Suppose that A,B⊂S such that Pr[A|B]=3/7, Pr[A]=3/10 and Pr[B′]=13/20. What is Pr[B|A′]? Write as a fraction

Q: Given f(x,y, z) = In(x² + y² + z²), show that ² f , ²f , ² f x² + y2 + z2

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Q: Suppose that f(0) = 1, ƒ(0.5) : 2.5, f(1) = 2, and f(0.25) = f(0.75) = a. Find a if the Composite…

A: Given:           x         0         0.25      0.5       0.75        1      f(x)     1        α…

Q: Using the Convolution Theorem, what is L[h(t)]?

A: In this question, we use the convolution theorem to find the Laplace transform of the given function…

Q: Let X=ℝ2 and define d,:ℝ2×ℝ2→ℝ d2((x1 ,y1),(x2,y)2)) = max{|x1 - x2|,|y1 - y2|}. Draw the…

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Q: Q4/Find Loplace transtorm of £(4)= et by using} defining fanotion ر م ) ) st e" dt

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Q: For the functions w = xy + yz + xz, x=u+ 2v, y=u- 2v, and z = uv, express dw dw and - using the…

A: Given: w=xy+yz+zx, x=u+2v, y=u-2v and z=uv

Q: let H = {n² |n E z*}, determine whether it is closed under

A: Given : H={n2|n∈Z+}   To Check:  H is closed under binary addition or not

Q: Let R be and bl#0) = iff a with unity - Let a l#0) in R- Show that and b an I.D are are associates-

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Q: let H = {n² |n e Z*}, determine whether it is closed under

A: Here, we have H=n2| n∈ℤ+. To show the set is closed under binary multiplication. This means we have…

Q: Let A = {x ∈ Z | 6 divides x} and B = {x ∈ Z | 3 divides x}. Prove that A ⊆ B, and then prove that…

A: We can prove using like showing every element in one set is an element of another set like that.

Q: Let f(t,y) = y+ 3t?e'. Then f satisfies a Lipschitz condition in y with L = 2, given that 1sts2.…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Given that n ≥ 2 , x ∈ Rn  Prove that there exists a y ∈ Rn in where y ≠ 0, and xy = 0

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Q: Show that F(n fla)] ds pleae do it frast

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Q: Prove that in the pairs of positive numbers ¤, y for æ² + y° = r the sum a+y is greatest when z = y.…

A: Here we solve the given problem of calculus.

Q: Use the I.V.T and Rolle's Theorem/M.V.T to prove that the equation below has a unique solution in…

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Q: OVESTON Prove that A is inveitine if at0 and at b l Gind The pivos 9 A %3D a a

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Q: . Show that z)= E kz is D: 1215 continuous io domain

A: The series can be shown as continuous in a domain if it converges. Therefore, the first calculate…

Q: Let X and Y be defined as follows: X = {a E Z | a = 3x for some x E Z}, and Y = {b E Z |b = 3y – 3…

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Q: find the values of c that satisfy Rolle's Theorem

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Q: J prove that for 0 <r<R

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Q: Suppose the Wronskian of f and g is W(t) = –2e®t, and f(t) = e²t is given. Find the general formula…

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Q: Find values a, b, c, d such that the function (x+ 1)³, -2 < r <-1 s(x) = { ar³ + bæ² + cx + d, -1 <…

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Q: The domain of the function f (x, y, z) = In(3ry – 6) is %3D - O {(x, y) E R² : xy 2} o {(z, y, z) E…

A: Given function is: f(x,y,z) = ln(3xy-6) We need to find the domain  for this function.This can be…

Q: Prove Va e Z, Vb e Z, 3|(a² + b² ) – 3|a ^ 3|b where xy means x divides y, i.e., there exists k e Z,…

A: In this question we use congruence modulo.The following  are useful in this question1) If  3 |…

Q: Where x = (X1, X2) E R². 3- N: R2 - → R defined by N(x) = /x1² + x2² is a norm on R². (x1, x2) E R².…

A: Let X=(x1,X2)€R^2

Q: if x, y>o such that x Sy then Vã svy Prove by direct method

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Q: Let H(x) be an antiderivative of 1sm z if H(5) = 7, then H(2) =

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Q: Find a general solution to (ax+b)y"+ a(ax +b)y' – y=(ax+b)D, where a,b >0 with ax+b>0 for all x on a…

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Q: ; Let x, y ER" be given. (a) lf ||x|| = ||y|| = 1 and x - y = 1, show that x = y. (b) If ||x|| ≤ 1…

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Q: Suppose that a) b) f(x, y) = [15x²y; 0<x<y<1 0; otherwise. Compute E(X | y), Var(X) and Var(Y).…

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Q: Given the FUchtion f (x) =x3 - Cox + 5. Find all the valve OF c in the interval (2,4) such that…

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Q: Suppose v(t) = 6t² - 3t on the interval [3, 5]. What is the displacement on [3, 5]? O 160 O 165 O…

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Q: Consider the formula A = Vx Vy.p(x,y) ^ ¬q(x, y). (b) Show that A is falsifiable (i.e. not valid) by…

A: We are given a formula as : A≡∀x∀y.p(x,y)∧¬q(x,y) We need to show that A is falsifiable by giving an…

Q: If Z = f(x + g(y)) , prove: Zx * Zyx = Zy * Zxx

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Q: For x, y, z, w > 0, prove that (x/z)+(y/z)+(z/w)+(w/x)≥4

A: It should by x/y, instead of x/z

Q: Decide if the statement is True or False. Justify your ans why not, and give an…

A: a) The poset (P(Z), ⊆)

Q: Find a general solution to (ax+b)y"+a(ax+b)y'- y3(ax+b)°, where a,b >0 with ax +b >0 for all x on a…

A: Given equation is  ax+b2y"+aax+by'-a2b2y=ax+b1b Cauchy Euler equation . To solve this put…

Q: find he querage vallwe of he fanction z-cor ox m De mternal ( )

A: fx=x-cos26x,   0, π6.

Q: find the root of the fnmetion ーX FCx)= ē^ _ x which lies betwen (o %3D

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Q: For p = (1, 0) and x = (x₁,x2,...,xn) ER", define ||2|p:= - ². |P Show that n jyjx|py|q for x, y…

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Q: the following "quation sutisfied Cauchy - Rieman equation es .4 W = Z

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1.…

Q: Show that if A and B are similar, then AT and BT are similar.

A: Let A and B are similar matrices. By definition of the similar matrices.  The matric A and B are…

Q: Find the discontinnity point of &Cz): ニ そzそ+

A: Given that, the function is fz=z+1z2+2z+1. Set z2+2z+1=0 to find the undefined points. Compare the…

Q: For Z= x²csc y,prove that Zxy is equal to Zyx

A: Given that,    z=x2csc y

Q: (a) Compute /(2) dr, given that f(b) 3 and that | af'(a) dr b(1 + f(-b)). (b) Computei (2) dz. given…

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Q: prove that for operatrs a and b which comute with thier commuters[a,b]=c,so that [a,c}=[b,c}=0 ,…

A: We know that ekABe-kA=B+kA,B+k22!A,A,B+... Given that A and B commute with their commutator then…

Q: Suppose that a) b) f(x, y) = [15x²y; 0<x<y<l 0; 0; otherwise. Compute E(X|y), Var(X) and Var(Y).…

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Q: Which of the following is a general solution to the followin x²y"+xy'+ (x²– 1)y=0 y=c,(x) +cY_,(x) O…

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