| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.07 |
| Score | 0% | 61% |
On average, the center for a basketball team hits 50% of his shots while a guard on the same team hits 55% of his shots. If the guard takes 25 shots during a game, how many shots will the center have to take to score as many points as the guard assuming each shot is worth the same number of points?
| 23 | |
| 27 | |
| 26 | |
| 59 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{55}{100} \) = \( \frac{55 x 25}{100} \) = \( \frac{1375}{100} \) = 13 shots
The center makes 50% of his shots so he'll have to take:
shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)
to make as many shots as the guard. Plugging in values for the center gives us:
center shots taken = \( \frac{13}{\frac{50}{100}} \) = 13 x \( \frac{100}{50} \) = \( \frac{13 x 100}{50} \) = \( \frac{1300}{50} \) = 26 shots
to make the same number of shots as the guard and thus score the same number of points.
What is -7y3 x y2?
| -6y6 | |
| -7y5 | |
| -7y3 | |
| -7y2 |
To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:
-7y3 x y2
(-7 x 1)y(3 + 2)
-7y5
Ezra loaned Jennifer $400 at an annual interest rate of 1%. If no payments are made, what is the total amount owed at the end of the first year?
| $412 | |
| $408 | |
| $416 | |
| $404 |
The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:
interest = annual interest rate x loan amount
i = (\( \frac{6}{100} \)) x $400
i = 0.01 x $400
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $400 + $4A machine in a factory has an error rate of 6 parts per 100. The machine normally runs 24 hours a day and produces 6 parts per hour. Yesterday the machine was shut down for 5 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 76 | |
| 91 | |
| 172.8 | |
| 107.2 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{6}{100} \) x 6 = \( \frac{6 \times 6}{100} \) = \( \frac{36}{100} \) = 0.36 errors per hour
So, in an average hour, the machine will produce 6 - 0.36 = 5.64 error free parts.
The machine ran for 24 - 5 = 19 hours yesterday so you would expect that 19 x 5.64 = 107.2 error free parts were produced yesterday.
A triathlon course includes a 300m swim, a 50.6km bike ride, and a 2.0km run. What is the total length of the race course?
| 31.4km | |
| 61.3km | |
| 52.9km | |
| 36.2km |
To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 300 meters to kilometers, divide the distance by 1000 to get 0.3km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.3km + 50.6km + 2.0km
total distance = 52.9km