| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.04 |
| Score | 0% | 61% |
If the ratio of home fans to visiting fans in a crowd is 3:1 and all 35,000 seats in a stadium are filled, how many home fans are in attendance?
| 24,000 | |
| 40,000 | |
| 23,250 | |
| 26,250 |
A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:
35,000 fans x \( \frac{3}{4} \) = \( \frac{105000}{4} \) = 26,250 fans.
In a class of 23 students, 15 are taking German and 8 are taking Spanish. Of the students studying German or Spanish, 7 are taking both courses. How many students are not enrolled in either course?
| 10 | |
| 11 | |
| 17 | |
| 7 |
The number of students taking German or Spanish is 15 + 8 = 23. Of that group of 23, 7 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 23 - 7 = 16 who are taking at least one language. 23 - 16 = 7 students who are not taking either language.
If \( \left|y - 5\right| \) - 1 = 6, which of these is a possible value for y?
| 3 | |
| -8 | |
| 12 | |
| 11 |
First, solve for \( \left|y - 5\right| \):
\( \left|y - 5\right| \) - 1 = 6
\( \left|y - 5\right| \) = 6 + 1
\( \left|y - 5\right| \) = 7
The value inside the absolute value brackets can be either positive or negative so (y - 5) must equal + 7 or -7 for \( \left|y - 5\right| \) to equal 7:
| y - 5 = 7 y = 7 + 5 y = 12 | y - 5 = -7 y = -7 + 5 y = -2 |
So, y = -2 or y = 12.
What is \( \frac{1}{9} \) x \( \frac{4}{8} \)?
| \(\frac{1}{12}\) | |
| \(\frac{1}{14}\) | |
| \(\frac{1}{6}\) | |
| \(\frac{1}{18}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{1}{9} \) x \( \frac{4}{8} \) = \( \frac{1 x 4}{9 x 8} \) = \( \frac{4}{72} \) = \(\frac{1}{18}\)
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 7 complete crews out on jobs?
| 13 | |
| 16 | |
| 6 | |
| 3 |
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. 7 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 7 x 2 = 14 total workers to staff the crews during the busy season. The company already employs 8 workers so they need to add 14 - 8 = 6 new staff for the busy season.