| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.16 |
| Score | 0% | 63% |
Convert b-2 to remove the negative exponent.
| \( \frac{1}{b^2} \) | |
| \( \frac{-1}{-2b} \) | |
| \( \frac{-1}{b^{-2}} \) | |
| \( \frac{-2}{b} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
What is \( \frac{12\sqrt{18}}{6\sqrt{6}} \)?
| 3 \( \sqrt{2} \) | |
| 2 \( \sqrt{3} \) | |
| \(\frac{1}{3}\) \( \sqrt{2} \) | |
| 3 \( \sqrt{\frac{1}{2}} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{12\sqrt{18}}{6\sqrt{6}} \)
\( \frac{12}{6} \) \( \sqrt{\frac{18}{6}} \)
2 \( \sqrt{3} \)
If the ratio of home fans to visiting fans in a crowd is 3:1 and all 40,000 seats in a stadium are filled, how many home fans are in attendance?
| 24,000 | |
| 30,000 | |
| 25,333 | |
| 33,000 |
A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:
40,000 fans x \( \frac{3}{4} \) = \( \frac{120000}{4} \) = 30,000 fans.
The total water usage for a city is 5,000 gallons each day. Of that total, 12% is for personal use and 37% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 1,300 | |
| 2,900 | |
| 13,600 | |
| 1,250 |
37% of the water consumption is industrial use and 12% is personal use so (37% - 12%) = 25% more water is used for industrial purposes. 5,000 gallons are consumed daily so industry consumes \( \frac{25}{100} \) x 5,000 gallons = 1,250 gallons.
A triathlon course includes a 100m swim, a 40.8km bike ride, and a 4.7km run. What is the total length of the race course?
| 57.1km | |
| 54.8km | |
| 45.6km | |
| 43km |
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 100 meters to kilometers, divide the distance by 1000 to get 0.1km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.1km + 40.8km + 4.7km
total distance = 45.6km