2. Prove or give a counterexample to • If X ≤Y then Var (X) < Var(Y) • Var(X-c) < Var (X + c) for c>0 . Var (X) ≤ Var(X)

Q: 6 7 5 576 Calculate the mean, variance, and standard deviation for this sample. Note: Please enter…

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Q: 2. Determine all values of x for which 0<= x2-11/x+1<=7 (include graph and intervals tables) *in…

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Q: x+ 6x +7 f(x) = {-x + 3 5 if x < -1 if -1<x<3 if x 2 3 f(2) = %3D f(-1) = S(-7) = S(3) =

A: The given step function is f(x)=x2+6x+7if x&lt;-1-x+3if -1≤x&lt;35if x≥3

Q: The function f is continuous on the interval -2 < x < 5 and is not continuous on the interval -2 ≤ x…

A: The function  is continuous on the interval and is not continuous on the interval . To find the…

Q: For all x, there exists y such that (y^2 <= x <(y+1)^2) when domain is N(natural number) I want to…

A: For all x, there exists a y, such that,  y2 ≤ x &lt; (y + 1)2   Given that x is a natural number,…

Q: (-3 if z 2

A: Here is a step by step solution of the problem. We have proved discontinuity at x=2 by evaluation…

Q: 5(x-3)&lt;2(3x-1)

A: Obtain the x values that satisfies the given inequality 5(x–3)&lt;2(3x–1).

Q: f(x) = 2* and g(x) = 2**2 %3D

A: We need to plot the given functions.

Q: 4. A function f may have the property that, for all numbers a and b in the domain of f, f(a) + f(b)…

A: GIVEN : f(a) + f(b) = f(a + b)

Q: x -4 ifx<2 Determine f(2) if f(x)= {2-x if 2 <x<4. x-2 if 4 <x

A: Given,           fx=x2-4if x≤22-xif 2&lt;x≤4x-2if 4&lt;xTo find : Determine f'+2.

Q: 1. State the domain and range of f(x) = /9(x - 4) + 2 D:[2,00) A. D:[4,00) В. D:[4,00) D:[2,00) D.…

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Q: Let f(x) = 4x%/1 and g(x) = 2x/² . Find (fg) (x) and L(x). Then evaluate fg and for x = 16. %3D…

A: Use function composition and division rule

Q: X~N(100,9). That is, E(X)=100 and Var(X)=9. Find Prob(60<X<80).

A: Given that  Given that.   X~N( μ , ?^2 )   μ=100    , ?=3   Z-score =( x - μ )/?

Q: ²-8 If f(x) = X-4' X = where is f not differentiable?

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Q: I do not know how to do this question or even what it's asking for.

A: Consider the given function,

Q: Find the domain of f(x)= Mostly sunny x|x€Rx‡¬ √10} 00 x|x€R_x#√10} Ox|x€R¸x*-√√10, 10}…

A: a2 - b2 = (a - b)(a + b)  and 10 = (10)1/2(10)1/2

Q: VxVx2((f(x1) = f(x2)) → (x1 = x2)) O composite O injective O surjective O bijective

A:

Q: What is true about the function f(x)= = a) f(x) → from above b) f(x) →2 from above c) f(x) → from…

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Q: Give the domain of f, the domain of g, and the domain of m, where m(x) = f[g(x)]. f(u) = In u;…

A: Given:  A  function  fu=ln u; gx=2x  mx=fgx To Find: Domain of f, g, m Domain is the set of all the…

Q: Where is the function f(x) = if x 0 removable discontinuity? Is it a jump discontinuity?

A: A jump discontinuity occurs when right and left limit exists but are unequal .

Q: 10. Evaluate | x In(x+12) « dr.

A:

Q: f(x) = - 4x+5 if -1<x<2 3x-8 if 2≤x≤4 The domain of the piecewise defined function fis [-1,2]U[2,4]

A: Given a piece wise function

Q: Suppose that f(x) = 3x² - 4x + 4 and Find the following: 1. (fog) (6) = Number 2. (fog)(0) = Number…

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Q: Which equation matches the graph of the piecewise function f(x) below?

A: Given,

Q: Which of the following statements below are true for f(x) = - 2(x - 1)(x - 2)(x + 3)(x + 4)? * i) as…

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Q: how many critical numbers does the funtion f ( x ) = | x 2 − 5 | have?

A: The graph of the function given below.

Q: Which of the following is an even function O f(x)= 3x^2 + 5x^3 + 10x^6 O f(x) = -7x^8 - 3x^4 + 5 O…

A: We have to check the even functions from the given functions.

Q: -4 if x1

A: The given function is: f(x)=-4        if  x&lt;-2(x+1)2-1    if  -2≤x≤1-14x+2if  x&gt;1

Q: O is a simple zero of f(x)= secx+e2 -2 %3D Select one: True O False

A:

Q: 3/4(8y-9)&lt;3

A: We multiply both sides by 4 first.

Q: What is the domain of x↦ (1)/(x^(2-25)) ? b. Explore x-> (1)/(x-|x|) to determine what inputs, if…

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Q: Let f(x) = -x4-9x³+2x+8. Find the open intervals on which is concave up (down). Then determine the…

A: For a given function f( x ) ( a ) inflection points by f''( x ) = 0 ( b ) For concave up , f''( x )…

Q: Suppose that To (2) centered at 3 for f(x)is given by Ts (2) = 7+3(2-3) + 2(x-3)² + 4(x-3)³ + (x-3)5…

A: Given that , T6x=7+3x-3+2x-32+4x-33+x-35+5x-36 and T6x centered at 3.

Q: if f(x,x2) =,0 < x, < 1,0 < x2 < 1, then f(x2/x,) = 1

A: Let X and Y be two continuous random variable with joint density function f(x,y). The marginal…