How many values x, y, z, w are there so that a +y+ z+w = 16 and x, y, z, w are all positive odd integers? Enter your answer here

Q: How many values x, y, z, w are there so that r +y+ z+w = 16 and x, y, z, w are all positive odd…

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Q: 1. Let, a, = 3, a2 = 4 and for n 2 3, a, = 2an-1+ an-2, express a, in terms of n.

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Q: (a) 1,2, ..., 16, i.e. such that the sum of all numbers in each row, each column and each diagonal…

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Q: How can you represent the set {(1, 3),(3, 1),(3, 3), (1, 1)}? (choose all correct answers - there…

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Q: Suppose x and y are integers. Show that If x y, then x | 3y - y + 5y. 1) What is your assumption? 2)…

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Q: Suppose ne N. Then the following equation is true: () - ) -)-) - + (-1 = 0. + 3 How can this…

A: Let's find.

Q: How many integers n where 1≤n≤1600 satisfy the condition ⌊n⌋\n.

A: Here, need n such that n/⌊n⌋ where 1≤n≤1600 and n is integer. Now, ⌊n⌋ is said to be floor function…

Q: Let, a, = 3, a2= 4 and for n2 3, a,= 2an-1+ an-2, express a, in terms of n. %3D

A: we have the nth term of A.P is given by  an=a+n-1d here,  a=3, d=4-3=1an=3+n-11=2+n we get,…

Q: 10. If the product of N consecutive posi- tive integers is divided by N, the remainder is always (A)…

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Q: 3. There are one hundred tickets in a box, numbered from 1 to 100. Draw once from the box. a. Is…

A: Define the events, A : The number is even B : The number is less or equal to 30 There are 1 to 100…

Q: How many even 4-digit numbers can be formed from the digits 1, 2, 6, 7, and 9 with no repetitions…

A: There is no repetition allowed.. At unit place we have two choices 2 or 6 In 10th place we have…

Q: 5n. Determine for which n n-2 For nz 2, let on =

A: Here we have to determine the n for which |an|<1 for all n≥2 where an=5nn2-2

Q: How many integers 2 ≤ n ≤ 65 have no prime divisor less than or equal to ¹/³?

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Q: How many numbers between 1 and 10000 have the digits 1,3, and 5 such that each digit appears exactly…

A: Here Numbers between 1 and 10,000 have digits 1,3,5 and each appears exactly once only

Q: How many mombers between 50 and 200 can be expressed as 4k-1, where k is an integer?

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Q: 1. Let, a, = 3, a2 = 4 and for n 2 3, a,= 2an-1+ an-2, express a, in terms of n.

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Q: 1 A1 5 a b C d for some integers а, b, с, d. What are the values of these integers (in order a, b,…

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Q: 3. Let r and y be positive integers. 4. Let a, b, c e Z. If c divides a +b,

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Q: 3. Let, a1 = 3, a2 = 4 and for n 2 3, an = 2an-1 + an-2 -5, express a, in terms of n. %3D

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Q: Droof that n! %3D1 オ=O K!(n=k)!

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Q: Let, a1 = 3, a2 = 4 and for n > 3, an = 2an-1 +an-2 +n², express an in terms of n. %3D

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Q: How many positive odd integers less than 10,000 can be written using the digits 3, 4, 6, 8, and 0?

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Q: Show that (n + 1)! > 2"+3, for n > 5.

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Q: is an integer greater than 1 Quantity a= the tens digit of N Quantity b= 0 which is greater or…

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Q: 2. Show that if a is an integer other than 0, then a) 1 divides a h) a divides 0

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Q: A positive integer is 4 less than another. If 3 times the reciprocal of the smaller integer is…

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Q: k is a prime number that has a ones digit of 7 and 0 <k < 100, how many values of k are possible?

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Q: how many positive integers n satisfy 22-5n>-3?

A: 22-5n&gt;-3

Q: Choose two distinct integers, x and y, between 0 and 9. Derive the number of 9- digit integers that…

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Q: 6. What is the sum of all 100 positive odd integers starting with 1? Apply your common sense if it…

A: Given n=100

Q: How many different ways could you choose any 4 gumballs from the 25 gumballs in the…

A: We can choose 4 gumballs from the 25 gumballs in 25C4 ways.

Q: let n be a positive integer not exceeding 20. How many values of n such that the equation x^2 +…

A: We have to find the values of n for which x^2+y^3n+1=1.

Q: The n in X" indicating the number of factors of X.

A: solution:

Q: Let i be a positive integer and A, = [-i+1,1[. Then N14= %3D

A: We have to find the first intersection first.

Q: How many integers from 1 to 99,999 contain exactly two consecutive 1s?

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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: How many can 3 digits be formed using the digits from 1 to 5 if the digit 2 is never there in the…

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Q: For any positive integer n and r = 1,2, ...,n, we have G) = (","') + C" - }). True O False

A: The expression nr can be presented in the factorial form as follows. nr=n!(n-r)!r! The expression…

Q: 2. Let, a, = 3, a2 = 4 and for n 2 3, an= 2an-1+ an-2 + 5, express a, in terms of n.

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Q: Find the sum of all integers from 41 to 83. The sum of all integers from 41 to 83 is

A: Detailed Solution and Explanation is given below....

Q: 51. If a, is no. of ways to split positive integer 'n' in all possible ways, then (A) (B) a, = a,…

A: As per the question we are given the sequence of numbers an such that an is the total number of ways…

Q: 58. The integer k is the product of four different prime numbers. If k divided by 22 is a multiple…

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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: Find the smallest positive integer N that satisifies all of the following conditions N is a square…

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

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Q: 5. What is the completion of (X, d). where X is the set of all rational numbers and d(xr, y)

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