Please answer this question from a discrete math textbook. A degree in computer science has 8 elective topics, and students must complete 2 or 3 of them in order to graduate. If 1000 students graduate, show that there is a group of at least 12 students that all completed the same electives.

Q: Let {an}_1 be a bounded sequence in R and ƒ : R → R be a continuous and increasing function. Prove…

A:

Q: Consider dM dt t 1+t subject to the condition M(0) = 0. Use the 7-step method to solve this problem…

A: Given information:The differential equation is dMdt+t1+tM=(1+t)2e−2t.The initial condition is…

Q: find the solution: x^2y'+2xy=2y^3

A: Given that the differential equation is                                        To find the solution…

Q: 1. A = { 1+2n 5n+7 :n=1,2,...} 2. B= [0,7] U {0, 12, 15}

A:

Q: For each deposit, find-the future value (that is, the final amount on deposit) when compounding…

A:

Q: dy (5) Find the general solution of the linear differential equation : - dr + (8x + 1)y= e 82.

A:

Q: Consider x² y² 100 25 the following equation of a quadric surface. . Find the intercepts with the…

A: The given quadratic surface is (a)Find the intercepts with three coordinate axes If they exist as…

Q: 1. Prove that if n is an integer and n is a multiple of 2, then 4n+ 24 is a multiple of 8. 2. Show…

A:

Q: fi(n) = n².5 f₂(n)=√√√2n f3(n)= n³ + 10 f4(n) = 10 fs(n) = 100n fo(n) = nlogn

A: We have to arrange the given grown function in ascending order.

Q: en decide if each of the following operations is defined (answer yes or no) + B + C + C B A C A C B…

A: (.) Given matrices are,  Matrix  is of order  .Matrix is of order .Matrix  is of order .

Q: Make a 3 x 4 matrix with rank equal to 1. -Make a 3 x 4 matrix with nullity equal to 1.

A:

Q: 3. Consider the surface defined by z = f(x, y), where: x²y 2(x² + y²) f(x, y) = Write down the…

A:

Q: side is the the (a) 1 (b) 3 Assume that (2,3, =) " where the left-hand product of two matrices. If…

A:

Q: Suppose the sequence {sn} is bounded above by M and {sn} converges to M. Prove sup{sn : n € N} = M.

A:

Q: Solve the congruence 15x - 5 = 8 (mod 52). If none exists, explain why. If there are one or more…

A: Given Linear congruence:1. 2. To check:The solution to the congruence exists or not. If exists, find…

Q: Consider the power series Σn" (x-4)". n=1 Find the radius of convergence R. If it is infinite, type…

A: The given series is .Here

Q: Let T: UV be a linear transformation. Use the rank-nullity theorem t complete the information in the…

A: The rank-nullity theorem says :

Q: Q): A fair coin is flipped ten times. What is the probability of observing exactly five heads in the…

A:

Q: Z₁ = 1-5i Z₂ = 3 + 2i Z2 3. Z3 = -7 + i 4. Z4 1.6i 1. 2.

A: Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Consider the following. P(x) = 2x4 − 21x3 + 35x2 + 93x + 35,    c = −1, 5 Show that the given…

A:

Q: 1. For each of the following sets, decide whether they are closed, bounded, compact (both) or…

A:

Q: n​ 2021, there were five women and four men on the Supreme Court in a country. In how many ways…

A: Number of women: Number of men: Condition: Five women sat next to each other

Q: Part B Here are three attempted inductive proofs of the correct theorem. None of them are correct.…

A: "Since you have posted multiple questions, we will provide the solution only to the first question…

Q: proof of The Cancellation Theorem for Limits

A: If  exists, and  is a function that is equal to  on an open interval containing  except possibly at…

Q: How do i approach the following question?  Let A and B be sets. Prove that A ∪ B = A ∩ B if and…

A:

Q: Solve the systems ODEs with initial condition yı (0) = 1 and y2 (0) = 0. y₁ = 4y2 + 5et 92-9₁-20e-t…

A: To solve the given system of differential equation, first we combine them to make a second order…

Q: 1. (2 points) Write a response that's at least five sentences to the following: A calculator display…

A:

Q: Determine whether the series converges or diverges: 5 1- En-0 (₂²+3/1) 2=0 2n 3n √n+1 2- En=1 √²+3…

A:

Q: a Find the general flow pattern of the network shown in the figure b. Assuming that the flow must be…

A:

Q: 5. If limn→∞ an 1 (a) limn→∞ bn (b) limn→∞ A and limno bn = B 0, prove B' an = bn B.

A:

Q: Suppose that ≺D,+,⋅≻ is a well-ordered integral domain. Then the least positive element in D is the…

A: Suppose that ≺D,+,⋅≻ is a well-ordered integral domain and let e be the least positive element in D.…

Q: The population of a southern city follows the exponential law. Use this information to answer parts…

A: Given exponential function The population get doubled in  month. The current population is We have…

Q: Prove that m^3 + 2n^2 =36 has no solution in positive integers.

A: Prove that  there is no solution for positive integers.Let if for for

Q: Math

A:

Q: Vectors ✓ = [3] V and W = [²] Find the area of the quadrilateral with vertices Ō, V, VW, and W.

A:

Q: Suppose that f(x, y) =x² + y² at which 0 ≤ x, y and 5x + 6y≤ 8. Please enter exact answers. 1.…

A:

Q: 5. Let y = √5r²+2+7, determine from first principles dy

A:

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT DON'T USE AI | DON'T USE AI | DON'T USE AI | DON'T USE AI | 2.…

A:

Q: (a) Let a and b be integers. Show that (3a + 2b)2 + (2a − 3b)2 = (3a − 2b)2 + (2a + 3b)2= 13(a2 +…

A:

Q: If then A-¹ = Given 6 = E 1 3 solve Ax = b. 0 x = A = 3 3 -1 -9 5 -8 5 3 -2

A:

Q: Show that Q(√2) = {r + s√2 | r, s € Q} is a field. Note that for any r, s E Q, r + s√2 € R (i.e. Q…

A:

Q: if $A$ and $B$ are events, then $\Pr[A\cap B]\geq \Pr[A]+\Pr[B]-1$

A:

Q: Find the B-coordinate vector of x E H where B = {b₁,b₂} is a basis of subspace H. b₁ = H b₂ = [6] 3…

A:

Q: Given: f = {(a,b),(b,a),(c,b)} a function from X = (a,b,c) to X a). Write f ∘ f as a set of…

A:

Q: Find the monthly payment for the loan. Purchase Price $3100 Down Payment $800 The monthly payment is…

A: Given that the data is:

Q: 1. Compute the Jacobian determinant of the transformation 4+5u cos v 2+3u sin v T(u, v) =

A: As per bartleby guidelines I am solving first question when multiple questions are given.Q 1-

Q: Prove or disprove: There exists a positive real number x such that x² <√√x-

A: Given statement isThere exist a positive real number x such that  x2&lt;x.This is an existential…

Q: 0 ences Determine the moments of inertia I, and I, of the area shown about vertical and horizontal…

A:

Q: 1 2 3 -00-00 B 1 A = [ 12 3 -1 3 ²-[] C= 4 1 5 2 1 3 E = 2-4 0 1 3 2 5 {]. 4 1 10 D 21 3 2 3 = [2…

A:

Q: 1. Consider the general linear second-order ODE Poy" +P1y + P2y = - (1) where po, P1, and p2 are…

A: /