| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.43 |
| Score | 0% | 69% |
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 9 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 88.2 | |
| 202.4 | |
| 84.6 | |
| 141 |
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 - 9 = 15 hours yesterday so you would expect that 15 x 5.88 = 88.2 error free parts were produced yesterday.
What is \( \sqrt{\frac{64}{4}} \)?
| \(\frac{3}{4}\) | |
| \(\frac{2}{7}\) | |
| 4 | |
| \(\frac{1}{3}\) |
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:
\( \sqrt{\frac{64}{4}} \)
\( \frac{\sqrt{64}}{\sqrt{4}} \)
\( \frac{\sqrt{8^2}}{\sqrt{2^2}} \)
\( \frac{8}{2} \)
4
Convert x-3 to remove the negative exponent.
| \( \frac{-1}{x^{-3}} \) | |
| \( \frac{-1}{-3x^{3}} \) | |
| \( \frac{3}{x} \) | |
| \( \frac{1}{x^3} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
What is the greatest common factor of 76 and 56?
| 31 | |
| 47 | |
| 20 | |
| 4 |
The factors of 76 are [1, 2, 4, 19, 38, 76] and the factors of 56 are [1, 2, 4, 7, 8, 14, 28, 56]. They share 3 factors [1, 2, 4] making 4 the greatest factor 76 and 56 have in common.
Simplify \( \frac{16}{64} \).
| \( \frac{1}{4} \) | |
| \( \frac{3}{4} \) | |
| \( \frac{5}{9} \) | |
| \( \frac{5}{16} \) |
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 64 are [1, 2, 4, 8, 16, 32, 64]. 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:
\( \frac{16}{64} \) = \( \frac{\frac{16}{16}}{\frac{64}{16}} \) = \( \frac{1}{4} \)