| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.30 |
| Score | 0% | 66% |
In a class of 34 students, 13 are taking German and 11 are taking Spanish. Of the students studying German or Spanish, 5 are taking both courses. How many students are not enrolled in either course?
| 15 | |
| 34 | |
| 19 | |
| 24 |
The number of students taking German or Spanish is 13 + 11 = 24. Of that group of 24, 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 24 - 5 = 19 who are taking at least one language. 34 - 19 = 15 students who are not taking either language.
If the ratio of home fans to visiting fans in a crowd is 5:1 and all 42,000 seats in a stadium are filled, how many home fans are in attendance?
| 27,333 | |
| 32,000 | |
| 39,200 | |
| 35,000 |
A ratio of 5:1 means that there are 5 home fans for every one visiting fan. So, of every 6 fans, 5 are home fans and \( \frac{5}{6} \) of every fan in the stadium is a home fan:
42,000 fans x \( \frac{5}{6} \) = \( \frac{210000}{6} \) = 35,000 fans.
Simplify \( \sqrt{28} \)
| 7\( \sqrt{14} \) | |
| 9\( \sqrt{7} \) | |
| 9\( \sqrt{14} \) | |
| 2\( \sqrt{7} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{28} \)
\( \sqrt{4 \times 7} \)
\( \sqrt{2^2 \times 7} \)
2\( \sqrt{7} \)
What is the distance in miles of a trip that takes 9 hours at an average speed of 30 miles per hour?
| 240 miles | |
| 420 miles | |
| 80 miles | |
| 270 miles |
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 distance:
distance = \( \text{speed} \times \text{time} \)
distance = \( 30mph \times 9h \)
270 miles
Convert z-5 to remove the negative exponent.
| \( \frac{-5}{z} \) | |
| \( \frac{1}{z^5} \) | |
| \( \frac{-1}{z^{-5}} \) | |
| \( \frac{-5}{-z} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.