| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.86 |
| Score | 0% | 57% |
Convert a-3 to remove the negative exponent.
| \( \frac{-1}{-3a} \) | |
| \( \frac{-1}{a^{-3}} \) | |
| \( \frac{1}{a^3} \) | |
| \( \frac{-3}{a} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
If a mayor is elected with 89% of the votes cast and 33% of a town's 48,000 voters cast a vote, how many votes did the mayor receive?
| 11,405 | |
| 9,504 | |
| 9,979 | |
| 14,098 |
If 33% of the town's 48,000 voters cast ballots the number of votes cast is:
(\( \frac{33}{100} \)) x 48,000 = \( \frac{1,584,000}{100} \) = 15,840
The mayor got 89% of the votes cast which is:
(\( \frac{89}{100} \)) x 15,840 = \( \frac{1,409,760}{100} \) = 14,098 votes.
If all of a roofing company's 12 workers are required to staff 4 roofing crews, how many workers need to be added during the busy season in order to send 6 complete crews out on jobs?
| 10 | |
| 11 | |
| 8 | |
| 6 |
In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 12 workers at the company now and that's enough to staff 4 crews so there are \( \frac{12}{4} \) = 3 workers on a crew. 6 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 6 x 3 = 18 total workers to staff the crews during the busy season. The company already employs 12 workers so they need to add 18 - 12 = 6 new staff for the busy season.
a(b + c) = ab + ac defines which of the following?
commutative property for division |
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distributive property for multiplication |
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distributive property for division |
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commutative property for multiplication |
The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.
What is 8\( \sqrt{9} \) x 5\( \sqrt{4} \)?
| 13\( \sqrt{4} \) | |
| 240 | |
| 13\( \sqrt{9} \) | |
| 40\( \sqrt{9} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
8\( \sqrt{9} \) x 5\( \sqrt{4} \)
(8 x 5)\( \sqrt{9 \times 4} \)
40\( \sqrt{36} \)
Now we need to simplify the radical:
40\( \sqrt{36} \)
40\( \sqrt{6^2} \)
(40)(6)
240