| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.24 |
| Score | 0% | 65% |
A machine in a factory has an error rate of 6 parts per 100. The machine normally runs 24 hours a day and produces 7 parts per hour. Yesterday the machine was shut down for 9 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 171 | |
| 98.7 | |
| 165.6 | |
| 115.4 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{6}{100} \) x 7 = \( \frac{6 \times 7}{100} \) = \( \frac{42}{100} \) = 0.42 errors per hour
So, in an average hour, the machine will produce 7 - 0.42 = 6.58 error free parts.
The machine ran for 24 - 9 = 15 hours yesterday so you would expect that 15 x 6.58 = 98.7 error free parts were produced yesterday.
What is the distance in miles of a trip that takes 8 hours at an average speed of 40 miles per hour?
| 490 miles | |
| 45 miles | |
| 495 miles | |
| 320 miles |
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 distance:
distance = \( \text{speed} \times \text{time} \)
distance = \( 40mph \times 8h \)
320 miles
If \(\left|a\right| = 7\), which of the following best describes a?
a = 7 |
|
a = 7 or a = -7 |
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a = -7 |
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none of these is correct |
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).
What is 4\( \sqrt{5} \) x 5\( \sqrt{3} \)?
| 20\( \sqrt{15} \) | |
| 9\( \sqrt{15} \) | |
| 9\( \sqrt{5} \) | |
| 20\( \sqrt{8} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
4\( \sqrt{5} \) x 5\( \sqrt{3} \)
(4 x 5)\( \sqrt{5 \times 3} \)
20\( \sqrt{15} \)
A factor is a positive __________ that divides evenly into a given number.
fraction |
|
improper fraction |
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integer |
|
mixed number |
A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.