| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.75 |
| Score | 0% | 55% |
\({b + c \over a} = {b \over a} + {c \over a}\) defines which of the following?
distributive property for multiplication |
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commutative property for multiplication |
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distributive property for division |
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commutative property for division |
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, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).
If a mayor is elected with 58% of the votes cast and 62% of a town's 29,000 voters cast a vote, how many votes did the mayor receive?
| 12,946 | |
| 10,428 | |
| 12,406 | |
| 10,608 |
If 62% of the town's 29,000 voters cast ballots the number of votes cast is:
(\( \frac{62}{100} \)) x 29,000 = \( \frac{1,798,000}{100} \) = 17,980
The mayor got 58% of the votes cast which is:
(\( \frac{58}{100} \)) x 17,980 = \( \frac{1,042,840}{100} \) = 10,428 votes.
On average, the center for a basketball team hits 25% of his shots while a guard on the same team hits 45% of his shots. If the guard takes 30 shots during a game, how many shots will the center have to take to score as many points as the guard assuming each shot is worth the same number of points?
| 22 | |
| 52 | |
| 65 | |
| 25 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 30 x \( \frac{45}{100} \) = \( \frac{45 x 30}{100} \) = \( \frac{1350}{100} \) = 13 shots
The center makes 25% of his shots so he'll have to take:
shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)
to make as many shots as the guard. Plugging in values for the center gives us:
center shots taken = \( \frac{13}{\frac{25}{100}} \) = 13 x \( \frac{100}{25} \) = \( \frac{13 x 100}{25} \) = \( \frac{1300}{25} \) = 52 shots
to make the same number of shots as the guard and thus score the same number of points.
In a class of 22 students, 13 are taking German and 7 are taking Spanish. Of the students studying German or Spanish, 6 are taking both courses. How many students are not enrolled in either course?
| 19 | |
| 13 | |
| 8 | |
| 10 |
The number of students taking German or Spanish is 13 + 7 = 20. Of that group of 20, 6 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 20 - 6 = 14 who are taking at least one language. 22 - 14 = 8 students who are not taking either language.
Convert 0.0009141 to scientific notation.
| 9.141 x 10-4 | |
| 0.914 x 10-3 | |
| 9.141 x 10-3 | |
| 9.141 x 104 |
A number in scientific notation has the format 0.000 x 10exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:
0.0009141 in scientific notation is 9.141 x 10-4