| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.14 |
| Score | 0% | 63% |
Solve for \( \frac{5!}{3!} \)
| 20 | |
| 1680 | |
| \( \frac{1}{840} \) | |
| \( \frac{1}{120} \) |
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:
\( \frac{5!}{3!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{3 \times 2 \times 1} \)
\( \frac{5 \times 4}{1} \)
\( 5 \times 4 \)
20
On average, the center for a basketball team hits 50% of his shots while a guard on the same team hits 70% of his shots. If the guard takes 15 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?
| 36 | |
| 25 | |
| 24 | |
| 20 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 15 x \( \frac{70}{100} \) = \( \frac{70 x 15}{100} \) = \( \frac{1050}{100} \) = 10 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 = \( \frac{10}{\frac{50}{100}} \) = 10 x \( \frac{100}{50} \) = \( \frac{10 x 100}{50} \) = \( \frac{1000}{50} \) = 20 shots
to make the same number of shots as the guard and thus score the same number of points.
Damon loaned Monty $300 at an annual interest rate of 6%. If no payments are made, what is the interest owed on this loan at the end of the first year?
| $21 | |
| $70 | |
| $60 | |
| $18 |
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 $300
i = 0.06 x $300
i = $18
A bread recipe calls for 3\(\frac{5}{8}\) cups of flour. If you only have \(\frac{1}{4}\) cup, how much more flour is needed?
| 2\(\frac{7}{8}\) cups | |
| 3\(\frac{1}{4}\) cups | |
| 3\(\frac{3}{8}\) cups | |
| \(\frac{5}{8}\) cups |
The amount of flour you need is (3\(\frac{5}{8}\) - \(\frac{1}{4}\)) cups. Rewrite the quantities so they share a common denominator and subtract:
(\( \frac{29}{8} \) - \( \frac{2}{8} \)) cups
\( \frac{27}{8} \) cups
3\(\frac{3}{8}\) cups
Convert x-5 to remove the negative exponent.
| \( \frac{-5}{x} \) | |
| \( \frac{1}{x^5} \) | |
| \( \frac{-1}{-5x^{5}} \) | |
| \( \frac{-1}{-5x} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.