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Improve your grades with Brainly! Use verified answers, tutor chat support, and textbook solutions to make the As start rolling in. Brainly, the AI Learning Companion. Learn with Brainly — the world’s most popular homework help app! Get quick solutions from students and Experts, while enjoying features that make studying fast, easy, and fun! In just seconds, you can find correct solutions with step-by-step explanations to help you understand concepts, boost your knowledge, and improve your grades. - Scan a pic of your math equation or word problem to get answers in seconds using Brainly’s Scan to Solve feature! - Improve your grades using 24/7 access to AI Tutor and Live Expert support. - Get Expert-Verified homework answers from Community Q&A. - Find personalized, in-depth answers powered by AI. Get ahead in school while earning points, finding study buddies, competing with other students, and climbing the leaderboards. – Do you struggle with math? Math Solver to the rescue! If you’re stuck and confused, just scan a pic of the question for a fast answer in seconds, plus a step-by-step explanation. Algebra, geometry, trigonometry, or calculus: no equation is too tough for Brainly! Solve math equations and word problems at any school level — including AP and college courses. – Why have just one study buddy when you can have millions? Never study alone again with Brainly Community Q&A, where you can ask any question for Expert-Verified answers from users around the world! Our large community of Experts is available 24/7 to help you with any question in math, science, history, English, & other subjects. Our network of reliable moderators ensures that all the answers you get are correct and easy to understand. We also allow parents and children to pair accounts as part of our commitment to safety. – Struggling with any particular subject or topic? A Live Expert* will help you get back on track! Get in-depth guidance and see all the steps to make homework easier and exams less stressful. Understand complex concepts in science & math with your own learning guide at your fingertips! And for personalized AI support, you can switch to the AI Tutor for on-demand help, available in seconds. *This feature is available if you have a Brainly Tutor Plan. – Do you spend a lot of time searching for textbook answers? Explore Brainly's library of solutions for structured, step-by-step answers written by Experts. Find explanations for practice questions in STEM textbooks and more by searching for your book's grade, title, author, or ISBN. – What if we told you that studying can be fun? Competition thrives on Brainly with learning-based leaderboards, badges, and achievements. Make tough questions a competition for others as you get rewards for answering the trickiest questions. Learning can take a lot of effort, but it doesn’t need to be all work and no play. – Get more out of Brainly with Brainly Plus & Brainly Tutor! Access to Brainly is 100% free. However, if you want to enjoy all of Brainly’s features without ads, upgrade to Brainly Plus or Brainly Tutor. *** Get fun updates from us on: Instagram @brainly Facebook @brainlygroup Tiktok @brainly For any problems, reach out to our support team: https://brainly.com/contact | [email protected] Marketing: https://brainly.com Terms of use: https://brainly.com/pages/terms_of_use Privacy policy: https://brainly.com/pages/privacy_policy
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Unit 1: Problem solving with arithmetic
Comparing with multiplication.
- Comparing with multiplication (Opens a modal)
- Comparing with multiplication and addition: giraffe (Opens a modal)
- Comparing with multiplication and addition: money (Opens a modal)
- Comparing with multiplication: magic (Opens a modal)
- Compare with multiplication Get 5 of 7 questions to level up!
- Compare with multiplication word problems Get 3 of 4 questions to level up!
Multiplication, division word problems
- Division word problem: field goals (Opens a modal)
- Multiplication word problem: pizza (Opens a modal)
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Multi-step word problems
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Mathematicians Are Edging Close to Solving One of the World's 7 Hardest Math Problems
And there’s $1 million at stake.
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- In new research, mathematicians have narrowed down one of the biggest outstanding problems in math.
- Huge breakthroughs in math and science are usually the work of many people over many years.
- Seven math problems were given a $1 million bounty each in 2000, and just one has been solved so far.
The “Millennium Problems” are seven infamously intractable math problems laid out in the year 2000 by the prestigious Clay Institute, each with $1 million attached as payment for a solution. They span all areas of math , as the Clay Institute was founded in 1998 to push the entire field forward with financial support for researchers and important breakthroughs.
