| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.09 |
| Score | 0% | 62% |
Convert y-5 to remove the negative exponent.
| \( \frac{1}{y^{-5}} \) | |
| \( \frac{1}{y^5} \) | |
| \( \frac{5}{y} \) | |
| \( \frac{-1}{y^{-5}} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 35% off." If Roger buys two shirts, each with a regular price of $48, how much will he pay for both shirts?
| $57.60 | |
| $55.20 | |
| $31.20 | |
| $79.20 |
By buying two shirts, Roger will save $48 x \( \frac{35}{100} \) = \( \frac{$48 x 35}{100} \) = \( \frac{$1680}{100} \) = $16.80 on the second shirt.
So, his total cost will be
$48.00 + ($48.00 - $16.80)
$48.00 + $31.20
$79.20
If a rectangle is twice as long as it is wide and has a perimeter of 36 meters, what is the area of the rectangle?
| 50 m2 | |
| 72 m2 | |
| 162 m2 | |
| 98 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 36 meters so the equation becomes: 2w + 2h = 36.
Putting these two equations together and solving for width (w):
2w + 2h = 36
w + h = \( \frac{36}{2} \)
w + h = 18
w = 18 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 18 - 2w
3w = 18
w = \( \frac{18}{3} \)
w = 6
Since h = 2w that makes h = (2 x 6) = 12 and the area = h x w = 6 x 12 = 72 m2
In a class of 19 students, 10 are taking German and 6 are taking Spanish. Of the students studying German or Spanish, 2 are taking both courses. How many students are not enrolled in either course?
| 11 | |
| 5 | |
| 17 | |
| 13 |
The number of students taking German or Spanish is 10 + 6 = 16. Of that group of 16, 2 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 16 - 2 = 14 who are taking at least one language. 19 - 14 = 5 students who are not taking either language.
Find the average of the following numbers: 12, 4, 12, 4.
| 11 | |
| 8 | |
| 10 | |
| 6 |
To find the average of these 4 numbers add them together then divide by 4:
\( \frac{12 + 4 + 12 + 4}{4} \) = \( \frac{32}{4} \) = 8