| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.72 |
| Score | 0% | 54% |
What is \( \frac{8}{5} \) - \( \frac{4}{9} \)?
| 2 \( \frac{8}{14} \) | |
| 2 \( \frac{4}{11} \) | |
| \( \frac{9}{17} \) | |
| 1\(\frac{7}{45}\) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 5 and 9 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{8 x 9}{5 x 9} \) - \( \frac{4 x 5}{9 x 5} \)
\( \frac{72}{45} \) - \( \frac{20}{45} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{72 - 20}{45} \) = \( \frac{52}{45} \) = 1\(\frac{7}{45}\)
Simplify \( \frac{36}{52} \).
| \( \frac{3}{5} \) | |
| \( \frac{5}{17} \) | |
| \( \frac{6}{17} \) | |
| \( \frac{9}{13} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] and the factors of 52 are [1, 2, 4, 13, 26, 52]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{36}{52} \) = \( \frac{\frac{36}{4}}{\frac{52}{4}} \) = \( \frac{9}{13} \)
What is \( 2 \)\( \sqrt{32} \) + \( 2 \)\( \sqrt{2} \)
| 4\( \sqrt{16} \) | |
| 4\( \sqrt{2} \) | |
| 4\( \sqrt{32} \) | |
| 10\( \sqrt{2} \) |
To add these radicals together their radicands must be the same:
2\( \sqrt{32} \) + 2\( \sqrt{2} \)
2\( \sqrt{16 \times 2} \) + 2\( \sqrt{2} \)
2\( \sqrt{4^2 \times 2} \) + 2\( \sqrt{2} \)
(2)(4)\( \sqrt{2} \) + 2\( \sqrt{2} \)
8\( \sqrt{2} \) + 2\( \sqrt{2} \)
Now that the radicands are identical, you can add them together:
8\( \sqrt{2} \) + 2\( \sqrt{2} \)On average, the center for a basketball team hits 45% of his shots while a guard on the same team hits 55% of his shots. If the guard takes 30 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 | |
| 80 | |
| 57 | |
| 32 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 30 x \( \frac{55}{100} \) = \( \frac{55 x 30}{100} \) = \( \frac{1650}{100} \) = 16 shots
The center makes 45% 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 = \( \frac{16}{\frac{45}{100}} \) = 16 x \( \frac{100}{45} \) = \( \frac{16 x 100}{45} \) = \( \frac{1600}{45} \) = 36 shots
to make the same number of shots as the guard and thus score the same number of points.
| 1 | |
| 2.0 | |
| 6.3 | |
| 8.1 |
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