| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.51 |
| Score | 0% | 70% |
A triathlon course includes a 500m swim, a 20.1km bike ride, and a 17.700000000000003km run. What is the total length of the race course?
| 53km | |
| 28.5km | |
| 29km | |
| 38.3km |
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 500 meters to kilometers, divide the distance by 1000 to get 0.5km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.5km + 20.1km + 17.700000000000003km
total distance = 38.3km
Find the average of the following numbers: 16, 14, 16, 14.
| 12 | |
| 17 | |
| 14 | |
| 15 |
To find the average of these 4 numbers add them together then divide by 4:
\( \frac{16 + 14 + 16 + 14}{4} \) = \( \frac{60}{4} \) = 15
Simplify \( \sqrt{50} \)
| 5\( \sqrt{4} \) | |
| 9\( \sqrt{4} \) | |
| 5\( \sqrt{2} \) | |
| 2\( \sqrt{2} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{50} \)
\( \sqrt{25 \times 2} \)
\( \sqrt{5^2 \times 2} \)
5\( \sqrt{2} \)
Simplify \( \frac{36}{64} \).
| \( \frac{8}{11} \) | |
| \( \frac{9}{16} \) | |
| \( \frac{5}{8} \) | |
| \( \frac{9}{17} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] and the factors of 64 are [1, 2, 4, 8, 16, 32, 64]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{36}{64} \) = \( \frac{\frac{36}{4}}{\frac{64}{4}} \) = \( \frac{9}{16} \)
Convert y-3 to remove the negative exponent.
| \( \frac{-1}{y^{-3}} \) | |
| \( \frac{-3}{y} \) | |
| \( \frac{1}{y^{-3}} \) | |
| \( \frac{1}{y^3} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.