| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.42 |
| Score | 0% | 68% |
What is the distance in miles of a trip that takes 1 hour at an average speed of 65 miles per hour?
| 420 miles | |
| 65 miles | |
| 250 miles | |
| 280 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 = \( 65mph \times 1h \)
65 miles
In a class of 26 students, 7 are taking German and 12 are taking Spanish. Of the students studying German or Spanish, 2 are taking both courses. How many students are not enrolled in either course?
| 24 | |
| 9 | |
| 19 | |
| 18 |
The number of students taking German or Spanish is 7 + 12 = 19. Of that group of 19, 2 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 19 - 2 = 17 who are taking at least one language. 26 - 17 = 9 students who are not taking either language.
What is \( \frac{-7z^8}{7z^3} \)?
| -z5 | |
| -z\(\frac{3}{8}\) | |
| -z11 | |
| -z-5 |
To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:
\( \frac{-7z^8}{7z^3} \)
\( \frac{-7}{7} \) z(8 - 3)
-z5
What is \( \frac{4}{3} \) - \( \frac{7}{9} \)?
| \( \frac{3}{7} \) | |
| \( \frac{1}{9} \) | |
| 2 \( \frac{2}{7} \) | |
| \(\frac{5}{9}\) |
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 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [9, 18, 27, 36, 45] making 9 the smallest multiple 3 and 9 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{4 x 3}{3 x 3} \) - \( \frac{7 x 1}{9 x 1} \)
\( \frac{12}{9} \) - \( \frac{7}{9} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{12 - 7}{9} \) = \( \frac{5}{9} \) = \(\frac{5}{9}\)
What is the least common multiple of 6 and 8?
| 48 | |
| 24 | |
| 21 | |
| 40 |
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 have in common.