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  • problem-solving

adjective as in analytic

Strongest matches

  • investigative

Weak matches

adjective as in analytical

  • interpretive
  • penetrating
  • explanatory
  • inquisitive
  • perspicuous
  • questioning
  • ratiocinative

adjective as in analytic/analytical

  • well-grounded

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Related words.

Words related to problem-solving are not direct synonyms, but are associated with the word problem-solving . Browse related words to learn more about word associations.

adjective as in logical

adjective as in examining and determining

adjective as in examining

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Example Sentences

“These are problem-solving products but that incorporate technology in a really subtle, unobtrusive way,” she says.

And it is a “problem-solving populism” that marries the twin impulses of populism and progressivism.

“We want a Republican Party that returns to problem-solving mode,” he said.

Problem-solving entails accepting realities, splitting differences, and moving forward.

It teaches female factory workers technical and life skills, such as literacy, communication and problem-solving.

Problem solving with class discussion is absolutely essential, and should occupy at least one third of the entire time.

In teaching by the problem-solving method Professor Lancelot 22 makes use of three types of problems.

Sequential Problem Solving is written for those with a whole brain thinking style.

Thus problem solving involves both the physical world and the interpersonal world.

Sequential Problem Solving begins with the mechanics of learning and the role of memorization in learning.

Synonym of the day

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On this page you'll find 87 synonyms, antonyms, and words related to problem-solving, such as: analytical, investigative, inquiring, rational, sound, and systematic.

From Roget's 21st Century Thesaurus, Third Edition Copyright © 2013 by the Philip Lief Group.

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Word Problems Involving the Mean of a Data Set

As we delve deeper into the world of statistics and probability, one specific term becomes very important to us: The mean. You've probably encountered this concept before -- even if you weren't aware of it. "Mean" essentially means the same thing as "average," and this number becomes very useful in a number of different fields. A baseball player's "batting average" tells you how skilled he or she is. The "average" return of an investment helps us understand how profitable it really is. As we can see, the mean is very useful in real-world applications. Let's tackle some word problems that show us how we can apply means to these real-world situations.

What is the mean?

We can find the mean of any data set with two easy steps:

  • Add all the data points together
  • Divide by the number of data points

Solving word problems involving means

Now let's put our knowledge to good use and solve a few word problems that involve means:

Consider the following data set: 4 , 8 , 20 , 25 , 32

If we add one more number ( x ) to this data set, we are left with a mean of 15. What is the value of this additional number?

First, let's try to add all of our numbers together: 4 + 8 + 20 + 25 + 32 + x

We don't know the value of x, so we can't complete this addition. But let's continue with the operation anyway:

If we add one more value (x) to our current data set, we get 6 total data points. This means that we need to divide the above sum by six:

4 + 8 + 20 + 25 + 32 + x + 6

We know that the end result is a mean of 15. So how can we solve this equation? Easy: We simplify it.

4 + 8 + 20 + 25 + 32 + x + 6 = 15

89 + x / 6 = 15

Now, all we need to do is multiply each side of the equation by 6:

6 × ( 89 + x ) / ( 6 ) = 15 × 6

89 + x = 90

The answer is 1.

We can even use our knowledge of means to help us set higher goals!

What happens if we know that we need an average of 90% or higher to get an "A" in math class?

What if our past test scores were 80%, 85%, 88%, and 95%?

We have one more test for the term. What score do we need to get an "A" average?

Right away, we know that our end result needs to be at least 90.

We also know that the total number of tests is 5.

With these values, we can find our minimum test score for an A average (x).

80 + 85 + 88 + 95 + x / 5

We can simplify this as 348 + x / 5

Now, all we need to do is multiply each side of the equation by 5:

5 × ( 348 + x ) / ( 5 ) = 90 × 5

Or: 348 + x = 450

Uh oh, looks like that value is 102. As we know, the highest possible score on a test is 100%. This means that it's theoretically impossible for us to get an A average this term -- unless, of course, we speak to our teacher about the possibility of doing additional work for extra credit. This highlights the importance of calculating means in order to plan effectively for the future.

Exercises such as this also show us how even a few low scores can seriously affect the overall average or mean.

The especially low score of 80% is 10 percentage points below our target grade, and this skews the data toward a lower mean. We can consider this value an outlier.

Topics related to the Word Problems Involving the Mean of a Data Set

Center and Variation of Data

Word Problems

Interpreting Data

Flashcards covering the Word Problems Involving the Mean of a Data Set

Statistics Flashcards

Common Core: High School - Statistics and Probability Flashcards

Practice tests covering the Word Problems Involving the Mean of a Data Set

Probability Theory Practice Tests

Common Core: High School - Statistics and Probability Diagnostic Tests

Tutoring helps your student gain confidence when solving word problems involving means

Tutoring gives your student the opportunity to go over a few more examples of word problems involving means. Sometimes, all it takes to reach for confidence in these concepts is a little extra time outside of class. Tutors can even cater to your student's learning style during these sessions, whether they prefer verbal or visual cues. Speak with Varsity Tutors' Educational Directors today to learn more about the possibilities of tutoring. We'll match your student with a suitable tutor.

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in problem solving the word of means

What Is Problem Solving?

You will often see beach clean-up drives being publicized in coastal cities. There are already dustbins available on the beaches,…

What Is Problem Solving?

You will often see beach clean-up drives being publicized in coastal cities. There are already dustbins available on the beaches, so why do people need to organize these drives? It’s evident that despite advertising and posting anti-littering messages, some of us don’t follow the rules.

Temporary food stalls and shops make it even more difficult to keep the beaches clean. Since people can’t ask the shopkeepers to relocate or prevent every single person from littering, the clean-up drive is needed.  This is an ideal example of problem-solving psychology in humans. ( 230-fifth.com ) So, what is problem-solving? Let’s find out.

What Is Problem-Solving?

At its simplest, the meaning of problem-solving is the process of defining a problem, determining its cause, and implementing a solution. The definition of problem-solving is rooted in the fact that as humans, we exert control over our environment through solutions. We move forward in life when we solve problems and make decisions. 

We can better define the problem-solving process through a series of important steps.

Identify The Problem: 

This step isn’t as simple as it sounds. Most times, we mistakenly identify the consequences of a problem rather than the problem itself. It’s important that we’re careful to identify the actual problem and not just its symptoms. 

Define The Problem: 

Once the problem has been identified correctly, you should define it. This step can help clarify what needs to be addressed and for what purpose.

Form A Strategy: 

Develop a strategy to solve your problem. Defining an approach will provide direction and clarity on the next steps. 

Organize The Information:  

Organizing information systematically will help you determine whether something is missing. The more information you have, the easier it’ll become for you to arrive at a solution.  

Allocate Resources:  

We may not always be armed with the necessary resources to solve a problem. Before you commit to implementing a solution for a problem, you should determine the availability of different resources—money, time and other costs.

Track Progress: 

The true meaning of problem-solving is to work towards an objective. If you measure your progress, you can evaluate whether you’re on track. You could revise your strategies if you don’t notice the desired level of progress. 

Evaluate The Results:  

After you spot a solution, evaluate the results to determine whether it’s the best possible solution. For example, you can evaluate the success of a fitness routine after several weeks of exercise.

Meaning Of Problem-Solving Skill

Now that we’ve established the definition of problem-solving psychology in humans, let’s look at how we utilize our problem-solving skills.  These skills help you determine the source of a problem and how to effectively determine the solution. Problem-solving skills aren’t innate and can be mastered over time. Here are some important skills that are beneficial for finding solutions.

Communication

Communication is a critical skill when you have to work in teams.  If you and your colleagues have to work on a project together, you’ll have to collaborate with each other. In case of differences of opinion, you should be able to listen attentively and respond respectfully in order to successfully arrive at a solution.

As a problem-solver, you need to be able to research and identify underlying causes. You should never treat a problem lightly. In-depth study is imperative because often people identify only the symptoms and not the actual problem.

Once you have researched and identified the factors causing a problem, start working towards developing solutions. Your analytical skills can help you differentiate between effective and ineffective solutions.

Decision-Making

You’ll have to make a decision after you’ve identified the source and methods of solving a problem. If you’ve done your research and applied your analytical skills effectively, it’ll become easier for you to take a call or a decision.

Organizations really value decisive problem-solvers. Harappa Education’s   Defining Problems course will guide you on the path to developing a problem-solving mindset. Learn how to identify the different types of problems using the Types of Problems framework. Additionally, the SMART framework, which is a five-point tool, will teach you to create specific and actionable objectives to address problem statements and arrive at solutions. 

Explore topics & skills such as Problem Solving Skills , PICK Chart , How to Solve Problems & Barriers to Problem Solving from our Harappa Diaries blog section and develop your skills.

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Definition of 'problem-solving'

Problem-solving in british english.

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Examples of 'problem-solving' in a sentence problem-solving

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Word Problems on Arithmetic Mean

Here we will learn to solve the three important types of word problems on arithmetic mean (average). The questions are mainly based on average (arithmetic mean), weighted average and average speed.

How to solve average (arithmetic mean) word problems?

To solve various problems we need to follow the uses of the formula for calculating average (arithmetic mean)

Average = (Sums of the observations)/(Number of observations)

Follow the explanation to solve the word problems on arithmetic mean (average):

1.  The heights of five runners are 160 cm, 137 cm, 149 cm, 153 cm and 161 cm respectively. Find the mean height per runner.

Mean height = Sum of the heights of the runners/number of runners

= (160 + 137 + 149 + 153 + 161)/5 cm

Hence, the mean height is 152 cm.

2. Find the mean of the first five prime numbers.

The first five prime numbers are 2, 3, 5, 7 and 11.

Mean = Sum of the first five prime numbers/number of prime numbers

= (2 + 3 + 5 + 7 + 11)/5

Hence, their mean is 5.6

3. Find the mean of the first six multiples of 4.

The first six multiples of 4 are 4, 8, 12, 16, 20 and 24.

Mean = Sum of the first six multiples of 4/number of multiples

= (4 + 8 + 12 + 16 + 20 + 24)/6

Hence, their mean is 14.

4. Find the arithmetic mean of the first 7 natural numbers.

The first 7 natural numbers are 1, 2, 3, 4, 5, 6 and 7.

Hence, their mean is 4.

5.  If the mean of 9, 8, 10, x, 12 is 15, find the value of x.

Mean of the given numbers = (9 + 8 + 10 + x + 12)/5 = (39 + x)/5

According to the problem, mean = 15 (given).

