Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following. F(x) = 0 if x < 0; x^2/25 if 0 <= x < 5; and 1 if x >= 5. Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.) (g) Calculate V(X) and σx. (Answer is not 1.391.)  (h) If the borrower is charged an amount h(X) = X2 when checkout duration is X, compute the expected charge E[h(X)].

Q: :-3 ifx 2 -3 2-1

A: The given piecewise function is,t(x)=-12x-3if x&lt;2-1if x≥2

Q: 3- Find the domain and ranges for V1/(1 – x3)

A: The given function is 11-x3  To find the domain and range of 11-x3

Q: Estimate how much the function f (x) = 1/1 + x2 will change if x decreases from 1 to .9.

A: Given: The function  f(x) = 11+x2 To find: How much the given function will change if x decreases…

Q: Determine if The following pairs of functions are of the same order. Justify your (a) /(0) = log1o…

A: If a pair of functions fx and gx are of same order, then limx→∞fg=N where N≠0 is a constant.

Q: of the function f(r) = (" – x)*. Find ao a. 12 Ob. O C. 6.

A: Let us consider the limit to be (0,2π) For the limit (-π,π)  the function is odd function so it will…

Q: Graph the given functions in the specified interval

A: We first solve the equation for y.   4y=x+4y=x+44y=x4+1

Q: Differentiate each of the following functions. i. y = 12x12 – 24 - ii. y = x5/6 – 28 - iii. y = 14…

A:

Q: Graph the functions

A: We make table for each potion  G(x)=1/x  x -3 -2 -1 -0.01 y -0.33 -0.5 -1 -100   G(x)=x…

Q: 4x f (x)=- x2 +4 %3D

A: f(x)=-4xx2+4

Q: 3. Check for monotonicity for the following functions. TR = -20² + 14Q %3D TC = 20 + 10 100 AC = Q +…

A:

Q: Evaluate the function f(x)=- 3.7521n x at x = 4. Round to 3 decimal places. (You may use your…

A:

Q: Given x0 = 0.1, y0 = 0.2, x1 = 0.2, y1 = 0.24, x2 = 0.3, y3 = 0.3. Find f [x0, x1] and f [x0, x1,…

A: Note: It is assumed that y2=0.3.   The formula for P1x is P1x=f(x0)+x-x0fx0, x1 and the formula for…

Q: Plot the following functions 1. y = -V2x +1 2. y = (x- 1)3 + 2

A:

Q: Evaluate the following function. If p (x) = 7 (4)" , find p (5)

A:

Q: It is estimated that 50% of chata are spam chats. Some software has been applied to filter these…

A: Solution

Q: Differentiate the following function with respect to x, fully simplifying the answer: y = 3sin(2x)/…

A:

Q: Differentiate each of the following functions using the quotient rule h (x) = %3D x2 - 2

A:

Q: Suppose you invest $250 at the end of each year for 10 years at an annual interest rate of r. The…

A: Ar=2501+r10-1r

Q: Graph the following functions.

A: The function: fx=-2x-1if x&lt;-11if -1≤x≤12x-1if x&gt;1

Q: Consider the following function.   Find values of a and b such that 1/7+x =a(1/1-bx) a= b=

A:

Q: 1. The function f gives the discharge rate of the Kalamazoo river in m³/s as a function of x miles…

A:

Q: Determine the value A (to 2 decimal places) of the following p.d.f.: A(1-x²) -1<x<1 s(x)= otherwise…

A: Solution

Q: Differentiate the following function. f(x) = - 2 e 4x d (-2e **) =D - 2 e 4*) %3D dx

A:

Q: Evaluate the following function. If p (x) = 4 (3)", find p (3)

A: p(x) = 4(3)x to find p(3) we will put value of variable x = 3 .

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.