| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.77 |
| Score | 0% | 55% |
What is 9\( \sqrt{2} \) x 2\( \sqrt{7} \)?
| 18\( \sqrt{9} \) | |
| 18\( \sqrt{14} \) | |
| 18\( \sqrt{2} \) | |
| 18\( \sqrt{7} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
9\( \sqrt{2} \) x 2\( \sqrt{7} \)
(9 x 2)\( \sqrt{2 \times 7} \)
18\( \sqrt{14} \)
In a class of 32 students, 12 are taking German and 14 are taking Spanish. Of the students studying German or Spanish, 5 are taking both courses. How many students are not enrolled in either course?
| 14 | |
| 29 | |
| 31 | |
| 11 |
The number of students taking German or Spanish is 12 + 14 = 26. Of that group of 26, 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 26 - 5 = 21 who are taking at least one language. 32 - 21 = 11 students who are not taking either language.
Convert b-3 to remove the negative exponent.
| \( \frac{1}{b^3} \) | |
| \( \frac{-1}{-3b} \) | |
| \( \frac{-1}{b^{-3}} \) | |
| \( \frac{-3}{-b} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
Solve 5 + (4 + 5) ÷ 3 x 4 - 52
| \(\frac{3}{5}\) | |
| \(\frac{1}{3}\) | |
| -8 | |
| \(\frac{2}{9}\) |
Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):
5 + (4 + 5) ÷ 3 x 4 - 52
P: 5 + (9) ÷ 3 x 4 - 52
E: 5 + 9 ÷ 3 x 4 - 25
MD: 5 + \( \frac{9}{3} \) x 4 - 25
MD: 5 + \( \frac{36}{3} \) - 25
AS: \( \frac{15}{3} \) + \( \frac{36}{3} \) - 25
AS: \( \frac{51}{3} \) - 25
AS: \( \frac{51 - 75}{3} \)
\( \frac{-24}{3} \)
-8
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 9 to 2 and the ratio of baseball to basketball cards is 9 to 1, what is the ratio of football to basketball cards?
| 81:2 | |
| 3:1 | |
| 7:1 | |
| 5:1 |
The ratio of football cards to baseball cards is 9:2 and the ratio of baseball cards to basketball cards is 9:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 81:18 and the ratio of baseball cards to basketball cards as 18:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 81:18, 18:2 which reduces to 81:2.