The call signs of radio and television stations in the United States generally begin with the letter W east of the Mississippi River and the letter K west of the Mississippi…

The call signs of radio and television stations in the United States generally begin with the letter W east of the Mississippi River and the letter K west of the Mississippi. Repetition of letters is allowed. How many different call signs are possible if each station uses a W or K followed by 3 letters?

Renting video games from The Video Vendor costs $6 per game with no annual membership fee…

Renting video games from The Video Vendor costs
$6 per game with no annual membership fee. Renting
video games from The Game Garage costs $3 per
game, but a customer must pay an additional $60 for
an annual membership. If n represents the number of
video games a customer rents in a year, which of the
following gives all values of n for which it costs less
to rent from The Game Garage than from The Video
Vendor?

at 7am a sewage treatment tank contains 3000000 gallons of water…

at 7am a sewage treatment tank contains 3000000 gallons of water. starting at 7am, x gallons per minute flow into the tank, and y gallons per minute flow out of the tank. no water enters or leaves the tank otherwise. which of the following functions f models the number of gallons of water in the sewage treatment plant at 8am?

In the “Proving Grounds” Quiz 1 #5 explanation, you state: “โ€ฆWe know that, as a general rule, the remainder when a polynomial f(x)ย is divided by x โ€“ย a is f(a).” Can you explain this further?

In the “Proving Grounds” Quiz 1 #5, this question is given:

p(x) = ax^2 + bx + c
q(x) = ax^2 + bx + d

The functions p(x) and q(x) are defined above, and a, b, c, and d are constants. If x โ€“ 3 is a factor of p(x) and d is 8 greater than c, what is the remainder when q(x) is divided by x โ€“ 3?

In your answer explanation, you state:
“โ€ฆWe know that, as a general rule, the remainder when a polynomial f(x)ย is divided by x โ€“ย a is f(a).”

Can you explain this further?

there are 50 questions on a quiz given to a class of a students…

there are 50 questions on a quiz given to a class of a students. Only 20% of the class answered all the questions on the quiz. Of the remaining students, half answered two-fifths of the questions and the other half answered three-fifths. What was the average number of questions answered on this quiz?