| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.43 |
| Score | 0% | 69% |
A machine in a factory has an error rate of 6 parts per 100. The machine normally runs 24 hours a day and produces 9 parts per hour. Yesterday the machine was shut down for 3 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 164.6 | |
| 177.7 | |
| 92.8 | |
| 158.1 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{6}{100} \) x 9 = \( \frac{6 \times 9}{100} \) = \( \frac{54}{100} \) = 0.54 errors per hour
So, in an average hour, the machine will produce 9 - 0.54 = 8.46 error free parts.
The machine ran for 24 - 3 = 21 hours yesterday so you would expect that 21 x 8.46 = 177.7 error free parts were produced yesterday.
What is the distance in miles of a trip that takes 7 hours at an average speed of 60 miles per hour?
| 250 miles | |
| 240 miles | |
| 420 miles | |
| 450 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 = \( 60mph \times 7h \)
420 miles
What is 7\( \sqrt{2} \) x 5\( \sqrt{9} \)?
| 35\( \sqrt{11} \) | |
| 12\( \sqrt{18} \) | |
| 105\( \sqrt{2} \) | |
| 12\( \sqrt{9} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
7\( \sqrt{2} \) x 5\( \sqrt{9} \)
(7 x 5)\( \sqrt{2 \times 9} \)
35\( \sqrt{18} \)
Now we need to simplify the radical:
35\( \sqrt{18} \)
35\( \sqrt{2 \times 9} \)
35\( \sqrt{2 \times 3^2} \)
(35)(3)\( \sqrt{2} \)
105\( \sqrt{2} \)
How many 6-passenger vans will it take to drive all 77 members of the football team to an away game?
| 3 vans | |
| 7 vans | |
| 6 vans | |
| 13 vans |
Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:
vans = \( \frac{77}{6} \) = 12\(\frac{5}{6}\)
So, it will take 12 full vans and one partially full van to transport the entire team making a total of 13 vans.
If a car travels 240 miles in 8 hours, what is the average speed?
| 35 mph | |
| 65 mph | |
| 30 mph | |
| 40 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)