Therefore, (39 + x)/5 = 15

⇒ 39 + x = 15 × 5

⇒ 39 + x = 75

⇒ 39 - 39 + x = 75 - 39

Hence, x = 36.

More examples on the worked-out word problems on arithmetic mean:

6. If the mean of five observations x, x + 4, x + 6, x + 8 and x + 12 is 16, find the value of x.

Solution: Mean of the given observations

= x + (x + 4) + (x + 6) + (x + 8) + (x + 12)/5

= (5x + 30)/5

According to the problem, mean = 16 (given).

Therefore, (5x + 30)/5 = 16

⇒ 5x + 30 = 16 × 5

⇒ 5x + 30 = 80

⇒ 5x + 30 - 30 = 80 - 30

Hence, x = 10.

148 + 153 + 146 + 147 + 154

7. The mean of 40 numbers was found to be 38. Later on, it was detected that a number 56 was misread as 36. Find the correct mean of given numbers.

Calculated mean of 40 numbers = 38.

Therefore, calculated sum of these numbers = (38 × 40) = 1520.

Correct sum of these numbers

= [1520 - (wrong item) + (correct item)]

= (1520 - 36 + 56)

Therefore, the correct mean = 1540/40 = 38.5.

8. The mean of the heights of 6 boys is 152 cm. If the individual heights of five of them are 151 cm, 153 cm, 155 cm, 149 cm and 154 cm, find the height of the sixth boy.

Mean height of 6 boys = 152 cm.

Sum of the heights of 6 boys = (152 × 6) = 912 cm

Sum of the heights of 5 boys = (151 + 153 + 155 + 149 + 154) cm = 762 cm.

Height of the sixth boy

= (sum of the heights of 6 boys) - (sum of the heights of 5 boys)

= (912 - 762) cm = 150 cm.

Arithmetic Mean

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Overview of the Problem-Solving Mental Process

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

in problem solving the word of means

Rachel Goldman, PhD FTOS, is a licensed psychologist, clinical assistant professor, speaker, wellness expert specializing in eating behaviors, stress management, and health behavior change.

in problem solving the word of means

  • Identify the Problem
  • Define the Problem
  • Form a Strategy
  • Organize Information
  • Allocate Resources
  • Monitor Progress
  • Evaluate the Results

Frequently Asked Questions

Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue.

The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything they can about the issue and then using factual knowledge to come up with a solution. In other instances, creativity and insight are the best options.

It is not necessary to follow problem-solving steps sequentially, It is common to skip steps or even go back through steps multiple times until the desired solution is reached.

In order to correctly solve a problem, it is often important to follow a series of steps. Researchers sometimes refer to this as the problem-solving cycle. While this cycle is portrayed sequentially, people rarely follow a rigid series of steps to find a solution.

The following steps include developing strategies and organizing knowledge.

1. Identifying the Problem

While it may seem like an obvious step, identifying the problem is not always as simple as it sounds. In some cases, people might mistakenly identify the wrong source of a problem, which will make attempts to solve it inefficient or even useless.

Some strategies that you might use to figure out the source of a problem include :

  • Asking questions about the problem
  • Breaking the problem down into smaller pieces
  • Looking at the problem from different perspectives
  • Conducting research to figure out what relationships exist between different variables

2. Defining the Problem

After the problem has been identified, it is important to fully define the problem so that it can be solved. You can define a problem by operationally defining each aspect of the problem and setting goals for what aspects of the problem you will address

At this point, you should focus on figuring out which aspects of the problems are facts and which are opinions. State the problem clearly and identify the scope of the solution.

3. Forming a Strategy

After the problem has been identified, it is time to start brainstorming potential solutions. This step usually involves generating as many ideas as possible without judging their quality. Once several possibilities have been generated, they can be evaluated and narrowed down.

The next step is to develop a strategy to solve the problem. The approach used will vary depending upon the situation and the individual's unique preferences. Common problem-solving strategies include heuristics and algorithms.

  • Heuristics are mental shortcuts that are often based on solutions that have worked in the past. They can work well if the problem is similar to something you have encountered before and are often the best choice if you need a fast solution.
  • Algorithms are step-by-step strategies that are guaranteed to produce a correct result. While this approach is great for accuracy, it can also consume time and resources.

Heuristics are often best used when time is of the essence, while algorithms are a better choice when a decision needs to be as accurate as possible.

4. Organizing Information

Before coming up with a solution, you need to first organize the available information. What do you know about the problem? What do you not know? The more information that is available the better prepared you will be to come up with an accurate solution.

When approaching a problem, it is important to make sure that you have all the data you need. Making a decision without adequate information can lead to biased or inaccurate results.

5. Allocating Resources

Of course, we don't always have unlimited money, time, and other resources to solve a problem. Before you begin to solve a problem, you need to determine how high priority it is.

If it is an important problem, it is probably worth allocating more resources to solving it. If, however, it is a fairly unimportant problem, then you do not want to spend too much of your available resources on coming up with a solution.

At this stage, it is important to consider all of the factors that might affect the problem at hand. This includes looking at the available resources, deadlines that need to be met, and any possible risks involved in each solution. After careful evaluation, a decision can be made about which solution to pursue.

6. Monitoring Progress

After selecting a problem-solving strategy, it is time to put the plan into action and see if it works. This step might involve trying out different solutions to see which one is the most effective.

It is also important to monitor the situation after implementing a solution to ensure that the problem has been solved and that no new problems have arisen as a result of the proposed solution.

Effective problem-solvers tend to monitor their progress as they work towards a solution. If they are not making good progress toward reaching their goal, they will reevaluate their approach or look for new strategies .

7. Evaluating the Results

After a solution has been reached, it is important to evaluate the results to determine if it is the best possible solution to the problem. This evaluation might be immediate, such as checking the results of a math problem to ensure the answer is correct, or it can be delayed, such as evaluating the success of a therapy program after several months of treatment.

Once a problem has been solved, it is important to take some time to reflect on the process that was used and evaluate the results. This will help you to improve your problem-solving skills and become more efficient at solving future problems.

A Word From Verywell​

It is important to remember that there are many different problem-solving processes with different steps, and this is just one example. Problem-solving in real-world situations requires a great deal of resourcefulness, flexibility, resilience, and continuous interaction with the environment.

Get Advice From The Verywell Mind Podcast

Hosted by therapist Amy Morin, LCSW, this episode of The Verywell Mind Podcast shares how you can stop dwelling in a negative mindset.

Follow Now : Apple Podcasts / Spotify / Google Podcasts

You can become a better problem solving by:

  • Practicing brainstorming and coming up with multiple potential solutions to problems
  • Being open-minded and considering all possible options before making a decision
  • Breaking down problems into smaller, more manageable pieces
  • Asking for help when needed
  • Researching different problem-solving techniques and trying out new ones
  • Learning from mistakes and using them as opportunities to grow

It's important to communicate openly and honestly with your partner about what's going on. Try to see things from their perspective as well as your own. Work together to find a resolution that works for both of you. Be willing to compromise and accept that there may not be a perfect solution.

Take breaks if things are getting too heated, and come back to the problem when you feel calm and collected. Don't try to fix every problem on your own—consider asking a therapist or counselor for help and insight.

If you've tried everything and there doesn't seem to be a way to fix the problem, you may have to learn to accept it. This can be difficult, but try to focus on the positive aspects of your life and remember that every situation is temporary. Don't dwell on what's going wrong—instead, think about what's going right. Find support by talking to friends or family. Seek professional help if you're having trouble coping.

Davidson JE, Sternberg RJ, editors.  The Psychology of Problem Solving .  Cambridge University Press; 2003. doi:10.1017/CBO9780511615771

Sarathy V. Real world problem-solving .  Front Hum Neurosci . 2018;12:261. Published 2018 Jun 26. doi:10.3389/fnhum.2018.00261

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

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Definition of problem noun from the Oxford Advanced Learner's Dictionary

  • big/serious/major problems
  • She has a lot of health problems .
  • financial/social/technical problems
  • Let me know if you have any problems .
  • The government must address the problem of child poverty.
  • We cannot tackle this problem effectively on our own.
  • We are dealing with a serious problem here.
  • Money isn't going to solve the problem .
  • (especially North American English) to fix a problem
  • If he chooses Mary it's bound to cause problems .
  • to pose/create a problem
  • The problem first arose in 2018.
  • problem with something There is a problem with this argument.
  • problem of something the problem of drug abuse
  • problem of doing something Most students face the problem of funding themselves while they are studying.
  • problem for somebody Unemployment is a very real problem for graduates now.
  • It’s a nice table! The only problem is (that) it’s too big for our room.
  • Part of the problem is the shape of the room.
  • Stop worrying about their marriage—it isn't your problem.
  • There's no history of heart problems (= disease connected with the heart) in our family.
  • the magazine’s problem page (= containing letters about readers’ problems and advice about how to solve them)
  • All the anti-depressant does is mask the problem.
  • Depression is a natural feeling if your problems seem intractable.
  • For years I've tried to overlook this problem.
  • Fortunately, it's easy to avoid any potential problems.
  • Framing the problem is an important step.
  • She believes she may have found a solution to the problem.
  • He developed a drinking problem.
  • She doesn't really see the problem.
  • He doesn't seem to understand my problem.
  • She had to undergo surgery to cure the problem with her knee.
  • He has been faced with all manner of problems in his new job.
  • Her new job had taken her mind off her family problems for a while.
  • I didn't imagine there would be a problem about getting tickets.
  • I don't anticipate any future problems in that regard.
  • I forgot my problems for a moment.
  • I'm glad you finally admitted your problem.
  • If the problem persists you should see a doctor.
  • Inadequate resources pose a problem for all members of staff.
  • Most people can see the ethical problem with accepting such an offer.
  • No one ever asked why or how the problem originated.
  • Our greatest problem is the lack of funds.
  • She had serious substance abuse problems with both cocaine and heroin.
  • She raised the problem of falling sales at the last meeting.
  • Success brings its own problems.
  • Systemic security problems have been identified.
  • The accident poses a terrible problem for the family.
  • The basic problem remains the lack of available housing.
  • The plan has been fraught with problems from the start.
  • The problem lies in the lack of communication between managers and staff.
  • Therein lies the problem.
  • The rail strike is a problem for all commuters.
  • The role of the sun in climate change is still a big unsolved problem.
  • The traffic in illegal drugs is a global problem.
  • These symptoms may indicate a serious problem.
  • They created a task force to study this problem.
  • They sold their car to ease their financial problems.
  • This illustrates another potential problem.
  • This underscores the biggest problem with electronic voting.
  • We need to get to the root of the problem before we can solve it.
  • We're faced with a whole host of new problems.
  • This is one of the great problems of cosmology: where did the overall structure of the universe come from?
  • present (somebody with)
  • behaviour/​behavior
  • problem about
  • problem for
  • an approach to a problem
  • the crux of the problem
  • the heart of the problem

