1. a)Why could x cause y b)why y could cause x

Q: Why must nCr always be less than or equal to nPr for any given n and r

A: Permutations and combinations are given.

Q: 1. Let A = {a, h, g}, and B = {3,6}. Answer each of the following questions. %3D (а) Ах В (b) В х В

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Q: Suppose P(A and B) = x, P(BlA) = y, and P(B) = z. What is P(A or B)?

A: According to the given information in this question We need to find the following probability

Q: A. let w-e te Find W2

A: We can solve this using u/v rule

Q: 2. K-5InX+3 find dw dr dw

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Q: 3 = adj A. If |A| = - %3D

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Q: 4.1c. Show that the product of two integers that can be represented by x2 +dy?, is always another…

A: Prove that the product of two integers of the form x2+dy2 is always of the form x2+dy2. Consider two…

Q: A car traveling along a street needs to pass through 4 intersections with traffic lights. If each…

A: Introduction: It is required to find the probability mass function of pmf of X.

Q: 2) Show = din (2) +C

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Q: What is AA-1, where (1 2) A = | 2 1 2 2 1

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Q: H.W 1. (xy' – y) cos (2) = -3x*

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Q: 14. Given P(A) = 0.25, P(B) = 0.28, and P(B|A) = 0.28, are A and B independent or dependent?

A: Given that: P(A) 0.25 P(B)=0.28 P(B|A) =0.28

Q: 1. Find values of x and y that make the following equation true. 1 3y] -15 7 3 -13 -15 10] -1 7 -2

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Q: 4. (4 – e 3*)³dx

A: Here we use the formula  ∫eaxdx=eaxa+C (a-b)3=a3-b3-3a2b+3ab2

Q: 2) classify ग 822 +y 8x2 02Z ०५२ 2

A: GivenA partial differential equation AimTo classify the given equation1) A linear partial…

Q: ZZ= X+y O x² +y² x² - y O

A: The given expression is zz. Let z=x+iy. Then, z=x-iy.

Q: x then ux is XX If u = V y %3D

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Q: If X is the number of heads obtained in four tosses of a coin, the 1 is 1+X mode of Y =

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Q: Show that, for all positive values of x and y, etty > e? ху

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Q: If (R – {0}, .) = (Q,.) then 1=0 1=-1 -1=0

A: For the given statement

Q: Ema thinks that (u) xw, exists. Paul disagrees with her. Who is right? Explain why.

A: Dot product gives a scalar value  .

Q: If f'(t) = 9t² + e' and f(0) = 4. Compute f(3).

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: | − x + 2| − 3 ≤4

A: Given  -x+2-3 ≤ 4 We have to find the values of x.

Q: and y= If a = 3, then x =

A: Solve using the properties of trigonometric rations

Q: 4. Suppose that P(A)=0.7 and P(B)= 0.5, and P([AUBY) =0.1. Find a) P(AOB) b) P(A| B) c) P(B|A)

A: Given data,P(A)=0.7P(B)=0.5P(A∪B)' =0.1P(A∪B)=1-P(A∪B)'=1-0.1=0.9

Q: 18

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Q: 3) Determine the rule writing it below and then complete the tablic 3

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Q: Find x, y, z and w if (::)-(; )-(.. ") 4 x + y 3 -1 2w z + w 3

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Q: X and  Y are randam variables then XeY is a randam variables.

A: Here, The X and Y are two random variables  Then XeY are also random variables we have to show Here…

Q: 1)Given P (A) = 0.25 and P (AU B)= 0.50. What must P (B) be if A and B are to be independent?

A: As per guideline expert have to answer first question only.

Q: Problem no10 Find gen. sol. I you +12y" +HOy² = 0 (0)²² (0)8 PPSH+vH¬"v

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Q: 6. If -2 determine all values of x and y for which A= A.

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Q: Question 18 Find - - -3 in terms of x and y &r & 16 کر ارولو

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Q: 12 2) (x-5) xdx

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Q: 4. Which relation between x and u yields 16+x² = 4/1+u?

A: Given:

Q: 5. If A = I then what is A?

A: Here given as A2=I Taking determinant both side A2=IA2=1A=±1 Thus A is non singular and inverse of A…

Q: 5) Find NV ir ZN -- 20 7) Find DW if YW-4

A: Consider that the centroid divides the median in the ratio 2:1 (5) ZNNV=2120NV=21NV=202NV=10

Q: Let 1 -2 1 -1 -3 1 3 A = -2 -1 1 -1 3 0 1 3 0 -4 Then nullity(A) = 2 4 3 O None

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Q: i) Find the projection of ū on i and the projection of ī on ū.

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Q: 5. A B Suppose that P(A)=0.4, P(B)=0.5 and P(AUB) = 0.42. Are A and B independen Yes, A and B are…

A: Given that  P(A) = 0.4 , P(B) = 0.5