| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.40 |
| Score | 0% | 68% |
Which of the following is an improper fraction?
\({2 \over 5} \) |
|
\(1 {2 \over 5} \) |
|
\({a \over 5} \) |
|
\({7 \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.
What is \( 8 \)\( \sqrt{27} \) + \( 3 \)\( \sqrt{3} \)
| 27\( \sqrt{3} \) | |
| 11\( \sqrt{81} \) | |
| 11\( \sqrt{27} \) | |
| 24\( \sqrt{9} \) |
To add these radicals together their radicands must be the same:
8\( \sqrt{27} \) + 3\( \sqrt{3} \)
8\( \sqrt{9 \times 3} \) + 3\( \sqrt{3} \)
8\( \sqrt{3^2 \times 3} \) + 3\( \sqrt{3} \)
(8)(3)\( \sqrt{3} \) + 3\( \sqrt{3} \)
24\( \sqrt{3} \) + 3\( \sqrt{3} \)
Now that the radicands are identical, you can add them together:
24\( \sqrt{3} \) + 3\( \sqrt{3} \)How many hours does it take a car to travel 270 miles at an average speed of 30 miles per hour?
| 8 hours | |
| 9 hours | |
| 7 hours | |
| 1 hour |
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 = \( \frac{270mi}{30mph} \)
9 hours
In a class of 25 students, 10 are taking German and 7 are taking Spanish. Of the students studying German or Spanish, 3 are taking both courses. How many students are not enrolled in either course?
| 25 | |
| 19 | |
| 17 | |
| 11 |
The number of students taking German or Spanish is 10 + 7 = 17. Of that group of 17, 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 17 - 3 = 14 who are taking at least one language. 25 - 14 = 11 students who are not taking either language.
If a car travels 120 miles in 2 hours, what is the average speed?
| 60 mph | |
| 65 mph | |
| 45 mph | |
| 30 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)