| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.99 |
| Score | 0% | 60% |
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 35% off." If Frank buys two shirts, each with a regular price of $36, how much will he pay for both shirts?
| $59.40 | |
| $23.40 | |
| $48.60 | |
| $43.20 |
By buying two shirts, Frank will save $36 x \( \frac{35}{100} \) = \( \frac{$36 x 35}{100} \) = \( \frac{$1260}{100} \) = $12.60 on the second shirt.
So, his total cost will be
$36.00 + ($36.00 - $12.60)
$36.00 + $23.40
$59.40
Which of these numbers is a factor of 40?
| 1 | |
| 38 | |
| 7 | |
| 32 |
The factors of a number are all positive integers that divide evenly into the number. The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40.
If \( \left|a - 5\right| \) - 8 = -2, which of these is a possible value for a?
| 11 | |
| 3 | |
| -5 | |
| -4 |
First, solve for \( \left|a - 5\right| \):
\( \left|a - 5\right| \) - 8 = -2
\( \left|a - 5\right| \) = -2 + 8
\( \left|a - 5\right| \) = 6
The value inside the absolute value brackets can be either positive or negative so (a - 5) must equal + 6 or -6 for \( \left|a - 5\right| \) to equal 6:
| a - 5 = 6 a = 6 + 5 a = 11 | a - 5 = -6 a = -6 + 5 a = -1 |
So, a = -1 or a = 11.
If \(\left|a\right| = 7\), which of the following best describes a?
a = -7 |
|
none of these is correct |
|
a = 7 |
|
a = 7 or a = -7 |
The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).
On average, the center for a basketball team hits 35% of his shots while a guard on the same team hits 55% 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?
| 45 | |
| 27 | |
| 23 | |
| 37 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{55}{100} \) = \( \frac{55 x 25}{100} \) = \( \frac{1375}{100} \) = 13 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 = \( \frac{13}{\frac{35}{100}} \) = 13 x \( \frac{100}{35} \) = \( \frac{13 x 100}{35} \) = \( \frac{1300}{35} \) = 37 shots
to make the same number of shots as the guard and thus score the same number of points.