| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.47 |
| Score | 0% | 69% |
What is \( \frac{15\sqrt{21}}{3\sqrt{3}} \)?
| 5 \( \sqrt{\frac{1}{7}} \) | |
| \(\frac{1}{5}\) \( \sqrt{\frac{1}{7}} \) | |
| \(\frac{1}{5}\) \( \sqrt{7} \) | |
| 5 \( \sqrt{7} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{15\sqrt{21}}{3\sqrt{3}} \)
\( \frac{15}{3} \) \( \sqrt{\frac{21}{3}} \)
5 \( \sqrt{7} \)
Which of the following is a mixed number?
\({5 \over 7} \) |
|
\({a \over 5} \) |
|
\(1 {2 \over 5} \) |
|
\({7 \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.
What is \( \sqrt{\frac{25}{81}} \)?
| \(\frac{1}{2}\) | |
| \(\frac{3}{4}\) | |
| 1\(\frac{3}{4}\) | |
| \(\frac{5}{9}\) |
To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:
\( \sqrt{\frac{25}{81}} \)
\( \frac{\sqrt{25}}{\sqrt{81}} \)
\( \frac{\sqrt{5^2}}{\sqrt{9^2}} \)
\(\frac{5}{9}\)
Bob loaned Jennifer $100 at an annual interest rate of 3%. If no payments are made, what is the total amount owed at the end of the first year?
| $103 | |
| $105 | |
| $108 | |
| $104 |
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 $100
i = 0.03 x $100
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $100 + $3A machine in a factory has an error rate of 3 parts per 100. The machine normally runs 24 hours a day and produces 7 parts per hour. Yesterday the machine was shut down for 2 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 213.4 | |
| 149.4 | |
| 124.1 | |
| 69 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{3}{100} \) x 7 = \( \frac{3 \times 7}{100} \) = \( \frac{21}{100} \) = 0.21 errors per hour
So, in an average hour, the machine will produce 7 - 0.21 = 6.79 error free parts.
The machine ran for 24 - 2 = 22 hours yesterday so you would expect that 22 x 6.79 = 149.4 error free parts were produced yesterday.