| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.82 |
| Score | 0% | 56% |
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 3 to 2 and the ratio of baseball to basketball cards is 3 to 1, what is the ratio of football to basketball cards?
| 7:8 | |
| 3:4 | |
| 9:2 | |
| 7:2 |
The ratio of football cards to baseball cards is 3:2 and the ratio of baseball cards to basketball cards is 3:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 9:6 and the ratio of baseball cards to basketball cards as 6:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 9:6, 6:2 which reduces to 9:2.
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?
| 5 | |
| 14 | |
| 16 | |
| 8 |
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 \( \frac{4c^7}{8c^3} \)?
| \(\frac{1}{2}\)c4 | |
| \(\frac{1}{2}\)c21 | |
| 2c10 | |
| 2c4 |
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:
\( \frac{4c^7}{8c^3} \)
\( \frac{4}{8} \) c(7 - 3)
\(\frac{1}{2}\)c4
a(b + c) = ab + ac defines which of the following?
distributive property for multiplication |
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commutative property for multiplication |
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commutative property for division |
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distributive property for division |
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.
Cooks are needed to prepare for a large party. Each cook can bake either 5 large cakes or 12 small cakes per hour. The kitchen is available for 2 hours and 23 large cakes and 430 small cakes need to be baked.
How many cooks are required to bake the required number of cakes during the time the kitchen is available?
| 14 | |
| 21 | |
| 5 | |
| 6 |
If a single cook can bake 5 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 5 x 2 = 10 large cakes during that time. 23 large cakes are needed for the party so \( \frac{23}{10} \) = 2\(\frac{3}{10}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 12 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 12 x 2 = 24 small cakes during that time. 430 small cakes are needed for the party so \( \frac{430}{24} \) = 17\(\frac{11}{12}\) cooks are needed to bake the required number of small cakes.
Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 3 + 18 = 21 cooks.