| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.50 |
| Score | 0% | 50% |
A tiger in a zoo has consumed 50 pounds of food in 5 days. If the tiger continues to eat at the same rate, in how many more days will its total food consumtion be 90 pounds?
| 5 | |
| 2 | |
| 4 | |
| 7 |
If the tiger has consumed 50 pounds of food in 5 days that's \( \frac{50}{5} \) = 10 pounds of food per day. The tiger needs to consume 90 - 50 = 40 more pounds of food to reach 90 pounds total. At 10 pounds of food per day that's \( \frac{40}{10} \) = 4 more days.
What is \( 5 \)\( \sqrt{80} \) - \( 2 \)\( \sqrt{5} \)
| 10\( \sqrt{400} \) | |
| 3\( \sqrt{400} \) | |
| 10\( \sqrt{5} \) | |
| 18\( \sqrt{5} \) |
To subtract these radicals together their radicands must be the same:
5\( \sqrt{80} \) - 2\( \sqrt{5} \)
5\( \sqrt{16 \times 5} \) - 2\( \sqrt{5} \)
5\( \sqrt{4^2 \times 5} \) - 2\( \sqrt{5} \)
(5)(4)\( \sqrt{5} \) - 2\( \sqrt{5} \)
20\( \sqrt{5} \) - 2\( \sqrt{5} \)
Now that the radicands are identical, you can subtract them:
20\( \sqrt{5} \) - 2\( \sqrt{5} \)A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 9 to 2 and the ratio of baseball to basketball cards is 9 to 1, what is the ratio of football to basketball cards?
| 7:2 | |
| 81:2 | |
| 5:4 | |
| 5:8 |
The ratio of football cards to baseball cards is 9:2 and the ratio of baseball cards to basketball cards is 9:1. 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 81:18 and the ratio of baseball cards to basketball cards as 18:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 81:18, 18:2 which reduces to 81:2.
On average, the center for a basketball team hits 25% of his shots while a guard on the same team hits 30% 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?
| 22 | |
| 30 | |
| 28 | |
| 18 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{30}{100} \) = \( \frac{30 x 25}{100} \) = \( \frac{750}{100} \) = 7 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 = \( \frac{7}{\frac{25}{100}} \) = 7 x \( \frac{100}{25} \) = \( \frac{7 x 100}{25} \) = \( \frac{700}{25} \) = 28 shots
to make the same number of shots as the guard and thus score the same number of points.
What is \( \frac{3}{4} \) + \( \frac{5}{10} \)?
| 1 \( \frac{9}{16} \) | |
| 2 \( \frac{1}{6} \) | |
| 1\(\frac{1}{4}\) | |
| 2 \( \frac{2}{20} \) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [20, 40, 60, 80] making 20 the smallest multiple 4 and 10 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{3 x 5}{4 x 5} \) + \( \frac{5 x 2}{10 x 2} \)
\( \frac{15}{20} \) + \( \frac{10}{20} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{15 + 10}{20} \) = \( \frac{25}{20} \) = 1\(\frac{1}{4}\)