| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.53 |
| Score | 0% | 71% |
What is the distance in miles of a trip that takes 4 hours at an average speed of 15 miles per hour?
| 60 miles | |
| 110 miles | |
| 400 miles | |
| 225 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 = \( 15mph \times 4h \)
60 miles
Simplify \( \sqrt{48} \)
| 2\( \sqrt{6} \) | |
| 4\( \sqrt{3} \) | |
| 9\( \sqrt{3} \) | |
| 7\( \sqrt{6} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{48} \)
\( \sqrt{16 \times 3} \)
\( \sqrt{4^2 \times 3} \)
4\( \sqrt{3} \)
The total water usage for a city is 35,000 gallons each day. Of that total, 19% is for personal use and 30% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 6,000 | |
| 9,450 | |
| 650 | |
| 3,850 |
30% of the water consumption is industrial use and 19% is personal use so (30% - 19%) = 11% more water is used for industrial purposes. 35,000 gallons are consumed daily so industry consumes \( \frac{11}{100} \) x 35,000 gallons = 3,850 gallons.
Simplify \( \frac{32}{72} \).
| \( \frac{4}{9} \) | |
| \( \frac{9}{16} \) | |
| \( \frac{6}{17} \) | |
| \( \frac{1}{2} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 72 are [1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72]. They share 4 factors [1, 2, 4, 8] making 8 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{32}{72} \) = \( \frac{\frac{32}{8}}{\frac{72}{8}} \) = \( \frac{4}{9} \)
Convert c-2 to remove the negative exponent.
| \( \frac{-1}{c^{-2}} \) | |
| \( \frac{2}{c} \) | |
| \( \frac{1}{c^{-2}} \) | |
| \( \frac{1}{c^2} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.