| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.16 |
| Score | 0% | 63% |
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 30 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 | |
| 20 | |
| 36 | |
| 26 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 30 x \( \frac{30}{100} \) = \( \frac{30 x 30}{100} \) = \( \frac{900}{100} \) = 9 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 = \( \frac{9}{\frac{25}{100}} \) = 9 x \( \frac{100}{25} \) = \( \frac{9 x 100}{25} \) = \( \frac{900}{25} \) = 36 shots
to make the same number of shots as the guard and thus score the same number of points.
What is the next number in this sequence: 1, 5, 13, 25, 41, __________ ?
| 61 | |
| 59 | |
| 52 | |
| 66 |
The equation for this sequence is:
an = an-1 + 4(n - 1)
where n is the term's order in the sequence, an is the value of the term, and an-1 is the value of the term before an. This makes the next number:
a6 = a5 + 4(6 - 1)
a6 = 41 + 4(5)
a6 = 61
What is the next number in this sequence: 1, 9, 17, 25, 33, __________ ?
| 45 | |
| 43 | |
| 33 | |
| 41 |
The equation for this sequence is:
an = an-1 + 8
where n is the term's order in the sequence, an is the value of the term, and an-1 is the value of the term before an. This makes the next number:
a6 = a5 + 8
a6 = 33 + 8
a6 = 41
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 7 to 2 and the ratio of baseball to basketball cards is 7 to 1, what is the ratio of football to basketball cards?
| 5:1 | |
| 1:2 | |
| 49:2 | |
| 5:4 |
The ratio of football cards to baseball cards is 7:2 and the ratio of baseball cards to basketball cards is 7:1. 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 49:14 and the ratio of baseball cards to basketball cards as 14:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 49:14, 14:2 which reduces to 49:2.
What is \( \frac{7}{4} \) + \( \frac{8}{8} \)?
| 1 \( \frac{4}{8} \) | |
| \( \frac{4}{8} \) | |
| \( \frac{1}{8} \) | |
| 2\(\frac{3}{4}\) |
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 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 4 and 8 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{7 x 2}{4 x 2} \) + \( \frac{8 x 1}{8 x 1} \)
\( \frac{14}{8} \) + \( \frac{8}{8} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{14 + 8}{8} \) = \( \frac{22}{8} \) = 2\(\frac{3}{4}\)