In a hand of 13 cards chosen at random from an ordinary deck of 52 cards, let X be the number of spades. Find E(X) and V ar(X). (Note: In the 52 cards, 13 of them are spades.)

Q: 2. Determine the power set p(A) = {{a, b}, {c}, {d, e, f}} 3. Suppose A = [7, e,0} and B = (0,1}.…

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Q: If y = 2x 8 xp a) -16x 8-8 8. -16r 7 Oc) 6- -16x (pO d. 6. 2x N +66 er F10 F11 F12 PrtSc F5 F7 F8…

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Q: If %₁ 7e45i and z2 = 300i, then the quotient = 22 X.

A: The given complex numbers z1=7e45i and z2=e300 i. To find the quotient of the complex numbers z1z2.

Q: Given that x² + y² + z² = 6 and (055) w w³ + z³ 5xy + 12. Find for x=1, y=0 and z=7. ( ($).

A: Given,                   and To find the value of for

Q: Find e if Z.! -2-2i

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Q: Solve the following: aDx aDy aDz Əx Əx Əx if D %3D 2хya, + x?а, + ху?а,

A: D=2xyax+x2ay+xy2az

Q: Use a separate sheet of paper for #3. Evaluate using an appropriate substitution. re2 In p dp-

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Q: For P(z>Z1) 0.20, which of the following is the nearest Z1? Please select one: a. 0.84 b. 1.96 c.…

A: Given P(z>Z1)=0.20

Q: dz If z = w", then is equal to: dw 7x7 w(1 – 49z8 In w) 7z'w7z²-1 7z8 w(1 – 49z7 In w)

A: topic - derivatives

Q: P. 12 F 15 6x W G- 9. x+8 H. 12x DO R.

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Q: Determine if S3 e S3 is solvable.

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Q: dx x²√4x² √ a. C. √4x² 4x √4+x² X + C + C e. None of the above. b. O d. 4x √4x² X √4+x² + C +C

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Q: 2) Find PF if RP = 14 E R (P F G

A: To find- Value of PF.

Q: Find a general formula for dr ax + b dx" cx +d

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Q: e) 36x* - 13x +1= 0.

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Q: S. If PH is 3 and AP is 2x +4 what is x? B oint 丰

A: Centroid of triangle divide each of median in ratio of 2;and 1

Q: 12. If IN = 2x + 10 and AT = 26, find x. %3D %3D В 丰 N A O 6 O 12 О 10 8. -

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Q: Suppose ∠BEC= 2x − 8 in the image below. Find the value of x.

A: Given that -  ∠BEC= 2x − 8

Q: Find N, A, and b.  k(x) =  11 2 + 7.5(1.06−x) ;    [0, 100] N  =    A  =    b  =

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Q: 9. If ANKF ~ ALZF, find NF. K x +3 4 N 15 L x +3 F

A: Given:

Q: 3) Find the mZT= %3D

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Q: 2. If (x + 1)7 = (x + 1)ª, for x > -1 and a is a constant, what is the value of a? а. b. C. 3 10 d.

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Q: C. Show that (1+i)*5 = 2*" (1 – i)

A: Polar form of complex numbers will be used in solving this problem. The typesetted solution in LaTeX…

Q: Given C(x,16) D(2,-4) E(-6,14) and F(-2,4) find the value of x, so that CD || EF

A: Given points are  C(x, 16), D(2, -4), E(-6, 14) and F(-2, 4) The slope of a line joining P(x1, y1)…

Q: e 2x 1+ ex dx

A: on solving this we get

Q: Define the variables x and t as x = 2.56, and t=6.7, then evaluate: a) 2x4 – 6x3 + 15x2 + 12 e 2x b)…

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Q: (a2xdx а. 2a2x + C 2a²x b. + C In a 1 a²x + C 2 In a d. None of the above C.

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Q: Suppose that az = 0 and Eb = 1. Find the values of k=1 k=1 a. 8a b. 250b; k=1 c. (az + 1) d. (b - 1)…

A: Given                            ∑k=1nak=0 and ∑k=1nbk=1 a) find ∑k=1n8ak…

Q: 10. For V=2, fi , first find and and then, compute t+p%.

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Q: In an experiment with three conditions, the means are 2, 4, and 9. What would be the value of L for…

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Q: E A

A: Topic = Geometry

Q: If e1x = 14, then x =

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Q: Det ermine whether the improper integral diverges or converges. (a) (x² + 4)³/2 d.x (b) xyx2 – 1 (c…

A: If the value of integral exists we say integral is converge As per our guideline we supposed to…