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  • \mathrm{Lauren's\:age\:is\:half\:of\:Joe's\:age.\:Emma\:is\:four\:years\:older\:than\:Joe.\:The\:sum\:of\:Lauren,\:Emma,\:and\:Joe's\:age\:is\:54.\:How\:old\:is\:Joe?}
  • \mathrm{Kira\:went\:for\:a\:drive\:in\:her\:new\:car.\:She\:drove\:for\:142.5\:miles\:at\:a\:speed\:of\:57\:mph.\:For\:how\:many\:hours\:did\:she\:drive?}
  • \mathrm{The\:sum\:of\:two\:numbers\:is\:249\:.\:Twice\:the\:larger\:number\:plus\:three\:times\:the\:smaller\:number\:is\:591\:.\:Find\:the\:numbers.}
  • \mathrm{If\:2\:tacos\:and\:3\:drinks\:cost\:12\:and\:3\:tacos\:and\:2\:drinks\:cost\:13\:how\:much\:does\:a\:taco\:cost?}
  • \mathrm{You\:deposit\:3000\:in\:an\:account\:earning\:2\%\:interest\:compounded\:monthly.\:How\:much\:will\:you\:have\:in\:the\:account\:in\:15\:years?}
  • How do you solve word problems?
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  • How do you identify word problems in math?
  • Word problems in math can be identified by the use of language that describes a situation or scenario. Word problems often use words and phrases which indicate that performing calculations is needed to find a solution. Additionally, word problems will often include specific information such as numbers, measurements, and units that needed to be used to solve the problem.
  • Is there a calculator that can solve word problems?
  • Symbolab is the best calculator for solving a wide range of word problems, including age problems, distance problems, cost problems, investments problems, number problems, and percent problems.
  • What is an age problem?
  • An age problem is a type of word problem in math that involves calculating the age of one or more people at a specific point in time. These problems often use phrases such as 'x years ago,' 'in y years,' or 'y years later,' which indicate that the problem is related to time and age.

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Word of the Day

What it means.

Obeisance is a synonym of homage that refers to an acknowledgement of another’s importance or superiority. Obeisance can also mean “a movement of the body (such as a bow) showing respect for someone or something.”

// The young singer paid obeisance to Otis Redding while on tour in Memphis by singing “(Sittin’ on) The Dock of the Bay.”

See the entry >

obeisance in Context

“Supreme Court rules establish specific guidelines by which these conferences must be conducted. But compliance is rare, and they are usually held in secret and undocumented. The clandestine nature of 402 proceedings conflicts with the judiciary’s general obeisance to concepts of transparency and public accountability in criminal cases.” — Jim Dey, The News-Gazette (Champaign-Urbana, Illinois), 3 Oct. 2023

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Challenging standardized test words.

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  • Late hour Loud sounds

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Did You Know?

When it first appeared in English in the 14th century, obeisance shared the same meaning as obedience . This makes sense given that obeisance can be traced back to the Anglo-French word obeir , a verb meaning “to obey” that is also an ancestor of English’s obey . The other senses of obeisance also date from the 14th century, but they have stood the test of time whereas the “obedience” sense is now obsolete... or is it? Recent evidence suggests that obeisance is starting to be used again as an (often disparaging) synonym of obedience ; for example, a politician deemed too easily swayed by others may be said to have pledged obeisance to party leaders or malign influences.

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Unscramble the letters to reveal a word that refers to an act of civility, respect, or reverence consisting of a slight lowering of the body with bending of the knees: YUCSTR

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Weltanschauung.

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Play Missing Letter: a crossword with a twist. Each of the 25 puzzle words start with a different letter of the alphabet. Which letter is missing?

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puzz 1

Can you solve it? The word game at the cutting edge of computer science

A crossword puzzle with a twist

UPDATE: You can read the solutions here

Today’s puzzle illuminates one of the smash hits of theoretical computer science, a mind-boggling result that left even experts in the field gobsmacked .

We’ll get to that result (the PCP theorem ) later. But first, to the challenge!

It’s a word puzzle. Crossword-style clues each point to a vertical column. The answer to each clue is a three-letter word, made up from the three letters that the clue points to.

Each clue points to the three letters in the answer.

Let’s solve this one together. An animal that’s three letters? How about “bat”?

proj-games 5

Each time we can put in a convincing answer we get a point for each letter. “Bat” gives us a score of 3.

Now let’s carry on. Here’s one way to complete the grid.

The red letters are ones not included in the solution.

Note that this grid is not a full solution. The three top clues are fully answered. I’ve highlighted the green arrows from the clue ‘verb’, which points to ‘pay’. But the three bottom clues are only partially solved. Food points to ‘pey’, not ‘pea’. However, we can award ourselves a point for any letters in a potentially correct answer, so ‘pey’ gets us 2 points, for the two correct letters in ‘pea’. Total score: 15 points.

Here’s how you could get a full solution, with a maximum score of 18. Of course, “cat” was a much more obvious place to start!

puzz 1

The point of this puzzle, says Dana Moshkovitz, professor of computer science at the University of Texas at Austin is that “it is OK to get a partial solution.” In fact, that is what makes it fun. The aim is to get the highest possible score.

Here are three examples, in increasing order of difficulty.

Slide16

I’ll be back at 5pm UK with full solutions. (There are possibly many full solutions.) Meanwhile, NO SPOILERS. Please discuss your favourite three letter words.

UPDATE: You can read the solutions here.

[If any enterprising reader wants to make an interactive version of this puzzle, please put the link below.]

UPDATE 2: two enterprising readers answered the challenge. Here’s one by Starwort who calls the puzzle Tangleword . And here’s one by Chris Ward .)

So, what have these puzzles got to do with one of the most important results in computer science? Bear with.

Fifty years ago, computer scientists discovered that many naturally occurring problems, such as how best to stack different sizes of suitcase in a car boot, become so complex once you scale them up that computers are unable to solve them in a reasonable time. It also turns out, surprisingly, that getting approximate answers to these suitcase-in-a-boot problems is just as hard.

The analogy with today’s puzzle is that the puzzle has a correct solution, but it also has “approximate” solutions. As we have seen, you can get full score, and you can also get partial scores. Imagine you were to scale up this type of puzzle with more clues, letters, and arrows. Distinguishing puzzles that give a perfect solution, and ones that give a partial solution is so complex that computers cannot do it in any reasonable time.

This field – the study of “hardness of approximation” – has deep connections to the PCP theorem, a stunning result that concerns mathematical proofs. Usually when you want to check a mathematical proof you need to check it line by line to see if there are no mistakes. Like when a teacher goes through your workings to make sure every piece of deduction is a logical step.

The PCP theorem, however, shows that you do not need to check a proof line by line in order to make sure there are no mistakes. Instead, you can rewrite the proof in such a way that you can check it by randomly choosing only two or three bits from the proof and checking only these bits, that is, checking at two or three points whether the bit is either a 0 or a 1. Just a couple of bits! For any mathematical proof!

The puzzle above is a simplified version of the PCP theorem, says Dana Moshkovitz, who came up with it as a way of introducing the subject to her students. She adds: “Practically *all* known results we have today about hardness of approximation start with the PCP theorem in the word puzzle form.”

Yes, this is a bit confusing, since the word puzzle is not itself about checking proofs. However, you can see the link if you consider each word as essentially a “check” of a full solution.

The PCP theorem (the letters stand for probabilistically checkable proof) was a huge theoretical advance, and one that promises important practical applications. For example, it permits a computer with a small memory to check very efficiently that a large computer has done something correctly, such as, say, an iphone checking the integrity of a program in the cloud. This technology is already being used in blockchains, such as by Israeli tech unicorn StarkWare .

If you want to learn more about the PCP theorem, here’s a great piece by Dana that was in XRDS, the student magazine of the Association for Computing Machinery.

I am currently science communicator in residence at the Simons Institute for the Theory of Computing, University of California, Berkeley.

I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me .

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in problem solving the word of means

Jumble 3/13/24 Answers - March 13 2024

Jumble has been entertaining folks since 1954 and has been a classic game where scrambled words require you to unscramble them in order to find key letters that leads to a final word to be unscrambled to answer the day’s pun! We have the answers for today’s Jumble , published on March 13th 2024 below.

Daily Jumble Answers Guide

There are multiple words that are scrambled and must be solved before you can get the final word that is a mix of letters found in the previous words.

Need help in the future? Use our Jumble Solver Tool to get the answer!

Daily Jumble Answer for March 13th 2024

Here are the answers to the 3/13/24 Jumble puzzle:

  • PLEEO -> ELOPE
  • SYHUK -> HUSKY
  • DNMETA -> TANDEM
  • IQUUEN -> UNIQUE

Some words that mean “be fond of” include enjoy, adore, relish, prefer —

  • LEHKTADNIE -> AND THE LIKE

Daily Jumble Solving Tips

  • Identify unique letters: Begin by scanning the jumbled letters for any unique characters, such as Q, X, or Z, which might help narrow down possible words.
  • Look for common letter patterns: Search for familiar letter combinations, such as “ing,” “ed,” “tion,” or “est,” as these can often help you identify parts of the word.
  • Rearrange letters: Physically rearrange the jumbled letters using paper or an online tool. This can help you visualize potential words more easily.
  • Form smaller words: Try to form smaller words using subsets of the given letters. This may help you recognize letter patterns that contribute to the final solution.
  • Use consonant and vowel patterns: Consider the usual arrangements of consonants and vowels in words. For example, consonants often surround vowels, and certain consonants tend to appear together (e.g., “th,” “ch,” “sh”).
  • Work on one word at a time: If the jumble consists of multiple words, focus on solving one word at a time. Solving one word may provide context clues for the others.
  • Apply context clues: If the jumble is part of a puzzle with a theme or accompanying image, use these context clues to guide your guesses.
  • Check word lengths: Take note of the length of the jumbled word. This can help eliminate possibilities and narrow down your search.
  • Eliminate incorrect combinations: As you try different letter arrangements, eliminate the combinations that do not form valid words or do not fit the context.
  • Take breaks: If you feel stuck, take a short break and come back to the jumble with fresh eyes. This may help you see new patterns or possibilities.

