| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.06 |
| Score | 0% | 61% |
A machine in a factory has an error rate of 9 parts per 100. The machine normally runs 24 hours a day and produces 10 parts per hour. Yesterday the machine was shut down for 8 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 97.6 | |
| 145.6 | |
| 118.4 | |
| 147.8 |
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 10 = \( \frac{9 \times 10}{100} \) = \( \frac{90}{100} \) = 0.9 errors per hour
So, in an average hour, the machine will produce 10 - 0.9 = 9.1 error free parts.
The machine ran for 24 - 8 = 16 hours yesterday so you would expect that 16 x 9.1 = 145.6 error free parts were produced yesterday.
Which of the following is an improper fraction?
\({7 \over 5} \) |
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\(1 {2 \over 5} \) |
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\({a \over 5} \) |
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\({2 \over 5} \) |
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.
This property states taht the order of addition or multiplication does not mater. For example, 2 + 5 and 5 + 2 are equivalent.
distributive |
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PEDMAS |
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commutative |
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associative |
The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.
Cooks are needed to prepare for a large party. Each cook can bake either 4 large cakes or 14 small cakes per hour. The kitchen is available for 4 hours and 30 large cakes and 340 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?
| 5 | |
| 10 | |
| 15 | |
| 9 |
If a single cook can bake 4 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 4 x 4 = 16 large cakes during that time. 30 large cakes are needed for the party so \( \frac{30}{16} \) = 1\(\frac{7}{8}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 14 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 14 x 4 = 56 small cakes during that time. 340 small cakes are needed for the party so \( \frac{340}{56} \) = 6\(\frac{1}{14}\) 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 2 + 7 = 9 cooks.
How many hours does it take a car to travel 260 miles at an average speed of 65 miles per hour?
| 4 hours | |
| 9 hours | |
| 5 hours | |
| 3 hours |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Solving for time:
time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{260mi}{65mph} \)
4 hours