| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.56 |
| Score | 0% | 51% |
A machine in a factory has an error rate of 3 parts per 100. The machine normally runs 24 hours a day and produces 8 parts per hour. Yesterday the machine was shut down for 6 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 184 | |
| 94.1 | |
| 121.6 | |
| 139.7 |
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 8 = \( \frac{3 \times 8}{100} \) = \( \frac{24}{100} \) = 0.24 errors per hour
So, in an average hour, the machine will produce 8 - 0.24 = 7.76 error free parts.
The machine ran for 24 - 6 = 18 hours yesterday so you would expect that 18 x 7.76 = 139.7 error free parts were produced yesterday.
A bread recipe calls for 3\(\frac{3}{4}\) cups of flour. If you only have 1\(\frac{1}{2}\) cups, how much more flour is needed?
| 2\(\frac{1}{8}\) cups | |
| 1\(\frac{1}{2}\) cups | |
| 1\(\frac{1}{4}\) cups | |
| 2\(\frac{1}{4}\) cups |
The amount of flour you need is (3\(\frac{3}{4}\) - 1\(\frac{1}{2}\)) cups. Rewrite the quantities so they share a common denominator and subtract:
(\( \frac{30}{8} \) - \( \frac{12}{8} \)) cups
\( \frac{18}{8} \) cups
2\(\frac{1}{4}\) cups
What is 6\( \sqrt{7} \) x 9\( \sqrt{2} \)?
| 54\( \sqrt{14} \) | |
| 54\( \sqrt{7} \) | |
| 15\( \sqrt{2} \) | |
| 54\( \sqrt{2} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
6\( \sqrt{7} \) x 9\( \sqrt{2} \)
(6 x 9)\( \sqrt{7 \times 2} \)
54\( \sqrt{14} \)
| 1 | |
| 5.4 | |
| 2.0 | |
| 6.0 |
1
How many 1 gallon cans worth of fuel would you need to pour into an empty 6 gallon tank to fill it exactly halfway?
| 6 | |
| 3 | |
| 3 | |
| 40 |
To fill a 6 gallon tank exactly halfway you'll need 3 gallons of fuel. Each fuel can holds 1 gallons so:
cans = \( \frac{3 \text{ gallons}}{1 \text{ gallons}} \) = 3