| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.44 |
| Score | 0% | 69% |
\({b + c \over a} = {b \over a} + {c \over a}\) defines which of the following?
distributive property for multiplication |
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commutative property for division |
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distributive property for division |
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commutative property for multiplication |
The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).
In a class of 18 students, 8 are taking German and 8 are taking Spanish. Of the students studying German or Spanish, 3 are taking both courses. How many students are not enrolled in either course?
| 12 | |
| 5 | |
| 11 | |
| 15 |
The number of students taking German or Spanish is 8 + 8 = 16. Of that group of 16, 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 16 - 3 = 13 who are taking at least one language. 18 - 13 = 5 students who are not taking either language.
If a car travels 360 miles in 6 hours, what is the average speed?
| 55 mph | |
| 40 mph | |
| 60 mph | |
| 65 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Convert x-4 to remove the negative exponent.
| \( \frac{-1}{x^{-4}} \) | |
| \( \frac{-4}{-x} \) | |
| \( \frac{1}{x^4} \) | |
| \( \frac{1}{x^{-4}} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
Damon loaned Diane $1,100 at an annual interest rate of 5%. If no payments are made, what is the total amount owed at the end of the first year?
| $1,199 | |
| $1,133 | |
| $1,155 | |
| $1,188 |
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 $1,100
i = 0.05 x $1,100
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $1,100 + $55