| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.31 |
| Score | 0% | 66% |
What is the greatest common factor of 32 and 28?
| 23 | |
| 4 | |
| 22 | |
| 19 |
The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 28 are [1, 2, 4, 7, 14, 28]. They share 3 factors [1, 2, 4] making 4 the greatest factor 32 and 28 have in common.
A triathlon course includes a 300m swim, a 20.9km bike ride, and a 12.5km run. What is the total length of the race course?
| 32.1km | |
| 34.8km | |
| 33.7km | |
| 56.1km |
To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 300 meters to kilometers, divide the distance by 1000 to get 0.3km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.3km + 20.9km + 12.5km
total distance = 33.7km
What is \( \frac{-4c^6}{6c^2} \)?
| -\(\frac{2}{3}\)c4 | |
| -\(\frac{2}{3}\)c3 | |
| -\(\frac{2}{3}\)c\(\frac{1}{3}\) | |
| -\(\frac{2}{3}\)c-4 |
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:
\( \frac{-4c^6}{6c^2} \)
\( \frac{-4}{6} \) c(6 - 2)
-\(\frac{2}{3}\)c4
If the ratio of home fans to visiting fans in a crowd is 4:1 and all 32,000 seats in a stadium are filled, how many home fans are in attendance?
| 28,333 | |
| 25,600 | |
| 25,333 | |
| 30,000 |
A ratio of 4:1 means that there are 4 home fans for every one visiting fan. So, of every 5 fans, 4 are home fans and \( \frac{4}{5} \) of every fan in the stadium is a home fan:
32,000 fans x \( \frac{4}{5} \) = \( \frac{128000}{5} \) = 25,600 fans.
What is the least common multiple of 4 and 6?
| 24 | |
| 12 | |
| 5 | |
| 6 |
The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] 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 [12, 24, 36, 48, 60] making 12 the smallest multiple 4 and 6 have in common.