| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.06 |
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On average, the center for a basketball team hits 35% of his shots while a guard on the same team hits 45% of his shots. If the guard takes 15 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?
| 11 | |
| 17 | |
| 12 | |
| 14 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 15 x \( \frac{45}{100} \) = \( \frac{45 x 15}{100} \) = \( \frac{675}{100} \) = 6 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 = \( \frac{6}{\frac{35}{100}} \) = 6 x \( \frac{100}{35} \) = \( \frac{6 x 100}{35} \) = \( \frac{600}{35} \) = 17 shots
to make the same number of shots as the guard and thus score the same number of points.
Solve for \( \frac{4!}{5!} \)
| \( \frac{1}{5} \) | |
| \( \frac{1}{1680} \) | |
| 6720 | |
| \( \frac{1}{15120} \) |
A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:
\( \frac{4!}{5!} \)
\( \frac{4 \times 3 \times 2 \times 1}{5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{5} \)
\( \frac{1}{5} \)
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 30% off." If Charlie buys two shirts, each with a regular price of $12, how much money will he save?
| $3.60 | |
| $2.40 | |
| $4.20 | |
| $3.00 |
By buying two shirts, Charlie will save $12 x \( \frac{30}{100} \) = \( \frac{$12 x 30}{100} \) = \( \frac{$360}{100} \) = $3.60 on the second shirt.
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 5% off." If Monty buys two shirts, each with a regular price of $18, how much will he pay for both shirts?
| $35.10 | |
| $0.90 | |
| $21.60 | |
| $17.10 |
By buying two shirts, Monty will save $18 x \( \frac{5}{100} \) = \( \frac{$18 x 5}{100} \) = \( \frac{$90}{100} \) = $0.90 on the second shirt.
So, his total cost will be
$18.00 + ($18.00 - $0.90)
$18.00 + $17.10
$35.10
Which of these numbers is a factor of 32?
| 15 | |
| 2 | |
| 7 | |
| 1 |
The factors of a number are all positive integers that divide evenly into the number. The factors of 32 are 1, 2, 4, 8, 16, 32.