| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.59 |
| Score | 0% | 52% |
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?
| 81:2 | |
| 5:8 | |
| 5:4 | |
| 3:1 |
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.
Solve 3 + (3 + 3) ÷ 3 x 2 - 52
| 1\(\frac{1}{5}\) | |
| 2\(\frac{1}{2}\) | |
| -18 | |
| 2 |
Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):
3 + (3 + 3) ÷ 3 x 2 - 52
P: 3 + (6) ÷ 3 x 2 - 52
E: 3 + 6 ÷ 3 x 2 - 25
MD: 3 + \( \frac{6}{3} \) x 2 - 25
MD: 3 + \( \frac{12}{3} \) - 25
AS: \( \frac{9}{3} \) + \( \frac{12}{3} \) - 25
AS: \( \frac{21}{3} \) - 25
AS: \( \frac{21 - 75}{3} \)
\( \frac{-54}{3} \)
-18
On average, the center for a basketball team hits 45% of his shots while a guard on the same team hits 65% of his shots. If the guard takes 20 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?
| 24 | |
| 23 | |
| 29 | |
| 33 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 20 x \( \frac{65}{100} \) = \( \frac{65 x 20}{100} \) = \( \frac{1300}{100} \) = 13 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 = \( \frac{13}{\frac{45}{100}} \) = 13 x \( \frac{100}{45} \) = \( \frac{13 x 100}{45} \) = \( \frac{1300}{45} \) = 29 shots
to make the same number of shots as the guard and thus score the same number of points.
A machine in a factory has an error rate of 8 parts per 100. The machine normally runs 24 hours a day and produces 5 parts per hour. Yesterday the machine was shut down for 9 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 190.1 | |
| 77.6 | |
| 135.4 | |
| 69 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{8}{100} \) x 5 = \( \frac{8 \times 5}{100} \) = \( \frac{40}{100} \) = 0.4 errors per hour
So, in an average hour, the machine will produce 5 - 0.4 = 4.6 error free parts.
The machine ran for 24 - 9 = 15 hours yesterday so you would expect that 15 x 4.6 = 69 error free parts were produced yesterday.
What is \( \frac{8}{3} \) - \( \frac{7}{7} \)?
| \( \frac{2}{21} \) | |
| 2 \( \frac{1}{9} \) | |
| 1\(\frac{2}{3}\) | |
| 1 \( \frac{1}{21} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [21, 42, 63, 84] making 21 the smallest multiple 3 and 7 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{8 x 7}{3 x 7} \) - \( \frac{7 x 3}{7 x 3} \)
\( \frac{56}{21} \) - \( \frac{21}{21} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{56 - 21}{21} \) = \( \frac{35}{21} \) = 1\(\frac{2}{3}\)