| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.99 |
| Score | 0% | 60% |
What is 8\( \sqrt{4} \) x 6\( \sqrt{8} \)?
| 48\( \sqrt{4} \) | |
| 48\( \sqrt{8} \) | |
| 192\( \sqrt{2} \) | |
| 48\( \sqrt{12} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
8\( \sqrt{4} \) x 6\( \sqrt{8} \)
(8 x 6)\( \sqrt{4 \times 8} \)
48\( \sqrt{32} \)
Now we need to simplify the radical:
48\( \sqrt{32} \)
48\( \sqrt{2 \times 16} \)
48\( \sqrt{2 \times 4^2} \)
(48)(4)\( \sqrt{2} \)
192\( \sqrt{2} \)
Which of the following is not a prime number?
9 |
|
5 |
|
2 |
|
7 |
A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.
Simplify \( \frac{16}{48} \).
| \( \frac{1}{3} \) | |
| \( \frac{6}{11} \) | |
| \( \frac{1}{2} \) | |
| \( \frac{5}{17} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 16 are [1, 2, 4, 8, 16] and the factors of 48 are [1, 2, 3, 4, 6, 8, 12, 16, 24, 48]. They share 5 factors [1, 2, 4, 8, 16] making 16 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{16}{48} \) = \( \frac{\frac{16}{16}}{\frac{48}{16}} \) = \( \frac{1}{3} \)
What is \( \frac{49\sqrt{32}}{7\sqrt{8}} \)?
| \(\frac{1}{7}\) \( \sqrt{\frac{1}{4}} \) | |
| 4 \( \sqrt{7} \) | |
| 7 \( \sqrt{4} \) | |
| \(\frac{1}{4}\) \( \sqrt{\frac{1}{7}} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{49\sqrt{32}}{7\sqrt{8}} \)
\( \frac{49}{7} \) \( \sqrt{\frac{32}{8}} \)
7 \( \sqrt{4} \)
On average, the center for a basketball team hits 50% of his shots while a guard on the same team hits 65% 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?
| 19 | |
| 17 | |
| 13 | |
| 12 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{65}{100} \) = \( \frac{65 x 10}{100} \) = \( \frac{650}{100} \) = 6 shots
The center makes 50% 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 = \( \frac{6}{\frac{50}{100}} \) = 6 x \( \frac{100}{50} \) = \( \frac{6 x 100}{50} \) = \( \frac{600}{50} \) = 12 shots
to make the same number of shots as the guard and thus score the same number of points.