| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.12 |
| Score | 0% | 62% |
What is \( \sqrt{\frac{49}{81}} \)?
| \(\frac{7}{9}\) | |
| 1\(\frac{3}{5}\) | |
| 1\(\frac{1}{6}\) | |
| 1\(\frac{1}{7}\) |
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:
\( \sqrt{\frac{49}{81}} \)
\( \frac{\sqrt{49}}{\sqrt{81}} \)
\( \frac{\sqrt{7^2}}{\sqrt{9^2}} \)
\(\frac{7}{9}\)
If a rectangle is twice as long as it is wide and has a perimeter of 30 meters, what is the area of the rectangle?
| 162 m2 | |
| 128 m2 | |
| 50 m2 | |
| 2 m2 |
The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 30 meters so the equation becomes: 2w + 2h = 30.
Putting these two equations together and solving for width (w):
2w + 2h = 30
w + h = \( \frac{30}{2} \)
w + h = 15
w = 15 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 15 - 2w
3w = 15
w = \( \frac{15}{3} \)
w = 5
Since h = 2w that makes h = (2 x 5) = 10 and the area = h x w = 5 x 10 = 50 m2
On average, the center for a basketball team hits 40% of his shots while a guard on the same team hits 60% 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 | |
| 15 | |
| 17 | |
| 19 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{60}{100} \) = \( \frac{60 x 10}{100} \) = \( \frac{600}{100} \) = 6 shots
The center makes 40% 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 = \( \frac{6}{\frac{40}{100}} \) = 6 x \( \frac{100}{40} \) = \( \frac{6 x 100}{40} \) = \( \frac{600}{40} \) = 15 shots
to make the same number of shots as the guard and thus score the same number of points.
What is \( \frac{2}{8} \) x \( \frac{2}{7} \)?
| \(\frac{4}{15}\) | |
| \(\frac{1}{6}\) | |
| \(\frac{1}{14}\) | |
| \(\frac{4}{7}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{2}{8} \) x \( \frac{2}{7} \) = \( \frac{2 x 2}{8 x 7} \) = \( \frac{4}{56} \) = \(\frac{1}{14}\)
Simplify \( \frac{36}{60} \).
| \( \frac{9}{20} \) | |
| \( \frac{1}{3} \) | |
| \( \frac{5}{13} \) | |
| \( \frac{3}{5} \) |
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 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]. They share 6 factors [1, 2, 3, 4, 6, 12] making 12 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{36}{60} \) = \( \frac{\frac{36}{12}}{\frac{60}{12}} \) = \( \frac{3}{5} \)