Use mathematical induction to show that the sum of the cubes of three consecutive integers is divisible by 9.

Q: Prove by mathematical induction that the sum of cubes of three consequtive positive integers n is…

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Q: Use mathematical induction to show that 5? − 1 is divisible by 4. Determine the starting value as…

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Q: Produce the least positive number that is divisible by​ 2, 3,​ 4, 5,​ 6, 7,​ 8, 9,​ 10, and 11.…

A: Given Produce the least positive number that is divisible 2, 3,​ 4, 5,​ 6, 7,​ 8, 9,​ 10, 11.…

Q: How many integers from 1000 through 9999 must you pick in order to be sure that there is at least…

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Q: A number that has exactly 2 factors (1 and itself) is called a number. * O factors O prime O…

A: We have asked if a number that has exactly 2 factors (1 and itself) then what kind of number is…

Q: How many 8-character passwords can be made using the letters A through Z if repeats are not allowed?…

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Q: What is the prime factorization of 72?

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Q: By using mathematical induction, proof  square root 2 + square root 3 is irrational.

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Q: How many words can be generated us

A: How many words can be generated using the letters of MARRIAGE.

Q: (a) Find the number of integers between 32 and 395 that are divisible by 6. (b) Find their sum.

A: (a) The first term of the integers between 32 and 395 is a1=36 which are divisible by 6   and the…

Q: EXAMPLE :- How many 3 digits number can be formed using digits 1,6,8,9,3,7 without repeating any…

A: Here use counting principle  Here total available digit 6

Q: How many different 9-digit phone numbers do not contain the digit 9? Assume that any digit in the…

A: Given data÷ How many different 9-digit phone numbers do not contain the digit 9. Assume that any…

Q: Briefly explain the differences between proof by contradiction and proof by mathematical induction.

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Q: Some automobiles have four-button locks. To gain entry, push each of the four buttons, in a…

A: Given,Some automobiles have four-button locks

Q: Find the formula for the nth term. 6, 11, 18, 27, 38, 51, ..

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Q: How many different 7-digit phone numbers do not contain the digit 8? Assume that any digit in the…

A: we know that we have 10 digits 0,1,,2,3,,4,5,6,7,8,9 if we do not use digit 8 then we left with9…

Q: 15. Explain when to use a permutation and when to use a combination

A: Permutation is used for lists (order matters) and Combination for groups (order doesn't matter). A…

Q: How many different 8-digit phone numbers do not contain the digit 9? Assume that any digit in the…

A: Please rate and feel free to ask any query about any part of the question.

Q: Sum of twin primes is divisible by 2. Select one: O True O False

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Q: How many different 7-digit phone numbers do not contain the digit 88? Assume that any digit in the…

A: Note: Hi there! Thank you for posting the question. As some information in the question seems to be…

Q: Find the smallest number greater than 200 with 14 positive divisors

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Q: Determine how we can use the decimal expansion of an integer n to determine whether n is divisible…

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

Q: 3.) Using matiematical induction, prove tiat lo" + 3 ·4*7+5 n+ 2 is divisible by 9 for n ?0

A: To prove the given statement by induction.

Q: ) Check all the numbers that are divisors. a.) 288

A: see 2nd step

Q: How many numbers from 1 to 1000 are not divisible by 2, 3 or 5?

A: We will count how many numbers are multiples of at least one of these three 2, 3 and 5 and then…

Q: B. Using induction, prove that 8" -1 is divisible by 7, where ne N

A: (B) 8n-1 is divisible by 7 Now for n=1 81-17=1 For n=2 82-17=64-17=637=9 Now, assume that 8n-1 is…

Q: what is the prime factorization of 76?

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Q: Find the smallest integer greater than 100 that is divisible by 3 but leaves the remainder 1, 5 when…

A: To find- Find the smallest integer greater than 100 that is divisible by 3 but leaves the remainder…

Q: Find the value of the permutation. 9P2 9P₂ = (Type a whole number.)

A: Formula of permutation : nPr = n!(n-r)!

Q: 3. Find a number with remainders of 3, 11, and 15, when divided by 10, 13, and 17, respectively.

A: Find a number with remainder of 3,11,15 when divided by 10,13,and 17 respectively.     Here i…

Q: Find the sum of all four-digit numbers that can be formed by the digits 1, 3, 5, 7, 9 without…

A: Answer: Option b)  666600

Q: = 55. Determine the value of n if (5)

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Q: n how many unique ways can we rearrange the letters in the word COEFFICIENT?

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Q: Evaluate the factorial expression.  7! - 2!=

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Q: How many modified perfect faro shuffles are needed to return the cards to their original position in…

A: The farro shuffle is a method of shuffling playing cards, in which half of the deck is held in each…

Q: Check all the numbers that are divisors

A: The divisors of 12,210 are 2,3 and 6 .

Q: Find the 15th term of the geometric 1,2,4, .. O 65, 536 O 8, 192 O 16, 384 O 32,768

A: Hence option (c) is correct.

Q: How many 6 digit numbers are divisible by 5? Assume repetition is allowed. 12000 180000 60000 200000

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Q: Find all integers that leaves the reminders 5,1, and 4 when divided by 8,5, and 9 respectively.

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Q: Find the prime factorization of 99. The prime factorization is

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Q: Rehan proved by mathematical induction that for all the positive integers, n^3+2n is divisible by 3.…

A: Show true for n=1 Let P(n):=n^3+2n be the statement now 3=1+2=(1)^3+2(1) 3 is definitely divisible…

Q: Use Mathematical Induction to show that 52n -1is divisible by 8,   ∀ ∈ n N.

A: Use Mathematical Induction to show that 52n -1is divisible by 8,   ∀ ∈ n N.

Q: What does the divisibility rule of 4 and 8 have in common ?

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Q: Evaluate the factorial expression  7!/5!

A: Given problem:- Evaluate the factorial expression  7!/5!

Q: The Greatest Common Divisor of two prime numbers a and b

A: Prime numbers are those numbers which have only two factors one factor is 1 and other factor is the…

Q: se mathematical induction to show    n ≥ 0, 7n - 1 is divisible by 6

A: Given: n≥0, 7n-1 To prove: 7n - 1 is divisible by 6

Q: the addition principle to determine how many integers in the list: 1,2,4•••,9999

A: Given :  list: 1,2,4•••,9999   Total Integers  = First digit - Last digit + 1   Total Number of 1…

Q: Check the divisibility of 6125,50105and32950by25

A: Check the divisibility of 6125,50105and32950by25   A number is divisible by 25 if the number formed…

Q: How many 8-character passwords can be made using the letters A through Z if repeats are not allowed?…

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Q: Find the sum of the divisors of 120. Generalise the result for an arbitrary natural number M

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