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Motocross Gear, Dirt Bike Gear, Motocross Apparel #answers #to #my #questions


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Latest, Top, Free, Best Mathematics Interview Questions and Answers – Mathematics Job


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Mathematics Interview Questions Answers

Below we have listed all the Mathematics Interview Questions and answers. Feel free to comment on any Mathematics Interview Questions or answer by the comment feature available on the page.

To buy an eBook containing 30,000 Interview Questions, with Answers, Click Here .
View All Mathematics Interview Questions & AnswersExam Mode / Learning Mode

Mathematics Interview Questions Answers

Mathematics is the science that deals with the logic of shape, quantity and arrangement. Math is all around us, in everything we do. It is the building block for everything in our daily lives, including mobile devices, architecture (ancient and modern), art, money, engineering, and even sports. At a naive level we can describe mathematics as a language that expresses relationships. This includes logic, measurement, algebra, calculus and geometry.

Highly Recommended, Hand Picked Mathematics Books


Fish Shop – Free Online Math Game #riddle #answers #search #engine


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Fish Shop – Multiplication

Fish Shop – Multiplication

Fish Shop – Multiplication Math Game

Content Skill: Multiplication Common Core State Standards: CCSS.Math.Content.3.OA.C.7 – Fluently multiply within 100, using strategies such as the relationship between multiplication and division or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Description

Welcome to your first day on the job at the fantastic Fish Shop. Learn the multiplication tables and have tons of fun in this multiplication.com classic. It’s been a student favorite at multiplication.com for years. In it you answer multiplication questions to sell fish to some some excited kids. This game is a great way to learn your multiplication facts and have fun at same time. Be sure not to take the wrong fish.

So grab your scoop and let’s get to work.

Instructions

After the game finishes loading, you’re welcomed to the fantastic fish shop. Click on one of the fish that represent levels to get started.

This screen is your welcome message to get the game started. You’re told that you must try to answer the questions correctly in order to keep the the kids from leaving angry. Customer service is always king in the fish business. Click the start button to get started.

Now comes the fun part. Customers will begin coming into the fish shop. Answer multiplication questions correctly by clicking on the fish tank represented by the correct answer, and you’ll give the kid the fish they’re looking for. Answer the multiplication question incorrectly, and you’ll give the kid a fish they didn’t want. You’ll see their facial expression change when they don’t get what they want. If you answer the question incorrectly two times the kids will leave in a huff. Notice there’s a indicator at the bottom left telling you how many customers have been happy or sad. And there’s an indicator telling you how many customers are left in this level.

After you successfully answered all the multiplication questions from level one, you now go to level two. But before you go to level two, you get to choose a new background for the fish shop. Click one of the three backgrounds and you’ll see the background change.

This screen will let you know that level two is a little tougher because you’ll have to answer to two multiplication questions for every kid. Click the start button to move on.

Now you need to answer the first multiplication equation represented by the fish at the bottom. Then after successfully answering the first multiplication question, answer the second multiplication question represent by the fish on the top.

After you finish level two, you will be able to now select the fish tank that will be shown in level III. Click one of the three fish tanks to move on.

This screen lets you know that these kids are pretty picky. Click the start button to get started answering questions in level III.

After you finish level III, you will see this congratulations screen letting you know that you have passed all three levels of the Fish Shop multiplication game. If you’d like to play again, simply click the “Play Again” button.


Mathematical Induction – Problems With Solutions #answer #to #life


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Mathematical Induction – Problems With Solutions

The principle of mathematical induction is used to prove that a given proposition (formula, equality, inequality?) is true for all positive integer numbers greater than or equal to some integer N.

Let us denote the proposition in question by P (n), where n is a positive integer. The proof involves two steps:

Step 1: We first establish that the proposition P (n) is true for the lowest possible value of the positive integer n.

Step 2: We assume that P (k) is true and establish that P (k+1) is also true

Use mathematical induction to prove that

1 + 2 + 3 +. + n = n (n + 1) / 2

for all positive integers n.

Solution to Problem 1:

  • Let the statement P (n) be

1 + 2 + 3 +. + n = n (n + 1) / 2

  • STEP 1: We first show that p (1) is true.

