Quiz about Math Models - Final

Question 1

A tourist decides to go cliff jumping in Hawaii from a cliff that is 7 yards from the water. The parabola below shows the path of the jumper.

What is the equation's axis of symmetry?

Accepted Answer

x = 2

Answer

x = 6

Answer

y = 7

Answer

y = 9

Question 2

A store is open for business while it is being renovated. The noise from the renovation is increasingly driving away customers. The daily revenue, r(d), the store has made, d, days since renovation began is modeled by the function, $$r\left(d\right)=10,000\left(0.9539\right)^d$$

What is the factor of decay in this function?

Accepted Answer

0.9539

Answer

0.0461

Answer

1.9539

Answer

10,000

Question 3

The amount of time required to assemble a television varies inversely with the number of robots used on the assembly line. If 20 robots are able to assemble a television in 40 minutes, how many minutes would it take 32 robots working at the same speed to assemble the television?

NOTE: $$y=\frac{k}{x}$$

k = constant

Accepted Answer

25

Answer

28

Answer

52

Answer

60

Question 4

The stem-and-leaf plot below shows the height of all the plants in Timothy's garden.

What is the difference between the tallest plant than the second shortest plant?

Accepted Answer

4.8 inches

Answer

2.0 inches

Answer

4.0 inches

Answer

7.0 inches

Question 5

William tossed a coin four times while waiting for his bus at the bus stop. The first time it landed on heads. The second time it landed on tails. The third and fourth time it landed on heads. If he were to toss the coin a fifth time, what are the chances that it will land on tails?

Accepted Answer

$$\frac{1}{2}$$

Answer

$$\frac{1}{4}$$

Answer

$$\frac{2}{5}$$

Answer

$$\frac{3}{4}$$

Question 6

According to Boyle's law, the pressure, P, of a compressed gas is inversely proportional to the volume, V, of the gas. If the pressure of a sample of gas is 20 psi when its volume is 500 cubic inches, what is the pressure when the gas is compressed to a volume of 400 cubic inches?

NOTE: $$y=\frac{k}{x}$$

Accepted Answer

25 psi

Answer

16 psi

Answer

40 psi

Answer

50 psi

Question 7

For each week of the summer vacation, Laura read at least two books. The number of books she read each week is shown in the list below.

3, 3, 4, 3, 5, 4, 3, 5, 4, 2

What is the mode of this list of numbers?

Accepted Answer

3

Answer

2

Answer

4

Answer

5

Question 8

A population of 850 birds decreases by roughly the same percentage every year. The table below shows data values for the size, y, of the population after x years.

A researcher uses technology to fit an exponential regression model to the data. If she uses her model to predict the size of the bird population after 20 years, which value will she most likely obtain?

HINT: Use the calculator for regression on this one.

Accepted Answer

722

Answer

704

Answer

709

Answer

728

Question 9

The total distance in centimeters a toy robot moves varies directly with the time in seconds. The toy robot moves a total distance of 264 centimeters in 11 seconds.

What is the time in seconds the toy robot moves when the total distance is 408 centimeters?

NOTE: $$y=kx$$

Accepted Answer

17 seconds

Answer

13 seconds

Answer

24 seconds

Answer

37 seconds

Question 10

Beth tossed two fair coins at the same time. She repeated this trial 160 times. According to theoretical probability, how many trials should Beth expect to result in both coins showing heads?

Accepted Answer

40

Answer

20

Answer

60

Answer

80

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