A professor has 15 books. They wish to distribute 4 books each to their 3 favorite students (so 12 in total). How many ways are there to do this? (All 15 books have different contents. We don’t care about the order of distribution, only who gets which books in the end.)

Q: (a) V16x"y 16 (b) Vóx(V6 + (245 - 3) (c)

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Q: Evaluate the line integral -ydx + xdy along the curve C C : y? = 24x from (24, 24) to (0,0). NOTE:…

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Q: 1. Consider the following scenario: Janet, Gail, Susan, and Lisa all walked away from the bus…

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Q: The complex number z is defined by z = 3·z + 4.j where z is real. a) Find, in terms of z, the real…

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Q: 2 sin V 4 - x 4 – X - 2

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Q: Question 3. Show your working in each case: (a) Find all the cluster points of the set M = {÷ +;: m,…

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Q: y"(t) = 4y(t) – e-tU (t – 1), y(0) = y (0) = 0.

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Q: Which of the following is NOT true about triangles? The longest side of any given triangle is called…

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Q: Determine all the singular points of the given differential equation. ( -2) x+(t+1)x'-(t-2)x=0…

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Q: 1. a) Find a linear transformation L: R³ → R³ whose kernel is spanned by the set -{{:) (:)} S =

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Q: E(-1)"+1 n2 + 3 n=1

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Q: Question 8. Define a relation - on the set of rational numbers Q by a ~ b iff Ja| = |b| (a) Prove…

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Q: . Let u = [1, 7, 4]), v = [1,5, 5), and w [35, 25, 20]. Find the critical point of f(x, y) = (x · u…

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Q: A 2nd order, homogeneous, constant coefficient differential equation has characteristic roots x=-1…

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Q: ) Define the alternating subgroup (A5, o) of Sz. Given a permutation a e A5, prove that the map 0:…

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Q: Which of the following is a convergent p-series? Select all that apply. Σ n =1 7" 4 n = 1 n² -2.7 Ση…

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Q: The following payoff table for a maximization problem is available. Decision Alternative State of…

A: By analysing following payoff table  We see that

Q: %3D y"(t) = 4y(t) – e-tU (t – 1), y(0) = y'(0) = 0.

A: Solution

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Q: 6 sin 5 |x cos xdx 2

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Q: fex) Cos X ノ

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Q: 8. Show that the gamma density function f(x, λ, r) integrates to 1

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Q: W3

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Q: Using t = x +1, find the parametric equations sets that represent the graphs of the rectangular…

A: y=2x-1As t=x+1⇒x=t-1⇒y=2(t-1)-1=2t-3  The parametric equations are x=t-1, y=2t-3…

Q: 2. Prove that if f be a nonnegative measurable function on E. Then f = 0 if and only if f =0 a.e. on…

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Q: c. Find all non-congruent solutions to x? = 1 (mod 15) d. Find all non-congruent solutions to x2 = 4…

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Q: Show that yrcos(x²) is asoktion to: xy"-y'+4x3y =0, and then use reduction of order to fond a second…

A: Given differential equation is ,                                   xy" - y' + 4x3y = 0 (.)  If  y =…

Q: 2 :B= 1 3. Consider the matrix If we apply the following operations in order to the rows of B what…

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Q: (j4+43)(20js (-35°)" 2cjs et @= Simplify o and write it in rectan 763 (32çis40°)

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Q: R.3. Let [a, b] be an interval on the real number line (with a < b). Prove that a,b]-[0,1].

A: We have to find a continuous bijective from a,b to 0,1 to show that a,b~0,1

Q: A credit card account had a $261 balance on March 5. A purchase of $196 was made on March 12, and a…

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Q: 6. An n x n matrix P is said to be orthogonal if P'P = In. (P'P is "the matrix product of…

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Q: Determine whether the sets S, and S, span the same subspace of R. S1 = {(2, 3, -2), (0, 2, 2), (4,…

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Q: 3. Prove that if E has finite measure and let {f.}be a sequence of measurable functions on E that…

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