| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.03 |
| Score | 0% | 61% |
On average, the center for a basketball team hits 30% of his shots while a guard on the same team hits 45% 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?
| 17 | |
| 11 | |
| 13 | |
| 7 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{45}{100} \) = \( \frac{45 x 10}{100} \) = \( \frac{450}{100} \) = 4 shots
The center makes 30% 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 = \( \frac{4}{\frac{30}{100}} \) = 4 x \( \frac{100}{30} \) = \( \frac{4 x 100}{30} \) = \( \frac{400}{30} \) = 13 shots
to make the same number of shots as the guard and thus score the same number of points.
In a class of 31 students, 13 are taking German and 11 are taking Spanish. Of the students studying German or Spanish, 6 are taking both courses. How many students are not enrolled in either course?
| 11 | |
| 13 | |
| 22 | |
| 10 |
The number of students taking German or Spanish is 13 + 11 = 24. Of that group of 24, 6 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 24 - 6 = 18 who are taking at least one language. 31 - 18 = 13 students who are not taking either language.
What is \( \frac{7}{2} \) + \( \frac{4}{10} \)?
| 2 \( \frac{6}{14} \) | |
| \( \frac{1}{9} \) | |
| 3\(\frac{9}{10}\) | |
| \( \frac{4}{10} \) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [10, 20, 30, 40, 50] making 10 the smallest multiple 2 and 10 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{7 x 5}{2 x 5} \) + \( \frac{4 x 1}{10 x 1} \)
\( \frac{35}{10} \) + \( \frac{4}{10} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{35 + 4}{10} \) = \( \frac{39}{10} \) = 3\(\frac{9}{10}\)
Convert z-3 to remove the negative exponent.
| \( \frac{-1}{-3z} \) | |
| \( \frac{1}{z^3} \) | |
| \( \frac{3}{z} \) | |
| \( \frac{-1}{z^{-3}} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
What is \( \sqrt{\frac{36}{25}} \)?
| \(\frac{4}{9}\) | |
| 1\(\frac{1}{5}\) | |
| 1\(\frac{3}{4}\) | |
| \(\frac{1}{2}\) |
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:
\( \sqrt{\frac{36}{25}} \)
\( \frac{\sqrt{36}}{\sqrt{25}} \)
\( \frac{\sqrt{6^2}}{\sqrt{5^2}} \)
\( \frac{6}{5} \)
1\(\frac{1}{5}\)