| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.07 |
| Score | 0% | 61% |
What is \( \frac{4}{5} \) x \( \frac{4}{7} \)?
| \(\frac{1}{18}\) | |
| \(\frac{3}{64}\) | |
| \(\frac{8}{21}\) | |
| \(\frac{16}{35}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{4}{5} \) x \( \frac{4}{7} \) = \( \frac{4 x 4}{5 x 7} \) = \( \frac{16}{35} \) = \(\frac{16}{35}\)
Convert y-2 to remove the negative exponent.
| \( \frac{-2}{-y} \) | |
| \( \frac{1}{y^2} \) | |
| \( \frac{-1}{-2y} \) | |
| \( \frac{-1}{-2y^{2}} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
In a class of 30 students, 15 are taking German and 12 are taking Spanish. Of the students studying German or Spanish, 5 are taking both courses. How many students are not enrolled in either course?
| 27 | |
| 15 | |
| 12 | |
| 8 |
The number of students taking German or Spanish is 15 + 12 = 27. Of that group of 27, 5 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 27 - 5 = 22 who are taking at least one language. 30 - 22 = 8 students who are not taking either language.
A machine in a factory has an error rate of 9 parts per 100. The machine normally runs 24 hours a day and produces 7 parts per hour. Yesterday the machine was shut down for 5 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 101.5 | |
| 134.4 | |
| 121 | |
| 77.4 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{9}{100} \) x 7 = \( \frac{9 \times 7}{100} \) = \( \frac{63}{100} \) = 0.63 errors per hour
So, in an average hour, the machine will produce 7 - 0.63 = 6.37 error free parts.
The machine ran for 24 - 5 = 19 hours yesterday so you would expect that 19 x 6.37 = 121 error free parts were produced yesterday.
| 4.8 | |
| 1 | |
| 0.8 | |
| 1.8 |
1