| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.15 |
| Score | 0% | 63% |
On average, the center for a basketball team hits 25% of his shots while a guard on the same team hits 35% of his shots. If the guard takes 10 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?
| 12 | |
| 7 | |
| 15 | |
| 5 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{35}{100} \) = \( \frac{35 x 10}{100} \) = \( \frac{350}{100} \) = 3 shots
The center makes 25% 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 = \( \frac{3}{\frac{25}{100}} \) = 3 x \( \frac{100}{25} \) = \( \frac{3 x 100}{25} \) = \( \frac{300}{25} \) = 12 shots
to make the same number of shots as the guard and thus score the same number of points.
Solve for \( \frac{5!}{6!} \)
| \( \frac{1}{30} \) | |
| 6 | |
| \( \frac{1}{3024} \) | |
| \( \frac{1}{6} \) |
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:
\( \frac{5!}{6!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6} \)
\( \frac{1}{6} \)
Convert y-5 to remove the negative exponent.
| \( \frac{-5}{y} \) | |
| \( \frac{1}{y^5} \) | |
| \( \frac{1}{y^{-5}} \) | |
| \( \frac{-1}{-5y} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
What is \( \sqrt{\frac{36}{36}} \)?
| \(\frac{5}{8}\) | |
| 2\(\frac{1}{2}\) | |
| 1 | |
| 4 |
To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:
\( \sqrt{\frac{36}{36}} \)
\( \frac{\sqrt{36}}{\sqrt{36}} \)
\( \frac{\sqrt{6^2}}{\sqrt{6^2}} \)
1
If \(\left|a\right| = 7\), which of the following best describes a?
a = 7 or a = -7 |
|
a = 7 |
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none of these is correct |
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a = -7 |
The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).