Confusing question. I think they want you to know that the independent variable, x, would be hours and the dependent variable, y, would be pay ($). Range refers to the smallest to largest values of the dependent variable, so it would be A) or B) cause those are in the correct units,...

f(x) = (x2/2) - 3x - (1/2)
df(x)/dx = x - 3
Mean Value Theorem: You want to find a point c in the interval [a,b] such that:
df(c)/dx = (f(b)-f(a))/(b-a)
In the interval [4,6]:
c - 3 = (f(6)-f(4))/(6-4)
c - 3 = (0 - -4)/(6-4)
c - 3 = 2
c...

If they win (45% chance), their chances of winning the next game = (0.45)(0.75)
If they lose (100% - 45%), their chances of winning the next game are = (1 - 0.45)(0.55)
Total = (0.45)(0.75) + (1 - 0.45)(0.55)

Your question is a bit vague, so it's hard to know what you're after. Here's a link to a Wyzant study guide on geometric transformations, including rotations.
https://www.wyzant.com/resources/files/496649/geometric_transformations
Maybe it will help you with learning...

Yes, you need a way to get an x2 into the numerator of the partial fraction so it's A/(x+2) + B/(x-2) + C. To put the C over the common denominator, you'll multiply it by (x2-4) and get Cx2-4C, so C=1. Then it reduces to a normal partial fraction with A = -B. ...

Let x = the smaller number.
The larger number is 8 more than the smaller number, so it's x+8. The sum of their squares is 104:
x2 + (x+8)2 = 104
x2 + x2 + 16x + 64 = 104
2x2 + 16x - 40 = 0
x2 + 8x - 20 = 0 ...

FOIL it out, Ma:
(x-5)(x+5) = x*x + 5x -5x + (5)(-5)
Can you finish it from here?

y=√(4x-x2)
I don't think you want to simplify it, I think you want to put it into the standard form for a circle:
(x-h)2 + (y-k)2 = r2
Square both sides:
y2 = 4x - x2
...

The general equation for a circle is:
(x-h)2 + (y-k)2 = r2
where (h,k) are the coordinates of the center of the circle and r is its radius. To find the particular equation for circle G, then, we need to find the center, (h,k), and the radius,...

30h + 50 ≤ 200
30h ≤ 150
h ≤ 5 hours

Use the distance formula to find the distance between the two points:
d = √((y2-y1)2+(x2-x1)2)
(x1,y1) = (-3,-7)
(x2,y2) = (1,-3)
Plug the points into the distance formula above and compute the distance, d, which is the length of a side. ...

K = mv2/2
Double the mass to 2m
K2m = 2mv2/2 = 2K It doubles the kinetic energy
Double the velocity to 2v:
K2v = m(2v)2/2 = 4mv2/2 = 4K ...

P(t) = P0·bt
P(t) = population at time t in millions
P0 = population in 1993 = 83 million
b = growth rate
t = years since 1993
P(t) = 83·bt
Now we'll use the two data points they gave us, (1993,83) and (2001,87), to find the value of b:
For...

Let g(x) be the transformed version of f(x). The general transformations are:
g(x) = a·f(b(x-c)) + d
a = vertical stretch. If a<0, it flips f(x) across the x-axis
b = horizontal stretch. If b<0, it flips f(x) across...

First, compute the circumference of Mercury's orbit:
C = 2·pi·r = 2(3.14159)(36,000,000) ≅ 540,353,936 miles (rounded to nearest mile)
Since it takes mercury 88 days to travel one full circumference, in one day Mercury travels...

Let m = men and h = horses. Since there were 19 heads, and both men and horses only have one head each:
m + h = 19
Men have 2 feet, horses have 4:
2m + 4h = 60
Solve the system of equations:
-2(m + h = 19)
2m...

P(t) = P0·(1+r)t
P(t) = Population in year t
Po = current population = 1543
r = rate (as a decimal) = 3.8% = 0.038
t = years from now = 5.2
P(t=5.2) = 1543·(1.038)5.2
Use your calculator to compute the answer. Round to nearest whole number...

Velocity = (angular velocity)*(radius) = (8pi/3 rad/min)*(125 ft) = _____ ft/min

You should do this one on your own Darcy just like the one I did for you earlier. One rotation = 2pi radians, 25 seconds = 25/60 = 5/12 of a minute. Divide radians by minutes.

One rotation = 2pi radians
45 seconds = (3/4) minute
Angular velocity has units of radians per minute, so divide the radians by the corresponding minutes:
Angular Velocity = 2pi/(3/4) = 8pi/3 radians/minute