| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.39 |
| Score | 0% | 68% |
The total water usage for a city is 45,000 gallons each day. Of that total, 17% is for personal use and 36% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 8,550 | |
| 3,150 | |
| 12,400 | |
| 5,200 |
36% of the water consumption is industrial use and 17% is personal use so (36% - 17%) = 19% more water is used for industrial purposes. 45,000 gallons are consumed daily so industry consumes \( \frac{19}{100} \) x 45,000 gallons = 8,550 gallons.
A machine in a factory has an error rate of 2 parts per 100. The machine normally runs 24 hours a day and produces 6 parts per hour. Yesterday the machine was shut down for 3 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 200.2 | |
| 123.5 | |
| 105.3 | |
| 109.5 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{2}{100} \) x 6 = \( \frac{2 \times 6}{100} \) = \( \frac{12}{100} \) = 0.12 errors per hour
So, in an average hour, the machine will produce 6 - 0.12 = 5.88 error free parts.
The machine ran for 24 - 3 = 21 hours yesterday so you would expect that 21 x 5.88 = 123.5 error free parts were produced yesterday.
Simplify \( \frac{16}{80} \).
| \( \frac{9}{19} \) | |
| \( \frac{1}{2} \) | |
| \( \frac{9}{13} \) | |
| \( \frac{1}{5} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 16 are [1, 2, 4, 8, 16] and the factors of 80 are [1, 2, 4, 5, 8, 10, 16, 20, 40, 80]. They share 5 factors [1, 2, 4, 8, 16] making 16 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{16}{80} \) = \( \frac{\frac{16}{16}}{\frac{80}{16}} \) = \( \frac{1}{5} \)
Which of the following is a mixed number?
\(1 {2 \over 5} \) |
|
\({7 \over 5} \) |
|
\({5 \over 7} \) |
|
\({a \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.
Convert y-5 to remove the negative exponent.
| \( \frac{-5}{-y} \) | |
| \( \frac{1}{y^5} \) | |
| \( \frac{-1}{-5y} \) | |
| \( \frac{-1}{-5y^{5}} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.