| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.17 |
| Score | 0% | 63% |
In a class of 28 students, 15 are taking German and 6 are taking Spanish. Of the students studying German or Spanish, 5 are taking both courses. How many students are not enrolled in either course?
| 23 | |
| 12 | |
| 14 | |
| 17 |
The number of students taking German or Spanish is 15 + 6 = 21. Of that group of 21, 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 21 - 5 = 16 who are taking at least one language. 28 - 16 = 12 students who are not taking either language.
Find the average of the following numbers: 8, 4, 10, 2.
| 1 | |
| 6 | |
| 9 | |
| 4 |
To find the average of these 4 numbers add them together then divide by 4:
\( \frac{8 + 4 + 10 + 2}{4} \) = \( \frac{24}{4} \) = 6
What is \( \frac{4}{3} \) - \( \frac{7}{5} \)?
| 1 \( \frac{7}{15} \) | |
| 2 \( \frac{3}{15} \) | |
| -\(\frac{1}{15}\) | |
| \( \frac{1}{15} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]. The first few multiples they share are [15, 30, 45, 60, 75] making 15 the smallest multiple 3 and 5 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{4 x 5}{3 x 5} \) - \( \frac{7 x 3}{5 x 3} \)
\( \frac{20}{15} \) - \( \frac{21}{15} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{20 - 21}{15} \) = \( \frac{-1}{15} \) = -\(\frac{1}{15}\)
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 15% off." If Frank buys two shirts, each with a regular price of $20, how much will he pay for both shirts?
| $28.00 | |
| $37.00 | |
| $26.00 | |
| $29.00 |
By buying two shirts, Frank will save $20 x \( \frac{15}{100} \) = \( \frac{$20 x 15}{100} \) = \( \frac{$300}{100} \) = $3.00 on the second shirt.
So, his total cost will be
$20.00 + ($20.00 - $3.00)
$20.00 + $17.00
$37.00
Simplify \( \sqrt{48} \)
| 5\( \sqrt{6} \) | |
| 9\( \sqrt{6} \) | |
| 4\( \sqrt{3} \) | |
| 6\( \sqrt{6} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{48} \)
\( \sqrt{16 \times 3} \)
\( \sqrt{4^2 \times 3} \)
4\( \sqrt{3} \)