| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.72 |
| Score | 0% | 54% |
On average, the center for a basketball team hits 35% of his shots while a guard on the same team hits 50% of his shots. If the guard takes 30 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?
| 43 | |
| 33 | |
| 31 | |
| 29 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 30 x \( \frac{50}{100} \) = \( \frac{50 x 30}{100} \) = \( \frac{1500}{100} \) = 15 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 = \( \frac{15}{\frac{35}{100}} \) = 15 x \( \frac{100}{35} \) = \( \frac{15 x 100}{35} \) = \( \frac{1500}{35} \) = 43 shots
to make the same number of shots as the guard and thus score the same number of points.
What is \( \frac{12\sqrt{14}}{4\sqrt{7}} \)?
| 3 \( \sqrt{2} \) | |
| \(\frac{1}{2}\) \( \sqrt{\frac{1}{3}} \) | |
| \(\frac{1}{3}\) \( \sqrt{\frac{1}{2}} \) | |
| 2 \( \sqrt{3} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{12\sqrt{14}}{4\sqrt{7}} \)
\( \frac{12}{4} \) \( \sqrt{\frac{14}{7}} \)
3 \( \sqrt{2} \)
Which of these numbers is a factor of 16?
| 4 | |
| 15 | |
| 13 | |
| 18 |
The factors of a number are all positive integers that divide evenly into the number. The factors of 16 are 1, 2, 4, 8, 16.
If the ratio of home fans to visiting fans in a crowd is 5:1 and all 49,000 seats in a stadium are filled, how many home fans are in attendance?
| 30,750 | |
| 29,250 | |
| 20,000 | |
| 40,833 |
A ratio of 5:1 means that there are 5 home fans for every one visiting fan. So, of every 6 fans, 5 are home fans and \( \frac{5}{6} \) of every fan in the stadium is a home fan:
49,000 fans x \( \frac{5}{6} \) = \( \frac{245000}{6} \) = 40,833 fans.
What is \( 6 \)\( \sqrt{125} \) - \( 7 \)\( \sqrt{5} \)
| 42\( \sqrt{5} \) | |
| 42\( \sqrt{25} \) | |
| 23\( \sqrt{5} \) | |
| 42\( \sqrt{125} \) |
To subtract these radicals together their radicands must be the same:
6\( \sqrt{125} \) - 7\( \sqrt{5} \)
6\( \sqrt{25 \times 5} \) - 7\( \sqrt{5} \)
6\( \sqrt{5^2 \times 5} \) - 7\( \sqrt{5} \)
(6)(5)\( \sqrt{5} \) - 7\( \sqrt{5} \)
30\( \sqrt{5} \) - 7\( \sqrt{5} \)
Now that the radicands are identical, you can subtract them:
30\( \sqrt{5} \) - 7\( \sqrt{5} \)