| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.51 |
| Score | 0% | 70% |
4! = ?
5 x 4 x 3 x 2 x 1 |
|
4 x 3 x 2 x 1 |
|
4 x 3 |
|
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 car travels 60 miles in 2 hours, what is the average speed?
| 30 mph | |
| 25 mph | |
| 75 mph | |
| 40 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Convert a-5 to remove the negative exponent.
| \( \frac{1}{a^5} \) | |
| \( \frac{-1}{a^{-5}} \) | |
| \( \frac{1}{a^{-5}} \) | |
| \( \frac{-1}{-5a} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
If \(\left|a\right| = 7\), which of the following best describes a?
a = 7 |
|
none of these is correct |
|
a = 7 or a = -7 |
|
a = -7 |
The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).
If a rectangle is twice as long as it is wide and has a perimeter of 48 meters, what is the area of the rectangle?
| 32 m2 | |
| 162 m2 | |
| 50 m2 | |
| 128 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 48 meters so the equation becomes: 2w + 2h = 48.
Putting these two equations together and solving for width (w):
2w + 2h = 48
w + h = \( \frac{48}{2} \)
w + h = 24
w = 24 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 24 - 2w
3w = 24
w = \( \frac{24}{3} \)
w = 8
Since h = 2w that makes h = (2 x 8) = 16 and the area = h x w = 8 x 16 = 128 m2