| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.23 |
| Score | 0% | 65% |
A machine in a factory has an error rate of 2 parts per 100. The machine normally runs 24 hours a day and produces 7 parts per hour. Yesterday the machine was shut down for 8 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 131 | |
| 138.2 | |
| 109.8 | |
| 109.2 |
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 7 = \( \frac{2 \times 7}{100} \) = \( \frac{14}{100} \) = 0.14 errors per hour
So, in an average hour, the machine will produce 7 - 0.14 = 6.86 error free parts.
The machine ran for 24 - 8 = 16 hours yesterday so you would expect that 16 x 6.86 = 109.8 error free parts were produced yesterday.
What is \( \frac{6z^5}{7z^3} \)?
| 1\(\frac{1}{6}\)z8 | |
| \(\frac{6}{7}\)z2 | |
| \(\frac{6}{7}\)z8 | |
| 1\(\frac{1}{6}\)z-2 |
To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:
\( \frac{6z^5}{7z^3} \)
\( \frac{6}{7} \) z(5 - 3)
\(\frac{6}{7}\)z2
If \(\left|a\right| = 7\), which of the following best describes a?
none of these is correct |
|
a = -7 |
|
a = 7 or a = -7 |
|
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).
If a car travels 315 miles in 9 hours, what is the average speed?
| 25 mph | |
| 15 mph | |
| 35 mph | |
| 40 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)What is \( \frac{7}{9} \) - \( \frac{3}{15} \)?
| 2 \( \frac{6}{45} \) | |
| \( \frac{3}{45} \) | |
| \(\frac{26}{45}\) | |
| 2 \( \frac{2}{45} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90] and the first few multiples of 15 are [15, 30, 45, 60, 75, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 9 and 15 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{7 x 5}{9 x 5} \) - \( \frac{3 x 3}{15 x 3} \)
\( \frac{35}{45} \) - \( \frac{9}{45} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{35 - 9}{45} \) = \( \frac{26}{45} \) = \(\frac{26}{45}\)