    Right Side = 1 (1 + 1) / 2 = 1

  • Both sides of the statement are equal hence p (1) is true.
  • STEP 2: We now assume that p (k) is true

    1 + 2 + 3 +. + k = k (k + 1) / 2

  • and show that p (k + 1) is true by adding k + 1 to both sides of the above statement

    1 + 2 + 3 +. + k + (k + 1) = k (k + 1) / 2 + (k + 1)

  • The last statement may be written as

    1 + 2 + 3 +. + k + (k + 1) = (k + 1)(k + 2) / 2

  • Which is the statement p(k + 1).
  • 1 2 + 2 2 + 3 2 +. + n 2 = n (n + 1) (2n + 1)/ 6

    For all positive integers n.

    Solution to Problem 2:

    • Statement P (n) is defined by

    1 2 + 2 2 + 3 2 +. + n 2 = n (n + 1) (2n + 1)/ 2

  • STEP 1: We first show that p (1) is true.

    Left Side = 1 2 = 1

    Right Side = 1 (1 + 1) (2*1 + 1)/ 6 = 1

  • Both sides of the statement are equal hence p (1) is true.
  • STEP 2: We now assume that p (k) is true

    1 2 + 2 2 + 3 2 +. + k 2 = k (k + 1) (2k + 1)/ 6

  • and show that p (k + 1) is true by adding (k + 1) 2 to both sides of the above statement

    1 2 + 2 2 + 3 2 +. + k 2 + (k + 1) 2 = k (k + 1) (2k + 1)/ 6 + (k + 1) 2

  • Set common denominator and factor k + 1 on the right side

    = (k + 1) [ k (2k + 1)+ 6 (k + 1) ] /6

  • Expand k (2k + 1)+ 6 (k + 1)

    = (k + 1) [ 2k 2 + 7k + 6 ] /6

  • Now factor 2k 2 + 7k + 6.

    = (k + 1) [ (k + 2) (2k + 3) ] /6

  • We have started from the statement P(k) and have shown that

    1 2 + 2 2 + 3 2 +. + k 2 + (k + 1) 2 = (k + 1) [ (k + 2) (2k + 3) ] /6

  • Which is the statement P(k + 1).
  • Use mathematical induction to prove that

    1 3 + 2 3 + 3 3 +. + n 3 = n 2 (n + 1) 2 / 4

    for all positive integers n.

    Solution to Problem 3:

    • Statement P (n) is defined by

    1 3 + 2 3 + 3 3 +. + n 3 = n 2 (n + 1) 2 / 4

  • STEP 1: We first show that p (1) is true.

    Left Side = 1 3 = 1

    Right Side = 1 2 (1 + 1) 2 / 4 = 1

  • hence p (1) is true.
  • STEP 2: We now assume that p (k) is true

    1 3 + 2 3 + 3 3 +. + k 3 = k 2 (k + 1) 2 / 4

  • add (k + 1) 3 to both sides

    1 3 + 2 3 + 3 3 +. + k 3 + (k + 1) 3 = k 2 (k + 1) 2 / 4 + (k + 1) 3

  • factor (k + 1) 2 on the right side

    = (k + 1) 2 [ k 2 / 4 + (k + 1) ]

  • set to common denominator and group

    = (k + 1) 2 [ k 2 + 4 k + 4 ] / 4

    = (k + 1) 2 [ (k + 2) 2 ] / 4

  • We have started from the statement P(k) and have shown that

    1 3 + 2 3 + 3 3 +. + k 3 + (k + 1) 3 = (k + 1) 2 [ (k + 2) 2 ] / 4

  • Which is the statement P(k + 1).
  • Prove that for any positive integer number n. n 3 + 2 n is divisible by 3

    Solution to Problem 4:

    • Statement P (n) is defined by

    n 3 + 2 n is divisible by 3

  • STEP 1: We first show that p (1) is true. Let n = 1 and calculate n 3 + 2n

    3 is divisible by 3

  • hence p (1) is true.
  • STEP 2: We now assume that p (k) is true

    k 3 + 2 k is divisible by 3

    is equivalent to

    k 3 + 2 k = 3 M. where M is a positive integer.

  • We now consider the algebraic expression (k + 1) 3 + 2 (k + 1); expand it and group like terms

    (k + 1) 3 + 2 (k + 1) = k 3 + 3 k 2 + 5 k + 3

    = [ k 3 + 2 k] + [3 k 2 + 3 k + 3]

    = 3 M + 3 [ k 2 + k + 1 ] = 3 [ M + k 2 + k + 1 ]

  • Hence (k + 1) 3 + 2 (k + 1) is also divisible by 3 and therefore statement P(k + 1) is true.
  • Prove that 3 n n 2 for n = 1, n = 2 and use the mathematical induction to prove that 3 n n 2 for n a positive integer greater than 2.

    Solution to Problem 5:

    • Statement P (n) is defined by
  • STEP 1: We first show that p (1) is true. Let n = 1 and calculate 3 1 and 1 2 and compare them
  • 3 is greater than 1 and hence p (1) is true.
  • Let us also show that P(2) is true.
  • Hence P(2) is also true.
  • STEP 2: We now assume that p (k) is true
  • Multiply both sides of the above inequality by 3

    3 * 3 k 3 * k 2

  • The left side is equal to 3 k + 1. For k , 2, we can write

    k 2 2 k and k 2 1

  • We now combine the above inequalities by adding the left hand sides and the right hand sides of the two inequalities

    2 k 2 2 k + 1

  • We now add k 2 to both sides of the above inequality to obtain the inequality

    3 k 2 k 2 + 2 k + 1

  • Factor the right side we can write

    3 * k 2 (k + 1) 2

  • If 3 * 3 k 3 * k 2 and 3 * k 2 (k + 1) 2 then

    3 * 3 k (k + 1) 2

  • Rewrite the left side as 3 k + 1

    3 k + 1 (k + 1) 2

  • Which proves tha P(k + 1) is true
  • Prove that n. 2 n for n a positive integer greater than or equal to 4. (Note: n! is n factorial and is given by 1 * 2 *. * (n-1)*n.)

    Solution to Problem 6:

    • Statement P (n) is defined by
  • STEP 1: We first show that p (4) is true. Let n = 4 and calculate 4. and 2 n and compare them
  • 24 is greater than 16 and hence p (4) is true.
  • STEP 2: We now assume that p (k) is true
  • Multiply both sides of the above inequality by k + 1

    k! (k + 1) 2 k (k + 1)

  • The left side is equal to (k + 1). For k , 4, we can write
  • Multiply both sides of the above inequality by 2 k to obtain

    2 k (k + 1) 2 * 2 k

  • The above inequality may be written

    2 k (k + 1) 2 k + 1

  • We have proved that (k + 1)! 2 k (k + 1) and 2 k (k + 1) 2 k + 1 we can now write
  • We have assumed that statement P(k) is true and proved that statment P(k+1) is also true.
  • Use mathematical induction to prove De Moivre’s theorem

    [ R (cos t + i sin t) ] n = R n (cos nt + i sin nt)

    for n a positive integer.

    Solution to Problem 7:

    • STEP 1: For n = 1

    [ R (cos t + i sin t) ] 1 = R 1 (cos 1*t + i sin 1*t)

  • It can easily be seen that the two sides are equal.
  • STEP 2: We now assume that the theorem is true for n = k, hence

    [ R (cos t + i sin t) ] k = R k (cos kt + i sin kt)

  • Multiply both sides of the above equation by R (cos t + i sin t)

    [ R (cos t + i sin t) ] k R (cos t + i sin t) = R k (cos kt + i sin kt) R (cos t + i sin t)

  • Rewrite the above as follows

    [ R (cos t + i sin t) ] k + 1 = R k + 1 [ (cos kt cos t – sin kt sin t) + i (sin kt cos t + cos kt sin t) ]

  • Trigonometric identities can be used to write the trigonometric expressions (cos kt cos t – sin kt sin t) and (sin kt cos t + cos kt sin t) as follows

    (cos kt cos t – sin kt sin t) = cos(kt + t) = cos(k + 1)t

    (sin kt cos t + cos kt sin t) = sin(kt + t) = sin(k + 1)t

  • Substitute the above into the last equation to obtain

    [ R (cos t + i sin t) ] k + 1 = R k + 1 [ cos (k + 1)t + sin(k + 1)t ]

  • It has been established that the theorem is true for n = 1 and that if it assumed true for n = k it is true for n = k + 1.

  • Motocross Kit #dictionary #and #thesaurus #free


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    POA Racing for Motocross Kit, Helmets, Clothing and More

    A Leading Lancashire Motocross shop who provides a wide range of Motocross equipment online, delivered direct to your door. POA Racing are a specialist Motocross shop who sells a wide range of Motocross equipment, MX kit, motocross helmets, motocross clothing and accessories including the Oakley Airbrake MX Googles .

