| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.91 |
| Score | 0% | 58% |
| 1 | |
| 0.8 | |
| 0.5 | |
| 2.7 |
1
If \(\left|a\right| = 7\), which of the following best describes a?
a = -7 |
|
none of these is correct |
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a = 7 |
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a = 7 or a = -7 |
The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).
Cooks are needed to prepare for a large party. Each cook can bake either 2 large cakes or 16 small cakes per hour. The kitchen is available for 4 hours and 20 large cakes and 400 small cakes need to be baked.
How many cooks are required to bake the required number of cakes during the time the kitchen is available?
| 8 | |
| 15 | |
| 10 | |
| 14 |
If a single cook can bake 2 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 2 x 4 = 8 large cakes during that time. 20 large cakes are needed for the party so \( \frac{20}{8} \) = 2\(\frac{1}{2}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 16 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 16 x 4 = 64 small cakes during that time. 400 small cakes are needed for the party so \( \frac{400}{64} \) = 6\(\frac{1}{4}\) cooks are needed to bake the required number of small cakes.
Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 3 + 7 = 10 cooks.
Simplify \( \frac{20}{52} \).
| \( \frac{1}{2} \) | |
| \( \frac{5}{12} \) | |
| \( \frac{5}{13} \) | |
| \( \frac{5}{9} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 20 are [1, 2, 4, 5, 10, 20] and the factors of 52 are [1, 2, 4, 13, 26, 52]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{20}{52} \) = \( \frac{\frac{20}{4}}{\frac{52}{4}} \) = \( \frac{5}{13} \)
A machine in a factory has an error rate of 5 parts per 100. The machine normally runs 24 hours a day and produces 8 parts per hour. Yesterday the machine was shut down for 5 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 144.4 | |
| 115.2 | |
| 110.7 | |
| 91 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{5}{100} \) x 8 = \( \frac{5 \times 8}{100} \) = \( \frac{40}{100} \) = 0.4 errors per hour
So, in an average hour, the machine will produce 8 - 0.4 = 7.6 error free parts.
The machine ran for 24 - 5 = 19 hours yesterday so you would expect that 19 x 7.6 = 144.4 error free parts were produced yesterday.