| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.67 |
| Score | 0% | 53% |
If the ratio of home fans to visiting fans in a crowd is 3:1 and all 31,000 seats in a stadium are filled, how many home fans are in attendance?
| 32,000 | |
| 23,250 | |
| 36,000 | |
| 37,600 |
A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:
31,000 fans x \( \frac{3}{4} \) = \( \frac{93000}{4} \) = 23,250 fans.
What is \( 6 \)\( \sqrt{18} \) + \( 2 \)\( \sqrt{2} \)
| 12\( \sqrt{9} \) | |
| 12\( \sqrt{18} \) | |
| 8\( \sqrt{9} \) | |
| 20\( \sqrt{2} \) |
To add these radicals together their radicands must be the same:
6\( \sqrt{18} \) + 2\( \sqrt{2} \)
6\( \sqrt{9 \times 2} \) + 2\( \sqrt{2} \)
6\( \sqrt{3^2 \times 2} \) + 2\( \sqrt{2} \)
(6)(3)\( \sqrt{2} \) + 2\( \sqrt{2} \)
18\( \sqrt{2} \) + 2\( \sqrt{2} \)
Now that the radicands are identical, you can add them together:
18\( \sqrt{2} \) + 2\( \sqrt{2} \)On average, the center for a basketball team hits 45% of his shots while a guard on the same team hits 60% 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?
| 21 | |
| 27 | |
| 52 | |
| 23 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 20 x \( \frac{60}{100} \) = \( \frac{60 x 20}{100} \) = \( \frac{1200}{100} \) = 12 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 = \( \frac{12}{\frac{45}{100}} \) = 12 x \( \frac{100}{45} \) = \( \frac{12 x 100}{45} \) = \( \frac{1200}{45} \) = 27 shots
to make the same number of shots as the guard and thus score the same number of points.
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 45% off." If Charlie buys two shirts, each with a regular price of $37, how much money will he save?
| $18.50 | |
| $14.80 | |
| $16.65 | |
| $1.85 |
By buying two shirts, Charlie will save $37 x \( \frac{45}{100} \) = \( \frac{$37 x 45}{100} \) = \( \frac{$1665}{100} \) = $16.65 on the second shirt.
If \(\left|a\right| = 7\), which of the following best describes a?
a = -7 |
|
a = 7 |
|
none of these is correct |
|
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).