| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.63 |
| Score | 0% | 53% |
The total water usage for a city is 20,000 gallons each day. Of that total, 20% is for personal use and 39% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 2,000 | |
| 3,800 | |
| 13,500 | |
| 7,350 |
39% of the water consumption is industrial use and 20% is personal use so (39% - 20%) = 19% more water is used for industrial purposes. 20,000 gallons are consumed daily so industry consumes \( \frac{19}{100} \) x 20,000 gallons = 3,800 gallons.
On average, the center for a basketball team hits 25% of his shots while a guard on the same team hits 40% of his shots. If the guard takes 30 shots during a game, how many shots will the center have to take to score as many points as the guard assuming each shot is worth the same number of points?
| 36 | |
| 24 | |
| 48 | |
| 39 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 30 x \( \frac{40}{100} \) = \( \frac{40 x 30}{100} \) = \( \frac{1200}{100} \) = 12 shots
The center makes 25% of his shots so he'll have to take:
shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)
to make as many shots as the guard. Plugging in values for the center gives us:
center shots taken = \( \frac{12}{\frac{25}{100}} \) = 12 x \( \frac{100}{25} \) = \( \frac{12 x 100}{25} \) = \( \frac{1200}{25} \) = 48 shots
to make the same number of shots as the guard and thus score the same number of points.
If there were a total of 350 raffle tickets sold and you bought 10 tickets, what's the probability that you'll win the raffle?
| 15% | |
| 3% | |
| 6% | |
| 12% |
You have 10 out of the total of 350 raffle tickets sold so you have a (\( \frac{10}{350} \)) x 100 = \( \frac{10 \times 100}{350} \) = \( \frac{1000}{350} \) = 3% chance to win the raffle.
Convert x-2 to remove the negative exponent.
| \( \frac{-1}{-2x} \) | |
| \( \frac{-2}{x} \) | |
| \( \frac{1}{x^{-2}} \) | |
| \( \frac{1}{x^2} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
What is \( 2 \)\( \sqrt{175} \) + \( 6 \)\( \sqrt{7} \)
| 8\( \sqrt{1225} \) | |
| 12\( \sqrt{7} \) | |
| 16\( \sqrt{7} \) | |
| 12\( \sqrt{175} \) |
To add these radicals together their radicands must be the same:
2\( \sqrt{175} \) + 6\( \sqrt{7} \)
2\( \sqrt{25 \times 7} \) + 6\( \sqrt{7} \)
2\( \sqrt{5^2 \times 7} \) + 6\( \sqrt{7} \)
(2)(5)\( \sqrt{7} \) + 6\( \sqrt{7} \)
10\( \sqrt{7} \) + 6\( \sqrt{7} \)
Now that the radicands are identical, you can add them together:
10\( \sqrt{7} \) + 6\( \sqrt{7} \)