| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.18 |
| Score | 0% | 64% |
What is \( \frac{20\sqrt{21}}{4\sqrt{7}} \)?
| 5 \( \sqrt{3} \) | |
| 3 \( \sqrt{5} \) | |
| \(\frac{1}{3}\) \( \sqrt{5} \) | |
| 3 \( \sqrt{\frac{1}{5}} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{20\sqrt{21}}{4\sqrt{7}} \)
\( \frac{20}{4} \) \( \sqrt{\frac{21}{7}} \)
5 \( \sqrt{3} \)
A machine in a factory has an error rate of 2 parts per 100. The machine normally runs 24 hours a day and produces 5 parts per hour. Yesterday the machine was shut down for 2 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 107.8 | |
| 81.9 | |
| 72 | |
| 147 |
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 5 = \( \frac{2 \times 5}{100} \) = \( \frac{10}{100} \) = 0.1 errors per hour
So, in an average hour, the machine will produce 5 - 0.1 = 4.9 error free parts.
The machine ran for 24 - 2 = 22 hours yesterday so you would expect that 22 x 4.9 = 107.8 error free parts were produced yesterday.
Find the average of the following numbers: 15, 9, 14, 10.
| 17 | |
| 15 | |
| 12 | |
| 7 |
To find the average of these 4 numbers add them together then divide by 4:
\( \frac{15 + 9 + 14 + 10}{4} \) = \( \frac{48}{4} \) = 12
The __________ is the greatest factor that divides two integers.
greatest common multiple |
|
absolute value |
|
least common multiple |
|
greatest common factor |
The greatest common factor (GCF) is the greatest factor that divides two integers.
A tiger in a zoo has consumed 135 pounds of food in 9 days. If the tiger continues to eat at the same rate, in how many more days will its total food consumtion be 225 pounds?
| 3 | |
| 8 | |
| 4 | |
| 6 |
If the tiger has consumed 135 pounds of food in 9 days that's \( \frac{135}{9} \) = 15 pounds of food per day. The tiger needs to consume 225 - 135 = 90 more pounds of food to reach 225 pounds total. At 15 pounds of food per day that's \( \frac{90}{15} \) = 6 more days.