Question

nc math 1—released items
questions 9 and 10 are gridded response items that require you to write your answers in the boxes provided on your answer sheet. write only one number or symbol in each box and fill in the circle in each column that matches what you have printed. fill in only one circle in each column.
9 the total cost, in dollars, of membership in a fitness center is given by the function $c(m) = 20m + 40$, where $m$ is the number of months a person is a member. in dollars, how much is the cost of a membership for 1 year?
10 water is being pumped into a 10-foot-tall cylindrical tank at a constant rate.

• the depth of the water is increasing linearly.
• at 1:30 p.m., the water depth was 2.4 feet.
• it is now 4:00 p.m., and the depth of the water is 3.9 feet.

what will the depth (in feet) of the water be at 5:00 p.m.?

Explanation:

Question 9

Step1: Convert 1 year to months

1 year has 12 months, so \( m = 12 \).

Step2: Substitute \( m = 12 \) into the cost function \( c(m)=20m + 40 \)

\( c(12)=20\times12 + 40 \)
\( = 240+40 \)
\( = 280 \)

Step1: Calculate the time elapsed

From 1:30 p.m. to 4:00 p.m., the time elapsed is \( 4:00 - 1:30 = 2.5 \) hours.

Step2: Find the rate of depth increase

The depth increased from 2.4 feet to 3.9 feet, so the increase in depth is \( 3.9 - 2.4 = 1.5 \) feet. The rate \( r \) is \( \frac{1.5}{2.5}=0.6 \) feet per hour.

Step3: Calculate the depth at 5:00 p.m.

From 4:00 p.m. to 5:00 p.m. is 1 hour. So the depth will increase by 0.6 feet. The depth at 4:00 p.m. is 3.9 feet, so at 5:00 p.m., the depth is \( 3.9+0.6 = 4.5 \) feet.

Answer:

280

Question 10