| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.34 |
| Score | 0% | 67% |
If a mayor is elected with 73% of the votes cast and 36% of a town's 24,000 voters cast a vote, how many votes did the mayor receive?
| 4,752 | |
| 4,579 | |
| 6,307 | |
| 5,270 |
If 36% of the town's 24,000 voters cast ballots the number of votes cast is:
(\( \frac{36}{100} \)) x 24,000 = \( \frac{864,000}{100} \) = 8,640
The mayor got 73% of the votes cast which is:
(\( \frac{73}{100} \)) x 8,640 = \( \frac{630,720}{100} \) = 6,307 votes.
Simplify \( \frac{40}{56} \).
| \( \frac{9}{14} \) | |
| \( \frac{1}{3} \) | |
| \( \frac{2}{7} \) | |
| \( \frac{5}{7} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40] and the factors of 56 are [1, 2, 4, 7, 8, 14, 28, 56]. They share 4 factors [1, 2, 4, 8] making 8 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{40}{56} \) = \( \frac{\frac{40}{8}}{\frac{56}{8}} \) = \( \frac{5}{7} \)
What is 2x7 + 9x7?
| 7x-7 | |
| 11x7 | |
| -7x-7 | |
| 11x14 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:
2x7 + 9x7
(2 + 9)x7
11x7
What is \( \frac{10\sqrt{20}}{2\sqrt{5}} \)?
| 5 \( \sqrt{\frac{1}{4}} \) | |
| \(\frac{1}{5}\) \( \sqrt{\frac{1}{4}} \) | |
| 5 \( \sqrt{4} \) | |
| \(\frac{1}{4}\) \( \sqrt{5} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{10\sqrt{20}}{2\sqrt{5}} \)
\( \frac{10}{2} \) \( \sqrt{\frac{20}{5}} \)
5 \( \sqrt{4} \)
A triathlon course includes a 300m swim, a 30.6km bike ride, and a 11.0km run. What is the total length of the race course?
| 45.3km | |
| 65.3km | |
| 41.9km | |
| 48.2km |
To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 300 meters to kilometers, divide the distance by 1000 to get 0.3km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.3km + 30.6km + 11.0km
total distance = 41.9km