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    Online Math Help – Learning Resources #maths #answers


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    Online Math Help Learning Resources

    Is math your favorite subject or your most hated topic in school? Are you looking for free online math help, math fun and other useful resources? In this site, you will find interesting quizzes, practice, homework help and other materials to keep you occupied; or fun facts, games, puzzles and other cool stuff to make this subject something to be enjoyed rather than dreaded. Have some fun while learning some key skills to improve your grades.

    For parents, teachers and educators, there are loads of materials here for teaching and learning online. Find interesting and fun stuff to help your kids, students and children to enjoy, appreciate and learn numbers, counting, arithmetic, fractions, computation, geometry, statistics, set theory, trigonometry and even algebra and matrices! Check out our Interactive Zone for dynamic online worksheets, exercises and other simulations.

    You can also use our free calculators and math tools to check your answers for many types of math problems: Basic Math, Pre-Algebra, Algebra, Trigonometry, Precalculus, Calculus, Statistics, Graphing and Matrices.

    Become a fan at our FaceBook page to follow our updates or to give us your feedback and comments. Do let us know how we can continue to improve our website.

    Are you looking for free math help that is suitable for a particular grade? Here, we have thousands of free math videos that are categorized according to grades. You can view the videos as many times as needed and learn math at your own speed. We also have free worksheets and games that will help you to understand the concepts better. Go to the menu for Grades.

    Do you need extra help in a particular math topic or maybe you did not understand your textbook? We have hundreds of free online math tutorials that can help you. Each tutorial will explain the math concepts and provide worked solutions. Videos are also included to help improve your learning. Go to the menu for Topics.

    For more specific key words, try our search engine below.

    Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

    You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

    What’s New?

    Our sub-site for interactive worksheets – Interactive Zone is now mobile-friendly!

    Sep 24, 2016 Construct rectangles from unit squares and determine the perimeters

    Sep 24, 2016 Line Plots and Rectangles

    Sep 15, 2016 SAT Study Tips: Writing and Language Test Section

    Jul 08, 2016 Algebra 2/Trigonometry Common Core Regents Exam – June 2016

    Jun 18, 2016 Math Palindrome

    Jun 18, 2016 GRE Practice Test 2 Quantitative Reasoning 1

    Jun 18, 2016 GRE Practice Test 2 Quantitative Reasoning 3

    Jun 18, 2016 GRE Practice Test 2 Quantitative Reasoning 2

    Jun 18, 2016 GRE Practice Test 2 Quantitative Reasoning 6

    Jun 18, 2016 GRE Practice Test 2 Quantitative Reasoning 4


    Free Online Thesaurus #jumble #puzzle #answers


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    Graphwords.com online thesaurus

    What is it?

    It’s an free English online thesaurus that helps you find the meanings of words and show connections among associated words. You can easily see the meaning of each by simply placing the mouse cursor over it.

    Underneath Graph Words lays the WordNet – a large lexical database of English. Nouns, verbs, adjectives and adverbs are grouped into sets of cognitive synonyms (synsets), each expressing a distinct concept. These meanings and semantic relationships are revealed graphically by the HTML5 canvas made available by Graph Words.

    Usage of this Online Thesaurus tool

    To search for associated words, type the word in the search box at the top of the window and press the “Draw” button. You may also press the enter key instead. After searching for a word, the main display will populate with thesaurus. The word you searched for will appear in the center of the display, and will be surrounded with words and meanings that are related to it.
    To save what is currently displayed in the Graph Words, you can press the “Save as image” button on the toolbar.

    Examples of thesaurus for popular words

    Color coding


    Online State-Specific Practice Tests and Benchmark Testing – USATestprep, Inc #answers #to


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    USATestprep, Inc.

    Teacher-developed

    USATestprep was founded by two teachers who believe that web-based technology could improve student test performance and curriculum mastery.

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    USATestprep is very user-friendly! Students and teachers can use the site effectively from the first day of purchase. We also offer a live online training session, as well as tutorial videos on every important aspect of our site.


    The Expert TA #the #answer


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    Every aspect of Expert TA is directed at evolving how students learn.

    Testimonials

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    Matt Evans, Ph.D. Associate Professor of Physics. University of Wisconsin, Eau Claire