| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.17 |
| Score | 0% | 63% |
If the ratio of home fans to visiting fans in a crowd is 5:1 and all 33,000 seats in a stadium are filled, how many home fans are in attendance?
| 30,750 | |
| 27,000 | |
| 27,500 | |
| 24,000 |
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:
33,000 fans x \( \frac{5}{6} \) = \( \frac{165000}{6} \) = 27,500 fans.
What is \( \frac{63\sqrt{12}}{9\sqrt{6}} \)?
| \(\frac{1}{2}\) \( \sqrt{7} \) | |
| \(\frac{1}{2}\) \( \sqrt{\frac{1}{7}} \) | |
| \(\frac{1}{7}\) \( \sqrt{\frac{1}{2}} \) | |
| 7 \( \sqrt{2} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{63\sqrt{12}}{9\sqrt{6}} \)
\( \frac{63}{9} \) \( \sqrt{\frac{12}{6}} \)
7 \( \sqrt{2} \)
A triathlon course includes a 500m swim, a 40.8km bike ride, and a 14.9km run. What is the total length of the race course?
| 50.4km | |
| 56.2km | |
| 62.9km | |
| 49.3km |
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 500 meters to kilometers, divide the distance by 1000 to get 0.5km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.5km + 40.8km + 14.9km
total distance = 56.2km
What is \( \frac{3}{8} \) x \( \frac{3}{5} \)?
| \(\frac{3}{56}\) | |
| 1\(\frac{4}{5}\) | |
| \(\frac{9}{40}\) | |
| \(\frac{1}{56}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{3}{8} \) x \( \frac{3}{5} \) = \( \frac{3 x 3}{8 x 5} \) = \( \frac{9}{40} \) = \(\frac{9}{40}\)
If all of a roofing company's 8 workers are required to staff 4 roofing crews, how many workers need to be added during the busy season in order to send 6 complete crews out on jobs?
| 19 | |
| 15 | |
| 4 | |
| 13 |
In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 8 workers at the company now and that's enough to staff 4 crews so there are \( \frac{8}{4} \) = 2 workers on a crew. 6 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 6 x 2 = 12 total workers to staff the crews during the busy season. The company already employs 8 workers so they need to add 12 - 8 = 4 new staff for the busy season.