Tamara knows that the arithmetic mean of her five quiz scores 4. is 95%. However‚ she has misplaced one of these quizzes. The ones she can find have scores of 100%‚ 100%‚ 99% and 98%. What is her score on the misplaced quiz? 5. How many integers between 100 and 300 have both 11 and 8 5. as factors? 6. One-half of a road construction 6. project was completed by 6 workers in 12 days. Working at the same rate‚ what is the smallest number of workers needed to finish
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‚ To type whole numbers‚ just use the number ‚ ‚ ‚ ‚ . The whole numbers‚ plus their respective negative values‚ make up this collection of numbers. Math Symbol: Z F On the number line: Smallest integer: None ( ‚ ← ddddddd→ ← 0 1 2 3 → Largest integer: None To type integers‚ use the number keys: ‚ etc.‚ but in addition to this‚ you can use the negation key: = Make sure you don’t mix up the negation (negative) key the subtraction key ‚ otherwise you get this error: ‚ ‚
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math.BigDecimal; import java.util.*; /** * * @author: Huma UmmulBanin Zaidi * @Project:Project1‚ Data Structure. * Running program looks like: This program finds sum or product of a LARGE numbers of integers. Enter as many integers > 0 as you would like. Enter the numbers: 1 3 5 7 7 5 3 1 Please select the number of one of these options: 1. Sum the numbers in the list 2. Multiply the numbers in the
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is the following; multiplication and division always produces larger and smaller values respectively. This is related to the order in which children are taught the concepts of multiplication‚ Division and extending the set of numbers from integers to non integers and fractions. Misconception | Demonstration of why this is incorrect | Multiplication always makes a number larger or it stays the same stays the samesolution larger than original number (5) | Multiplication can make numbers smaller
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for prime triplets * Continue till all Prime Triplets are printed Question 2: A unique digit integer is a positive integer (without leading zeros) with no duplicate digits. For example 7‚ 135‚ 214 are all unique digit integers whereas 33‚ 3121‚ 300 are not. Given two positive integers m and n‚ where m<n‚ write a program to determine how many unique digit integers are there in the range between m and n (both inclusive) and output them. Algorithm: * Start * To input
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Lemma: If n is a positive integer‚ [pic] proof: [pic] [pic] [pic] = an − bn. Theorem: If 2n + 1 is an odd prime‚ then n is a power of 2. proof: If n is a positive integer but not a power of 2‚ then n = rs where [pic]‚ [pic]and s is odd. By the preceding lemma‚ for positive integer m‚ [pic] where [pic]means "evenly divides". Substituting a = 2r‚ b = − 1‚ and m = s and using that s is odd‚ [pic] and thus [pic] Because 1
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GMAT Club Math Book Facebook gmatclub.com/mathbook facebook.com/ gmatclubforum Table of Contents Number Theory ..................................................................................................................... 3 INTEGERS................................................................................................................................................... 3 IRRATIONAL NUMBERS ............................................................................
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Section 4.1 Divisibility and Modular Arithmetic 87 CHAPTER 4 Number Theory and Cryptography SECTION 4.1 Divisibility and Modular Arithmetic 2. a) 1 | a since a = 1 · a. b) a | 0 since 0 = a · 0. 4. Suppose a | b ‚ so that b = at for some t ‚ and b | c‚ so that c = bs for some s. Then substituting the first equation into the second‚ we obtain c = (at)s = a(ts). This means that a | c‚ as desired. 6. Under the hypotheses‚ we have c = as and d = bt for some s and t . Multiplying
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question paper. Each question carries 5 marks. • Answer all questions. • Time allotted: 2 hours. QUESTIONS 1. What is the smallest positive integer k such that k(33 + 43 + 53 ) = an for some positive integers a and n‚ with n > 1? n √ 2. Let Sn = k=0 1 √ . What is the value of k+1+ k 99 1 ? n=1 Sn + Sn−1 3. It is given that the equation x2 + ax + 20 = 0 has integer roots. What is the sum of all possible values of a? 4. Three points X‚ Y‚ Z are on a striaght line such that XY = 10 and XZ = 3. What
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a negative sign (-).These numbers are sometimes called directed numbers or signed numbers. e.g. 1.2 - FUNDAMENTAL OPERATIONS ON INTEGERS 1.2.1 – ADDITION OF INTEGERS To add integers with the same sign ‚add without regard to the signs.Then affix the common sign of the integers.To add two integers with different signs ‚consider the distance of each integer from zero (that is‚ consider the absolute value of each addend).Subtract the shorter distance from the longer distance. In the answer
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