| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.61 |
| Score | 0% | 52% |
In a class of 24 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?
| 20 | |
| 22 | |
| 12 | |
| 10 |
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. 24 - 14 = 10 students who are not taking either language.
Which of the following is not a prime number?
7 |
|
5 |
|
9 |
|
2 |
A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 3 to 2 and the ratio of baseball to basketball cards is 3 to 1, what is the ratio of football to basketball cards?
| 7:6 | |
| 7:8 | |
| 5:8 | |
| 9:2 |
The ratio of football cards to baseball cards is 3:2 and the ratio of baseball cards to basketball cards is 3:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 9:6 and the ratio of baseball cards to basketball cards as 6:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 9:6, 6:2 which reduces to 9:2.
On average, the center for a basketball team hits 40% of his shots while a guard on the same team hits 55% of his shots. If the guard takes 15 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?
| 22 | |
| 20 | |
| 17 | |
| 32 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 15 x \( \frac{55}{100} \) = \( \frac{55 x 15}{100} \) = \( \frac{825}{100} \) = 8 shots
The center makes 40% 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 = \( \frac{8}{\frac{40}{100}} \) = 8 x \( \frac{100}{40} \) = \( \frac{8 x 100}{40} \) = \( \frac{800}{40} \) = 20 shots
to make the same number of shots as the guard and thus score the same number of points.
What is \( 7 \)\( \sqrt{45} \) + \( 2 \)\( \sqrt{5} \)
| 9\( \sqrt{9} \) | |
| 14\( \sqrt{5} \) | |
| 23\( \sqrt{5} \) | |
| 14\( \sqrt{225} \) |
To add these radicals together their radicands must be the same:
7\( \sqrt{45} \) + 2\( \sqrt{5} \)
7\( \sqrt{9 \times 5} \) + 2\( \sqrt{5} \)
7\( \sqrt{3^2 \times 5} \) + 2\( \sqrt{5} \)
(7)(3)\( \sqrt{5} \) + 2\( \sqrt{5} \)
21\( \sqrt{5} \) + 2\( \sqrt{5} \)
Now that the radicands are identical, you can add them together:
21\( \sqrt{5} \) + 2\( \sqrt{5} \)