| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.98 |
| Score | 0% | 60% |
| 7.2 | |
| 1 | |
| 8.0 | |
| 0.5 |
1
A machine in a factory has an error rate of 3 parts per 100. The machine normally runs 24 hours a day and produces 10 parts per hour. Yesterday the machine was shut down for 7 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 164.9 | |
| 203.7 | |
| 191.1 | |
| 167.2 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{3}{100} \) x 10 = \( \frac{3 \times 10}{100} \) = \( \frac{30}{100} \) = 0.3 errors per hour
So, in an average hour, the machine will produce 10 - 0.3 = 9.7 error free parts.
The machine ran for 24 - 7 = 17 hours yesterday so you would expect that 17 x 9.7 = 164.9 error free parts were produced yesterday.
A tiger in a zoo has consumed 75 pounds of food in 5 days. If the tiger continues to eat at the same rate, in how many more days will its total food consumtion be 135 pounds?
| 4 | |
| 7 | |
| 9 | |
| 5 |
If the tiger has consumed 75 pounds of food in 5 days that's \( \frac{75}{5} \) = 15 pounds of food per day. The tiger needs to consume 135 - 75 = 60 more pounds of food to reach 135 pounds total. At 15 pounds of food per day that's \( \frac{60}{15} \) = 4 more days.
What is \( \frac{-2z^7}{3z^4} \)?
| -\(\frac{2}{3}\)z\(\frac{4}{7}\) | |
| -1\(\frac{1}{2}\)z-3 | |
| -\(\frac{2}{3}\)z3 | |
| -\(\frac{2}{3}\)z11 |
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:
\( \frac{-2z^7}{3z^4} \)
\( \frac{-2}{3} \) z(7 - 4)
-\(\frac{2}{3}\)z3
What is (c2)5?
| c10 | |
| 2c5 | |
| c3 | |
| 5c2 |
To raise a term with an exponent to another exponent, retain the base and multiply the exponents:
(c2)5