| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.35 |
| Score | 0% | 67% |
The total water usage for a city is 15,000 gallons each day. Of that total, 12% is for personal use and 38% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 3,900 | |
| 2,200 | |
| 9,500 | |
| 5,500 |
38% of the water consumption is industrial use and 12% is personal use so (38% - 12%) = 26% more water is used for industrial purposes. 15,000 gallons are consumed daily so industry consumes \( \frac{26}{100} \) x 15,000 gallons = 3,900 gallons.
Diane scored 84% on her final exam. If each question was worth 3 points and there were 150 possible points on the exam, how many questions did Diane answer correctly?
| 48 | |
| 38 | |
| 28 | |
| 42 |
Diane scored 84% on the test meaning she earned 84% of the possible points on the test. There were 150 possible points on the test so she earned 150 x 0.84 = 126 points. Each question is worth 3 points so she got \( \frac{126}{3} \) = 42 questions right.
What is \( \frac{20\sqrt{6}}{4\sqrt{3}} \)?
| \(\frac{1}{2}\) \( \sqrt{5} \) | |
| \(\frac{1}{5}\) \( \sqrt{2} \) | |
| 2 \( \sqrt{5} \) | |
| 5 \( \sqrt{2} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{20\sqrt{6}}{4\sqrt{3}} \)
\( \frac{20}{4} \) \( \sqrt{\frac{6}{3}} \)
5 \( \sqrt{2} \)
What is -7x5 x 4x7?
| -3x7 | |
| -28x12 | |
| -3x5 | |
| -3x12 |
To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:
-7x5 x 4x7
(-7 x 4)x(5 + 7)
-28x12
What is the least common multiple of 2 and 4?
| 6 | |
| 2 | |
| 4 | |
| 7 |
The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40]. The first few multiples they share are [4, 8, 12, 16, 20] making 4 the smallest multiple 2 and 4 have in common.