| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.84 |
| Score | 0% | 57% |
If a mayor is elected with 64% of the votes cast and 37% of a town's 38,000 voters cast a vote, how many votes did the mayor receive?
| 10,545 | |
| 8,998 | |
| 11,810 | |
| 8,577 |
If 37% of the town's 38,000 voters cast ballots the number of votes cast is:
(\( \frac{37}{100} \)) x 38,000 = \( \frac{1,406,000}{100} \) = 14,060
The mayor got 64% of the votes cast which is:
(\( \frac{64}{100} \)) x 14,060 = \( \frac{899,840}{100} \) = 8,998 votes.
What is \( \frac{3}{9} \) ÷ \( \frac{2}{7} \)?
| 10\(\frac{1}{2}\) | |
| \(\frac{2}{5}\) | |
| 1\(\frac{1}{6}\) | |
| \(\frac{4}{63}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{3}{9} \) ÷ \( \frac{2}{7} \) = \( \frac{3}{9} \) x \( \frac{7}{2} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{3}{9} \) x \( \frac{7}{2} \) = \( \frac{3 x 7}{9 x 2} \) = \( \frac{21}{18} \) = 1\(\frac{1}{6}\)
What is \( \frac{3}{2} \) - \( \frac{3}{8} \)?
| 1 \( \frac{2}{6} \) | |
| 1\(\frac{1}{8}\) | |
| 2 \( \frac{4}{11} \) | |
| \( \frac{5}{8} \) |
To subtract 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 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 2 and 8 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{3 x 4}{2 x 4} \) - \( \frac{3 x 1}{8 x 1} \)
\( \frac{12}{8} \) - \( \frac{3}{8} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{12 - 3}{8} \) = \( \frac{9}{8} \) = 1\(\frac{1}{8}\)
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 25 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?
| 37 | |
| 23 | |
| 30 | |
| 29 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{45}{100} \) = \( \frac{45 x 25}{100} \) = \( \frac{1125}{100} \) = 11 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 = \( \frac{11}{\frac{30}{100}} \) = 11 x \( \frac{100}{30} \) = \( \frac{11 x 100}{30} \) = \( \frac{1100}{30} \) = 37 shots
to make the same number of shots as the guard and thus score the same number of points.
What is \( \frac{1c^9}{5c^4} \)?
| \(\frac{1}{5}\)c5 | |
| \(\frac{1}{5}\)c2\(\frac{1}{4}\) | |
| \(\frac{1}{5}\)c-5 | |
| \(\frac{1}{5}\)c13 |
To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:
\( \frac{c^9}{5c^4} \)
\( \frac{1}{5} \) c(9 - 4)
\(\frac{1}{5}\)c5