| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.20 |
| Score | 0% | 64% |
What is \( \sqrt{\frac{49}{36}} \)?
| 1\(\frac{1}{6}\) | |
| \(\frac{2}{3}\) | |
| 1 | |
| \(\frac{5}{6}\) |
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:
\( \sqrt{\frac{49}{36}} \)
\( \frac{\sqrt{49}}{\sqrt{36}} \)
\( \frac{\sqrt{7^2}}{\sqrt{6^2}} \)
\( \frac{7}{6} \)
1\(\frac{1}{6}\)
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 10% off." If Damon buys two shirts, each with a regular price of $21, how much money will he save?
| $4.20 | |
| $2.10 | |
| $1.05 | |
| $8.40 |
By buying two shirts, Damon will save $21 x \( \frac{10}{100} \) = \( \frac{$21 x 10}{100} \) = \( \frac{$210}{100} \) = $2.10 on the second shirt.
A machine in a factory has an error rate of 7 parts per 100. The machine normally runs 24 hours a day and produces 7 parts per hour. Yesterday the machine was shut down for 4 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 162.5 | |
| 130.2 | |
| 133.9 | |
| 115.4 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{7}{100} \) x 7 = \( \frac{7 \times 7}{100} \) = \( \frac{49}{100} \) = 0.49 errors per hour
So, in an average hour, the machine will produce 7 - 0.49 = 6.51 error free parts.
The machine ran for 24 - 4 = 20 hours yesterday so you would expect that 20 x 6.51 = 130.2 error free parts were produced yesterday.
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 10% off." If Charlie buys two shirts, each with a regular price of $29, how much will he pay for both shirts?
| $55.10 | |
| $31.90 | |
| $36.25 | |
| $2.90 |
By buying two shirts, Charlie will save $29 x \( \frac{10}{100} \) = \( \frac{$29 x 10}{100} \) = \( \frac{$290}{100} \) = $2.90 on the second shirt.
So, his total cost will be
$29.00 + ($29.00 - $2.90)
$29.00 + $26.10
$55.10
What is 6c5 x 5c5?
| 30c25 | |
| 30c10 | |
| 11c5 | |
| 30c0 |
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:
6c5 x 5c5
(6 x 5)c(5 + 5)
30c10