| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.08 |
| Score | 0% | 62% |
Convert y-5 to remove the negative exponent.
| \( \frac{5}{y} \) | |
| \( \frac{-1}{-5y} \) | |
| \( \frac{-1}{-5y^{5}} \) | |
| \( \frac{1}{y^5} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
If a mayor is elected with 55% of the votes cast and 58% of a town's 27,000 voters cast a vote, how many votes did the mayor receive?
| 12,215 | |
| 8,143 | |
| 8,613 | |
| 9,396 |
If 58% of the town's 27,000 voters cast ballots the number of votes cast is:
(\( \frac{58}{100} \)) x 27,000 = \( \frac{1,566,000}{100} \) = 15,660
The mayor got 55% of the votes cast which is:
(\( \frac{55}{100} \)) x 15,660 = \( \frac{861,300}{100} \) = 8,613 votes.
Simplify \( \frac{16}{64} \).
| \( \frac{7}{13} \) | |
| \( \frac{1}{4} \) | |
| \( \frac{2}{3} \) | |
| \( \frac{9}{13} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 16 are [1, 2, 4, 8, 16] and the factors of 64 are [1, 2, 4, 8, 16, 32, 64]. They share 5 factors [1, 2, 4, 8, 16] making 16 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{16}{64} \) = \( \frac{\frac{16}{16}}{\frac{64}{16}} \) = \( \frac{1}{4} \)
If the ratio of home fans to visiting fans in a crowd is 5:1 and all 42,000 seats in a stadium are filled, how many home fans are in attendance?
| 31,500 | |
| 35,000 | |
| 39,200 | |
| 39,167 |
A ratio of 5:1 means that there are 5 home fans for every one visiting fan. So, of every 6 fans, 5 are home fans and \( \frac{5}{6} \) of every fan in the stadium is a home fan:
42,000 fans x \( \frac{5}{6} \) = \( \frac{210000}{6} \) = 35,000 fans.
If \( \left|x - 8\right| \) - 8 = 3, which of these is a possible value for x?
| 3 | |
| 19 | |
| 9 | |
| -21 |
First, solve for \( \left|x - 8\right| \):
\( \left|x - 8\right| \) - 8 = 3
\( \left|x - 8\right| \) = 3 + 8
\( \left|x - 8\right| \) = 11
The value inside the absolute value brackets can be either positive or negative so (x - 8) must equal + 11 or -11 for \( \left|x - 8\right| \) to equal 11:
| x - 8 = 11 x = 11 + 8 x = 19 | x - 8 = -11 x = -11 + 8 x = -3 |
So, x = -3 or x = 19.