| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.81 |
| Score | 0% | 56% |
Convert z-5 to remove the negative exponent.
| \( \frac{-1}{-5z^{5}} \) | |
| \( \frac{1}{z^5} \) | |
| \( \frac{-1}{-5z} \) | |
| \( \frac{-5}{z} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
What is \( 3 \)\( \sqrt{32} \) - \( 8 \)\( \sqrt{2} \)
| -5\( \sqrt{64} \) | |
| 24\( \sqrt{16} \) | |
| -5\( \sqrt{-12} \) | |
| 4\( \sqrt{2} \) |
To subtract these radicals together their radicands must be the same:
3\( \sqrt{32} \) - 8\( \sqrt{2} \)
3\( \sqrt{16 \times 2} \) - 8\( \sqrt{2} \)
3\( \sqrt{4^2 \times 2} \) - 8\( \sqrt{2} \)
(3)(4)\( \sqrt{2} \) - 8\( \sqrt{2} \)
12\( \sqrt{2} \) - 8\( \sqrt{2} \)
Now that the radicands are identical, you can subtract them:
12\( \sqrt{2} \) - 8\( \sqrt{2} \)If the ratio of home fans to visiting fans in a crowd is 2:1 and all 50,000 seats in a stadium are filled, how many home fans are in attendance?
| 24,750 | |
| 33,333 | |
| 30,000 | |
| 24,000 |
A ratio of 2:1 means that there are 2 home fans for every one visiting fan. So, of every 3 fans, 2 are home fans and \( \frac{2}{3} \) of every fan in the stadium is a home fan:
50,000 fans x \( \frac{2}{3} \) = \( \frac{100000}{3} \) = 33,333 fans.
A bread recipe calls for 2\(\frac{1}{8}\) cups of flour. If you only have \(\frac{1}{8}\) cup, how much more flour is needed?
| 1\(\frac{1}{2}\) cups | |
| 2 cups | |
| 1\(\frac{3}{8}\) cups | |
| 1\(\frac{7}{8}\) cups |
The amount of flour you need is (2\(\frac{1}{8}\) - \(\frac{1}{8}\)) cups. Rewrite the quantities so they share a common denominator and subtract:
(\( \frac{17}{8} \) - \( \frac{1}{8} \)) cups
\( \frac{16}{8} \) cups
2 cups
In a class of 27 students, 10 are taking German and 14 are taking Spanish. Of the students studying German or Spanish, 3 are taking both courses. How many students are not enrolled in either course?
| 13 | |
| 19 | |
| 6 | |
| 15 |
The number of students taking German or Spanish is 10 + 14 = 24. Of that group of 24, 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 24 - 3 = 21 who are taking at least one language. 27 - 21 = 6 students who are not taking either language.