| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.39 |
| Score | 0% | 68% |
Roger loaned Ezra $1,100 at an annual interest rate of 8%. If no payments are made, what is the interest owed on this loan at the end of the first year?
| $84 | |
| $88 | |
| $42 | |
| $45 |
The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:
interest = annual interest rate x loan amount
i = (\( \frac{6}{100} \)) x $1,100
i = 0.08 x $1,100
i = $88
Alex loaned Jennifer $1,300 at an annual interest rate of 8%. If no payments are made, what is the total amount owed at the end of the first year?
| $1,391 | |
| $1,352 | |
| $1,313 | |
| $1,404 |
The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:
interest = annual interest rate x loan amount
i = (\( \frac{6}{100} \)) x $1,300
i = 0.08 x $1,300
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $1,300 + $104How many hours does it take a car to travel 250 miles at an average speed of 50 miles per hour?
| 5 hours | |
| 9 hours | |
| 2 hours | |
| 6 hours |
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 time:
time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{250mi}{50mph} \)
5 hours
What is \( \frac{2}{2} \) - \( \frac{2}{6} \)?
| \( \frac{1}{4} \) | |
| 1 \( \frac{2}{6} \) | |
| 2 \( \frac{8}{6} \) | |
| \(\frac{2}{3}\) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [6, 12, 18, 24, 30] making 6 the smallest multiple 2 and 6 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{2 x 3}{2 x 3} \) - \( \frac{2 x 1}{6 x 1} \)
\( \frac{6}{6} \) - \( \frac{2}{6} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{6 - 2}{6} \) = \( \frac{4}{6} \) = \(\frac{2}{3}\)
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 6 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 152.3 | |
| 87.3 | |
| 102.9 | |
| 114 |
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 - 6 = 18 hours yesterday so you would expect that 18 x 8.46 = 152.3 error free parts were produced yesterday.