| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.24 |
| Score | 0% | 65% |
In a class of 36 students, 15 are taking German and 11 are taking Spanish. Of the students studying German or Spanish, 2 are taking both courses. How many students are not enrolled in either course?
| 22 | |
| 18 | |
| 12 | |
| 31 |
The number of students taking German or Spanish is 15 + 11 = 26. Of that group of 26, 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 26 - 2 = 24 who are taking at least one language. 36 - 24 = 12 students who are not taking either language.
What is the greatest common factor of 68 and 20?
| 3 | |
| 4 | |
| 20 | |
| 12 |
The factors of 68 are [1, 2, 4, 17, 34, 68] and the factors of 20 are [1, 2, 4, 5, 10, 20]. They share 3 factors [1, 2, 4] making 4 the greatest factor 68 and 20 have in common.
What is \( \frac{7a^8}{9a^2} \)?
| 1\(\frac{2}{7}\)a-6 | |
| 1\(\frac{2}{7}\)a6 | |
| \(\frac{7}{9}\)a-6 | |
| \(\frac{7}{9}\)a6 |
To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:
\( \frac{7a^8}{9a^2} \)
\( \frac{7}{9} \) a(8 - 2)
\(\frac{7}{9}\)a6
The __________ is the smallest positive integer that is a multiple of two or more integers.
greatest common factor |
|
least common factor |
|
least common multiple |
|
absolute value |
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.
Convert a-4 to remove the negative exponent.
| \( \frac{1}{a^4} \) | |
| \( \frac{1}{a^{-4}} \) | |
| \( \frac{-1}{a^{-4}} \) | |
| \( \frac{-4}{-a} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.