| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.16 |
| Score | 0% | 63% |
Solve for \( \frac{2!}{3!} \)
| 210 | |
| \( \frac{1}{20} \) | |
| 7 | |
| \( \frac{1}{3} \) |
A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:
\( \frac{2!}{3!} \)
\( \frac{2 \times 1}{3 \times 2 \times 1} \)
\( \frac{1}{3} \)
\( \frac{1}{3} \)
On average, the center for a basketball team hits 30% of his shots while a guard on the same team hits 40% of his shots. If the guard takes 20 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?
| 27 | |
| 32 | |
| 16 | |
| 19 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 20 x \( \frac{40}{100} \) = \( \frac{40 x 20}{100} \) = \( \frac{800}{100} \) = 8 shots
The center makes 30% 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 = \( \frac{8}{\frac{30}{100}} \) = 8 x \( \frac{100}{30} \) = \( \frac{8 x 100}{30} \) = \( \frac{800}{30} \) = 27 shots
to make the same number of shots as the guard and thus score the same number of points.
How many 8-passenger vans will it take to drive all 76 members of the football team to an away game?
| 5 vans | |
| 4 vans | |
| 10 vans | |
| 12 vans |
Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:
vans = \( \frac{76}{8} \) = 9\(\frac{1}{2}\)
So, it will take 9 full vans and one partially full van to transport the entire team making a total of 10 vans.
What is \( \frac{3}{5} \) ÷ \( \frac{2}{8} \)?
| 2\(\frac{2}{5}\) | |
| \(\frac{9}{64}\) | |
| \(\frac{4}{63}\) | |
| 12 |
To divide fractions, invert the second fraction and then multiply:
\( \frac{3}{5} \) ÷ \( \frac{2}{8} \) = \( \frac{3}{5} \) x \( \frac{8}{2} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{3}{5} \) x \( \frac{8}{2} \) = \( \frac{3 x 8}{5 x 2} \) = \( \frac{24}{10} \) = 2\(\frac{2}{5}\)
If all of a roofing company's 8 workers are required to staff 2 roofing crews, how many workers need to be added during the busy season in order to send 7 complete crews out on jobs?
| 13 | |
| 19 | |
| 1 | |
| 20 |
In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 8 workers at the company now and that's enough to staff 2 crews so there are \( \frac{8}{2} \) = 4 workers on a crew. 7 crews are needed for the busy season which, at 4 workers per crew, means that the roofing company will need 7 x 4 = 28 total workers to staff the crews during the busy season. The company already employs 8 workers so they need to add 28 - 8 = 20 new staff for the busy season.