| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.26 |
| Score | 0% | 65% |
In a class of 37 students, 14 are taking German and 15 are taking Spanish. Of the students studying German or Spanish, 7 are taking both courses. How many students are not enrolled in either course?
| 15 | |
| 22 | |
| 33 | |
| 19 |
The number of students taking German or Spanish is 14 + 15 = 29. Of that group of 29, 7 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 29 - 7 = 22 who are taking at least one language. 37 - 22 = 15 students who are not taking either language.
If a mayor is elected with 56% of the votes cast and 47% of a town's 13,000 voters cast a vote, how many votes did the mayor receive?
| 3,972 | |
| 4,155 | |
| 3,544 | |
| 3,422 |
If 47% of the town's 13,000 voters cast ballots the number of votes cast is:
(\( \frac{47}{100} \)) x 13,000 = \( \frac{611,000}{100} \) = 6,110
The mayor got 56% of the votes cast which is:
(\( \frac{56}{100} \)) x 6,110 = \( \frac{342,160}{100} \) = 3,422 votes.
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?
| 72 m2 | |
| 32 m2 | |
| 162 m2 | |
| 2 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
What is the distance in miles of a trip that takes 6 hours at an average speed of 25 miles per hour?
| 320 miles | |
| 360 miles | |
| 150 miles | |
| 330 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 = \( 25mph \times 6h \)
150 miles
What is (z2)3?
| z6 | |
| z5 | |
| z-1 | |
| 3z2 |
To raise a term with an exponent to another exponent, retain the base and multiply the exponents:
(z2)3