| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.98 |
| Score | 0% | 60% |
In a class of 30 students, 12 are taking German and 12 are taking Spanish. Of the students studying German or Spanish, 2 are taking both courses. How many students are not enrolled in either course?
| 8 | |
| 28 | |
| 13 | |
| 26 |
The number of students taking German or Spanish is 12 + 12 = 24. Of that group of 24, 2 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 24 - 2 = 22 who are taking at least one language. 30 - 22 = 8 students who are not taking either language.
If all of a roofing company's 20 workers are required to staff 5 roofing crews, how many workers need to be added during the busy season in order to send 7 complete crews out on jobs?
| 16 | |
| 9 | |
| 8 | |
| 17 |
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 20 workers at the company now and that's enough to staff 5 crews so there are \( \frac{20}{5} \) = 4 workers on a crew. 7 crews are needed for the busy season which, at 4 workers per crew, means that the roofing company will need 7 x 4 = 28 total workers to staff the crews during the busy season. The company already employs 20 workers so they need to add 28 - 20 = 8 new staff for the busy season.
On average, the center for a basketball team hits 50% of his shots while a guard on the same team hits 55% of his shots. If the guard takes 20 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?
| 20 | |
| 19 | |
| 33 | |
| 22 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 20 x \( \frac{55}{100} \) = \( \frac{55 x 20}{100} \) = \( \frac{1100}{100} \) = 11 shots
The center makes 50% 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 = \( \frac{11}{\frac{50}{100}} \) = 11 x \( \frac{100}{50} \) = \( \frac{11 x 100}{50} \) = \( \frac{1100}{50} \) = 22 shots
to make the same number of shots as the guard and thus score the same number of points.
The __________ is the greatest factor that divides two integers.
least common multiple |
|
greatest common multiple |
|
greatest common factor |
|
absolute value |
The greatest common factor (GCF) is the greatest factor that divides two integers.
A triathlon course includes a 500m swim, a 40.4km bike ride, and a 11.8km run. What is the total length of the race course?
| 52.7km | |
| 58.9km | |
| 56.1km | |
| 52km |
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 + 40.4km + 11.8km
total distance = 52.7km