100! + 101! + …..200! is divisible by 11 Select one: O True O False

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

A:

Q: Examine the properties of the operation o defined by the equation xoy= x2+y2 in the N natural…

A: Given: The equation x∘y=x2+y2 in the N natural numbers set

Q: 8. Given 1, 2, 3, 4, 5, 6, 7, 0, 9, how many 4-digit numbers can be formed if it must be divisible…

A: We have to solve question number 8

Q: How many different​ three-digit numbers can be formed using the digits 3, 6, 1, 7, 8, 2, and 4…

A: How many different​ three-digit numbers can be formed using the digits 3, 6, 1, 7, 8, 2, and 4…

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: How many 4-digit number can be formed with the digits 5,2,3,0,4,6 and 7 which are divisible by 5 and…

A:

Q: 2) 10! + 1 is not divisible by 11 a) True b) False a) True O b) False O O

A: A number is said to be divisible by another number if we can divide the number without getting any…

Q: Marshall had d dogs that he put into 4 different areas. How do you write this as a divison sentence?

A: Consider the provided question, Given, Marshall had d dogs that he put into 4 different areas. We…

Q: 3. Let n be an integer greater than 2. Explain why n! +2, n! +3, n! +4, n! + (n – 1), n! +n are all…

A: We have to explain that n!+2, n!+3,…,n!+n-1,n!+n are all composite numbers.

Q: 9.) Is 9" + 3 is divisible by 4? PROVE IT!

A: Given : 9n+3 is divisible by 4. To Prove: The given statement is true for n=k+1. Consider Tn=9n+3.…

Q: In a contest where 7 contestants are entered, in how many ways can the distinct prizes be awarded

A: Ans- Given,In a contest where 7 contestants are entered, In how many ways can the distinct prizes be…

Q: If mis divisible by 9 and 4, then mis divisible by 12.

A:

Q: i Regular MA license plates have 3 digits followed by 3 (uppercase) letters, e.g. '924 VXA' or 4…

A: We have to use sum and product rule to solve given questions- (I) Concept: Since total number of…

Q: How many positive integers between 100 and 999 inclusive   d) are not divisible by either 3 or 4?…

A: The set: A∪B contains all the elements that are present in set A or B. The set A-B contains all the…

Q: How many positive integers between 50 and 100 a) are divisible by 7? Which integers are these? b)…

A:

Q: A) How many integers, greater than or equal to10000 but less than or equal to 39999, can be formed…

A: Note :- We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

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: 6. How many integers from 1 through 100 must you pick in order to be sure of getting one that is…

A:

Q: (b) An integer is divisible by 3 if and only if the sum of its digits is divisible by 3.

A:

Q: Suppose that n=24.35.112.133. How many divisors does n have?

A: Given,  n = 24 35 112 133 Then (4+1)(5+1)(2+1)(3+1) = 5×6×3×4=360 It has 360 number of divisors

Q: There are 12 teams, each representing a different country, in a women’s Olympic basketball…

A: GivenNo.of teams =12No.of medals = 3   (i.e.,Gold,Silver,bronze)

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: 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: 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: What is the greatest common divisor of 24 and 44? n If n is a natural number such that gcd(800, n) =…

A:

Q: Let S = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Suppose six integers are chosen from S. Must there be two…

A: Consider the following given set:S = {3,4,5,6,7,8,9,10,11,12}Suppose six integers are chosen from…

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

A: Concept: Combination: The method of combination is used to decide the wide variety of approaches to…

Q: In how many different ways can you arrange 3 chemistry books, 5 physies books, and 5 biology books…

A: (1) We have to arrange 3 chemistry books, 5 physics books, and 5 biology books on a shelf. The books…

Q: How many integers greater than 130 but less than 640 are divisible by 7? O None of these. O 72 O 73…

A: Correct ans is = 73 Please find attachment for the details solution

Q: Please Prove whether it is True or False. The value of nª - n² is divisible by 6 for any integer…

A: To prove that whether the given statement is true or false

Q: Q2:- A) How Many ways you can write 12 digits number from the digits 1,2,3,4,5,6,7,8,9,10,11,12 if…

A:

Q: .76 How many six-digit numbers with different digits belonging to the set ${0,1,2,3,4,5,5}$ and…

A: 6 digit forming a 6 digit number  The total number of 6 digit different numbers = 6!-5! = 720-120 =…

Q: a- The first ten multiples of 3 are : ---- ----- b- The first ten multiples of 6 are : c- The first…

A: We are solving the first three subparts and for the next subparts post the question again and…

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: 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: 3. There are seven students who always compare their CS test grades. They discovered that either the…

A: It is given that there are seven students who always compare their CS test grades. They discovered…

Q: How many positive integers less than 2ˆ{20} are not divisible by 7, 11 or 13. Use…

A: The solution is given below

Q: Find the number of 13-card hands drawn from a 52-card deck that are void in exactly one suit.…

A: Solution :-

Q: Users of the online system for a Bank are required to set a password that is 10 character-long. Each…

A: Introduction: Considering the letters are not case-sensitive, each letter indicates a single choice,…

Q: What is |A| if 3 5

A:

Q: by

A:

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: How many natural number that are less or equal to 1000 and that are not multiplea of 3,5or7 exist

A: To find: Number of natural numbers ≤1000 that are not multiple of 3 or 5 or 7.

Q: How many five-digit numbers are there composed of different digits belonging to the set…

A: Givenset is {0,1,2,3,4}

Q: 1. A small town has only 500 residents. Must there be 2 residents who have the same birthday? Why?…

A: (1) A small town has only 500 residents. Claim: There are 2 residents who have the same birthday.…

Q: nd her brother has 8 visitors. In how many ways can they be seated including Clara and her brother…

A: Carla has = 6 visitors Her brother has = 8 visitors we have to find  how many ways can they be…

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

A:

Q: How many seven-digit numbers are there with non-repeating digits belonging to the set…

A: Solution:3.75. From the given information, a set of numbers is {0, 1, 2, 3, 4, 5, 6}

Q: 30. What are the first five terms in the recursive seguence defined by 02 3 O 12, 3, -1, -4,-53 O…

A: