| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.21 |
| Score | 0% | 64% |
In a class of 23 students, 13 are taking German and 9 are taking Spanish. Of the students studying German or Spanish, 5 are taking both courses. How many students are not enrolled in either course?
| 12 | |
| 10 | |
| 6 | |
| 20 |
The number of students taking German or Spanish is 13 + 9 = 22. Of that group of 22, 5 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 22 - 5 = 17 who are taking at least one language. 23 - 17 = 6 students who are not taking either language.
If a mayor is elected with 61% of the votes cast and 69% of a town's 21,000 voters cast a vote, how many votes did the mayor receive?
| 7,825 | |
| 11,737 | |
| 8,839 | |
| 10,868 |
If 69% of the town's 21,000 voters cast ballots the number of votes cast is:
(\( \frac{69}{100} \)) x 21,000 = \( \frac{1,449,000}{100} \) = 14,490
The mayor got 61% of the votes cast which is:
(\( \frac{61}{100} \)) x 14,490 = \( \frac{883,890}{100} \) = 8,839 votes.
Which of the following is an improper fraction?
\({2 \over 5} \) |
|
\({a \over 5} \) |
|
\(1 {2 \over 5} \) |
|
\({7 \over 5} \) |
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?
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).
What is \( \frac{1}{6} \) ÷ \( \frac{4}{7} \)?
| 1\(\frac{3}{4}\) | |
| \(\frac{7}{24}\) | |
| \(\frac{1}{16}\) | |
| \(\frac{3}{16}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{1}{6} \) ÷ \( \frac{4}{7} \) = \( \frac{1}{6} \) x \( \frac{7}{4} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{1}{6} \) x \( \frac{7}{4} \) = \( \frac{1 x 7}{6 x 4} \) = \( \frac{7}{24} \) = \(\frac{7}{24}\)