| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.85 |
| Score | 0% | 57% |
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 10% off." If Frank buys two shirts, each with a regular price of $41, how much will he pay for both shirts?
| $36.90 | |
| $59.45 | |
| $77.90 | |
| $4.10 |
By buying two shirts, Frank will save $41 x \( \frac{10}{100} \) = \( \frac{$41 x 10}{100} \) = \( \frac{$410}{100} \) = $4.10 on the second shirt.
So, his total cost will be
$41.00 + ($41.00 - $4.10)
$41.00 + $36.90
$77.90
\({b + c \over a} = {b \over a} + {c \over a}\) defines which of the following?
commutative property for division |
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distributive property for division |
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commutative property for multiplication |
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distributive property for multiplication |
The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).
A machine in a factory has an error rate of 9 parts per 100. The machine normally runs 24 hours a day and produces 7 parts per hour. Yesterday the machine was shut down for 6 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 104.5 | |
| 106.7 | |
| 114.7 | |
| 96.6 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{9}{100} \) x 7 = \( \frac{9 \times 7}{100} \) = \( \frac{63}{100} \) = 0.63 errors per hour
So, in an average hour, the machine will produce 7 - 0.63 = 6.37 error free parts.
The machine ran for 24 - 6 = 18 hours yesterday so you would expect that 18 x 6.37 = 114.7 error free parts were produced yesterday.
What is \( 9 \)\( \sqrt{8} \) - \( 4 \)\( \sqrt{2} \)
| 5\( \sqrt{4} \) | |
| 36\( \sqrt{2} \) | |
| 14\( \sqrt{2} \) | |
| 36\( \sqrt{16} \) |
To subtract these radicals together their radicands must be the same:
9\( \sqrt{8} \) - 4\( \sqrt{2} \)
9\( \sqrt{4 \times 2} \) - 4\( \sqrt{2} \)
9\( \sqrt{2^2 \times 2} \) - 4\( \sqrt{2} \)
(9)(2)\( \sqrt{2} \) - 4\( \sqrt{2} \)
18\( \sqrt{2} \) - 4\( \sqrt{2} \)
Now that the radicands are identical, you can subtract them:
18\( \sqrt{2} \) - 4\( \sqrt{2} \)If a car travels 200 miles in 8 hours, what is the average speed?
| 25 mph | |
| 30 mph | |
| 55 mph | |
| 40 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)