| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.12 |
| Score | 0% | 62% |
Simplify \( \sqrt{8} \)
| 4\( \sqrt{2} \) | |
| 2\( \sqrt{2} \) | |
| 5\( \sqrt{2} \) | |
| 6\( \sqrt{2} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{8} \)
\( \sqrt{4 \times 2} \)
\( \sqrt{2^2 \times 2} \)
2\( \sqrt{2} \)
a(b + c) = ab + ac defines which of the following?
commutative property for multiplication |
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distributive property for division |
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commutative property for division |
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distributive property for multiplication |
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.
On average, the center for a basketball team hits 50% of his shots while a guard on the same team hits 60% of his shots. If the guard takes 25 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?
| 29 | |
| 37 | |
| 30 | |
| 48 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{60}{100} \) = \( \frac{60 x 25}{100} \) = \( \frac{1500}{100} \) = 15 shots
The center makes 50% 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 = \( \frac{15}{\frac{50}{100}} \) = 15 x \( \frac{100}{50} \) = \( \frac{15 x 100}{50} \) = \( \frac{1500}{50} \) = 30 shots
to make the same number of shots as the guard and thus score the same number of points.
In a class of 29 students, 7 are taking German and 12 are taking Spanish. Of the students studying German or Spanish, 5 are taking both courses. How many students are not enrolled in either course?
| 18 | |
| 15 | |
| 29 | |
| 21 |
The number of students taking German or Spanish is 7 + 12 = 19. Of that group of 19, 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 19 - 5 = 14 who are taking at least one language. 29 - 14 = 15 students who are not taking either language.
What is \( \sqrt{\frac{81}{81}} \)?
| 1\(\frac{1}{4}\) | |
| \(\frac{1}{2}\) | |
| 1 | |
| 4 |
To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:
\( \sqrt{\frac{81}{81}} \)
\( \frac{\sqrt{81}}{\sqrt{81}} \)
\( \frac{\sqrt{9^2}}{\sqrt{9^2}} \)
1