| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.29 |
| Score | 0% | 66% |
What is \( \frac{10\sqrt{18}}{5\sqrt{6}} \)?
| \(\frac{1}{2}\) \( \sqrt{3} \) | |
| \(\frac{1}{3}\) \( \sqrt{\frac{1}{2}} \) | |
| \(\frac{1}{3}\) \( \sqrt{2} \) | |
| 2 \( \sqrt{3} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{10\sqrt{18}}{5\sqrt{6}} \)
\( \frac{10}{5} \) \( \sqrt{\frac{18}{6}} \)
2 \( \sqrt{3} \)
If a car travels 195 miles in 3 hours, what is the average speed?
| 65 mph | |
| 55 mph | |
| 30 mph | |
| 40 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)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 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?
| 48 | |
| 26 | |
| 33 | |
| 54 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{60}{100} \) = \( \frac{60 x 25}{100} \) = \( \frac{1500}{100} \) = 15 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 = \( \frac{15}{\frac{45}{100}} \) = 15 x \( \frac{100}{45} \) = \( \frac{15 x 100}{45} \) = \( \frac{1500}{45} \) = 33 shots
to make the same number of shots as the guard and thus score the same number of points.
The __________ is the smallest positive integer that is a multiple of two or more integers.
least common multiple |
|
absolute value |
|
least common factor |
|
greatest common factor |
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.
Ezra loaned Alex $1,500 at an annual interest rate of 1%. If no payments are made, what is the interest owed on this loan at the end of the first year?
| $24 | |
| $15 | |
| $18 | |
| $6 |
The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:
interest = annual interest rate x loan amount
i = (\( \frac{6}{100} \)) x $1,500
i = 0.01 x $1,500
i = $15