That wraps up the answers for today’s Daily Jumble. If you need answers to past puzzles, please find our ongoing Daily Jumble Answers guide , which also includes answers to the most recent puzzles. You can play at Chicago Tribune or USA Today online .

The post Jumble 3/13/24 Answers – March 13 2024 appeared first on Try Hard Guides .

Jumble has been entertaining folks since 1954 and has been a classic game where scrambled words require you to unscramble them in order to find key letters that leads to a final word to be unscrambled to answer the day’s pun! We have the answers for today’s Jumble, published on March 13th 2024 below. Daily […]

illustration

Biden's State of the Union address, annotated and fact-checked

By Zachary B. Wolf and Sean O’Key, CNN

Published March 8, 2024

It may have been President Joe Biden’s final State of the Union address. Or possibly the last of his first term. As Biden and former President Donald Trump prepare for a 2024 general election rematch, a vigorous Biden went off script at times, directly addressing Republicans and making the case that his administration has improved the country and people’s lives.

Here’s what he said and key ad-libs, along with context and fact checks from CNN’s fact check team.

Good evening.

Mr. Speaker. Madam Vice President. Members of Congress. My Fellow Americans.

In January 1941, President Franklin Roosevelt came to this chamber to speak to the nation.

He said, “I address you at a moment unprecedented in the history of the Union."

Hitler was on the march. War was raging in Europe.

President Roosevelt’s purpose was to wake up the Congress and alert the American people that this was no ordinary moment.

Freedom and democracy were under assault in the world.

Roosevelt’s “Four Freedoms” speech closed with a vision of spreading American democracy to the world. That’s a very Biden sentiment .

Tonight I come to the same chamber to address the nation.

Now it is we who face an unprecedented moment in the history of the Union.

And yes, my purpose tonight is to both wake up this Congress, and alert the American people that this is no ordinary moment either.

It’s notable that Biden was essentially comparing the threat against democracy today, both here and abroad, to the threat posed by Adolf Hitler in Germany in 1941.

Not since President Lincoln and the Civil War have freedom and democracy been under assault here at home as they are today.

What makes our moment rare is that freedom and democracy are under attack, both at home and overseas, at the very same time.

Biden’s challenge in this election is to make Americans believe his quest to save democracy is an urgent matter. The rise of Trump from the political desert suggests many Americans are tiring of the message.

Overseas, Putin of Russia is on the march, invading Ukraine and sowing chaos throughout Europe and beyond.

If anybody in this room thinks Putin will stop at Ukraine, I assure you, he will not.

But Ukraine can stop Putin if we stand with Ukraine and provide the weapons it needs to defend itself. That is all Ukraine is asking. They are not asking for American soldiers.

In fact, there are no American soldiers at war in Ukraine. And I am determined to keep it that way.

This was an important pledge for Americans to hear. French President Emmanuel Macron recently suggested European troops could be called to Ukraine .

But now assistance for Ukraine is being blocked by those who want us to walk away from our leadership in the world.

The Senate passed a bill to give Ukraine an additional $60 billion in US aid, but Speaker Mike Johnson, who sat over Biden’s left shoulder during the speech, has not schedule d a vote in the House .

It wasn’t that long ago when a Republican President, Ronald Reagan, thundered, “Mr. Gorbachev, tear down this wall."

Now, my predecessor, a former Republican President, tells Putin, “Do whatever the hell you want."

Reagan’s words were an important moment in US history. Watch it here. Trump, he who shall not be named in this speech, said recently that he told a European leader that Russia should be able to “ do whatever the hell they want ” to European countries that don’t spend enough on defense.

A former American President actually said that, bowing down to a Russian leader.

It’s outrageous. It’s dangerous. It’s unacceptable.

This “bowing down” line has become a staple of Biden’s speeches.

America is a founding member of NATO the military alliance of democratic nations created after World War II to prevent war and keep the peace.

Today, we’ve made NATO stronger than ever.

We welcomed Finland to the Alliance last year, and just this morning, Sweden officially joined NATO, and their Prime Minister is here tonight.

Mr. Prime Minister, welcome to NATO, the strongest military alliance the world has ever known.

Sweden was able to join NATO after Turkey and Hungary dropped objections. Coincidentally, Trump is set to meet with Hungary’s Putin-friendly prime minister, Viktor Orban, at Mar-a-Lago on Friday.

I say this to Congress: we must stand up to Putin. Send me the Bipartisan National Security Bill.

History is watching.

If the United States walks away now, it will put Ukraine at risk.

Europe at risk. The free world at risk, emboldening others who wish to do us harm.

My message to President Putin is simple.

We will not walk away. We will not bow down. I will not bow down.

History is watching, just like history watched three years ago on January 6th.

This was an important turn, from standing up to Putin to the threat of insurrectionists at home. Trump’s affinity for Putin is no secret. Trump argues he would be able to contain Putin better than Biden.

Insurrectionists stormed this very Capitol and placed a dagger at the throat of American democracy.

Many of you were here on that darkest of days.

We all saw with our own eyes these insurrectionists were not patriots.

They had come to stop the peaceful transfer of power and to overturn the will of the people.

Everyone saw it, but many Republican lawmakers now downplay the threat posed by the January 6, 2021, insurrection. Johnson was among the lawmakers who objected to the counting of electoral votes in key states Biden won in 2020.

January 6th and the lies about the 2020 election, and the plots to steal the election, posed the gravest threat to our democracy since the Civil War.

But they failed. America stood strong and democracy prevailed.

But we must be honest the threat remains and democracy must be defended.

My predecessor and some of you here seek to bury the truth of January 6th.

I will not do that.

A lot of Americans might want to move on from 2020, but Biden will try to remind them at every turn. He’ll get help from Trump, who is also still very focused on 2020. Trump has fashioned his campaign as a weapon of “retribution.”

This is a moment to speak the truth and bury the lies.

And here’s the simplest truth. You can’t love your country only when you win.

As I’ve done ever since being elected to office, I ask you all, without regard to party, to join together and defend our democracy!

Remember your oath of office to defend against all threats foreign and domestic.

Respect free and fair elections! Restore trust in our institutions! And make clear –political violence has absolutely no place in America!

Biden frequently uses this line about having to love your country when you lose too. The erosion of faith in US institutions is a troubling development reflected in multiple polls .

And history is watching another assault on freedom.

Joining us tonight is Latorya Beasley, a social worker from Birmingham, Alabama . 14 months ago tonight, she and her husband welcomed a baby girl thanks to the miracle of IVF.

She scheduled treatments to have a second child, but t he Alabama Supreme Court shut down IVF treatments across the state , unleashed by the Supreme Court decision overturning Roe v. Wade.

She was told her dream would have to wait.

Here’s a list of all of the people who sat with first lady Jill Biden.

Notably, some Alabama clinics have resumed treatment under a bipartisan law hastily passed in that state. But Democrats will continue to make this argument about abortion restrictions being an assault on freedom.

What her family has gone through should never have happened. And unless Congress acts, it could happen again.

So tonight, let’s stand up for families like hers!

To my friends across the aisle, don’t keep families waiting any longer. Guarantee the right to IVF nationwide!

This will be an interesting request to monitor, since it could theoretically gain bipartisan support.

Like most Americans, I believe Roe v. Wade got it right. And I thank Vice President Harris for being an incredible leader, defending reproductive freedom and so much more.

But my predecessor came to office determined to see Roe v. Wade overturned.

He’s the reason it was overturned. In fact, he brags about it.

Look at the chaos that has resulted.

Most Americans support abortion rights in some form, but the parties are hopelessly split. It will help Trump with his base to brag about overturning Roe v. Wade. It will help Biden with his base to blame Trump.

Joining us tonight is Kate Cox, a wife and mother from Dallas.

When she became pregnant again, the fetus had a fatal condition.

Her doctors told Kate that her own life and her ability to have children in the future were at risk if she didn’t act.

Because Texas law banned abortion, Kate and her husband had to leave the state to get the care she needed.

What her family has gone through should never have happened as well. But it is happening to so many others.

CNN’s Betsy Klein notes that Biden leaned on the personal stories of two of the guests in the first lady’s box: Latorya Beasley, an Alabama mother who had to pause in vitro fertilization treatment, and Kate Cox , the Texas mother of two who had to leave her state for access to a lifesaving abortion. And he pointed to a patchwork of abortion rights laws around the country.

But Republicans would have as much trouble passing a nationwide abortion ban as Democrats would have passing a bill to codify Roe v. Wade.

There are state laws banning the right to choose, criminalizing doctors, and forcing survivors of rape and incest to leave their states as well to get the care they need.

Many of you in this Chamber and my predecessor are promising to pass a national ban on reproductive freedom.

My God, what freedoms will you take away next?

In its decision to overturn Roe v. Wade the Supreme Court majority wrote, “Women are not without – electoral or political power.”

No kidding.

Clearly, those bragging about overturning Roe v. Wade have no clue about the power of women in America.

They found out though when reproductive freedom was on the ballot and won in 2022, 2023, and they will find out again, in 2024.

Democratic candidates will do everything they can to raise the abortion rights issue during the general election. Even voters in red states have chosen to support abortion rights when given the chance. There could be abortion-related ballot questions in key states, including Florida .

If Americans send me a Congress that supports the right to choose , I promise you, I will restore Roe v. Wade as the law of the land again!

This math doesn’t work. Passing legislation to protect abortion rights nationwide and restore Roe would surely require 60 votes in the Senate. Democrats currently have 51 seats, and there are few opportunities for pickups in 2024. Two Republicans, Sens. Susan Collins of Maine and Lisa Murkowski of Alaska, publicly support a national abortion rights law. That’s not nearly enough.

America cannot go back. I am here tonight to show the way forward. Because I know how far we’ve come.

Four years ago next week, before I came to office, our country was hit by the worst pandemic and the worst economic crisis in a century.

Remember the fear. Record job losses. Remember the spike in crime. And the murder rate.

A raging virus that would take more than 1 million American lives and leave millions of loved ones behind.

Biden’s figure needs context. Many lives were lost to Covid-19 during the Trump administration, but the US didn’t reach its millionth death until May 2022 when Biden was in office.

A mental health crisis of isolation and loneliness.

A president, my predecessor, who failed the most basic duty. Any President owes the American people the duty to care.

That is unforgivable.

I came to office determined to get us through one of the toughest periods in our nation’s history .

It is sometimes hard to remember that the Covid-19 pandemic started during the Trump administration and dominated the start of the Biden administration.

