| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.82 |
| Score | 0% | 56% |
What is \( \frac{5c^8}{2c^2} \)?
| 2\(\frac{1}{2}\)c6 | |
| \(\frac{2}{5}\)c10 | |
| 2\(\frac{1}{2}\)c16 | |
| 2\(\frac{1}{2}\)c10 |
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:
\( \frac{5c^8}{2c^2} \)
\( \frac{5}{2} \) c(8 - 2)
2\(\frac{1}{2}\)c6
Solve 3 + (5 + 2) ÷ 2 x 4 - 42
| \(\frac{2}{3}\) | |
| 1 | |
| \(\frac{4}{5}\) | |
| \(\frac{5}{6}\) |
Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):
3 + (5 + 2) ÷ 2 x 4 - 42
P: 3 + (7) ÷ 2 x 4 - 42
E: 3 + 7 ÷ 2 x 4 - 16
MD: 3 + \( \frac{7}{2} \) x 4 - 16
MD: 3 + \( \frac{28}{2} \) - 16
AS: \( \frac{6}{2} \) + \( \frac{28}{2} \) - 16
AS: \( \frac{34}{2} \) - 16
AS: \( \frac{34 - 32}{2} \)
\( \frac{2}{2} \)
1
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 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?
| 20 | |
| 24 | |
| 13 | |
| 27 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 15 x \( \frac{45}{100} \) = \( \frac{45 x 15}{100} \) = \( \frac{675}{100} \) = 6 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 = \( \frac{6}{\frac{25}{100}} \) = 6 x \( \frac{100}{25} \) = \( \frac{6 x 100}{25} \) = \( \frac{600}{25} \) = 24 shots
to make the same number of shots as the guard and thus score the same number of points.
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?
| 3:2 | |
| 9:2 | |
| 3:4 | |
| 9:8 |
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.
Which of the following is an improper fraction?
\({7 \over 5} \) |
|
\(1 {2 \over 5} \) |
|
\({a \over 5} \) |
|
\({2 \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.