| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.02 |
| Score | 0% | 60% |
If the ratio of home fans to visiting fans in a crowd is 2:1 and all 47,000 seats in a stadium are filled, how many home fans are in attendance?
| 28,000 | |
| 31,333 | |
| 25,600 | |
| 35,000 |
A ratio of 2:1 means that there are 2 home fans for every one visiting fan. So, of every 3 fans, 2 are home fans and \( \frac{2}{3} \) of every fan in the stadium is a home fan:
47,000 fans x \( \frac{2}{3} \) = \( \frac{94000}{3} \) = 31,333 fans.
Simplify \( \sqrt{175} \)
| 9\( \sqrt{7} \) | |
| 5\( \sqrt{7} \) | |
| 3\( \sqrt{7} \) | |
| 3\( \sqrt{14} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{175} \)
\( \sqrt{25 \times 7} \)
\( \sqrt{5^2 \times 7} \)
5\( \sqrt{7} \)
\({b + c \over a} = {b \over a} + {c \over a}\) defines which of the following?
commutative property for multiplication |
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commutative property for division |
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distributive property for multiplication |
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distributive 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, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).
What is 5c3 - 8c3?
| 3c3 | |
| -3c-3 | |
| -3c3 | |
| 13c3 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:
5c3 - 8c3
(5 - 8)c3
-3c3
In a class of 19 students, 9 are taking German and 5 are taking Spanish. Of the students studying German or Spanish, 3 are taking both courses. How many students are not enrolled in either course?
| 8 | |
| 19 | |
| 15 | |
| 12 |
The number of students taking German or Spanish is 9 + 5 = 14. Of that group of 14, 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 14 - 3 = 11 who are taking at least one language. 19 - 11 = 8 students who are not taking either language.