And we have. It doesn’t make the news but in thousands of cities and towns the American people are writing the greatest comeback story never told.

So let’s tell that story here and now.

America’s comeback is building a future of American possibilities, building an economy from the middle out and the bottom up , not the top down, investing in all of America, in all Americans to make sure everyone has a fair shot and we leave no one behind!

Republicans frequently try to label Biden as a socialist for spending taxpayer money. But Democrats and Biden argue the public has an interest in trying to make sure opportunities are accessible to everyone.

The pandemic no longer controls our lives. The vaccines that saved us from COVID are now being used to help beat cancer.

Turning setback into comeback.

That's America!

I inherited an economy that was on the brink. Now our economy is the envy of the world!

15 million new jobs in just three years - that's a record!

Biden’s claim is correct: the US economy added about 14.8 million jobs between Biden’s first full month in office, February 2021, and January 2024, more jobs than were added in any previous four-year presidential term. However, it’s important to note that Biden took office in an unusual pandemic context that makes meaningful comparison to other periods very difficult.

Unemployment at 50-year lows.

This needs context. The unemployment rate did hit a five-decade low during two months of early 2023 , 3.4%, and it has since remained close to that level — but the latest available unemployment rate, 3.7% for January, is higher than the rate was during nine months under President Donald Trump in 2019 and pre-pandemic 2020. (The rate then skyrocketed on account of the pandemic, and it was 6.4% the month Biden took office in January 2021.)

A record 16 million Americans are starting small businesses and each one is an act of hope.

With historic job growth and small business growth for Black, Hispanic, and Asian-Americans.

800,000 new manufacturing jobs in America and counting.

Biden’s figure is correct. The US economy added 791,000 manufacturing jobs from Biden’s first full month in office, February 2021, through January 2024, the last month for which Bureau of Labor Statistics data is available — though it’s worth noting that the growth largely occurred in 2021 and 2022 (with 746,000 manufacturing jobs added starting in February 2021) before a relatively flat 2023.

More people have health insurance today than ever before.

The racial wealth gap is the smallest it’s been in 20 years.

Wages keep going up and inflation keeps coming down!

Inflation has dropped from 9% to 3% – the lowest in the world!

Convincing Americans that their economy is good and improving may be Biden’s most important task in his reelection campaign. Because despite all of that data he rattled off, people are having trouble making ends meet. He’ll have more work to do to convince them .

And trending lower.

And now instead of importing foreign products and exporting American jobs, we’re exporting American products and creating American jobs – right here in America where they belong!

And the American people are beginning to feel it.

Consumer studies show consumer confidence is soaring.

Buy American has been the law of the land since the 1930s.

Past administrations including my predecessor failed to Buy American.

Not any more.

On my watch, federal projects like helping to build American roads bridges and highways will be made with American products built by American workers creating good-paying American jobs!

Thanks to my Chips and Science Act the United States is investing more in research and development than ever before.

Biden did oversee the passage of multiple, bipartisan bills to improve the country. The bipartisan infrastructure law is meant to improve things across the country. Propping up a semiconductor chip industry is also meant to make the US more independent from China.

During the pandemic a shortage of semiconductor chips drove up prices for everything from cell phones to automobiles.

Well instead of having to import semiconductor chips, which America invented I might add, private companies are now investing billions of dollars to build new chip factories here in America!

Creating tens of thousands of jobs many of them paying over $100,000 a year and don’t require a college degree.

In fact my policies have attracted $650 Billion of private sector investments in clean energy and advanced manufacturing creating tens of thousands of jobs here in America!

Thanks to our Bipartisan Infrastructure Law, 46,000 new projects have been announced across your communities – modernizing our roads and bridges, ports and airports, and public transit systems.

A futuristic airport terminal, a fish passage and ski town bus lanes: Here are some of the projects being built through the infrastructure law.

Removing poisonous lead pipes so every child can drink clean water without risk of getting brain damage.

Providing affordable high speed internet for every American no matter where you live.

Urban, suburban, and rural communities — in red states and blue.

Record investments in tribal communities.

Because of my investments, family farms are better be able to stay in the family and children and grandchildren won’t have to leave home to make a living.

It’s transformative.

A great comeback story is Belvidere, Illinois. Home to an auto plant for nearly 60 years.

Before I came to office the plant was on its way to shutting down.

Thousands of workers feared for their livelihoods. Hope was fading.

Then I was elected to office and we raised Belvidere repeatedly with the auto company knowing unions make all the difference.

The UAW worked like hell to keep the plant open and get those jobs back. And together, we succeeded!

Instead of an auto factory shutting down an auto factory is re-opening and a new state-of-the art battery factory is being built to power those cars.

Instead of a town being left behind it’s a community moving forward again!

Because instead of watching auto jobs of the future go overseas 4,000 union workers with higher wages will be building that future, in Belvidere, here in America!

Here tonight is UAW President, Shawn Fain, a great friend, and a great labor leader.

And Dawn Simms, a third generation UAW worker in Belvidere.

Shawn, I was proud to be the first President in American history to walk a picket line.

Biden attended a U nited A uto W orkers rally in Belvidere with UAW President Shawn Fain last year. He also became the first president to join a picket line when he stood with workers in Michigan.

And today Dawn has a job in her hometown providing stability for her family and pride and dignity.

Showing once again, Wall Street didn’t build this country!

The middle class built this country! And unions built the middle class!

Both Biden and Trump will try to argue they are looking out for the middle class. The turn of White voters without college degrees away from Democrats and toward Republicans has been a major shift in politics that drove the rise of Trump.

When Americans get knocked down, we get back up!

We keep going!

That’s America! That’s you, the American people!

It’s because of you America is coming back!

It’s because of you, our future is brighter!

Never has a State of the Union transcript included so many exclamations. Biden presented as a vigorous and energized leader here, far from the doddering old man he has been portrayed as by Republicans.

And it’s because of you that tonight we can proudly say the State of our Union is strong and getting stronger!

Tonight I want to talk about the future of possibilities that we can build together.

A future where the days of trickle-down economics are over and the wealthy and biggest corporations no longer get all the breaks.

I grew up in a home where not a lot trickled down on my Dad’s kitchen table.

That’s why I’m determined to turn things around so the middle class does well the poor have a way up and the wealthy still does well.

After earlier praising Reagan’s foreign policy, here Biden trashed the guiding principle of Reagan’s economic policy (and Republicans who have worked tirelessly to cut taxes for a generation).

We all do well.

And there’s more to do to make sure you’re feeling the benefits of all we’re doing.

Americans pay more for prescription drugs than anywhere else.

It’s wrong and I’m ending it.

With a law I proposed and signed and not one Republican voted for we finally beat Big Pharma!

This is the Inflation Reduction Act , a post-Covid-19 recovery plan that Democrats loaded up with other policy priorities and were able to pass without Republican votes by bending budget rules.

Democrats had been trying for years to pass a law that would allow Medicare to negotiate prescription drug prices . This is a first step.

Instead of paying $400 a month for insulin seniors with diabetes only have to pay $35 a month!

And now I want to cap the cost of insulin at $35 a month for every American who needs it!

For years people have talked about it but I finally got it done and gave Medicare the power to negotiate lower prices for prescription drugs just like the VA does for our veterans.

That’s not just saving seniors money.

It’s saving taxpayers money cutting the federal deficit by $160 billion because Medicare will no longer have to pay exorbitant prices to Big Pharma.

It’s true that two of the main drug price provisions in the Inflation Reduction Act, which Democrats pushed through Congress in 2022, are expected to reduce the deficit by $160 billion, according to the nonpartisan Congressional Budget Office. In total, the law’s drug measures are expected to reduce the deficit by $237 billion, though delaying the implementation of a Trump administration drug rebate rule accounts for the difference.

This year Medicare is negotiating lower prices for some of the costliest drugs on the market that treat everything from heart disease to arthritis.

Now it’s time to go further and give Medicare the power to negotiate lower prices for 500 drugs over the next decade.

That will not only save lives it will save taxpayers another $200 Billion!

Starting next year that same law caps total prescription drug costs for seniors on Medicare at $2,000 a year even for expensive cancer drugs that can cost $10,000, $12,000, $15,000 a year.

Now I want to cap prescription drug costs at $2,000 a year for everyone!

Another major contrast between Trump and Biden. Trump still wants to repeal the Affordable Care Act . Biden seemed to be veering toward “Medicare for All” here.

Folks Obamacare, known as the Affordable Care Act is still a very big deal.

Over one hundred million of you can no longer be denied health insurance because of pre-existing conditions.

But my predecessor and many in this chamber want to take that protection away by repealing the Affordable Care Act I won’t let that happen!

We stopped you 50 times before and we will stop you again!

In fact I am protecting it and expanding it.

I enacted tax credits that save $800 per person per year reducing health care premiums for millions of working families.

Those tax credits expire next year.

I want to make those savings permanent!

Women are more than half of our population but research on women’s health has always been underfunded.

That’s why we’re launching the first-ever White House Initiative on Women’s Health Research, led by Jill who is doing an incredible job as First Lady.

Creating a commission or new office is a classic State of the Union maneuver. That this speech focused on women’s health is not surprising since Democrats are so focused on the issue.

Pass my plan for $12 Billion to transform women’s health research and benefit millions of lives across America!

I know the cost of housing is so important to you .

If inflation keeps coming down mortgage rates will come down as well.

But I’m not waiting.

I want to provide an annual tax credit that will give Americans $400 a month for the next two years as mortgage rates come down to put toward their mortgage when they buy a first home or trade up for a little more space.

My Administration is also eliminating title insurance fees for federally backed mortgages.

When you refinance your home this can save you $1,000 or more.

These are all very specific ideas to put people at ease about the cost of buying and renting, major issues that are affecting how people view the economy . But Biden can’t accomplish all of this. He will need Congress to enact tax credits. He will need inflation to continue to come down to bring down mortgage rates .

For millions of renters, we’re cracking down on big landlords who break antitrust laws by price-fixing and driving up rents.

I’ve cut red tape so more builders can get federal financing, which is already helping build a record 1.7 million housing units nationwide.

Now pass my plan to build and renovate 2 million affordable homes and bring those rents down!

To remain the strongest economy in the world we need the best education system in the world.

I want to give every child a good start by providing access to pre-school for 3- and 4-year-olds.

He’s actually wanted to enact universal pre-K for some time. But Democrats could not come up with the votes to include that program in the Inflation Reduction Act.

