| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.54 |
| Score | 0% | 51% |
Find the average of the following numbers: 11, 9, 11, 9.
| 10 | |
| 13 | |
| 14 | |
| 5 |
To find the average of these 4 numbers add them together then divide by 4:
\( \frac{11 + 9 + 11 + 9}{4} \) = \( \frac{40}{4} \) = 10
On average, the center for a basketball team hits 45% of his shots while a guard on the same team hits 50% of his shots. If the guard takes 25 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 | |
| 27 | |
| 60 | |
| 28 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{50}{100} \) = \( \frac{50 x 25}{100} \) = \( \frac{1250}{100} \) = 12 shots
The center makes 45% 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 = \( \frac{12}{\frac{45}{100}} \) = 12 x \( \frac{100}{45} \) = \( \frac{12 x 100}{45} \) = \( \frac{1200}{45} \) = 27 shots
to make the same number of shots as the guard and thus score the same number of points.
Which of the following statements about exponents is false?
all of these are false |
|
b0 = 1 |
|
b1 = 1 |
|
b1 = b |
A number with an exponent (be) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b1 = b) and a base with an exponent of 0 equals 1 ( (b0 = 1).
What is \( 8 \)\( \sqrt{50} \) - \( 9 \)\( \sqrt{2} \)
| 31\( \sqrt{2} \) | |
| -1\( \sqrt{50} \) | |
| 72\( \sqrt{50} \) | |
| -1\( \sqrt{25} \) |
To subtract these radicals together their radicands must be the same:
8\( \sqrt{50} \) - 9\( \sqrt{2} \)
8\( \sqrt{25 \times 2} \) - 9\( \sqrt{2} \)
8\( \sqrt{5^2 \times 2} \) - 9\( \sqrt{2} \)
(8)(5)\( \sqrt{2} \) - 9\( \sqrt{2} \)
40\( \sqrt{2} \) - 9\( \sqrt{2} \)
Now that the radicands are identical, you can subtract them:
40\( \sqrt{2} \) - 9\( \sqrt{2} \)A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 5 to 2 and the ratio of baseball to basketball cards is 5 to 1, what is the ratio of football to basketball cards?
| 5:8 | |
| 9:6 | |
| 25:2 | |
| 3:8 |
The ratio of football cards to baseball cards is 5:2 and the ratio of baseball cards to basketball cards is 5:1. 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 25:10 and the ratio of baseball cards to basketball cards as 10:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 25:10, 10:2 which reduces to 25:2.