| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.97 |
| Score | 0% | 59% |
How many hours does it take a car to travel 375 miles at an average speed of 75 miles per hour?
| 6 hours | |
| 4 hours | |
| 5 hours | |
| 1 hour |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Solving for time:
time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{375mi}{75mph} \)
5 hours
This property states taht the order of addition or multiplication does not mater. For example, 2 + 5 and 5 + 2 are equivalent.
commutative |
|
distributive |
|
associative |
|
PEDMAS |
The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.
On average, the center for a basketball team hits 50% of his shots while a guard on the same team hits 60% 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?
| 12 | |
| 22 | |
| 29 | |
| 17 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{60}{100} \) = \( \frac{60 x 10}{100} \) = \( \frac{600}{100} \) = 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.
What is 3b6 x 2b2?
| 6b8 | |
| 5b6 | |
| 5b8 | |
| 6b6 |
To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:
3b6 x 2b2
(3 x 2)b(6 + 2)
6b8
What is \( 6 \)\( \sqrt{125} \) + \( 2 \)\( \sqrt{5} \)
| 32\( \sqrt{5} \) | |
| 12\( \sqrt{25} \) | |
| 8\( \sqrt{5} \) | |
| 12\( \sqrt{625} \) |
To add these radicals together their radicands must be the same:
6\( \sqrt{125} \) + 2\( \sqrt{5} \)
6\( \sqrt{25 \times 5} \) + 2\( \sqrt{5} \)
6\( \sqrt{5^2 \times 5} \) + 2\( \sqrt{5} \)
(6)(5)\( \sqrt{5} \) + 2\( \sqrt{5} \)
30\( \sqrt{5} \) + 2\( \sqrt{5} \)
Now that the radicands are identical, you can add them together:
30\( \sqrt{5} \) + 2\( \sqrt{5} \)