| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.01 |
| Score | 0% | 60% |
What is \( \sqrt{\frac{16}{81}} \)?
| \(\frac{2}{7}\) | |
| 1\(\frac{1}{3}\) | |
| \(\frac{1}{4}\) | |
| \(\frac{4}{9}\) |
To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:
\( \sqrt{\frac{16}{81}} \)
\( \frac{\sqrt{16}}{\sqrt{81}} \)
\( \frac{\sqrt{4^2}}{\sqrt{9^2}} \)
\(\frac{4}{9}\)
Which of these numbers is a factor of 28?
| 29 | |
| 30 | |
| 23 | |
| 2 |
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 34 students, 12 are taking German and 14 are taking Spanish. Of the students studying German or Spanish, 2 are taking both courses. How many students are not enrolled in either course?
| 10 | |
| 33 | |
| 22 | |
| 12 |
The number of students taking German or Spanish is 12 + 14 = 26. Of that group of 26, 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 26 - 2 = 24 who are taking at least one language. 34 - 24 = 10 students who are not taking either language.
If the ratio of home fans to visiting fans in a crowd is 4:1 and all 35,000 seats in a stadium are filled, how many home fans are in attendance?
| 28,333 | |
| 26,400 | |
| 28,000 | |
| 28,667 |
A ratio of 4:1 means that there are 4 home fans for every one visiting fan. So, of every 5 fans, 4 are home fans and \( \frac{4}{5} \) of every fan in the stadium is a home fan:
35,000 fans x \( \frac{4}{5} \) = \( \frac{140000}{5} \) = 28,000 fans.
A machine in a factory has an error rate of 4 parts per 100. The machine normally runs 24 hours a day and produces 7 parts per hour. Yesterday the machine was shut down for 3 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 141.1 | |
| 104.9 | |
| 109.2 | |
| 114.7 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{4}{100} \) x 7 = \( \frac{4 \times 7}{100} \) = \( \frac{28}{100} \) = 0.28 errors per hour
So, in an average hour, the machine will produce 7 - 0.28 = 6.72 error free parts.
The machine ran for 24 - 3 = 21 hours yesterday so you would expect that 21 x 6.72 = 141.1 error free parts were produced yesterday.