| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.73 |
| Score | 0% | 55% |
On average, the center for a basketball team hits 35% of his shots while a guard on the same team hits 40% of his shots. If the guard takes 10 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?
| 16 | |
| 18 | |
| 11 | |
| 9 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{40}{100} \) = \( \frac{40 x 10}{100} \) = \( \frac{400}{100} \) = 4 shots
The center makes 35% 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 = \( \frac{4}{\frac{35}{100}} \) = 4 x \( \frac{100}{35} \) = \( \frac{4 x 100}{35} \) = \( \frac{400}{35} \) = 11 shots
to make the same number of shots as the guard and thus score the same number of points.
Convert x-4 to remove the negative exponent.
| \( \frac{-1}{-4x} \) | |
| \( \frac{-1}{-4x^{4}} \) | |
| \( \frac{1}{x^4} \) | |
| \( \frac{4}{x} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 40% off." If Alex buys two shirts, each with a regular price of $37, how much will he pay for both shirts?
| $22.20 | |
| $14.80 | |
| $59.20 | |
| $40.70 |
By buying two shirts, Alex will save $37 x \( \frac{40}{100} \) = \( \frac{$37 x 40}{100} \) = \( \frac{$1480}{100} \) = $14.80 on the second shirt.
So, his total cost will be
$37.00 + ($37.00 - $14.80)
$37.00 + $22.20
$59.20
If the ratio of home fans to visiting fans in a crowd is 4:1 and all 31,000 seats in a stadium are filled, how many home fans are in attendance?
| 35,250 | |
| 24,800 | |
| 26,250 | |
| 22,000 |
A ratio of 4:1 means that there are 4 home fans for every one visiting fan. So, of every 5 fans, 4 are home fans and \( \frac{4}{5} \) of every fan in the stadium is a home fan:
31,000 fans x \( \frac{4}{5} \) = \( \frac{124000}{5} \) = 24,800 fans.
The __________ is the smallest positive integer that is a multiple of two or more integers.
least common multiple |
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absolute value |
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least common factor |
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greatest common factor |
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.