Studies show that children who go to pre-school are nearly 50% more likely to finish high school and go on to earn a 2- or 4-year degree no matter their background.

I want to expand high-quality tutoring and summer learning time and see to it that every child learns to read by third grade.

I’m also connecting businesses and high schools so students get hands-on experience and a path to a good-paying job whether or not they go to college.

And I want to make college more affordable.

Let’s continue increasing Pell Grants for working- and middle-class families and increase our record investments in HBCUs and Hispanic and Minority-serving Institutions

I fixed student loan programs to reduce the burden of student debt for nearly 4 Million Americans including nurses firefighters and others in public service like Keenan Jones a public-school educator in Minnesota who’s here with us tonight.

Biden has done quite a bit to forgive federal student loan debt, canceling about $138 billion so far. Here’s a good visualization of that . But his most expansive plan, which he hoped to do through executive action and would have canceled up to $20,000 for borrowers who make less than $125,000 a year, was rejected by the Supreme Court.

He’s educated hundreds of students so they can go to college now he can help his own daughter pay for college.

Such relief is good for the economy because folks are now able to buy a home start a business even start a family.

While we’re at it I want to give public school teachers a raise!

Now let me speak to a question of fundamental fairness for all Americans.

I’ve been delivering real results in a fiscally responsible way.

I’ve already cut the federal deficit by over one trillion dollars.

Biden’s claim leaves out such critical context that it is misleading. While the annual federal budget deficit was more than $1 trillion lower in the 2023 fiscal year than it was in both the 2020 fiscal year (under President Donald Trump) and the 2021 fiscal year (partially under Trump and partially under Biden), analysts have repeatedly noted that Biden’s own actions, including laws he has signed and executive orders he has issued, have had the overall effect of worsening annual deficits, not reducing them. As in past remarks , Biden didn’t explain that the primary reason the deficit fell by a record amount during his tenure was that it had skyrocketed to a record high at the end of Trump’s term because of bipartisan emergency pandemic relief spending, then fell as expected when that spending expired as planned.

I signed a bipartisan budget deal that will cut another trillion dollars over the next decade.

And now it’s my goal to cut the federal deficit $3 trillion more by making big corporations and the very wealthy finally pay their fair share.

Look, I’m a capitalist.

If you want to make a million bucks – great!

Just pay your fair share in taxes.

A fair tax code is how we invest in the things –

that make a country great, health care, education, defense, and more.

But here’s the deal.

The last administration enacted a $2 Trillion tax cut that overwhelmingly benefits the very wealthy and the biggest corporations and exploded the federal deficit.

They added more to the national debt than in any presidential term in American history.

Biden’s numbers are correct; the national debt rose from about $19.9 trillion to about $27.8 trillion during Trump’s tenure, an increase of about 39% and more than in any other four-year presidential term, in part because of Trump’s major tax cuts. But it is an oversimplification to blame presidents alone for debt incurred during their tenures. Some of the Trump-era increase in the debt was due to the trillions of dollars in emergency Covid-19 pandemic relief spending that passed with bipartisan support and because of spending required by safety-net programs, such as Medicare, Medicaid and Social Security, that were created by previous presidents.

For folks at home does anybody really think the tax code is fair?

Do you really think the wealthy and big corporations need another $2 trillion in tax breaks?

I sure don’t. I’m going to keep fighting like hell to make it fair!

Under my plan nobody earning less than $400,000 will pay an additional penny in federal taxes.

Nobody. Not one penny.

In fact the Child Tax Credit I passed during the pandemic cut taxes for millions of working families and cut child poverty in HALF.

Restore the Child Tax Credit because no child should go hungry in this country!

The way to make the tax code fair is to make big corporations and the very wealthy finally pay their share.

In 2020 55 of the biggest companies in America made $40 billion in profits and paid zero in federal income taxes.

Not any more!

Thanks to the law I wrote and signed big companies now have to pay a minimum of 15%.

Biden’s “not anymore” claim is false, an exaggeration. While his 15% corporate minimum tax will reduce the number of big companies that don’t pay any federal taxes, it’s not true that “not anymore” will any big company — such as the ones on the list of 55 companies Biden mentioned — ever do so. That’s because the minimum tax, on the “book income” companies report to investors, only applies to companies with at least $1 billion in average annual income. According to the Institute on Taxation and Economic Policy, only 14 of the companies on its list of 55 non-payers reported having US pre-tax income of at least $1 billion.

But that’s still less than working people pay in federal taxes.

It’s time to raise the corporate minimum tax to at least 21% so every big corporation finally begins to pay their fair share.

I also want to end the tax breaks for Big Pharma, Big Oil, private jets, and massive executive pay!

End it now!

There are 1,000 billionaires in America.

You know what the average federal tax rate for these billionaires is? 8.2 percent!

That’s far less than the vast majority of Americans pay.

No billionaire should pay a lower tax rate than a teacher, a sanitation worker, a nurse!

That’s why I’ve proposed a minimum tax of 25% for billionaires. Just 25%.

That would raise $500 Billion over the next 10 years.

Imagine what that could do for America. Imagine a future with affordable child care so millions of families can get the care they need and still go to work and help grow the economy.

Imagine a future with paid leave because no one should have to choose between working and taking care of yourself or a sick family member.

Imagine a future with home care and elder care so seniors and people living with disabilities can stay in their homes and family caregivers get paid what they deserve!

Tonight, let’s all agree once again to stand up for seniors!

Many of my Republican friends want to put Social Security on the chopping block.

If anyone here tries to cut Social Security or Medicare or raise the retirement age I will stop them!

Working people who built this country pay more into Social Security than millionaires and billionaires do. It’s not fair.

We have two ways to go on Social Security.

Republicans will cut Social Security and give more tax cuts to the wealthy.

Biden went off script here, engaging in a back-and-forth with Republicans on the House floor. Republicans jeered when he said they would cut Social Security . Many in their party say they will do no such thing.

“That’s the proposal — oh no? You guys don’t want another $2 trillion tax cut?” Biden said. “I kind of thought that’s what your plan was. Well, that's good to hear.”

I will protect and strengthen Social Security and make the wealthy pay their fair share!

Too many corporations raise their prices to pad their profits charging you more and more for less and less.

That’s why we’re cracking down on corporations that engage in price gouging or deceptive pricing from food to health care to housing.

In fact, snack companies think you won’t notice when they charge you just as much for the same size bag but with fewer chips in it.

Pass Senator Bob Casey’s bill to put a stop to shrinkflation !

While a lot of people seem to blame Biden for inflation and cite government spending, he’d like to blame corporations.

CNN’s Bryan Mena notes while there is evidence that companies have reduced the size of their products, according to Labor Department data, the reason is usually to cut costs during times of high inflation and is a widespread practice. Companies do this because consumers are more sensitive to price changes than the size of a product becoming smaller, according to research. “Shrinkflation” due to corporate greed is a hasty generalization.

I’m also getting rid of junk fees those hidden fees added at the end of your bills without your knowledge. My administration just announced we’re cutting credit card late fees from $32 to just $8.

The banks and credit card companies don’t like it.

I’m saving American families $20 billion a year with all of the junk fees I’m eliminating .

And I’m not stopping there.

If this sounded familiar, that’s because he talked about junk fees at last year’s State of the Union .

My Administration has proposed rules to make cable, travel, utilities and online ticket sellers tell you the total price upfront so there are no surprises.

It matters.

This was his chance to say the words “ Taylor Swift .” Fail.

And so does this.

In November, my team began serious negotiations with a bipartisan group of Senators.

The result was a bipartisan bill with the toughest set of border security reforms we’ve ever seen in this country .

He went off script again here. CNN’s Priscilla Alvarez notes that Biden baited Republicans with praise for the bipartisan Senate border bill .

“Oh, you don’t like that bill, huh? That conservatives got together and said it was a good bill. I’ll be darned. That’s amazing,” Biden said, as some Republicans grumbled in the crowd.

Republican Sen. James Lankford, a key negotiator on the bipartisan border deal who faced pushback from members of his own party, stared ahead, appearing to nod as Biden ticked through elements of the bill -- including how it would shore up federal resources and include an emergency authority that would allow him to shut down the border if certain triggers are met.

That bipartisan deal would hire 1,500 more border security agents and officers.

100 more immigration judges to help tackle a backload of 2 million cases.

4,300 more asylum officers and new policies so they can resolve cases in 6 months instead of 6 years.

100 more high-tech drug detection machines to significantly increase the ability to screen and stop vehicles from smuggling fentanyl into America.

This bill would save lives and bring order to the border.

It would also give me as President new emergency authority to temporarily shut down the border when the number of migrants at the border is overwhelming.

The Border Patrol Union endorsed the bill.

The Chamber of Commerce endorsed the bill.

I believe that given the opportunity a majority of the House and Senate would endorse it as well.

But unfortunately, politics have derailed it so far.

I’m told my predecessor called Republicans in Congress and demanded they block the bill . He feels it would be a political win for me and a political loser for him.

It’s not about him or me.

Biden was interrupted here by GOP Rep. Marjorie Taylor Greene, who shouted at him about Laken Riley , the Georgia nursing student killed, allegedly by an undocumented immigrant. It’s an incident that has driven claims that migrants are criminals.

Biden picked up a pin that read “Say Her Name Laken Riley” and directly addressed the parents of Laken Riley, who had been invited to the speech by a congressman.

“Lincoln (sic) Riley, an innocent young woman who was killed by an illegal. That's right. But how many of the thousands of people being killed by illegals - to her parents, I say my heart goes out to you. Having lost children myself, I understand.”

It is interesting that Biden also referred to the undocumented migrant who is suspected in Riley’s killing with the derogatory term “illegal.” Read more.

It’d be a winner for America!

My Republican friends you owe it to the American people to get this bill done.

We need to act.

And if my predecessor is watching instead of playing politics and pressuring members of Congress to block this bill, join me in telling Congress to pass it!

We can do it together. But here’s what I will not do.

I will not demonize immigrants saying they “poison the blood of our country” as he said in his own words.

I will not separate families.

I will not ban people from America because of their faith.

Trump’s rhetoric on immigration has gotten increasingly heated. He frequently refers to people crossing the border as “murderers,” for instance. The “poisoning the blood” line Trump uses is similar to a passage in Hitler’s manifesto “Mein Kampf.”

Unlike my predecessor, on my first day in office I introduced a comprehensive plan to fix our immigration system, secure the border, and provide a pathway to citizenship for Dreamers and so much more.

Because unlike my predecessor, I know who we are as Americans.

