Philip can paint a room in 9 hours. If Esteban helps Philip, they can paint the room in 3.6 hours. Use the function 3.6 9 + 3.6 x to find how long it would take Esteban to paint the room alone?

A. 6 hours
Correct! If Esteban paints the room in 6 hours alone, he and Philip can paint the room in 3.6 hours together.

B. 3 hours
Incorrect. Esteban cannot paint the room in less time alone than working with Philip.

C. 8 hours
Incorrect. It would take 4.2 hours, not 3.6 hours, for these two men to paint the room together if Esteban takes this long alone.

D. 4 hours
Incorrect. It would take 2.8 hours, not 3.6 hours, for these two men to paint the room together if Esteban takes this long alone.

The chemist's assistant needs to add an 80% acid solution to 20 milliliters of a solution that is 18% acid, using the function f(x) = 20(0.18) + x(0.80) 20 + x. With the percent of acid, f(x), a function of x, the amount of the 80% acid solution added, which graph correctly tells the assistant how much of the 80% solution needs to be added to have a resulting solution that is 60% acid?

Correct! The function has been correctly entered into the calculator and correctly shows the point indicating that 42 ml of the 80% solution will result in a 60% acid solution.	Incorrect. The function has been incorrectly entered as a linear function. When 0.40 ml is substituted into the function, we do not get a resulting solution of 60% acid.
Incorrect. The function has been incorrectly entered as a linear function.	Incorrect. The point shown gives the amount of 80% acid solution to get a resulting solution that is 50% acid instead of the 60% needed.

Scuba divers are under intense pressure caused by the weight of the water above them. To compensate, divers fill their tanks with air containing less oxygen than Earth's atmosphere. The recommended percent, p, of oxygen in the air a diver breathes is given by p = 660 d + 33, where d is the depth, in feet. Which choice does not accurately depict the depth at which a diver would need a tank with 3% oxygen?

Incorrect. This table correctly reflects the function values and shows that the depth of 187 feet would require 3% oxygen and we are looking for a choice that is incorrect.	Incorrect. This graph correctly reflects the function values and shows that the depth of 187 feet would require 3% oxygen and we are looking for a choice that is incorrect.
Incorrect. These steps correctly depict the algebraic solution showing that the depth of 187 feet would require 3% oxygen and we are looking for a choice that is incorrect.	Correct! This graph incorrectly reflects the function values so this choice is what we want.

A certain company uses a drill press to remove the core out of a metal cylinder to make it hollow. The height of the cylinder is a function of the radius, having the equation h = V π(r² − 4), where V is the volume of the cylinder. If the volume of the cylinder is 500 units³ and the height is 8 units, what is the radius?

A. 4.89 units
Correct! 500 divided by π multiplied by 4.89 squared minus 4 almost equals 7.99, which gives us the height of 8 units.

B. 23.89 units
Incorrect. You forgot that the radius was squared. You need to take the square root of this value.

C. 2.65 units
Incorrect. You substituted the height in place of the radius.

D.10.75 units
Incorrect. 500 divided by π multiplied by 10.75 squared minus 4 almost equals 1.43, which does not give us the height of 8 units.