| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.87 |
| Score | 0% | 57% |
In a class of 14 students, 7 are taking German and 5 are taking Spanish. Of the students studying German or Spanish, 3 are taking both courses. How many students are not enrolled in either course?
| 12 | |
| 5 | |
| 11 | |
| 13 |
The number of students taking German or Spanish is 7 + 5 = 12. Of that group of 12, 3 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 12 - 3 = 9 who are taking at least one language. 14 - 9 = 5 students who are not taking either language.
If a rectangle is twice as long as it is wide and has a perimeter of 18 meters, what is the area of the rectangle?
| 72 m2 | |
| 98 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 18 meters so the equation becomes: 2w + 2h = 18.
Putting these two equations together and solving for width (w):
2w + 2h = 18
w + h = \( \frac{18}{2} \)
w + h = 9
w = 9 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 9 - 2w
3w = 9
w = \( \frac{9}{3} \)
w = 3
Since h = 2w that makes h = (2 x 3) = 6 and the area = h x w = 3 x 6 = 18 m2
Monica scored 91% on her final exam. If each question was worth 3 points and there were 210 possible points on the exam, how many questions did Monica answer correctly?
| 62 | |
| 64 | |
| 68 | |
| 55 |
Monica scored 91% on the test meaning she earned 91% of the possible points on the test. There were 210 possible points on the test so she earned 210 x 0.91 = 192 points. Each question is worth 3 points so she got \( \frac{192}{3} \) = 64 questions right.
How many hours does it take a car to travel 325 miles at an average speed of 65 miles per hour?
| 4 hours | |
| 5 hours | |
| 1 hour | |
| 6 hours |
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 time:
time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{325mi}{65mph} \)
5 hours
What is \( 2 \)\( \sqrt{20} \) + \( 7 \)\( \sqrt{5} \)
| 14\( \sqrt{100} \) | |
| 11\( \sqrt{5} \) | |
| 14\( \sqrt{20} \) | |
| 14\( \sqrt{4} \) |
To add these radicals together their radicands must be the same:
2\( \sqrt{20} \) + 7\( \sqrt{5} \)
2\( \sqrt{4 \times 5} \) + 7\( \sqrt{5} \)
2\( \sqrt{2^2 \times 5} \) + 7\( \sqrt{5} \)
(2)(2)\( \sqrt{5} \) + 7\( \sqrt{5} \)
4\( \sqrt{5} \) + 7\( \sqrt{5} \)
Now that the radicands are identical, you can add them together:
4\( \sqrt{5} \) + 7\( \sqrt{5} \)