| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.17 |
| Score | 0% | 63% |
If all of a roofing company's 6 workers are required to staff 2 roofing crews, how many workers need to be added during the busy season in order to send 5 complete crews out on jobs?
| 7 | |
| 11 | |
| 9 | |
| 12 |
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 6 workers at the company now and that's enough to staff 2 crews so there are \( \frac{6}{2} \) = 3 workers on a crew. 5 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 5 x 3 = 15 total workers to staff the crews during the busy season. The company already employs 6 workers so they need to add 15 - 6 = 9 new staff for the busy season.
The total water usage for a city is 30,000 gallons each day. Of that total, 22% is for personal use and 34% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 4,400 | |
| 6,000 | |
| 12,000 | |
| 3,600 |
34% of the water consumption is industrial use and 22% is personal use so (34% - 22%) = 12% more water is used for industrial purposes. 30,000 gallons are consumed daily so industry consumes \( \frac{12}{100} \) x 30,000 gallons = 3,600 gallons.
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 40% off." If Alex buys two shirts, each with a regular price of $28, how much money will he save?
| $11.20 | |
| $14.00 | |
| $8.40 | |
| $5.60 |
By buying two shirts, Alex will save $28 x \( \frac{40}{100} \) = \( \frac{$28 x 40}{100} \) = \( \frac{$1120}{100} \) = $11.20 on the second shirt.
a(b + c) = ab + ac defines which of the following?
distributive property for division |
|
commutative property for division |
|
distributive property for multiplication |
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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 \( \frac{5z^5}{7z^4} \)?
| \(\frac{5}{7}\)z-1 | |
| 1\(\frac{2}{5}\)z | |
| \(\frac{5}{7}\)z20 | |
| \(\frac{5}{7}\)z |
To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:
\( \frac{5z^5}{7z^4} \)
\( \frac{5}{7} \) z(5 - 4)
\(\frac{5}{7}\)z