| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.60 |
| Score | 0% | 72% |
What is -b6 x 6b5?
| -6b5 | |
| 5b30 | |
| -6b11 | |
| 5b11 |
To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:
-b6 x 6b5
(-1 x 6)b(6 + 5)
-6b11
If a car travels 630 miles in 9 hours, what is the average speed?
| 45 mph | |
| 70 mph | |
| 40 mph | |
| 25 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)A machine in a factory has an error rate of 2 parts per 100. The machine normally runs 24 hours a day and produces 10 parts per hour. Yesterday the machine was shut down for 2 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 104.2 | |
| 152 | |
| 148.4 | |
| 215.6 |
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 10 = \( \frac{2 \times 10}{100} \) = \( \frac{20}{100} \) = 0.2 errors per hour
So, in an average hour, the machine will produce 10 - 0.2 = 9.8 error free parts.
The machine ran for 24 - 2 = 22 hours yesterday so you would expect that 22 x 9.8 = 215.6 error free parts were produced yesterday.
What is the distance in miles of a trip that takes 6 hours at an average speed of 45 miles per hour?
| 120 miles | |
| 270 miles | |
| 315 miles | |
| 275 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 = \( 45mph \times 6h \)
270 miles
Simplify \( \sqrt{175} \)
| 5\( \sqrt{7} \) | |
| 6\( \sqrt{14} \) | |
| 3\( \sqrt{7} \) | |
| 8\( \sqrt{14} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{175} \)
\( \sqrt{25 \times 7} \)
\( \sqrt{5^2 \times 7} \)
5\( \sqrt{7} \)