Suppose that X, Y , and Z. If Pr(X) = 19/40, Pr(Y ) = 11/40, Pr(Z) = 2/5, Pr(X ∩ Y ) = 1/5, Pr(X ∩ Z) = 3/10, Pr(Y ∩ Z) = 3/20, and Pr(X ∩ Y ∩ Z) = 1/10. Complete the following Venn diagram and find the following values: (a) Pr[X' ∩ Y ∩ Z ' ] (b) Pr[X' ∩ (Y ∪ Z ' )] (c) Pr[X']

Q: 5) Construct AD'E'F', the reflection of ADEF across line l. F.

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Q: 6. Make a 3D sketch for each of the following. a. 7= (2,4, 1) + s(2,3,-2) b. 7= (1,2,0) + t(1,-1,3)…

A: To Do: Make a 3D sketch of the following: (a) r→=2, 4, 1+s2, 3, -2 (b) r→=1, 2, 0+t1, -1, 3 (c)…

Q: Deiermine the equation of the circle graphed below. y. Enter your search term. 10 8 (7, 7) 5(2, 4).…

A: The graph of the circle is To evaluate: The equation of the circle.

Q: 9. Find the point C such that AC = ² AB. 4

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Q: If a = (1, 2, 1) and b cross products. 1. a × b : = 2. b xa = = (12, 15, 1), find the following

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Q: Find the distance from the poinst (-5, 2, -3) to the z-axis.

A: Given:  Point: ( -5 , 2 , -3)

Q: Use symmetry to evaluate the followingintegrals.

A: The given integral is, ∫-22x3-4xx2+1dx The function is f(x)=x3-4xx2+1 When function f(x) is…

Q: d. e. the angle between vectors AB and AC the direction cosines of AC

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Q: 1. Find the set of V and the set of E for the graph K1. b j K1 V = E =

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Q: 9. 11 Let a1 = -6 a2 -4 |, and a3 = 11 -3 -4 The set {a1, a2, a3} will span R° unless h =

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Q: 7) Find the number of paths that spell the word "Electron" below. E C R R N RI

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Q: The polnt (6, n) les on the crcle whose equation Is (x - 2)2 +(y + 1) =52. Find the values of n. The…

A:

Q: 4. Let A Sketch the collection of points Ar for i in the unit square.

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Q: Produce the following graphics by using Mathematica. Hint:Use appropriate data such as (1, 2.2) to…

A: Solution: First graph is

Q: Solve y'=+x

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Q: Question 7: Suppose that K,H ≤ G such that G = HK and Hn and hk = kh, VhEH and kE K. Show that G≈ H

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Q: 7π 4 decimals to at least one decimal place. Convert the point (r, 0, z) (x, y, z): = = 6, " to…

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Q: Plot these points: y 8 8 6. 1. 1 4 3 44

A: Given dataset is :

Q: Let x be a data set such that ĩ = 3 and S = 15. a) If y = 5x + 2, find: i. ỹ ii. S; b) If z = x - y,…

A: x is a data set with, Mean, x = 3 Sample Variance, Sx2 = 15 Let, y = ax+b we know,  y = ax +b And,…

Q: .In AWXY, if ZX = ZY , WX = 9x – 11, XY = 4x + 1, and WY = 7x- 3, find x and the each side. measure…

A: Given that <X = <Y , so the opposite sides of them are equal.  WX=WY Or, 9x-11=7x-3 Or,…

Q: H.

A: In the given question we have to find the shortest path from A to J and we also determine the length…

Q: 103 Let = 2+j"8 and z, = 4+ j06. Show that a. + =2 = =, +z2 b. 1- 2 = =-2 с. d.

A:

Q: 4) Which of the following is a graph of F(r, y) = ? A or B? B

A: To find the graph of given F.

Q: 1. Determine for each of the following which of the figures labeled (1) through classified under the…

A: Since we are given with the multiple number of question and our guideline is solve first kindly…

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.