| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.58 |
| Score | 0% | 72% |
Which of the following is not a prime number?
2 |
|
5 |
|
7 |
|
9 |
A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.
What is the distance in miles of a trip that takes 1 hour at an average speed of 70 miles per hour?
| 55 miles | |
| 240 miles | |
| 70 miles | |
| 450 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 = \( 70mph \times 1h \)
70 miles
4! = ?
4 x 3 x 2 x 1 |
|
4 x 3 |
|
3 x 2 x 1 |
|
5 x 4 x 3 x 2 x 1 |
A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
In a class of 25 students, 6 are taking German and 12 are taking Spanish. Of the students studying German or Spanish, 6 are taking both courses. How many students are not enrolled in either course?
| 18 | |
| 12 | |
| 13 | |
| 25 |
The number of students taking German or Spanish is 6 + 12 = 18. Of that group of 18, 6 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 18 - 6 = 12 who are taking at least one language. 25 - 12 = 13 students who are not taking either language.
What is \( \frac{6}{2} \) - \( \frac{6}{6} \)?
| 1 \( \frac{7}{11} \) | |
| 2 \( \frac{4}{11} \) | |
| 2 \( \frac{8}{14} \) | |
| 2 |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [6, 12, 18, 24, 30] making 6 the smallest multiple 2 and 6 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{6 x 3}{2 x 3} \) - \( \frac{6 x 1}{6 x 1} \)
\( \frac{18}{6} \) - \( \frac{6}{6} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{18 - 6}{6} \) = \( \frac{12}{6} \) = 2