| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.08 |
| Score | 0% | 62% |
4! = ?
4 x 3 x 2 x 1 |
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4 x 3 |
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3 x 2 x 1 |
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5 x 4 x 3 x 2 x 1 |
A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
A factor is a positive __________ that divides evenly into a given number.
improper fraction |
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mixed number |
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integer |
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fraction |
A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.
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 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?
| 24 | |
| 48 | |
| 41 | |
| 28 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 20 x \( \frac{60}{100} \) = \( \frac{60 x 20}{100} \) = \( \frac{1200}{100} \) = 12 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 = \( \frac{12}{\frac{50}{100}} \) = 12 x \( \frac{100}{50} \) = \( \frac{12 x 100}{50} \) = \( \frac{1200}{50} \) = 24 shots
to make the same number of shots as the guard and thus score the same number of points.
What is \( 4 \)\( \sqrt{50} \) + \( 4 \)\( \sqrt{2} \)
| 24\( \sqrt{2} \) | |
| 16\( \sqrt{25} \) | |
| 8\( \sqrt{100} \) | |
| 8\( \sqrt{25} \) |
To add these radicals together their radicands must be the same:
4\( \sqrt{50} \) + 4\( \sqrt{2} \)
4\( \sqrt{25 \times 2} \) + 4\( \sqrt{2} \)
4\( \sqrt{5^2 \times 2} \) + 4\( \sqrt{2} \)
(4)(5)\( \sqrt{2} \) + 4\( \sqrt{2} \)
20\( \sqrt{2} \) + 4\( \sqrt{2} \)
Now that the radicands are identical, you can add them together:
20\( \sqrt{2} \) + 4\( \sqrt{2} \)In a class of 28 students, 7 are taking German and 10 are taking Spanish. Of the students studying German or Spanish, 4 are taking both courses. How many students are not enrolled in either course?
| 24 | |
| 12 | |
| 21 | |
| 15 |
The number of students taking German or Spanish is 7 + 10 = 17. Of that group of 17, 4 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 17 - 4 = 13 who are taking at least one language. 28 - 13 = 15 students who are not taking either language.