Show that V ar(aX + b) = a2V ar(X).  V ar(c) = 0 for any constant c.

Q: Let f(x) = V9x – 10 . Determine f-(x). f-(x)%3D

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Q: Let f(x) = 4x + 3. Determine (f ofo f)(x). (f o f o f)(x)

A: Composite functions: composite functions are the functions substituted inside the other function.…

Q: Suppose that Var(X) = 742.23, Var(Y) = 8890.5, and Cov(X,Y) = 2191.72. What is Var(.51X + .49Y)?

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

Q: Let f(x) = cx3.8 and suppose that f(2) = 16. Find the value of c.

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Q: The integrating factor of y= 2x' is dx

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Q: 8 Use definition L{f(t)} = - S% e- 0 -st f(t) dt to find L{3t}

A: From definition of Laplace integral  for function ,, Here

Q: For function i, i(x+4)=3x+1. Find i(-1)

A: Given function is

Q: that Var(X) = 727.48, Var(X) = 9536.23, and Cov(

A: Given,           Var(X) = 727.48, Var(Y) = 9536.23, and Cov(X, Y) = 2236.37 To the value of…

Q: Find f (VF + xJ dx

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Q: If f(x) = Vx+1 %3D 1 g(x) =- X+4 1 h(x) = - X Then find (fogoh)(x)

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Q: If f(x.y)= x?+2xy+5y² then дудх

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Q: Let f(x) = 4x - 8x. Find F(x), the antiderivative function, if F(1) = 3.

A: Let f(x)=4x2-8xTo find the antiderivative function F(x)if F(1)=3

Q: For what values of x is Ax) concave down if f "(x) = 3x' – 14x² + &r?

A: Given that, f''x=3x3-14x2+8x For what value of x is fx concave down.

Q: : Find a2f and a2f of the following: дх ду ду дх (1) f(x,y) = In(x?y) + ху (2) f(x,y) = e-3x*y³ +…

A: While finding partial derivative in multivariable function, if we have to find the partial…

Q: Integrate

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Q: Let f(x) = cx4.2 and suppose that f(5) = 30. Find the value of c.

A: Given f(x) = cx4.2

Q: Let f(x) = x²+ Ax + B. By knowing that f(1) = 5 and f'(1) = 5, find the values for A and B.

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Q: arg(z) = 1/4

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Q: Let f(x) = x² 4. Find f(3 - V13) – 6x – . %3D

A: Given:            fx=x2-6x-4 Find; f3-13 f3-13 =3-13 2-63-13-4 Simplify using : a-b2=a2-2ab+b2 3-13…

Q: e) k(x) = (2x-1) ³x

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Q: Suppose that Var(X) = 861.99, Var(X) = 9517.33, and Cov(X,Y) = 2449.18. What is Var(.37X + .63Y)?

A: Solution

Q: Find the differentiate

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Q: Find an antiderivative of (3x3+9x5)/x6 in the variable x where x does not equal 0.

A: From the given problem:   3x3+9x5x6   So,    3x3+9x5x6=∫3x3+9x5x6dx   We can simply write as:…

Q: Given f(x) = x2, is f the independent variable? Why or why not?

A: fx=x2

Q: If V(x) represents the volume of water, in cubic inches, in a tank when the height of the water is x…

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Q: Compare the values of Ay and dy if f(x) = x³ + x². 2x + 1 - æ is changes from 2 to 2.05.

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Q: Find an antiderivative of the given function. f(x) = 5(7x + 1)(7) Select one: A. (7x + 1)4 7 O B.…

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Q: Find Df,Rf/f(x). X 3 √x + √ X

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Q: f(x+1): = 71 Sx+3 ZX-7

A: Step 1: Step 2: Step 3: Step 4:

Q: The following table is based on information from the U.S. Census Bureau regarding the type of health…

A: HealthInsuranceCoverage<18(A)18-44(B)45-64(C)>64(D)TotalPrivate…

Q: r {(2) = In(V32" + 5x° + + 6), find f'(r). Use exact values. If

A: Given function is fx=ln3x6+5x3+67      =ln3x6+5x3+617=17ln3x6+5x3+6

Q: Linearize f(x)=√√√2-x for a = 1 and use it to approximate the value of √1.6. L(x) =

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