| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.23 |
| Score | 0% | 65% |
What is \( 2 \)\( \sqrt{48} \) - \( 7 \)\( \sqrt{3} \)
| 14\( \sqrt{3} \) | |
| -5\( \sqrt{-7} \) | |
| -5\( \sqrt{144} \) | |
| \( \sqrt{3} \) |
To subtract these radicals together their radicands must be the same:
2\( \sqrt{48} \) - 7\( \sqrt{3} \)
2\( \sqrt{16 \times 3} \) - 7\( \sqrt{3} \)
2\( \sqrt{4^2 \times 3} \) - 7\( \sqrt{3} \)
(2)(4)\( \sqrt{3} \) - 7\( \sqrt{3} \)
8\( \sqrt{3} \) - 7\( \sqrt{3} \)
Now that the radicands are identical, you can subtract them:
8\( \sqrt{3} \) - 7\( \sqrt{3} \)A machine in a factory has an error rate of 2 parts per 100. The machine normally runs 24 hours a day and produces 10 parts per hour. Yesterday the machine was shut down for 6 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 188.1 | |
| 159.8 | |
| 176.4 | |
| 87.4 |
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 - 6 = 18 hours yesterday so you would expect that 18 x 9.8 = 176.4 error free parts were produced yesterday.
What is the distance in miles of a trip that takes 4 hours at an average speed of 15 miles per hour?
| 40 miles | |
| 105 miles | |
| 70 miles | |
| 60 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 = \( 15mph \times 4h \)
60 miles
Damon loaned Monty $200 at an annual interest rate of 3%. If no payments are made, what is the interest owed on this loan at the end of the first year?
| $49 | |
| $6 | |
| $135 | |
| $14 |
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 $200
i = 0.03 x $200
i = $6
What is c4 x 7c2?
| 7c-2 | |
| 7c6 | |
| 8c8 | |
| 8c4 |
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:
c4 x 7c2
(1 x 7)c(4 + 2)
7c6