Suppose that A,B⊂S such that Pr[A|B]=25, Pr[A]=12 and Pr[B′]=12. What is Pr[B|A′]?

Q: Find dy for each of the fo llowing (4) y In (tax? tbx +c )

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Q: A fair coin is tossed two times independently. Let H₁ = {1₁ (1, if head is obtained at the ith toss…

A: When head is obtained at 1st toss then H1= 1  When head is not obtained at 1st toss then  H1= 0 When…

Q: 2. Let f:Z→Z be the function given by fAn) =3n+1. a. Is fone-to-one? Briefly explain why. b. Is…

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Q: Let u = (-3, 1) and v = (0,3). Compute the following: u.v= • = | | i|| 2 = −1 (u · v) • (−1ū) · v ū⋅…

A: Step 1:Step 2: Dot Product (·):The dot product measures how much two vectors are aligned with each…

Q: Let P = v?R/(R +r)² as in Example 8. Calculate dP/dr, assuming that r is variable and R is constant.

A: Given:

Q: Sp

A: The question is asking to verify the statement that for all real numbers x and y, the product xy is…

Q: and B =

A: (2/5,1/5,1/2)

Q: Evaluate f (tcos² ti+1/tj+sec² tk) dt

A: To solve the following

Q: Find ||F||. F(x, y, z) = i + j + k

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Q: Which of the following is the parent function for a) f(x) = x b) flx) = x c) fx) = Ix| d) flx) = Vx

A: Given function is y=23x2. We have to find the parent function of y=23x2. The parent function is…

Q: Let F ____ {(a, b]: a, b E Q). Show that a(F) = B(R).

A:

Q: If Sc F · dr = Sc(x + 4y?) dæ + (x²y) dy, what is F?

A: Given ∫F→dr→=∫x+4y2dx+x2ydy

Q: Determine U(Z[x]).

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Q: Let u > 0 be harmonic in R². Show that u is a constant.

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Q: Evaluate dx V In(8-x)) at x = 1. = 1.

A: We have to find: ddxln(8-x2)3   at x = 1.

Q: Consider the following. u = (-5, 5, 4) v = (0, 1, 6) Find u x v.

A:

Q: Sp

A: The question is asking if the product of two real numbers x and y, represented as 'xy', is equal to…

Q: Verify that ||v-w||^2=1 when ||v||=2, ||w||=1, and v*w=2

A: By the definition of inner product and norm we can derive the following formula : ‖u-v‖2=⟨u-v,u-v⟩…

Q: Let r = xi + yj + zk and r = |rl. If F = find div(F). (Enter your answer in terms of r and p.) p'…

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Q: Suppose X and Y are independent. Find Pr[X Compliment |Y ] if Pr[X ∩ Y ] = .42 and Pr[Y ] = .6.

A: According to the provided information,