| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.83 |
| Score | 0% | 57% |
The total water usage for a city is 15,000 gallons each day. Of that total, 17% is for personal use and 39% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 2,850 | |
| 2,500 | |
| 3,300 | |
| 5,200 |
39% of the water consumption is industrial use and 17% is personal use so (39% - 17%) = 22% more water is used for industrial purposes. 15,000 gallons are consumed daily so industry consumes \( \frac{22}{100} \) x 15,000 gallons = 3,300 gallons.
Which of these numbers is a factor of 28?
| 9 | |
| 6 | |
| 29 | |
| 14 |
The factors of a number are all positive integers that divide evenly into the number. The factors of 28 are 1, 2, 4, 7, 14, 28.
In a class of 36 students, 14 are taking German and 11 are taking Spanish. Of the students studying German or Spanish, 2 are taking both courses. How many students are not enrolled in either course?
| 20 | |
| 13 | |
| 29 | |
| 32 |
The number of students taking German or Spanish is 14 + 11 = 25. Of that group of 25, 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 25 - 2 = 23 who are taking at least one language. 36 - 23 = 13 students who are not taking either language.
A machine in a factory has an error rate of 6 parts per 100. The machine normally runs 24 hours a day and produces 9 parts per hour. Yesterday the machine was shut down for 7 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 122.2 | |
| 113.1 | |
| 109.5 | |
| 143.8 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{6}{100} \) x 9 = \( \frac{6 \times 9}{100} \) = \( \frac{54}{100} \) = 0.54 errors per hour
So, in an average hour, the machine will produce 9 - 0.54 = 8.46 error free parts.
The machine ran for 24 - 7 = 17 hours yesterday so you would expect that 17 x 8.46 = 143.8 error free parts were produced yesterday.
On average, the center for a basketball team hits 50% of his shots while a guard on the same team hits 60% 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?
| 39 | |
| 24 | |
| 40 | |
| 57 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 20 x \( \frac{60}{100} \) = \( \frac{60 x 20}{100} \) = \( \frac{1200}{100} \) = 12 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 = \( \frac{12}{\frac{50}{100}} \) = 12 x \( \frac{100}{50} \) = \( \frac{12 x 100}{50} \) = \( \frac{1200}{50} \) = 24 shots
to make the same number of shots as the guard and thus score the same number of points.