| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.36 |
| Score | 0% | 67% |
In a class of 29 students, 10 are taking German and 12 are taking Spanish. Of the students studying German or Spanish, 3 are taking both courses. How many students are not enrolled in either course?
| 10 | |
| 22 | |
| 18 | |
| 26 |
The number of students taking German or Spanish is 10 + 12 = 22. Of that group of 22, 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 22 - 3 = 19 who are taking at least one language. 29 - 19 = 10 students who are not taking either language.
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 20% off." If Charlie buys two shirts, each with a regular price of $30, how much will he pay for both shirts?
| $54.00 | |
| $39.00 | |
| $31.50 | |
| $33.00 |
By buying two shirts, Charlie will save $30 x \( \frac{20}{100} \) = \( \frac{$30 x 20}{100} \) = \( \frac{$600}{100} \) = $6.00 on the second shirt.
So, his total cost will be
$30.00 + ($30.00 - $6.00)
$30.00 + $24.00
$54.00
What is \( \frac{7}{6} \) + \( \frac{9}{8} \)?
| \( \frac{9}{12} \) | |
| 2 \( \frac{1}{24} \) | |
| 2 \( \frac{6}{14} \) | |
| 2\(\frac{7}{24}\) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 6 and 8 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{7 x 4}{6 x 4} \) + \( \frac{9 x 3}{8 x 3} \)
\( \frac{28}{24} \) + \( \frac{27}{24} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{28 + 27}{24} \) = \( \frac{55}{24} \) = 2\(\frac{7}{24}\)
How many hours does it take a car to travel 30 miles at an average speed of 30 miles per hour?
| 8 hours | |
| 1 hour | |
| 3 hours | |
| 6 hours |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Solving for time:
time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{30mi}{30mph} \)
1 hour
What is \( \frac{3}{8} \) x \( \frac{3}{6} \)?
| \(\frac{1}{25}\) | |
| \(\frac{8}{27}\) | |
| \(\frac{1}{6}\) | |
| \(\frac{3}{16}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{3}{8} \) x \( \frac{3}{6} \) = \( \frac{3 x 3}{8 x 6} \) = \( \frac{9}{48} \) = \(\frac{3}{16}\)