| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.10 |
| Score | 0% | 62% |
What is the greatest common factor of 56 and 24?
| 22 | |
| 4 | |
| 17 | |
| 8 |
The factors of 56 are [1, 2, 4, 7, 8, 14, 28, 56] and the factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24]. They share 4 factors [1, 2, 4, 8] making 8 the greatest factor 56 and 24 have in common.
If a mayor is elected with 65% of the votes cast and 65% of a town's 17,000 voters cast a vote, how many votes did the mayor receive?
| 7,183 | |
| 9,835 | |
| 8,840 | |
| 6,630 |
If 65% of the town's 17,000 voters cast ballots the number of votes cast is:
(\( \frac{65}{100} \)) x 17,000 = \( \frac{1,105,000}{100} \) = 11,050
The mayor got 65% of the votes cast which is:
(\( \frac{65}{100} \)) x 11,050 = \( \frac{718,250}{100} \) = 7,183 votes.
On average, the center for a basketball team hits 50% of his shots while a guard on the same team hits 55% 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?
| 28 | |
| 22 | |
| 31 | |
| 48 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 20 x \( \frac{55}{100} \) = \( \frac{55 x 20}{100} \) = \( \frac{1100}{100} \) = 11 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 = \( \frac{11}{\frac{50}{100}} \) = 11 x \( \frac{100}{50} \) = \( \frac{11 x 100}{50} \) = \( \frac{1100}{50} \) = 22 shots
to make the same number of shots as the guard and thus score the same number of points.
What is -6x2 x 9x4?
| -54x-2 | |
| -54x2 | |
| -54x6 | |
| 3x8 |
To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:
-6x2 x 9x4
(-6 x 9)x(2 + 4)
-54x6
In a class of 20 students, 9 are taking German and 8 are taking Spanish. Of the students studying German or Spanish, 4 are taking both courses. How many students are not enrolled in either course?
| 17 | |
| 7 | |
| 10 | |
| 11 |
The number of students taking German or Spanish is 9 + 8 = 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. 20 - 13 = 7 students who are not taking either language.