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

Q: For what values of nn will the number of ways of selecting nn items from 60 exceed the number of…

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Q: Question 1:  How many ways can they line up so there is always atleast 1 duck between any two geese.

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Q: Let a and b be ranges of numbers in a number line such that –1 < a < 5 and 6 < b< 10. - If a is…

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Q: The following “Theorem” is obviously not true. Explain what’s wrong with the proof. [5]  Theorem: 1…

A: We see in the proof that it is a fact that n2 &gt; n when n &gt; 1. That means n2 is larger than n…

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: Prove that if a>b then a+c > b+c

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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: N is a natural number. How many values of 'n' can take if ( n! ) Is a multiple of 2 power 25 but not…

A: The highest power of 2 that will multiple of n! is n2+n22+n23+n24+n25+... and so on If we take n=20,…

Q: -1<9+n<7

A: Given,           -1 &lt; 9 + n &lt; 7

Q: Using the result you proved in the question above, find a list of 200 consecutive composite…

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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: Find the smallest number n for which n! is larger than the population of the world.

A: World population is 7.98 billion till October 2022 It according to worldometer by United States.…

Q: A certain affects virus 0.8% of the population. A test used to detect the virus in a person is…

A: Obtain the probability that the person has virus given that they have tested positive. The…

Q: Consider sum 1+5+9+13+...+81 what is a6

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Q: O Disprove the following claim: "For all integers z, z2 +1 is odd" Use that Odd(r) 2k + 1} %3D

A: For all integers x , let x^2 + 1 is odd

Q: Discrete Mathematics How many n-digit numbers are there with at least one of the digits 1 or 2 or 3…

A: when 1 is absent,  There are 8 digits at first i.e. 2,3,4,...,9. So upto n, there are (n-2) digits.…

Q: V5 +3 v3 - E-2 where k is an integer to be found. V5 + V3 Without using a calculator, show that Cs…

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Q: п For all integers n > 1, 1.2 2.3 п(п+ 1) п+ 1

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Q: If n3 + 7 is an odd integer then O n is an odd integer. O n is sometimes even and sometimes odd. O n…

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Q: -10 -9 -8 -6 8 7 6 -3- -4 -5 -7 8 m n 10 11

A: To write down that the given statements are true or false.

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: If n is prime, then 2" – 1 is prime.

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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: Question 14, 6.2.53 University Law School accepts 1 out of every 7 applicants. If the school…

A: Let's find how many Students accepted.

Q: 2. What are the two largest positive integers n satisfying n - 1 | n²-A?

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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: Which of the follow could be the units digit of 7n where n is a positive integer? Select all…

A: Given that, n is a positive integer.   So n varies from 1 to infinity.....   Now 71 = 7  72 = 49  73…

Q: If n is a positive integer, then 2 n - [a] »] + [a + ²] + [a + ² ] -- - + [a + ¹ = ¹] - =] = n n =…

A: Given: nis a positive integer. To Prove: α+α+1n+α+2n . . . +α+n-1n=nα

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: Use the method of direct proof to prove the statement below. Suppose a is an integer. If 5|2a, then…

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Q: Statement: The difference of two even numbers is positive. Which of the following provides a…

A: First option is not correct because 7 - 2 and 7 is odd number and in statement they ask for two even…