We are the only nation in the world with a heart and soul that draws from old and new.

Home to Native Americans whose ancestors have been here for thousands of years. Home to people from every place on Earth.

Some came freely.

Some chained by force.

Some when famine struck, like my ancestral family in Ireland.

Some to flee persecution.

Some to chase dreams that are impossible anywhere but here in America.

That’s America, where we all come from somewhere, but we are all Americans.

We can fight about the border, or we can fix it. I’m ready to fix it.

Send me the border bill now!

Biden both eloquently talked about how the US is a nation of immigrants and also called on Congress to give him the power to close the border. His shift on the issue has been remarkable.

A transformational moment in our history happened 59 years ago today in Selma, Alabama.

Hundreds of foot soldiers for justice marched across the Edmund Pettus Bridge, named after a Grand Dragon of the KKK, to claim their fundamental right to vote.

They were beaten bloodied and left for dead.

Our late friend and former colleague John Lewis was at the march.

We miss him.

Joining us tonight are other marchers who were there including Betty May Fikes, known as the "Voice of Selma”.

A daughter of gospel singers and preachers, she sang songs of prayer and protest on that Bloody Sunday,

to help shake the nation’s conscience. Five months later, the Voting Rights Act was signed into law.

But 59 years later, there are forces taking us back in time.

Voter suppression. Election subversion. Unlimited dark money. Extreme gerrymandering.

John Lewis was a great friend to many of us here. But if you truly want to honor him and all the heroes who marched with him, then it’s time for more than just talk.

Pass and send me the Freedom to Vote Act and the John Lewis Voting Rights Act!

If Democrats could not pass a new national voting standard when they controlled the House during Biden’s first two years in office, they will not be able to do it now, while Republicans control the chamber.

And stop denying another core value of America our diversity across American life.

Banning books.

It’s wrong!

Instead of erasing history, let’s make history!

I want to protect other fundamental rights!

Pass the Equality Act, and my message to transgender Americans: I have your back!

Pass the PRO Act for workers rights! And raise the federal minimum wage because every worker has the right to earn a decent living!

We are also making history by confronting the climate crisis, not denying it.

I’m taking the most significant action on climate ever in the history of the world.

I am cutting our carbon emissions in half by 2030.

The climate crisis may be an existential problem for humanity, but it did not rate mention in the first half of this State of the Union address. That said, Biden, with help from the Inflation Reduction Act, has done more than previous presidents to address the issue. But n ot enough to satisfy activists . Trump, meanwhile, likes to poke fun at climate efforts.

Creating tens of thousands of clean-energy jobs, like the IBEW workers building and installing 500,000 electric vehicle charging stations.

Conserving 30% of America’s lands and waters by 2030.

Taking historic action on environmental justice for fence-line communities smothered by the legacy of pollution.

And patterned after the Peace Corps and Ameri Corps, I’ve launched a Climate Corps to put 20,000 young people to work at the forefront of our clean energy future.

I’ll triple that number this decade.

All Americans deserve the freedom to be safe, and America is safer today than when I took office.

The year before I took office, murders went up 30% nationwide the biggest increase in history.

That was then.

Now, through my American Rescue Plan, which every Republican voted against, I’ve made the largest investment in public safety ever.

Last year, the murder rate saw the sharpest decrease in history, and violent crime fell to one of the lowest levels in more than 50 years.

This is true, at least based on preliminary 2023 data that should be treated with caution. The preliminary 2023 data published by the FBI, running through the third quarter of the year, showed that violent crime was down 8.2% compared to the same period in 2022 — a decline that would be “historically large” for a year, crime data expert Jeff Asher wrote in a December article. The data generally confirms Biden’s description of violent crime falling across the nation, though some communities have seen increases. Asher wrote: “The quarterly data shows violent crime down in big cities, small cities, suburban counties, and rural counties, pretty much across the board.”

But we have more to do.

Help cities and towns invest in more community police officers, more mental health workers, and more community violence intervention.

Give communities the tools to crack down on gun crime, retail crime, and carjacking.

Keep building public trust, as I’ve been doing by taking executive action on police reform, and calling for it to be the law of the land, directing my Cabinet to review the federal classification of marijuana, and expunging thousands of convictions for mere possession , because no one should be jailed for using or possessing marijuana!

Biden’s mass clemency for federal offenses of simple marijuana possession, announced before the m idterm elections in 2022 , was seen as a first step to national decriminalization.

To take on crimes of domestic violence, I am ramping up federal enforcement of the Violence Against Women Act, that I proudly wrote, so we can finally end the scourge of violence against women in America!

And there’s another kind of violence I want to stop.

With us tonight is Jasmine, whose 9-year-old sister Jackie was murdered with 21 classmates and teachers at her elementary school in Uvalde, Texas.

Soon after it happened, Jill and I went to Uvalde and spent hours with the families.

We heard their message, and so should everyone in this chamber do something.

I did do something by establishing the first-ever Office of Gun Violence Prevention in the White House that Vice President Harris is leading.

Meanwhile, my predecessor told the NRA he’s proud he did nothing on guns when he was President.

After another school shooting in Iowa he said we should just “get over it.”

I say we must stop it.

I’m proud we beat the NRA when I signed the most significant gun safety law in nearly 30 years!

Now we must beat the NRA again!

I’m demanding a ban on assault weapons and high-capacity magazines!

Pass universal background checks!

Again, none of this will happen without a major change in Congress.

None of this violates the Second Amendment or vilifies responsible gun owners.

As we manage challenges at home, we’re also managing crises abroad including in the Middle East.

I know the last five months have been gut-wrenching for so many people, for the Israeli people, the Palestinian people, and so many here in America.

This crisis began on October 7th with a massacre by the terrorist group Hamas.

1,200 innocent people women and girls men and boys slaughtered, many enduring sexual violence.

The deadliest day for the Jewish people since the Holocaust.

250 hostages taken.

Here in the chamber tonight are American families whose loved ones are still being held by Hamas.

I pledge to all the families that we will not rest until we bring their loved ones home.

We will also work around the clock to bring home Evan and Paul, Americans being unjustly detained all around the world.

Israel has a right to go after Hamas.

This is an incredibly important issue for Biden. Nothing else splits Democrats at the moment like Israel. Biden is a self-proclaimed Zionist. While he has increasingly called out the conservative government of Israeli Prime Minister Benjamin Netanyahu, it’s not nearly enough to satisfy the large portion of Democrats who are motivated by the plight of Palestinians who are stuck and starving in Gaza .

Hamas could end this conflict today by releasing the hostages, laying down arms, and surrendering those responsible for October 7th.

Israel has an added burden because Hamas hides and operates among the civilian population. But Israel also has a fundamental responsibility to protect innocent civilians in Gaza.

This war has taken a greater toll on innocent civilians than all previous wars in Gaza combined.

More than 30,000 Palestinians have been killed.

Most of whom are not Hamas.

Thousands and thousands are innocent women and children.

Girls and boys also orphaned.

Nearly 2 million more Palestinians under bombardment or displaced.

Homes destroyed, neighborhoods in rubble, cities in ruin.

Families without food, water, medicine.

It’s heartbreaking.

We’ve been working non-stop to establish an immediate ceasefire that would last for at least six weeks.

It is notable that while Biden said the US is working for an immediate ceasefire, he did not say permanent. Israel wants the ability to revisit any ceasefire after six weeks.

Biden’s optimism for a ceasefire seems to have cooled. He had previously predicted there would be a ceasefire by this past Monday. In the meantime, the world was horrified by the killing of more than 100 Palestinians trying to get food from an Israeli aid truck.

As Biden spoke, House Democratic Rep. Rashida Tlaib — the sole Palestinian American member of Congress — held a sign reading “Ceasefire Now.”

It would get the hostages home, ease the intolerable humanitarian crisis, and build toward something more enduring.

The United States has been leading international efforts to get more humanitarian assistance into Gaza.

Tonight, I’m directing the U.S. military to lead an emergency mission to establish a temporary pier in the Mediterranean on the Gaza coast that can receive large ships carrying food, water, medicine and temporary shelters.

No U.S. boots will be on the ground.

This temporary pier would enable a massive increase in the amount of humanitarian assistance getting into Gaza every day.

This pier sounds like an incredible engineering feat. It’s not clear how soon it can be achieved. Also, this was the second time in the speech where Biden pledged that US troops will not get involved in an international conflict.

But Israel must also do its part.

Israel must allow more aid into Gaza and ensure that humanitarian workers aren’t caught in the cross fire.

To the leadership of Israel I say this.

Humanitarian assistance cannot be a secondary consideration or a bargaining chip.

Protecting and saving innocent lives has to be a priority.

As we look to the future, the only real solution is a two-state solution.

I say this as a lifelong supporter of Israel and the only American president to visit Israel in wartime.

This is a public warning to Israel and an insistence that Israel must allow a Palestinian state. But it is not particularly stern considering the tens of thousands of Palestinians who have died .

There is no other path that guarantees Israel’s security and democracy.

There is no other path that guarantees Palestinians can live with peace and dignity.

There is no other path that guarantees peace between Israel and all of its Arab neighbors, including Saudi Arabia.

Creating stability in the Middle East also means containing the threat posed by Iran.

That’s why I built a coalition of more than a dozen countries to defend international shipping and freedom of navigation in the Red Sea.

I’ve ordered strikes to degrade Houthi capabilities and defend U.S. Forces in the region.

As Commander in Chief, I will not hesitate to direct further measures to protect our people and military personnel.

The strikes have not so far had a deterrent effect.

For years, all I’ve heard from my Republican friends and so many others is China’s on the rise and America is falling behind.

They’ve got it backward.

America is rising.

We have the best economy in the world.

Since I’ve come to office, our GDP is up.

He is welcome to say this. Most Americans do not currently seem to believe it.

And our trade deficit with China is down to the lowest point in over a decade.

We’re standing up against China’s unfair economic practices.

And standing up for peace and stability across the Taiwan Strait.

I’ve revitalized our partnerships and alliances in the Pacific.

I’ve made sure that the most advanced American technologies can’t be used in China’s weapons.

Frankly for all his tough talk on China, it never occurred to my predecessor to do that.

We want competition with China, but not conflict.

And we’re in a stronger position to win the competition for the 21st Century against China or anyone else for that matter.

Here at home I’ve signed over 400 bipartisan bills.

But there’s more to do to pass my Unity Agenda.

Strengthen penalties on fentanyl trafficking.

Pass bipartisan privacy legislation to protect our children online.

