| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.17 |
| Score | 0% | 63% |
In a class of 23 students, 13 are taking German and 10 are taking Spanish. Of the students studying German or Spanish, 6 are taking both courses. How many students are not enrolled in either course?
| 18 | |
| 10 | |
| 6 | |
| 17 |
The number of students taking German or Spanish is 13 + 10 = 23. Of that group of 23, 6 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 - 6 = 17 who are taking at least one language. 23 - 17 = 6 students who are not taking either language.
Find the average of the following numbers: 13, 5, 12, 6.
| 8 | |
| 11 | |
| 13 | |
| 9 |
To find the average of these 4 numbers add them together then divide by 4:
\( \frac{13 + 5 + 12 + 6}{4} \) = \( \frac{36}{4} \) = 9
The __________ is the smallest positive integer that is a multiple of two or more integers.
least common multiple |
|
greatest common factor |
|
absolute value |
|
least common factor |
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.
Simplify \( \sqrt{50} \)
| 6\( \sqrt{2} \) | |
| 4\( \sqrt{2} \) | |
| 5\( \sqrt{2} \) | |
| 9\( \sqrt{2} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{50} \)
\( \sqrt{25 \times 2} \)
\( \sqrt{5^2 \times 2} \)
5\( \sqrt{2} \)
If \( \left|c - 8\right| \) - 7 = -9, which of these is a possible value for c?
| -4 | |
| 15 | |
| -15 | |
| 6 |
First, solve for \( \left|c - 8\right| \):
\( \left|c - 8\right| \) - 7 = -9
\( \left|c - 8\right| \) = -9 + 7
\( \left|c - 8\right| \) = -2
The value inside the absolute value brackets can be either positive or negative so (c - 8) must equal - 2 or --2 for \( \left|c - 8\right| \) to equal -2:
| c - 8 = -2 c = -2 + 8 c = 6 | c - 8 = 2 c = 2 + 8 c = 10 |
So, c = 10 or c = 6.