| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.14 |
| Score | 0% | 63% |
In a class of 35 students, 15 are taking German and 8 are taking Spanish. Of the students studying German or Spanish, 3 are taking both courses. How many students are not enrolled in either course?
| 15 | |
| 34 | |
| 18 | |
| 25 |
The number of students taking German or Spanish is 15 + 8 = 23. Of that group of 23, 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 23 - 3 = 20 who are taking at least one language. 35 - 20 = 15 students who are not taking either language.
If a mayor is elected with 85% of the votes cast and 46% of a town's 39,000 voters cast a vote, how many votes did the mayor receive?
| 12,558 | |
| 13,814 | |
| 9,867 | |
| 15,249 |
If 46% of the town's 39,000 voters cast ballots the number of votes cast is:
(\( \frac{46}{100} \)) x 39,000 = \( \frac{1,794,000}{100} \) = 17,940
The mayor got 85% of the votes cast which is:
(\( \frac{85}{100} \)) x 17,940 = \( \frac{1,524,900}{100} \) = 15,249 votes.
Which of the following is a mixed number?
\({5 \over 7} \) |
|
\({7 \over 5} \) |
|
\(1 {2 \over 5} \) |
|
\({a \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.
If \(\left|a\right| = 7\), which of the following best describes a?
none of these is correct |
|
a = 7 or a = -7 |
|
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 42 meters, what is the area of the rectangle?
| 72 m2 | |
| 128 m2 | |
| 2 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 42 meters so the equation becomes: 2w + 2h = 42.
Putting these two equations together and solving for width (w):
2w + 2h = 42
w + h = \( \frac{42}{2} \)
w + h = 21
w = 21 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 21 - 2w
3w = 21
w = \( \frac{21}{3} \)
w = 7
Since h = 2w that makes h = (2 x 7) = 14 and the area = h x w = 7 x 14 = 98 m2