Let P₂ (R) be the vector space of polynomials of degree at most 2. Which of the following are elements (ie "vectors") of P2 (R)? Choose all that apply. 01+ 2x 01²-3 01+2x+3x² B 01+2+² +2³ O

Q: Show that if A × B = B × A then A = B

A:

Q: Show by an example that (AB)" B™A".

A:

Q: 25) Find the gcd of 10563 and 10563105.

A: We have to find the gcd of given number.

Q: Suppose Var(X) = 32, Var(Y) = 47, and X and Y are independent. What is Var(.15X + .85Y)?

A: Given, a  and . and  are independent random variables.It is required to find the .To solve this…

Q: Suppose P(A) = 0.48 and P(B) = 0.62. Can A and B be mutually exclusive? Why or why not.

A: We know that, mutually exclusive events are  events which can not happen at the same time.

Q: if P(A and B)=P(A)*P(B) then P(A and B) cannot equal P(A)+P(B) True or False

A: It is given that  P(A and B) = P(A)*P(B)

Q: uppose Var(X) = 93, Var(Y) = 98, and X and Y are independent. What is Var(.6X + .4Y)?

A: Answer: - Given,  Var(X) = 93, Var(Y) = 98, and X and Y are independent.                 What is…

Q: Show that Z10 = ⟨3⟩ = ⟨7⟩ = ⟨9⟩a. Is Z10 = ⟨2⟩?

A: We have to find the condition according to the given condition

Q: Which of the following is equivalent to 3x²(-2x)e-x² + e-x²16x O -16xe-x²(x² - 1) O 16xe-x²(x² + 1)…

A: Given query is to simplify the expression.

Q: Create an example of a permutation and a combination (one of each) and use them to communicate the…

A: Solution: Robert wants to color his three triangles with different colors. He has a total of 12…

Q: If fx)x3x+1 then fx) (In x]3x (3x+1}x3x (2x+ In xr3x+ 1 3x13r 3 Inx 3x+13 In x

A: Note:Hi there! Thank you for posting the question. The first line in the image is not very clear.…

Q: Suppose Var(X) = 88, Var(Y) = 17, and X and Y are independent. What is Var(.28X + .72Y)?

A:

Q: so-Z of what is 21

A:

Q: Use the substitution method to evaluate V1-22dx

A:

Q: Differentiate 2xー4x -

A:

Q: Suppose the multiplication cx is defined to produce (cx1, 0) instead of (cx1, cx2 ). With the usual…

A: The multiplication cx where x∈ℝ2 is defined as cx=cx1, 0 because x=x1, x2 where x1 and x2 belong to…

Q: What is the order of Z11?

A: Recall the fact that order is the number of elements in that group. Note that ,…

Q: 1. Which of the following are in grouped form? (You can pick more than one) * x+4 (x+2)(x-7)…

A: See attached file for a step by step explanation.

Q: I have to identify the recursive and explicit rule. I need to select two

A: Answer: Option F f(n)=f(n-1) . r Option A f(n)=3. 4n-1

Q: Did you use the product rule as well? I would like some clarification on the steps.

A:

Q: 4) Which expression is equivalent to 1&r-50? 1) 2(3x + 5)² 2) 2(3х - 5)2 3) 2(3х - 5)(3х + 5) 4)…

A: we have to identify which expression is equivalent to the given expression

Q: Compute the following. (a) P6, 2. (b) C6, 2. (c) P6, 6.

A: P(n,r)=n!n-r!C(n,r)=n!n-r!.r!

Q: Suppose Var(X) = 43, Var(Y) = 36, and X and Y are independent. What is Var(.67X + .33Y)?

A: GivenX and Y are independentVar(X)=43Var(Y)=36

Q: Suppose Var(X) = 4, Var(Y) = 78, and X and Y are independent. What is Var(.58X + .42Y)?

A: Answer: - Given, Var(X) = 4, Var(Y) = 78, and X and Y are independent.                What is…

Q: Compute r2

A: Given the calculated values, t value, t = 2.17

Q: How do we know that -1 and -2 will be in the field?

A: Given F is field, So,  0, 1∈F ( since a field F must contain zero element and unity ) A field is…

Q: (AUB) = ACNBC. Show that P(ACNBC) = 1- P(A) - P(B) + P(ANB)

A: P(Ac∩Bc)=1−P(A)−P(B)+P(A∩B)

Q: Suppose Var(X) = 71, Var(Y) = 12, and X and Y are independent. What is Var(.59X + .41Y)?

A: The objective of this question is to find the variance of the linear combination of two independent…

Q: Suppose P(AIB) = X and P(A n B) = 8 What is P(B)?

A: P(A|B) = 14P(A∩B) = 18P(B) = ?