| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.46 |
| Score | 0% | 69% |
If \(\left|a\right| = 7\), which of the following best describes a?
none of these is correct |
|
a = 7 |
|
a = -7 |
|
a = 7 or 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).
In a class of 22 students, 5 are taking German and 5 are taking Spanish. Of the students studying German or Spanish, 2 are taking both courses. How many students are not enrolled in either course?
| 12 | |
| 13 | |
| 15 | |
| 14 |
The number of students taking German or Spanish is 5 + 5 = 10. Of that group of 10, 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 10 - 2 = 8 who are taking at least one language. 22 - 8 = 14 students who are not taking either language.
Simplify \( \frac{32}{80} \).
| \( \frac{5}{7} \) | |
| \( \frac{10}{11} \) | |
| \( \frac{5}{14} \) | |
| \( \frac{2}{5} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 80 are [1, 2, 4, 5, 8, 10, 16, 20, 40, 80]. They share 5 factors [1, 2, 4, 8, 16] making 16 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{32}{80} \) = \( \frac{\frac{32}{16}}{\frac{80}{16}} \) = \( \frac{2}{5} \)
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 50% off." If Bob buys two shirts, each with a regular price of $29, how much money will he save?
| $14.50 | |
| $1.45 | |
| $13.05 | |
| $2.90 |
By buying two shirts, Bob will save $29 x \( \frac{50}{100} \) = \( \frac{$29 x 50}{100} \) = \( \frac{$1450}{100} \) = $14.50 on the second shirt.
What is \( \frac{2}{5} \) ÷ \( \frac{4}{6} \)?
| \(\frac{3}{35}\) | |
| 2\(\frac{2}{5}\) | |
| \(\frac{1}{10}\) | |
| \(\frac{3}{5}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{2}{5} \) ÷ \( \frac{4}{6} \) = \( \frac{2}{5} \) x \( \frac{6}{4} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{2}{5} \) x \( \frac{6}{4} \) = \( \frac{2 x 6}{5 x 4} \) = \( \frac{12}{20} \) = \(\frac{3}{5}\)