| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.77 |
| Score | 0% | 55% |
4! = ?
3 x 2 x 1 |
|
4 x 3 x 2 x 1 |
|
4 x 3 |
|
5 x 4 x 3 x 2 x 1 |
A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
If a rectangle is twice as long as it is wide and has a perimeter of 6 meters, what is the area of the rectangle?
| 50 m2 | |
| 2 m2 | |
| 18 m2 | |
| 8 m2 |
The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 6 meters so the equation becomes: 2w + 2h = 6.
Putting these two equations together and solving for width (w):
2w + 2h = 6
w + h = \( \frac{6}{2} \)
w + h = 3
w = 3 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 3 - 2w
3w = 3
w = \( \frac{3}{3} \)
w = 1
Since h = 2w that makes h = (2 x 1) = 2 and the area = h x w = 1 x 2 = 2 m2
On average, the center for a basketball team hits 30% of his shots while a guard on the same team hits 50% 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?
| 40 | |
| 21 | |
| 48 | |
| 50 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{50}{100} \) = \( \frac{50 x 25}{100} \) = \( \frac{1250}{100} \) = 12 shots
The center makes 30% 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 = \( \frac{12}{\frac{30}{100}} \) = 12 x \( \frac{100}{30} \) = \( \frac{12 x 100}{30} \) = \( \frac{1200}{30} \) = 40 shots
to make the same number of shots as the guard and thus score the same number of points.
What is \( 6 \)\( \sqrt{18} \) - \( 9 \)\( \sqrt{2} \)
| 54\( \sqrt{9} \) | |
| 9\( \sqrt{2} \) | |
| 54\( \sqrt{18} \) | |
| -3\( \sqrt{36} \) |
To subtract these radicals together their radicands must be the same:
6\( \sqrt{18} \) - 9\( \sqrt{2} \)
6\( \sqrt{9 \times 2} \) - 9\( \sqrt{2} \)
6\( \sqrt{3^2 \times 2} \) - 9\( \sqrt{2} \)
(6)(3)\( \sqrt{2} \) - 9\( \sqrt{2} \)
18\( \sqrt{2} \) - 9\( \sqrt{2} \)
Now that the radicands are identical, you can subtract them:
18\( \sqrt{2} \) - 9\( \sqrt{2} \)Convert 8,438,000 to scientific notation.
| 8.438 x 105 | |
| 8.438 x 106 | |
| 8.438 x 10-6 | |
| 84.38 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:
8,438,000 in scientific notation is 8.438 x 106