| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.23 |
| Score | 0% | 65% |
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 4 large cakes or 11 small cakes per hour. The kitchen is available for 3 hours and 34 large cakes and 490 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?
| 18 | |
| 10 | |
| 8 | |
| 13 |
If a single cook can bake 4 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 4 x 3 = 12 large cakes during that time. 34 large cakes are needed for the party so \( \frac{34}{12} \) = 2\(\frac{5}{6}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 11 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 11 x 3 = 33 small cakes during that time. 490 small cakes are needed for the party so \( \frac{490}{33} \) = 14\(\frac{28}{33}\) 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 + 15 = 18 cooks.
Find the average of the following numbers: 15, 11, 14, 12.
| 10 | |
| 15 | |
| 16 | |
| 13 |
To find the average of these 4 numbers add them together then divide by 4:
\( \frac{15 + 11 + 14 + 12}{4} \) = \( \frac{52}{4} \) = 13
In a class of 21 students, 9 are taking German and 9 are taking Spanish. Of the students studying German or Spanish, 5 are taking both courses. How many students are not enrolled in either course?
| 8 | |
| 21 | |
| 12 | |
| 20 |
The number of students taking German or Spanish is 9 + 9 = 18. Of that group of 18, 5 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 18 - 5 = 13 who are taking at least one language. 21 - 13 = 8 students who are not taking either language.
Alex loaned Latoya $1,400 at an annual interest rate of 2%. If no payments are made, what is the total amount owed at the end of the first year?
| $1,484 | |
| $1,428 | |
| $1,526 | |
| $1,414 |
The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:
interest = annual interest rate x loan amount
i = (\( \frac{6}{100} \)) x $1,400
i = 0.02 x $1,400
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $1,400 + $28