| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.01 |
| Score | 0% | 60% |
What is (a5)3?
| a15 | |
| a2 | |
| a8 | |
| 3a5 |
To raise a term with an exponent to another exponent, retain the base and multiply the exponents:
(a5)3A triathlon course includes a 500m swim, a 20.1km bike ride, and a 10.9km run. What is the total length of the race course?
| 51.4km | |
| 46km | |
| 31.5km | |
| 45.4km |
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 500 meters to kilometers, divide the distance by 1000 to get 0.5km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.5km + 20.1km + 10.9km
total distance = 31.5km
What is \( \frac{4}{5} \) ÷ \( \frac{2}{8} \)?
| \(\frac{2}{21}\) | |
| \(\frac{1}{6}\) | |
| 6\(\frac{2}{5}\) | |
| 3\(\frac{1}{5}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{4}{5} \) ÷ \( \frac{2}{8} \) = \( \frac{4}{5} \) x \( \frac{8}{2} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{4}{5} \) x \( \frac{8}{2} \) = \( \frac{4 x 8}{5 x 2} \) = \( \frac{32}{10} \) = 3\(\frac{1}{5}\)
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?
| 33 | |
| 26 | |
| 25 | |
| 38 |
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.
Cooks are needed to prepare for a large party. Each cook can bake either 3 large cakes or 11 small cakes per hour. The kitchen is available for 3 hours and 35 large cakes and 480 small cakes need to be baked.
How many cooks are required to bake the required number of cakes during the time the kitchen is available?
| 14 | |
| 12 | |
| 10 | |
| 19 |
If a single cook can bake 3 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 3 x 3 = 9 large cakes during that time. 35 large cakes are needed for the party so \( \frac{35}{9} \) = 3\(\frac{8}{9}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 11 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 11 x 3 = 33 small cakes during that time. 480 small cakes are needed for the party so \( \frac{480}{33} \) = 14\(\frac{6}{11}\) cooks are needed to bake the required number of small cakes.
Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 4 + 15 = 19 cooks.