But the only solved Millennium Problem so far, the Poincare conjecture, illustrates one of the funny pitfalls inherent to offering a large cash prize for math. The winner, Grigori Perelman, refused the Clay prize as well as the prestigious Fields Medal. He withdrew from mathematics and public life in 2006, and even in 2010, he still insisted his contribution was the same as the mathematician whose work laid the foundation on which he built his proof, Richard Hamilton.
Math, all sciences, and arguably all human inquiries are filled with pairs or groups that circle the same finding at the same time until one officially makes the breakthrough. Think about Sir Isaac Newton and Gottfried Leibniz, whose back-and-forth about calculus led to the combined version of the field we still study today. Rosalind Franklin is now mentioned in the same breath as her fellow discoverers of DNA, James Watson and Francis Crick. Even the Bechdel Test for women in media is sometimes called the Bechdel-Wallace Test, because humans are almost always in collaboration.
That’s what makes this new paper so important. Two mathematicians—Larry Guth of the Massachusetts Institute of Technology (MIT) and James Maynard of the University of Oxford—collaborated on the new finding about how certain polynomials are formed and how they reach out into the number line. Maynard is just 37, and won the Fields Medal himself in 2022. Guth, a decade older, has won a number of important prizes with a little less name recognition.
The Riemann hypothesis is not directly related to prime numbers , but it has implications that ripple through number theory in different ways (including with prime numbers). Basically, it deals with where and how the graph of a certain function of complex numbers crosses back and forth across axes. The points where the function crosses an axis is called a “zero,” and the frequency with which those zeroes appear is called the zero density.
In the far reaches of the number line, prime numbers become less and less predictable (in the proverbial sense). They are not, so far, predictable in the literal sense—a fact that is an underpinning of modern encryption , where data is protected by enormous strings of integers made by multiplying enormous prime numbers together. The idea of a periodic table of primes, of any kind of template that could help mathematicians better understand where and how large primes cluster together or not, is a holy grail.
In the new paper, Maynard and Guth focus on a new limitation of Dirichlet polynomials. These are special series of complex numbers that many believe are of the same type as the function involved in the Riemann hypothesis involves. In the paper, they claim they’ve proven that these polynomials have a certain number of large values, or solutions , within a tighter range than before.
In other words, if we knew there might be an estimated three Dirichlet values between 50 and 100 before, now we may know that range to be between 60 and 90 instead. The eye exam just switched a blurry plate for a slightly less blurry one, but we still haven’t found the perfect prescription. “If one knows some more structure about the set of large values of a Dirichlet polynomial, then one can hope to have improved bound,” Maynard and Guth conclude.
No, this is not a final proof of the Riemann hypothesis. But no one is suggesting it is. In advanced math, narrowing things down is also vital. Indeed, even finding out that a promising idea turns out to be wrong can have a lot of value—as it has a number of times in the related Twin Primes Conjecture that still eludes mathematicians.
In a collaboration that has lasted 160 years and counting, mathematicians continue to take each step together and then, hopefully, compare notes.
![Headshot of Caroline Delbert Headshot of Caroline Delbert](https://hips.hearstapps.com/rover/profile_photos/a22690a4-8f27-4d35-88eb-eee99009129c_1572980876.png?fill=1:1&resize=120:*)
Caroline Delbert is a writer, avid reader, and contributing editor at Pop Mech. She's also an enthusiast of just about everything. Her favorite topics include nuclear energy, cosmology, math of everyday things, and the philosophy of it all.
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10 of the Hardest Math Problems Ever Solved
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Computer Science > Computation and Language
Title: dart-math: difficulty-aware rejection tuning for mathematical problem-solving.
