Consider the continuous random variable X whose pdf is given by f(2)=√15.50(2). (a) Find the value of k that makes f(x) a pdf. (b) Find E(X). (e) Find V(X). (d) Find P(X ≤ 4).

Q: Find f such that f'(x) = 4x² + 3x-3 and f(0) = 9.

A: (1) f′(x)=4x2+3x−3f(x)=∫f′(x)dxf(x)=∫(4x2+3x−3)dxUsing the Power Rule∫xndx=xn+1n+1+C

Q: Let f(x) = (sin(x))*. Find the value of (a) 1 (b) 2 (c) 2 (d) 2 (e) 0

A: The given function is fx=sinxx. To find the value of f'π2, first take the logarithmic of fx=sinxx on…

Q: Pr[A'nB]=0.4 and Pr[(AUB)']=0.5. determine Pr[A]

A: GivenP(A'∩B)=0.4P(A∪B)'=0.5

Q: Let h(x) = 3x² + x -x² + 3x - 3 what is h' (2)?

A: We need to find out h'(2).

Q: :1 S* d(x³). 3

A:

Q: (b). Use the definition of the derivative to evaluate f (x)=x". [Hint: Use the Binomial Theorem:…

A: Given: i. fx=xnii. a+bn=an+nan-1b+nn-12!an-2b2+·····+nabn-1+bn. To Find: Use definition of…

Q: If "C, = "C,, then n is equal to 4.

A:

Q: Let f(1) = 1, g(1) = -3,h(1) = 2, f'(1) = -1,g'(1) = 2, and h'(1 d f(x) g(x) dx h(x) Find when x =…

A: Please refer to the image below

Q: 4. If fdx = f(x)[In(x) + 1] + C, then f(1) =

A: We have, ∫lnxx2dx = fxlnx+1+C To evaluate : The value of f1

Q: If f(t) = 9t+1, find f"(5). %3D

A:

Q: Q3. (a) Mention the engineering application of interpolation and integration. (b) The

A: To Find the engineering applications of interpolation and integration

Q: Find f. (x+ 1) (b) f'(x) = f(1) = 5 3.

A:

Q: Estimate Af. Use a calculator to compute the error and percentage error. Af = f'(a)Ax f(x) = V1+x a…

A:

Q: Determine the number of outcomes in the event. Then decide whether the event is a simple event or…

A: A computer is used to randomly select a number between 1 and 1000. Event A is selecting a number…

Q: Let F(x) =Cx41D, fCx)=X,and gox)=x+1 True or fals e (gof)(x) = FCX).

A:

Q: 7. f(4) = 34. Find f such that f'(x) = %3D %3D f(x) =|

A: f'(x)=7xIntegrate on both sides∫f'(x) dx=∫7x…

Q: Consider the function h(z), for which h(4) = -12 and h'(4) = -7. %3D h(z) Find f'(4) for the…

A: To Determine: find f'4 Given: consider the function h(x) for which h4=-12 and h'4=-7 also…

Q: f(x) 132. Let h (x) = g(x) Find a. h' (1), b. h' (3) , and с. h' (4).

A: Given

Q: Let f(x) = In[x4(x +9)6(x2 + 4)3]. Find f'(x). f'(x) =

A: Given,

Q: Use the Mean Value Theorem to prove that f'(x) = 0.01 has a solution in the (-4, -3) interval.…

A: We use cubic formula to calculate the value of c

Q: 1) Find the average value of the function f(x) = 3-4x + 5x² over the interval [-1, 3].

A: The function is given by fx = 3-4x+5x2 To determine: The average value of the function over interval…

Q: Find the probability and interpret the results. If convenient, use technology to find the…

A: Mean(µ) = 61000Standard deviations (σ) = 5500  Sample size (n) = 34

Q: Compute f(x)dx f(x) = { 2x if x <1 4 if x 21

A:

Q: If f is a function such that f(2) = 5 and f'(x) ≥ 3 for all x, what are the possible values of f(7)?

A: The given condition for the function is:

Q: K Find f such that f'(x) = 8x-5, f(5) = 0. f(x) = 0

A:

Q: Find P(A and B')

A: P(A) = P(B) = 0.33 P(A or B) = 0.43

Q: Find f such that f'(x) = 4x – 3, f(4) = 0. %3D %3D f(x) = D %3D

A: Given that: f'(x)=4x-3, f(4)=0

Q: Find the average value of the function f(x)= (3x +15.x-7) (2.x +5) over the given interval [1,3].

A:

Q: 5 Find f such that f'(x) = - √x f(16) = 49.

A: f′(x)=5x,f(16)=49