| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.33 |
| Score | 0% | 67% |
20 members of a bridal party need transported to a wedding reception but there are only 4 4-passenger taxis available to take them. How many will need to find other transportation?
| 4 | |
| 2 | |
| 8 | |
| 9 |
There are 4 4-passenger taxis available so that's 4 x 4 = 16 total seats. There are 20 people needing transportation leaving 20 - 16 = 4 who will have to find other transportation.
a(b + c) = ab + ac defines which of the following?
distributive property for division |
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commutative property for division |
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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.
If all of a roofing company's 8 workers are required to staff 4 roofing crews, how many workers need to be added during the busy season in order to send 8 complete crews out on jobs?
| 8 | |
| 6 | |
| 2 | |
| 7 |
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 8 workers at the company now and that's enough to staff 4 crews so there are \( \frac{8}{4} \) = 2 workers on a crew. 8 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 8 x 2 = 16 total workers to staff the crews during the busy season. The company already employs 8 workers so they need to add 16 - 8 = 8 new staff for the busy season.
What is -3a5 + 5a5?
| -8a5 | |
| 2a5 | |
| 8a5 | |
| 2a10 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:
-3a5 + 5a5
(-3 + 5)a5
2a5
In a class of 24 students, 7 are taking German and 6 are taking Spanish. Of the students studying German or Spanish, 3 are taking both courses. How many students are not enrolled in either course?
| 23 | |
| 17 | |
| 16 | |
| 14 |
The number of students taking German or Spanish is 7 + 6 = 13. Of that group of 13, 3 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 13 - 3 = 10 who are taking at least one language. 24 - 10 = 14 students who are not taking either language.