Use trial-and-error to determine the smallest integer n for which the given statement is true. 6n < 2n 6. 4 5 O 7

Q: Let R be the set of 50 distinct positive integers. These integers are divided by 23. Show that at…

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Q: Let n be a positive integer. Show that in any set of n consecutive integers there is exactly one…

A: Let  be an integer, then  are n consecutive integers .Since  for any integer :When  then  and  are…

Q: In a leap year there are 29 days in February instead of 28 days. That means there are 366 days in a…

A: Given in a Leap year there are 29 days in February instead of 28 days and the total days in a leap…

Q: 24 Evaluate the following. 5! 120 15 720

A: 24)  To evaluate: 5!

Q: 33. Is it possible to have a combination of nickels, dimes, and quarters that add up to $4.72?…

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Q: 1. 80.5 3.5

A: 1. 80.5÷ 3.5

Q: Suppose ʼn is a positive whole number. Simplify [n+1)! — n! × n. On! O 1 On + 1

A: 'n' is a positive whole number. We have to solve  (n+1)!-n!×n Remember : n!=n.(n-1)........3.2.1

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: Evaluate the following. 9! =

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Q: Discrete Math: Prove the claim using a valid strategy. Use the definitions of even and odd.  Claim…

A: To prove a mathematical statement, there are three methods. The basic method is direct proof. If the…

Q: Prove that if 7 divides n with remainder 1, 7 divides n² + 2n + 7 with remainder 3.

A: Given, if 7 divides n with remainder 1. We have to prove that 7 divides n2+2n+7 with remainder 3.

Q: How many even 3-digit numbers can be formed from the digits 1, 2, 3, 6, and 9 with no repetitions…

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Q: Let n be any integer. If n=3k+5 for some integer k. Does 91 6n-3 No, because 6n-3= 18k+30-3 which is…

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Q: What is n? Input Output -1 1 2 4 2 8 4 32 3.

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Q: How many different 10-letter words (real or imaginary) can be formed from the following letters? N,…

A: Given letters areN , I, R, E, C, Q, I, R, Y, Fletter 'I' is repeated 2 timesletter 'R' is repeated 2…

Q: For any integer n, n² + 5 is not divisible by 4.

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Q: Suppose that n is a positive integer with the properties: • for any integers a, b, c, • n is not…

A: Suppose that n is a positive integer with the properties:1). for any integers a, b, c    2). n is…

Q: Determine the set of values of n for which n²-1 n² +1 and are positive integers. 2 2

A: First, we simplify the given expressions. The expression 2/2 simplifies to 1, which is a positive…

Q: Use permutations to solve. From a cooler with 9 different kinds of soda, 3 are selected for 3…

A: The formula of permutation is: Prn=n!n-r! This is the required answer.

Q: Suppose that c and d are integers where 12c = 25d. Then 12|d and 25|c.

A: We have to check whether given statement is true or false?

Q: Evaluate the expression. 8

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Q: Ten teams are competing in a relay race in which the top three teams win unique prizes.  How many…

A: There are three places to pick, so we have to pick 3 teams from 10 teams.  Since it is ranking, so…

Q: 4. Use a combinatorial argument to show that () n 1 -2) n + 22 n 2 3 -

A: Given: nn-2=n3+12n2n-2n

Q: Without computing each sum, find which is greater, O or E, and by how much. O 5+7+9+11+...+101 E = 4…

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