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: Sketch the trace at z = 0. = 1 25 16 2 -6 -4 4 -6 -4 6 4 -6 4 -아 -8 -6 -4 -2 4

A: topic - sketch of a equation

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

A:

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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)…

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

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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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A: Given:  Point: ( -5 , 2 , -3)

Q: Use symmetry to evaluate the followingintegrals.

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Q: 2. Let b 1, and graph C ate- using different values for a. Explain the effect of the parameter a.

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

A:

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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 =

A:

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

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Q: Determine the amplitude of the following graph. 5 4 3 1 37 51 37 47 57 бл 11T 2 2 2 2 2 2 -1 -2 -3

A:

Q: if zi = ayi for i=1,2,...,n, show that z=ay

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A: Solution: First graph is

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Q: Determine the amplitude of the following graph. 1 -10A -157 -57 -51 5л 15л 10л 2 257 157 357 207 457…

A: Given:

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

A:

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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.

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A: since you have posted multiple question in this question which are not interlinked so i have solved…

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.

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”.