| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.68 |
| Score | 0% | 54% |
On average, the center for a basketball team hits 25% of his shots while a guard on the same team hits 30% 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?
| 32 | |
| 36 | |
| 17 | |
| 16 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 30 x \( \frac{30}{100} \) = \( \frac{30 x 30}{100} \) = \( \frac{900}{100} \) = 9 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 = \( \frac{9}{\frac{25}{100}} \) = 9 x \( \frac{100}{25} \) = \( \frac{9 x 100}{25} \) = \( \frac{900}{25} \) = 36 shots
to make the same number of shots as the guard and thus score the same number of points.
If \(\left|a\right| = 7\), which of the following best describes a?
a = -7 |
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none of these is correct |
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a = 7 |
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a = 7 or a = -7 |
The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).
What is \( 5 \)\( \sqrt{48} \) + \( 8 \)\( \sqrt{3} \)
| 13\( \sqrt{144} \) | |
| 40\( \sqrt{144} \) | |
| 28\( \sqrt{3} \) | |
| 40\( \sqrt{48} \) |
To add these radicals together their radicands must be the same:
5\( \sqrt{48} \) + 8\( \sqrt{3} \)
5\( \sqrt{16 \times 3} \) + 8\( \sqrt{3} \)
5\( \sqrt{4^2 \times 3} \) + 8\( \sqrt{3} \)
(5)(4)\( \sqrt{3} \) + 8\( \sqrt{3} \)
20\( \sqrt{3} \) + 8\( \sqrt{3} \)
Now that the radicands are identical, you can add them together:
20\( \sqrt{3} \) + 8\( \sqrt{3} \)In a class of 28 students, 14 are taking German and 13 are taking Spanish. Of the students studying German or Spanish, 7 are taking both courses. How many students are not enrolled in either course?
| 8 | |
| 27 | |
| 22 | |
| 16 |
The number of students taking German or Spanish is 14 + 13 = 27. Of that group of 27, 7 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 27 - 7 = 20 who are taking at least one language. 28 - 20 = 8 students who are not taking either language.
The total water usage for a city is 10,000 gallons each day. Of that total, 17% is for personal use and 49% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 8,250 | |
| 6,500 | |
| 3,200 | |
| 7,000 |
49% of the water consumption is industrial use and 17% is personal use so (49% - 17%) = 32% more water is used for industrial purposes. 10,000 gallons are consumed daily so industry consumes \( \frac{32}{100} \) x 10,000 gallons = 3,200 gallons.