A 19. n? + n is divisible by 2. 20. n + 2n is divisible by 3. 21. n? – n + 2 is divisible by 2. 22. n(n + 1) (n + 2) is divisible by 6.

Q: Consider the 6-digit numbers, with distinct digits (no repetition), that can be formed using the…

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Q: 15) n(n*+5) is divisible by for each integer

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Q: 7 ´a³b° is The simplified form of the expression O a2 63 42 O a2 63 21 O a 46?c 1 O a2'b63c 42 O…

A: Given:     To determine: The simplified form of the given expression.

Q: Which of the following rules is used to find the number of positive integers less than 1000 that are…

A: To Determine: which of the following rules is used to find the number of positive integers less than…

Q: 3. Describe the to Example: 4, 8, 12, 16, 20 ... Adding 4 to the previous pattern. a. 2, 5, 8, 11…

A: (a)2, 5, 8, 11  ...2+3=55+3=88+3=11Adding 3 to the pervious pattern.   Ans

Q: Q4 : Consider the 5 - digit numbers , with distinct digits ( no repetition ) , that can be formed…

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Q: How many terms are there in the G.P. 3, 6, 12, 24, .... 384. '

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Q: 2. 6n - 1 is divisible by 5 for n any positive integer

A:

Q: How many five-digit numbers are there with different digits and simultaneously: a) divisible by 4 b)…

A: For the number to be divisible by 4, the last two digits must be a multiple of 4.Hence The last two…

Q: A boy imagined a four digit multiple 0f 5 with different digits.if the first digit is erased the…

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Q: divisible by 3 for

A:

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: *-

A: Given: 3x=π4+nπ

Q: How many three-digit numbers with different digits are divisible by: a) 25 b) $4 ?$

A: We have to find how many three digit numbers are divisible by: 25 4

Q: composite. 10. Suppose that n = 2³ × 5² × 7 × 17³. Give the prime factorization of n² and nº (Hint:…

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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: 8. What is the value of the 13th coefficient in the expansion of (a+b)5? 1,365 455 O 3,003 O 105

A: given(a+b)15 we have to calculate 13th coefficientwe know Binomial nth term formulaTr+1=Cran-rbrnfor…

Q: 8- The simple expression of the 21 a b c 3a³b²c² is

A: Given,  21a-3b5c83a5b-2c7

Q: What is 14 7/8% of $2.70?

A:

Q: Which of the followig is true about the divisibilty test for 8? a. For divisibility by 8, we must…

A: As we know that For 2 we check unit digit     {2=21}For 4  we check last two digit is divisible by 4…

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: a) n(n+1)(n+2)is divisible by 6 b) n(n+1)(n+2)(n+3) is divisible by 24 c) 5" -3" is divisible by 2

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Q: termine if 345 is divisible by 5, 6,

A: Introduction: 5 times divisible Numbers with a one-place digit of 0 or 5. 6 times divisible. A…

Q: a. Is 4 5 {4}?b. How many elements are in the set {3, 4, 3, 5}?c. How many elements are in the set…

A: (a)To verify that 4 = {4}.It is known that a set cannot be equal to number.{4} is a set with one…

Q: How many positive integers greater than 5 and less than 2020 are divisible by 7? are divisible by…

A: 1) Here , 2020/7 = 288.57 So 288 multiples of 7 are there between 5 to 2020 So , 288 integers are…

Q: 3. What is the quotient and what is

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Q: a) Arrange the digits 0, 1, 1, 1, 2, 4, 5, 6, 7 to make a 9-digit number that is divisible by 2, 3,…

A: (a) Divisibility test of 2: The last digit of the number will be 0, 2, 4,  6, 8. So, the required…

Q: 8. Show that 4 29! +5! is divisible by 31.

A: We have to prove that 4.29!+5! is divisible by 31.

Q: a.b = b.a is commutative property of Addition صواب İhi

A: a.b=b.a is commutative property of Addition

Q: (d) an 10"+1 +3 x 4"-1+5 is divisible by 9 for all n2 1,

A:

Q: (b) Give two different interpretations of the bino- mial coefficient (") for non-negative integers n…

A: First we will give two different interpretations of the binomial coefficient nk for non-negative…

Q: 2. What is the prime factorization of 15x y? O 3.5 2y O 3.5 x y Y O 15 - x * y Y 3-5 22 y y

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Q: divisibility

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Q: 5349 is added to 3957. Then 7062 is subtracted from the sum. The result is not divisible by. 5349 को…

A: Given: 5349 is added to 3957. Sum=5349+3957=9306 Then, 7062 is subtracted from the sum.  Resulted…

Q: The number n= 6,34d,217 is divisible by 11. Since its alternating sum of digits is 6 - 3+4 -d +2-1…

A: Divisibility by 11

Q: 22 Evaluate. (n - 1)!, where n = 3 2 5 6

A: This can be solved as follows:

Q: rn is not divisible by 3k +1 or n = 3k + 2.

A: Introduction: If a number a is divided by b, then there must exist an integer k such that, b=ak.

Q: 25.07 is divisible by what?

A: IF ANY NUMBER HAS FACTORS MORE THAN TWO THEN IT IS CALLED A COMPOSITE NUMBER.

Q: 3 Determine a16 when a, =, d = - 1. 3 a16 when a, =5. d= - 1. %3D (Type an integer or a simplified…

A: The first term of A.P is a1=35 and the common difference is d=-1.

Q: 4503 is divisible by 2,3,,5,6,9or 10

A: 4503 is divisible by 2, 3, 5, 6, 9 or 10.

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: 5. The GCF of any even number and any number divisible by 3 number is always 6. Falls

A: Let us consider the two numbers      a = 2      b = 3

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: V. How many different ways can the letters of each word can be arranged?

A: HERE USE COUNTING PRINCIPLE

Q: For Americans using library services, the American Library Association (ALA) claims that 67% borrow…

A: ALA claims 67% borrow books i.e. p = 0.67 sample size  : n = 101  x : number of borrowed books = 78…

Q: 30 Evaluate > Ak +2 k=1

A:

Q: 3. How many different arrangements are there using all the letters in the word COMBINATORICS. A.…

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Q: ove that n’ +5n is divisible by 6 for all n E N.

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.