| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.27 |
| Score | 0% | 65% |
Simplify \( \sqrt{50} \)
| 3\( \sqrt{2} \) | |
| 7\( \sqrt{4} \) | |
| 4\( \sqrt{4} \) | |
| 5\( \sqrt{2} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{50} \)
\( \sqrt{25 \times 2} \)
\( \sqrt{5^2 \times 2} \)
5\( \sqrt{2} \)
Convert 2,414,000 to scientific notation.
| 2.414 x 10-6 | |
| 2.414 x 106 | |
| 2.414 x 107 | |
| 24.14 x 105 |
A number in scientific notation has the format 0.000 x 10exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:
2,414,000 in scientific notation is 2.414 x 106
What is the least common multiple of 3 and 9?
| 9 | |
| 21 | |
| 18 | |
| 25 |
The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [9, 18, 27, 36, 45] making 9 the smallest multiple 3 and 9 have in common.
On average, the center for a basketball team hits 40% of his shots while a guard on the same team hits 55% 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?
| 29 | |
| 55 | |
| 28 | |
| 34 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 20 x \( \frac{55}{100} \) = \( \frac{55 x 20}{100} \) = \( \frac{1100}{100} \) = 11 shots
The center makes 40% 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 = \( \frac{11}{\frac{40}{100}} \) = 11 x \( \frac{100}{40} \) = \( \frac{11 x 100}{40} \) = \( \frac{1100}{40} \) = 28 shots
to make the same number of shots as the guard and thus score the same number of points.
What is the distance in miles of a trip that takes 5 hours at an average speed of 75 miles per hour?
| 60 miles | |
| 140 miles | |
| 40 miles | |
| 375 miles |
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 distance:
distance = \( \text{speed} \times \text{time} \)
distance = \( 75mph \times 5h \)
375 miles