| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.51 |
| Score | 0% | 50% |
The __________ is the smallest positive integer that is a multiple of two or more integers.
absolute value |
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least common factor |
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least common multiple |
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greatest common factor |
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.
On average, the center for a basketball team hits 45% of his shots while a guard on the same team hits 65% of his shots. If the guard takes 20 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 | |
| 41 | |
| 28 | |
| 57 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 20 x \( \frac{65}{100} \) = \( \frac{65 x 20}{100} \) = \( \frac{1300}{100} \) = 13 shots
The center makes 45% 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 = \( \frac{13}{\frac{45}{100}} \) = 13 x \( \frac{100}{45} \) = \( \frac{13 x 100}{45} \) = \( \frac{1300}{45} \) = 29 shots
to make the same number of shots as the guard and thus score the same number of points.
If the ratio of home fans to visiting fans in a crowd is 3:1 and all 36,000 seats in a stadium are filled, how many home fans are in attendance?
| 32,000 | |
| 27,000 | |
| 20,667 | |
| 28,667 |
A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:
36,000 fans x \( \frac{3}{4} \) = \( \frac{108000}{4} \) = 27,000 fans.
What is -5b4 + 3b4?
| -2b16 | |
| -8b4 | |
| -2b4 | |
| -2b-8 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:
-5b4 + 3b4
(-5 + 3)b4
-2b4
What is \( 6 \)\( \sqrt{28} \) + \( 6 \)\( \sqrt{7} \)
| 36\( \sqrt{196} \) | |
| 36\( \sqrt{7} \) | |
| 18\( \sqrt{7} \) | |
| 12\( \sqrt{28} \) |
To add these radicals together their radicands must be the same:
6\( \sqrt{28} \) + 6\( \sqrt{7} \)
6\( \sqrt{4 \times 7} \) + 6\( \sqrt{7} \)
6\( \sqrt{2^2 \times 7} \) + 6\( \sqrt{7} \)
(6)(2)\( \sqrt{7} \) + 6\( \sqrt{7} \)
12\( \sqrt{7} \) + 6\( \sqrt{7} \)
Now that the radicands are identical, you can add them together:
12\( \sqrt{7} \) + 6\( \sqrt{7} \)