Use generating functions to find the number of integer solutions to e1 + e2 + €3 +e4+€g = 38, such that ep E {3,4,5, 6, 7,8} for ke {1,2,3,4, 5}.

Q: Consider nonnegative integer solutions of the equation xi + x2 + x3 + x4 + x5 + æ6 = 30.

A: The non-negative integer equation is x1+x2+x3+x4+x5+x6=30Since ,xi-number varying from 0 to…

Q: How many integer solutions are there to the equation with x₁ > 1, 2 > 2, x3 > 2, x4 > 0 ? X1 + x₂ +…

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Q: Identify the solution to an=2an-1+ an-2-2an-3 with ag = 3, a₁ = 6, and a2 = 0 for all integers n ≥…

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Q: Find the index of 12Z in 3Z

A: The integers are

Q: Find the number of positive integers X smaller than 12849 which have exactly 2022 positive divisors

A: Theory : Total no of divisor of a number, If its prime factorization, given by ∏i=1hpiai Where p is…

Q: How many non-negative integer solutions (O is allowed) are there to r +y+ z = 24?

A: The given equation is, x+y+z= 24 We know that, For equation,  x1+x2+......xr=n  There are n+r-1Cr-1…

Q: How many solutions there are to this equation xl+x2+x3+x4 + x5= 30, each x is an integer that is at…

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Q: How many non-negative integer solutions are there to the equation rị + *2 + x3 = 21

A:

Q: Let A - -5 -2 -5 -10 -5 -7 -20 -7-22| Solve the equation using an LU factorization of and b - Ax = b…

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Q: replacement, what is the probability that the roots of the equation x²+²x+2=0 are real

A: If P and q  are chosen randomly from the set {1,2,3,4, 5, 6, 7, 8, 9, 10} with replacement.

Q: Which of the following is equivalent to 3x²(-2x)e-x² + e-x²16x O -16xe-x²(x² - 1) O 16xe-x²(x² + 1)…

A: Given query is to simplify the expression.

Q: 5. Find all integer solutions to 6s+ 14t+21u = 1.

A:

Q: Given A= 2n + 1-2, show that for any 4, the number of ways you can have the same value of a given…

A: Given: Objective: Show that for any value of , the number of ways to have the same value for a given…

Q: 3.9b + a3 + 27 - 3a2 + 5a3 - 2a2 + 2.1b + 7

A:

Q: Determine the number of solutions of the equation x₁ + x2 + x3 + x4 + X5 = 15 in positive integers…

A:

Q: Find all integer solutions to 25s+ 14t = 1. O

A: Given equation25s + 14t = 1We have to find all integer solutions for s and t.

Q: 5 -1 2 Compute A-613 and (613)A, where A = -3 3 -7 -3 1 1 A-613 = (613)A= -1 -1 2 -3 -3 -7 -3 1 -5

A: A=5-12-33-7-311A-6I3=5-12-33-7-311-6100010001A-6I3=5-12-33-7-311-600060006A-6I3=5-6-12-33-6-7-311-6A…

Q: If A=-1 4 -3 -7/ -1 and A¹=/? ? (22 a ? What is the value of the element a? Give your answer…

A:

Q: compute 2A

A:

Q: Find 1- fext=/4+|3*

A: To solve this question we need have some standard formulas of differentiation

Q: How many integer solutions to x1 + x2 + x3 + x4 x₁ ≥ 4, x2 ≥ 2, x3 ≥ 5 and x4 ≥ 3? > = 31 are there…

A: Find change all inequality to grater then equal to 0. Then use the theorem

Q: n)+3<10

A:

Q: Solve 65x ≡ 2(mod243) by inverse method

A: Given, 65x≡2mod 243 Here gcd65,243=1 Now find the inverse of 65 mod 243.…

Q: How many solutions there are to this equation x1+x2+x3+x5+x4 = 30, each x, is an integer that is at…

A: Answer : None of them.

Q: Solve for X, show all calculation in binary number system only X = ((1110)₂-(0011)₂) (10011010)₂)…

A:

Q: Find the solution to an=2an-1+an-2-2an-3 for n=3,4,5,...with a0=3, a1=6 and a2=0

A: Find the solution to an=2an-1+an-2-2an-3 for n=3,4,5,...with a0=3, a1=6 and a2=0

Q: How many solutions are there to the equation X₁ + x₂ + x3 = 21, if each x; is a positive integer?…

A:

Q: Find three even numbers less than 400, each of which can be expressed as asum of consecutive…

A: The objective is to obtain 3 even numbers less than 400 such that they can be expressed as a sum of…

Q: Compute A -213 and (213)A, where A = A-213= 5 - 4 -4 -1 2 3 - 5 1 3

A: In this question, we will compute the matrix.

Q: How many consecutive zeroes are there at the end of 100! (100 factorial). For example, 12! -…

A: How many consecutive zeroes are there at the end of 100! We know that…

Q: For this problem, you need the total, n, of the sum of all digits in your student ID. For example,…

A: We have n=(2+0+4+6+9+4+3+4)=32. We will find the number of solutions S   to the equation…

Q: compute BA

A:

Q: of T2, T-:

A: Consider Tn={n, n2}, where n is an integer. The objective is to find the number of elements in each…

Q: Find the solution to an=2an-1+an-2-2an-3 for n=3,4,5,...with a0=3, à1=6 and a2=0

A:

Q: How many integer solutions are there to the equation x+y+z=10 if x, y, and z are all bigger than -2?

A: Given, x+y+z=10 x,y,z&gt;-2

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

A: 22-5n&gt;-3

Q: Find the number of 5-tuples (a, b, c, d, e) of positive odd integers that are solutions to the…

A: The idea is to transform this into a known counting problem