Using the digits 1, 2, 5, 6, 8, and 9 only once, place a digit in each blank so that: a.The least sum is obtained. b.The greatest sum is obtained.

Q: v prime number p, if p is less than or equal to Vn then n is not divisible by p.

A: (b) We have to find out the negation of given statement. The given statement is "n is not divisible…

Q: 0. How many handshakes are performed if all 100 senators shake each of the other senator's hand? Is…

A: We are going to use the following observations.

Q: An experiment Consist of tossing a coin 144 times. Let X be the number of tails. Find P(X>84).

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Q: A researching team conduct a survey, where out of 76 Americans surveyed, only 2 had seen or sensed…

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Q: 1. Let all of the numbers given below be correctly rounded to shown. For each calculation, determine…

A: (c) Let's firstly evaluate the values: 2.747(6.83)=18.76201 Thus, the least possible measure for…

Q: A student earned grades of A, C, B, A, and D. Those courses had these corresponding numbers of…

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Q: Find all possible values of p∗ if p∗ approximates 0.25 × 10^−2 to at least 3 significant digits

A: To approximate : 0.25×10-2 up to 3 significant digits   0.25×10-2=0.0025

Q: Given 4 numbers with the sum of 9 900 let the second exceed the 1st by 1/7th ,let the third exceed…

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Q: Fermat's little theorem states that if p is a prime number, then for any integer a, the number a P…

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Q: Slips of paper marked with the numbers 1, 2, 3, 4, and 5 are placedin a box. After being mixed, two…

A: Slips of paper marked with the numbers 1, 2, 3, 4, and 5 are placedin a box. After being mixed, two…

Q: Show that there exists i and j with i + j such that p, divides p;. а. b. Show that there exists i…

A: Given: It is given that let p1,p2,...., p51 be their final exam scores . Hence each pi is an integer…

Q: Express Ine sum, dipperence , produict and quotient of the following Compley numbers 2,= -2ji 2マ:11…

A: To solve for complex number

Q: n open-top box is to be constructed from a sheet of tin that measures 22 inches by 12 inches by…

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Q: Use one of the methods: direct proof, contraposition, contradiction, or a counterexample to prove or…

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Q: Determine whether the statement is true or false. 27€{2,3,4,...15) Choose the correct answer below.…

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Q: Use the formula for „P, to solve the following question. A club with nine members is to choose three…

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Q: DISCRETE MATH - Inclusion-exclusion principle, Euler's totient function, permutations How many…

A: (a) Total number divisible by 2 from 1 to 1000 10002=500....(1) similarly total nos divided by 3…

Q: Using only a simple calculator, find the values of k such that det(M)=0, where M=⎣ −4 k 0 1 1 k 1 1…

A: Find k for given matrix.

Q: Answers have attached. Please provide full-explained workings, thank you.

A: The sum of the series, 1+2+3,…n is given by,

Q: A grant from an alumnus to a university specified that the university was to receive $800,000 during…

A: NOTE: Refresh your page if you can't see any equations. . the university was to receive $800,000…

Q: f we want to prove by contradiction that there is an infinite number of prime numbers, we must…

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Q: 1. A party banner contains 21 colourful equilateral triangles. In the middle of the banner is the…

A: Given that, there are 21 colourful equilateral triangles. Also the biggest triangle with base 300 mm…

Q: U= the set of natural numbers between 10 and 20 A= Even numbers B= Multiples of 3 where the number…

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Q: Bob is a stamp collector. His collection consists of three books. Two-tenths of his stamps are in…

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Q: 1/q + 1/r + 1/p =1/m p, q, r are pr

A: Given: An expression 1q+1r+1p=1m, where p, q, r be the primes and m be the natural numbers. To find:…

Q: et S be the set of positive integers less than 500. Find the number of integers in S that are…

A: Given query is to find the number of integers.

Q: List all numbers from the given set that are c. integers f. real numbers a. natural numbers b. whole…

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Q: a. Use the formula S, = (a, + a,) to show that the sum of the first n positive integers is S, = (1 +…

A: The given formula is,

Q: Find the sum of the odd integers between 228 and 60

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Q: Theorem: If a and b are consecutive integers, then the Choose a match sum a + b is odd. Proof:…

A: Solution is here

Q: 50 is Greater than 3 and less than 4 O Greater than 5 and less than 6 O Greater than 7 and less than…

A: Please refer the attached image for complete solution. THANK YOU.

Q: 150 workers were engaged to finish a piece of work in a certain number of days. Four workers dropped…

A: Given:    150 workers engaged.      4 workers drop the second day and 4 more dropped the thrid day…

Q: 5. Equivalence Prove that the following are equivalent for all a, b e R: (i) a is less than b, (ii)…

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Q: Decide whether R \ Q is countable or uncountable, and prove your answer. You can use what you know…

A: To prove that R \ Q is countable or uncountable.

Q: Four points A, B, C, and D are arranged along a number line such that AB > AC and BC < BD. Draw a…

A: Four points A, B, C, and D are arranged along a number line such that AB &gt; AC and BC &lt; BD.…

Q: 5. Equivalence Prove that the following are equivalent for all a, be R: (i) a is less than b, (ii)…

A: Q5. (i) =&gt; (ii) a is less than b  So, a &lt; b  So, a + a &lt; a + b  So, 2a &lt; a + b  So, a…

Q: List all numbers from the given set that are c. integers f. real numbers a. natural numbers b. whole…

A: The given set is -3 , 45 , 9 , -2 , 0 , π , 0.6 , 1.4 (a) Natural numbers : The numbers which are…

Q: Three applicants for encoder were asked to type a manuscript 5 times to determine their typing…

A: we can check consistency by variance. Data which has more variability is less consistent. Data which…

Q: (vii) at least one of the car (viii) none of the car.

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Q: The Infinite Monkey Theorem states that a monkey hitting keys completely at random on a typewriter…

A: he infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for…

Q: The Infinite Monkey Theorem states that a monkey hitting keys completely at random on a typewriter…

A: Suppose a monkey is seated in front of a KEYBOARD WITH 28 CHARACTERS. Suppose the monkey types only…

Q: 2. Some boxes of a certain brand of breakfast cereal include a voucher for a free video rental…

A: As per the guidelines we are allowed to solve maximum of 1 question If you need help with other…

Q: (a) Count the number of six-digit numbers that have all their digits in either nonincreasing or non-…

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Q: Show work A large box that is 24 in. X 18 in. X 16 in. is filled with books that are 8 in. X 5 in. X…

A: To determine the solution to this problem, first we have to find the volume of the box of given…

Q: Ilentipy R:aRb>ab is an odd nomber greater than or equal to 5, in the setA={384,5e the Properties e…

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Q: A man leaving P60,000 to his children and grandchildren seven in allI. The children receive 1/3 of…

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Q: Using only a simple calculator, find the values of k such that det(M)=0 where M=[6 k 0 1 1 k 1 1−7].…

A: We will first calculate the determinant of the given matrix and then equate it to zero to find the…

Q: -1 (a) Determine the set of values of n for which n² +1 and 2 are positive integers. A 'Pythagorean…

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Q: 5000 people voted in an election. Candidate Smith claimed 52% of the votes. How many votes does…

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Q: three positive n umberu whoce Find the is and the the maximum Sum OF Sum numbers is 100 OF there…

A: This is a problem of conditional maximum. So, we have to use Lagrange multipliers in this problem as…