Abstract: Solving mathematical problems requires advanced reasoning abilities and presents notable challenges for large language models. Previous works usually synthesize data from proprietary models to augment existing datasets, followed by instruction tuning to achieve top-tier results. However, our analysis of these datasets reveals severe biases towards easy queries, with frequent failures to generate any correct response for the most challenging queries. Hypothesizing that difficult queries are crucial to learn complex reasoning, we propose Difficulty-Aware Rejection Tuning (DART), a method that allocates difficult queries more trials during the synthesis phase, enabling more extensive training on difficult samples. Utilizing DART, we have created new datasets for mathematical problem-solving that focus more on difficult queries and are substantially smaller than previous ones. Remarkably, our synthesis process solely relies on a 7B-sized open-weight model, without reliance on the commonly used proprietary GPT-4. We fine-tune various base models on our datasets ranging from 7B to 70B in size, resulting in a series of strong models called DART-MATH. In comprehensive in-domain and out-of-domain evaluation on 6 mathematical benchmarks, DART-MATH outperforms vanilla rejection tuning significantly, being superior or comparable to previous arts, despite using much smaller datasets and no proprietary models. Furthermore, our results position our synthetic datasets as the most effective and cost-efficient publicly available resources for advancing mathematical problem-solving.
Comments: | Preprint. Data and model checkpoints are available at |
Subjects: | Computation and Language (cs.CL); Artificial Intelligence (cs.AI) |
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(or [cs.CL] for this version) |
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Get math homework help 24/7. Post your math homework questions and get expert-verified answers fast! Learn faster and improve your grades with Brainly! All Mathematics History English Biology Chemistry Physics Social Studies Advanced Placement (AP) SAT Geography Health Arts Business Computers and Technology
Brainly is the knowledge-sharing community where hundreds of millions of students and experts put their heads together to crack their toughest homework questions. ... "I struggled with math, but Brainly helped me overcome it by providing . step-by-step explanations. for complex problems." ...
Brainly, the AI Learning Companion. Brainly is a powerful Math solver app that can help you with your school doubts. Solve Math problems in Algebra, Trigonometry, & Geometry with correct & expert-verified answers instantly. With Brainly, you can find solutions to your math homework. Math answers have never been easier to find!
An example of problem-solving steps in math is provided. Explanation: Problem-solving Steps: Problem-solving is a series of sequential steps used to respond to a well-structured problem. While there is no simple step-by-step method that works for every problem, the general procedures facilitate problem-solving and make it more meaningful ...
Math Solver to the rescue! If you're stuck and confused, just scan a pic of the question for a fast answer in seconds, plus a step-by-step explanation. Algebra, geometry, trigonometry, or calculus: no equation is too tough for Brainly! Solve math equations and word problems at any school level — including AP and college courses.
Solution. This problem can be viewed as either a linear function or as an arithmetic sequence. The table of values give us a few clues towards a formula. The problem allows us to begin the sequence at whatever n n −value we wish. It's most convenient to begin at n = 0 n = 0 and set a0 = 1500 a 0 = 1500.
Free math problem solver answers your algebra homework questions with step-by-step explanations. Mathway. Visit Mathway on the web. Start 7-day free trial on the app. Start 7-day free trial on the app. Download free on Amazon. Download free in Windows Store. Take a photo of your math problem on the app. get Go. Algebra. Basic Math.
Answer: mark as brainliest!. Step-by-step explanation: To solve arithmetic problems easily, understand the problem statement clearly, break it down into smaller steps, use appropriate mathematical operations, check your work for accuracy, and practice regularly to enhance your skills.
Also, a good, general understanding of what the problem means should be sought. Choose a strategy to solve the problem. Some of the possible strategies will be discussed in the rest of this article. Carry out the problem solving strategy. If the first problem solving technique you try doesn't work, try another. Check the solution.
Problem solving with arithmetic | Khan Academy. 2 units · 15 skills. Unit 2 Factors, multiples, and patterns. Course challenge. Test your knowledge of the skills in this course. Start Course challenge. Math Content. Operations and Algebraic Thinking 201-210.
