10 use n= n1c 16 +hlk-1 + h 16 +no pug of Rul e cf divisibility for 7 16,21

Q: How many distinguishable permutation can be made from the letters of the word MATH? Ɔ 12 ) 18 O 20 O…

A:

Q: The order of permutation (13)(27)(8)(1237)(648)(5) is 04 O 12 18 O 2 07 O None of them

A:

Q: A. If p + 2 is a prime number, prove that p? + 3 is divisible by 4.

A: Let p≠2 be a prime number.

Q: If a number N is divisible by both 4 and 12, then which of the following must be true? i. N is…

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Q: Let p > 5 be the prime number. Prove that the expression p – 10p +9 is divisible by 1920.

A: We have to prove that the expression p4-10p2+9 is divisible by 1920.

Q: 14. Use the indirect method (contrapositive) to show that "If a + b is an odd integer, then a or b…

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Q: If n has a prime factorization n = pi*p2² ... p" then the sum Eajn d³P(d) is equal to: a1. az

A: Euler's phi function is widely used in number theory and algebra. This function represents the…

Q: Let P(n) be the assertion that: for any integer n 2 1, 7" - 1 is divisible by 6. Part 1 Part 2. In…

A: Principle of Mathematical Induction :Let P(n) be a statement .step 1 : For n=1 is true .step 2 : Let…

Q: (10) The following element is prime in (Ze,+,.) = .... .. (а) 2 (b) 4 (c) 12 (d) No Choice (а) (b)…

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Q: 2. If P (n) : "2.4z + 3""" is divisible by k for all ne N" is true, then the value of k is

A: The solution is given below:

Q: If a number N is divisible by both 4 and 12, then which of the following must be true? i. Nis…

A: Thanks for the question :) And your upvote will be really appreciable ;)

Q: If p + 2 is a prime number, prove that p² + 3 is divisible by 4.

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Q: 6. Find the number of different 8-letter arrangements that can be made from the letters of the word…

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Q: 5. Let a, b, c, and d be any four integers. Assume that 2 divides a, that 3 divides b, that 5…

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Q: Consider the following. (a) In how many different ways can a player select a diamond and a spade…

A: The total number of ways selecting 2 cards is, C252=52!2!52-2!=52×51×50!2!×50!=1275

Q: For each positive integer n, let P(n) be the property 5n − 1 is divisible by 4. Write P(0). Is P(0)…

A: Replace the values of n by given values

Q: 4. How many permutations of the letters ABCDEFG contain: a) the string GD? b) the string AFC? c) the…

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Q: How can we use R to compute the number of ways we can pick a card from the suit heah a standard deck…

A: Total number of cards in standard deck of cards = 52 There are 4 suits of cards in standard deck of…

Q: Suppose a,b,n are integers and n>0 s.t. 63a^5b^4=3575n^3, what is the smallest possible n. Explain…

A: The objective is to find the smallest value of n such that 63a5b4=3575n3.

Q: and kanin re the Ten candidales Dea Scommillee How many. Nup can A committee five be chosen Keyin…

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Q: 11. When the marchers in the annual Mathematics Department Parade lined up 4 abreast, there was 1…

A: let the number of Persons in department be x. according to the given Problem, x≡1(mod 4)x≡2(mod…

Q: 5. Evaluate [62³e¹dA; R= [0, 2] × [0, 2] R

A:

Q: 2. Prove that n = aŋɑp-1 aza,a, is divisible by 8 if and only if aza,a, is divisible by 8. A…

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Q: 9. Find the sum of all'integers between 90 and 190 if each integer Is divisible by 17 (Hint. The…

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Q: 11.7.50 In how many distinct ways can the letters of the word MAMAS be arranged? ways

A: We know the number of permutations of n objects, where n1 of objects are identical ,.......,nr of…

Q: 9. 10. What is t divisors?

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Q: (a) the first digit is 6 and the other digits are different from 6 and different from each other,…

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Q: a) Find how many numbers in A are not divisible by 13 and 7. (b) Find the number of subsets B C A…

A: Given that                       A=1, 2, . . . , 999

Q: 10. Using the digits 2, 4, 6, 7 and 9, how many five-digit numbers can be formed if the number is…

A: Solve by p and c

Q: matan or? K1921 (4Tt (0,007)2) (4TT (1,25)2) LoIS0late 92

A: The given equation is:mgtanϕ r2kq24π0.0072=q24π1.252

Q: Prove that 9? −1 is divisible by 8,for all n ≥ 1

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Q: Suppose you have 45 books (10 history books, 25 novels and 10 math books). Assume that all 45 books…

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Q: 2. a. How many strings of hexadecimal digits consist of from one through three digits? (Recall that…

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Q: The number n= 6,34d,217 is divisible by 11. Since its alternating sum of digits is 6-…

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Q: N is an integer such that N div 13 = -11 and N is not a multiple of 13. What is IN| div %3D 13? 11…

A: See the solution below.

Q: If  n×k divisible by 4, then n is divisible by 4 or k is divisible by 4. Which of the following is…

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Q: . How many four-digit numbers are there with different digits and simultaneously: (a) divisible by…

A: Given: Total number of digits = 10 (0 to 9) Number of digits in a number = 4

Q: Is 7, 8, 9, 11 are pairwise relatively prime. صواب ihi

A: Two nos. a and b are said to be relatively prime iff gcd(a,b)=1

Q: 2.3 How many integers between 0 and 500: 1. Have distinct digits? 2. Are divisible by 3? 3. Are…

A: NOTE** As per bartleby guideline for more than three sub parts asked only first three are to be…

Q: 27. How many distinguishable permutations are there for the letters of MATHEMATICS taken all…

A: Given that  Word : MATHEMATICS Number of letters in the word (n) = 11 Number of times distinct…

Q: Does 9|54? O Yes, because 6 = 54 O Yes, because 54 = 9 · 5. O Yes, because 54 = 9 · 6. %3D O No,…

A: Correct Answer =>  Option C :- yes, because 54 = 9•5

Q: (a) At a glance, determine the digit d so that 64,275,67d is divisible by 4. Is there more than one…

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Q: Show by induction that 21" – 8" is divisible by 13 for all n> 0

A: For the solution follow the next steps.

Q: The greatest common divisor of 9n + 10 and 10n +9 is Oa 10 or 19 оь. 19 O. None d. 1 or 19 Oe. 1

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Q: Show by induction that 19" – 8" is divisible by 11 for all n >0

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Q: 123. A SUKUEY OF 300 KIDS N BOSTON SHOWED THAT 3 EAT AT TACO BELL 102 EAT AT DEL TACOni 45 EAT AT…

A: We have to find given event for students..

Q: 3. A divisibility test for divisibility by 13: а. Prove that 13|(10x + y) if and only if 13|(x +…

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Q: (3) Prove the following by contraposition. If n? is not divisible by 3, then n is not divisible by…

A: Statement:if A then B Contrapositive statement:if not B then not A