| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.04 |
| Score | 0% | 61% |
On average, the center for a basketball team hits 25% of his shots while a guard on the same team hits 45% 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?
| 24 | |
| 27 | |
| 13 | |
| 11 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 15 x \( \frac{45}{100} \) = \( \frac{45 x 15}{100} \) = \( \frac{675}{100} \) = 6 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 = \( \frac{6}{\frac{25}{100}} \) = 6 x \( \frac{100}{25} \) = \( \frac{6 x 100}{25} \) = \( \frac{600}{25} \) = 24 shots
to make the same number of shots as the guard and thus score the same number of points.
What is \( \frac{2}{7} \) x \( \frac{1}{6} \)?
| \(\frac{16}{45}\) | |
| \(\frac{1}{21}\) | |
| \(\frac{1}{3}\) | |
| \(\frac{8}{15}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{2}{7} \) x \( \frac{1}{6} \) = \( \frac{2 x 1}{7 x 6} \) = \( \frac{2}{42} \) = \(\frac{1}{21}\)
If \(\left|a\right| = 7\), which of the following best describes a?
a = -7 |
|
a = 7 |
|
a = 7 or a = -7 |
|
none of these is correct |
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).
What is (a3)2?
| 2a3 | |
| a-1 | |
| a6 | |
| a5 |
To raise a term with an exponent to another exponent, retain the base and multiply the exponents:
(a3)2What is \( 8 \)\( \sqrt{48} \) - \( 8 \)\( \sqrt{3} \)
| 64\( \sqrt{16} \) | |
| 0\( \sqrt{48} \) | |
| 24\( \sqrt{3} \) | |
| 0\( \sqrt{-7} \) |
To subtract these radicals together their radicands must be the same:
8\( \sqrt{48} \) - 8\( \sqrt{3} \)
8\( \sqrt{16 \times 3} \) - 8\( \sqrt{3} \)
8\( \sqrt{4^2 \times 3} \) - 8\( \sqrt{3} \)
(8)(4)\( \sqrt{3} \) - 8\( \sqrt{3} \)
32\( \sqrt{3} \) - 8\( \sqrt{3} \)
Now that the radicands are identical, you can subtract them:
32\( \sqrt{3} \) - 8\( \sqrt{3} \)