Ask Math questions from the largest social learning community and get all your Math doubts & problems solved. Brainly.in #1 social learning platform.
To solve the arithmetic problem without using a calculator, we add the given numbers in base 10 (decimal) to get the result.Then, we convert the decimal result to hexadecimal by repeatedly dividing it by 16 and taking remainders. The hexadecimal representation of the result is 24.. To solve the arithmetic problem without using a calculator, we need to perform the addition in base 10 (decimal ...
Brainly User Brainly User Answer: To solve arithmetic problems easily, understand the problem statement clearly, break it down into smaller steps, use appropriate mathematical operations, check your work for accuracy, and practice regularly to enhance your skills. Hope it helps.
Quick Math Helper & Science Solutions | Get Homework Answers for School Doubts
The Math Calculator will evaluate your problem down to a final solution. You can also add, subtraction, multiply, and divide and complete any arithmetic you need. Step 2: Click the blue arrow to submit and see your result! Math Calculator from Mathway will evaluate various math problems from basic arithmetic to advanced trigonometric expressions.
Problem solving for arithmetic sequence. Answer: The arithmetic sequence formula is given as, an=a1+ (n−1)d a n = a 1 + ( n − 1 ) d where, an a n = a general term, a1 a 1 = first term, and and d is the common difference. This is to find the general term in the sequence. Step-by-step explanation:
Examples of arithmetic series problem solving with solution - 405720. answered Examples of arithmetic series problem solving with solution See answer Advertisement Advertisement MargiebeltraN MargiebeltraN 5,9,13,17 n=10 a1=5 d=4 S10=10/2 [2(5)+(10-1)4] =5(10+36) =5(46) S10=230 ... Get the Brainly App
Solve Complex Math Problems Instantly with a Click of your Smartphone's Camera Math Solver is the First in a Suite of New Products Arriving to the Brainly Community in 2021 January 27, 2021 — New York — Ask any high school student which subject is the hardest to find quality help with online, and you will undoubtedly hear that math ...
To solve the arithmetic problems: 1. Learn the tables at least up to 20. 2. Practise questions regularly at least 10 to 20 questions. 3. Make a formula chart of the arithmetic chapters like AP, GP, important identities. 4. Paste the formula chart in your room to revise it regularly. 5. Don't just take it as a burden, learn by enjoying ...
Mathematicians Are Edging Close to Solving One of the World's 7 Hardest Math Problems And there's $1 million at stake. By Caroline Delbert Published: Jul 09, 2024 10:15 AM EDT
Answer. A square pyramid has 5 faces. 4 of which are triangles, while the 5th is a square. It is not possible to draw a square pyramid where all faces are triangle. From the question, we have: Shape: Square Pyramid. Faces: Triangles. A square pyramid is called a square pyramid because the base face is a square, while the other faces are triangle.
Solving mathematical problems requires advanced reasoning abilities and presents notable challenges for large language models. Previous works usually synthesize data from proprietary models to augment existing datasets, followed by instruction tuning to achieve top-tier results. However, our analysis of these datasets reveals severe biases towards easy queries, with frequent failures to ...
Arithmetic sequence Get the answers you need, now! 9847701256 9847701256 24.07.2021 Math Secondary School answered Arithmetic sequence See answer Advertisement Advertisement sweetysuvarnakarottu sweetysuvarnakarottu An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant k. ... Get the Brainly App ...
Physics requires both speed and accuracy in solving arithmetic problems. The ability to quickly and accurately solve equations is crucial in physics, as it helps in understanding and analyzing natural phenomena. Physics problem-solving skills also involve estimating and assessing the significance of numerical answers.
Step-by-step explanation: To solve profit and loss arithmetic problems, follow these steps:1. Understand the Problem: Read the problem carefully to understand what is given and what needs to be found.2. Identify the Given Values: Identify the cost price (CP), selling price (SP), profit (if any), or loss (if any) mentioned in the problem.3.