CNN's Brian Fung notes that this call for a bill to regulate social media platforms is the third time in as many years that Biden has criticized the social media industry in his State of the Union speech.

Notably, however, Biden’s call specifically highlighted legislation to protect children’s privacy — not any of the myriad bills circulating that would impose targeted restrictions on social media companies .

The House could vote soon on a separate bill meant to pressure TikTok’s China-linked parent company to spin off the app used by 170 million Americans.

Harness the promise of A.I. and protect us from its peril.

Ban A.I. voice impersonation and more!

Fung also notes that Biden knows personally about this. A fake robocall campaign cloned his voice and targeted thousands of New Hampshire primary voters in what authorities have described as an AI-enabled election meddling attempt.

But US lawmakers have struggled to advance any meaningful AI legislation in the roughly one year since Senate Majority Leader Chuck Schumer made a rare and personal effort to put AI at the top of the congressional agenda.

Even as disinformation experts warn of AI’s threats to elections and public discourse, few expect Congress to pass legislation reining in the AI industry during a divisive election year.

And keep our one truly sacred obligation, to train and equip those we send into harm’s way and care for them and their families when they come home, and when they don’t.

That’s why I signed the PACT Act, one of the most significant laws ever, helping millions of veterans who were exposed to toxins and who now are battling more than 100 cancers.

Many of them didn’t come home.

We owe them and their families.

And we owe it to ourselves to keep supporting our new health research agency called ARPA-H and remind us that we can do big things like end cancer as we know it!

Let me close with this.

I know I may not look like it, but I’ve been around a while.

And when you get to my age certain things become clearer than ever before.

I know the American story.

Again and again I’ve seen the contest between competing forces in the battle for the soul of our nation.

Between those who want to pull America back to the past and those who want to move America into the future.

My lifetime has taught me to embrace freedom and democracy.

A future based on the core values that have defined America.

Honesty. Decency. Dignity. Equality.

To respect everyone. To give everyone a fair shot. To give hate no safe harbor.

Now some other people my age see a different story.

An American story of resentment, revenge, and retribution.

That’s not me.

Biden put forward an energetic persona in this speech. And he pointed out that Trump is his age. Actually, Trump is four years younger.

The name “Trump” did not appear in the speech. But he was clearly top of mind. Trump has promised to be his supporters’ “retribution” and still does not admit to losing the 2020 election. Biden’s burden will be to convince voters who are wavering that trying to upend democracy should disqualify Trump.

I was born amid World War II when America stood for freedom in the world.

I grew up in Scranton, Pennsylvania and Claymont, Delaware among working people who built this country.

I watched in horror as two of my heroes, Dr. King and Bobby Kennedy, were assassinated and their legacies inspired me to pursue a career in service.

A public defender, county councilman, elected United States Senator at 29, then Vice President, to our first Black President, now President, with our first woman Vice President.

In my career I’ve been told I’m too young and I’m too old.

Whether young or old, I’ve always known what endures.

Our North Star.

The very idea of America, that we are all created equal and deserve to be treated equally throughout our lives.

We’ve never fully lived up to that idea, but we’ve never walked away from it either.

And I won’t walk away from it now.

My fellow Americans the issue facing our nation isn’t how old we are it’s how old our ideas are?

Hate, anger, revenge, retribution are among the oldest of ideas.

But you can’t lead America with ancient ideas that only take us back.

To lead America, the land of possibilities, you need a vision for the future of what America can and should be.

Tonight you’ve heard mine.

I see a future where we defend democracy not diminish it.

I see a future where we restore the right to choose and protect other freedoms not take them away.

I see a future where the middle class finally has a fair shot and the wealthy finally have to pay their fair share in taxes.

I see a future where we save the planet from the climate crisis and our country from gun violence.

Above all, I see a future for all Americans!

I see a country for all Americans!

And I will always be a president for all Americans!

Because I believe in America!

I believe in you the American people.

You’re the reason I’ve never been more optimistic about our future!

The speech ended with many more exclamations and a vigorous Biden pumping people up.

So let’s build that future together!

Let’s remember who we are!

We are the United States of America.

There is nothing beyond our capacity when we act together!

May God bless you all.

May God protect our troops.

IMAGES

  1. Herbert Simon Quote: “Solving a problem simply means representing it so

    in problem solving the word of means

  2. What Is Problem-Solving? Steps, Processes, Exercises to do it Right

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  3. Introduction to Problem Solving Skills

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  4. Problem Solving Cycle

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  5. Problem solving infographic 10 steps concept Vector Image

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  6. problem solving methods

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COMMENTS

  1. PDF Glossary of Problem-Solving Terms

    Mess A set of related but as yet undifferentiated problems. By definition, a mess is amenable to analysis, that is, the set of problems can be sorted out or differentiated from one another. Model A means of representing the structure of the situation in which the problem is embedded, typically in diagram form (e.g.,

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    The meaning of PROBLEM-SOLVING is the process or act of finding a solution to a problem. How to use problem-solving in a sentence.

  3. 80 Synonyms & Antonyms for problem-solving

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    Tutoring helps your student gain confidence when solving word problems involving means. Tutoring gives your student the opportunity to go over a few more examples of word problems involving means. Sometimes, all it takes to reach for confidence in these concepts is a little extra time outside of class. Tutors can even cater to your student's ...

  5. Why is the word "of" equivalent to multiplying in fraction word problems?

    Rewrite the word of as multiplication and solve as follows. This answer tells you how much of the whole pie Doreen ate: Doreen = 1/6 * 4/5 = 4/30* Now what I don't understand is the part where 1/6 is multiplied into 4/5 when it should, the book says that in almost all fraction word problems the word "of" almost always means "multiplication" and ...

  6. What is Problem Solving

    At its simplest, the meaning of problem-solving is the process of defining a problem, determining its cause, and implementing a solution. The definition of problem-solving is rooted in the fact that as humans, we exert control over our environment through solutions. We move forward in life when we solve problems and make decisions.

  7. PROBLEM-SOLVING definition

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  8. PROBLEM-SOLVING

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  9. What exactly do we mean by the term 'problem solving'?

    Just like creativity, problem solving is a key skill required across all sectors and at all levels. However, while the word 'creativity' can seem to refer to a very broad range of meanings, the term 'problem solving' can, in contrast, seem overly narrow. A well-defined problem can be understood, agreed upon and then solved, often using approaches that are familiar or well-practiced.

  10. PROBLEM-SOLVING definition and meaning

    The act or process of finding solutions to problems, esp by using a scientific or analytical.... Click for English pronunciations, examples sentences, video.

  11. Problem solving

    Definition. The term problem solving has a slightly different meaning depending on the discipline. For instance, it is a mental process in psychology and a computerized process in computer science. There are two different types of problems: ill-defined and well-defined; different approaches are used for each. Well-defined problems have specific ...

  12. What Are Problem-Solving Skills? Definition and Examples

    Problem-Solving Skills Definition. Problem-solving skills are the ability to identify problems, brainstorm and analyze answers, and implement the best solutions. An employee with good problem-solving skills is both a self-starter and a collaborative teammate; they are proactive in understanding the root of a problem and work with others to ...

  13. Word Problems on Arithmetic Mean

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  14. problem-solving noun

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  15. The Problem-Solving Process

    Allocate Resources. Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue. The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off ...

  16. problem noun

    a thing that is difficult to deal with or to understand. big/serious/major problems; She has a lot of health problems.; financial/social/technical problems; Let me know if you have any problems.; The government must address the problem of child poverty.; We cannot tackle this problem effectively on our own.; We are dealing with a serious problem here.; Money isn't going to solve the problem.

  17. What is Problem Solving? Steps, Process & Techniques

    Finding a suitable solution for issues can be accomplished by following the basic four-step problem-solving process and methodology outlined below. Step. Characteristics. 1. Define the problem. Differentiate fact from opinion. Specify underlying causes. Consult each faction involved for information. State the problem specifically.

  18. Word Problems Calculator

    An age problem is a type of word problem in math that involves calculating the age of one or more people at a specific point in time. These problems often use phrases such as 'x years ago,' 'in y years,' or 'y years later,' which indicate that the problem is related to time and age.

  19. PDF Key Words for Solving Word Problems

    The hardest part of solving a word problem is actually understanding the problem and determining the operation (or operations) that needs to be performed. Listed below are a few of the most commonly used key words in word problems and the operations that they signal. Keep in mind that same key words may signal more than one operation.

  20. What is another word for problem-solving

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  22. a means of solving a problem or dealing with a difficult situation

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  23. Problem Solving in Nursing: Strategies for Your Staff

    Here are some essentials for building a culture of innovation that encourages problem solving: Present problems as opportunities instead of obstacles. Strive to be a positive role model. Support creative thinking and staff collaboration. Encourage feedback and embrace new ideas. Respect staff knowledge and abilities.

  24. Word of the Day: Obeisance

    Obeisance is a synonym of homage that refers to an acknowledgement of another's importance or superiority. Obeisance can also mean "a movement of the body (such as a bow) showing respect for someone or something.". // The young singer paid obeisance to Otis Redding while on tour in Memphis by singing " (Sittin' on) The Dock of the Bay

  25. What is Evidence-Based Practice in Nursing?

    Evidence-based practice in nursing involves providing holistic, quality care based on the most up-to-date research and knowledge rather than traditional methods, advice from colleagues, or personal beliefs. Nurses can expand their knowledge and improve their clinical practice experience by collecting, processing, and implementing research findings.

  26. Leadership in Nursing: Qualities & Why It Matters

    Professionalism and Leadership: Leaders in nursing build vital relationships and collaborate with various health care teams on sensitive topics. Using critical thinking skills allows those in nursing leadership roles to analyze decisions impacting the organization. They then clearly explain the rationale in a manner that encourages staff support.

  27. Can you solve it? The word game at the cutting edge of computer science

    Problem 1. Problem 2. In this puzzle, the clues are more ambiguous: Some clues are synonyms for the answer, and some are descriptions of the answer. Thus 'exclamation' refers to an exclamation ...

  28. Jumble 3/13/24 Answers

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  29. Biden's State of the Union address, annotated and fact-checked

    This math doesn't work. Passing legislation to protect abortion rights nationwide and restore Roe would surely require 60 votes in the Senate. Democrats currently have 51 seats, and there are ...

  30. The New York Times Crossword

    Down. 1 Bird in a Poe poem. 2 Biblical garden. 3 Where the invading aliens come from in H.G. Wells's "The War of the Worlds". 4 When a high schooler might take a limo. 5 Ready for picking.