| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.84 |
| Score | 0% | 57% |
On average, the center for a basketball team hits 30% of his shots while a guard on the same team hits 35% of his shots. If the guard takes 10 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?
| 15 | |
| 7 | |
| 11 | |
| 10 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{35}{100} \) = \( \frac{35 x 10}{100} \) = \( \frac{350}{100} \) = 3 shots
The center makes 30% 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 = \( \frac{3}{\frac{30}{100}} \) = 3 x \( \frac{100}{30} \) = \( \frac{3 x 100}{30} \) = \( \frac{300}{30} \) = 10 shots
to make the same number of shots as the guard and thus score the same number of points.
In a class of 25 students, 11 are taking German and 7 are taking Spanish. Of the students studying German or Spanish, 4 are taking both courses. How many students are not enrolled in either course?
| 22 | |
| 25 | |
| 11 | |
| 16 |
The number of students taking German or Spanish is 11 + 7 = 18. Of that group of 18, 4 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 18 - 4 = 14 who are taking at least one language. 25 - 14 = 11 students who are not taking either language.
A triathlon course includes a 100m swim, a 40.7km bike ride, and a 13.7km run. What is the total length of the race course?
| 54.2km | |
| 24.4km | |
| 54.5km | |
| 25.9km |
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 100 meters to kilometers, divide the distance by 1000 to get 0.1km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.1km + 40.7km + 13.7km
total distance = 54.5km
What is \( \frac{-3c^9}{6c^4} \)?
| -2c-5 | |
| -\(\frac{1}{2}\)c2\(\frac{1}{4}\) | |
| -\(\frac{1}{2}\)c5 | |
| -\(\frac{1}{2}\)c-5 |
To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:
\( \frac{-3c^9}{6c^4} \)
\( \frac{-3}{6} \) c(9 - 4)
-\(\frac{1}{2}\)c5
A machine in a factory has an error rate of 7 parts per 100. The machine normally runs 24 hours a day and produces 6 parts per hour. Yesterday the machine was shut down for 5 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 114.2 | |
| 106 | |
| 85.5 | |
| 162.5 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{7}{100} \) x 6 = \( \frac{7 \times 6}{100} \) = \( \frac{42}{100} \) = 0.42 errors per hour
So, in an average hour, the machine will produce 6 - 0.42 = 5.58 error free parts.
The machine ran for 24 - 5 = 19 hours yesterday so you would expect that 19 x 5.58 = 106 error free parts were produced yesterday.