| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.10 |
| Score | 0% | 62% |
Which of these numbers is a factor of 32?
| 7 | |
| 1 | |
| 19 | |
| 10 |
The factors of a number are all positive integers that divide evenly into the number. The factors of 32 are 1, 2, 4, 8, 16, 32.
4! = ?
5 x 4 x 3 x 2 x 1 |
|
3 x 2 x 1 |
|
4 x 3 x 2 x 1 |
|
4 x 3 |
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.
What is \( \frac{1a^9}{6a^2} \)?
| 6a11 | |
| \(\frac{1}{6}\)a7 | |
| \(\frac{1}{6}\)a4\(\frac{1}{2}\) | |
| \(\frac{1}{6}\)a18 |
To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:
\( \frac{a^9}{6a^2} \)
\( \frac{1}{6} \) a(9 - 2)
\(\frac{1}{6}\)a7
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?
| 5:8 | |
| 7:8 | |
| 3:6 | |
| 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 25% of his shots while a guard on the same team hits 45% of his shots. If the guard takes 10 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?
| 7 | |
| 16 | |
| 9 | |
| 10 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{45}{100} \) = \( \frac{45 x 10}{100} \) = \( \frac{450}{100} \) = 4 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 = \( \frac{4}{\frac{25}{100}} \) = 4 x \( \frac{100}{25} \) = \( \frac{4 x 100}{25} \) = \( \frac{400}{25} \) = 16 shots
to make the same number of shots as the guard and thus score the same number of points.