| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.62 |
| Score | 0% | 52% |
The total water usage for a city is 25,000 gallons each day. Of that total, 17% is for personal use and 41% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 14,499 | |
| 6,000 | |
| 9,450 | |
| 10,000 |
41% of the water consumption is industrial use and 17% is personal use so (41% - 17%) = 24% more water is used for industrial purposes. 25,000 gallons are consumed daily so industry consumes \( \frac{24}{100} \) x 25,000 gallons = 6,000 gallons.
If the ratio of home fans to visiting fans in a crowd is 4:1 and all 33,000 seats in a stadium are filled, how many home fans are in attendance?
| 20,000 | |
| 26,400 | |
| 35,833 | |
| 24,800 |
A ratio of 4:1 means that there are 4 home fans for every one visiting fan. So, of every 5 fans, 4 are home fans and \( \frac{4}{5} \) of every fan in the stadium is a home fan:
33,000 fans x \( \frac{4}{5} \) = \( \frac{132000}{5} \) = 26,400 fans.
What is the next number in this sequence: 1, 4, 10, 19, 31, __________ ?
| 46 | |
| 51 | |
| 48 | |
| 45 |
The equation for this sequence is:
an = an-1 + 3(n - 1)
where n is the term's order in the sequence, an is the value of the term, and an-1 is the value of the term before an. This makes the next number:
a6 = a5 + 3(6 - 1)
a6 = 31 + 3(5)
a6 = 46
If a rectangle is twice as long as it is wide and has a perimeter of 18 meters, what is the area of the rectangle?
| 2 m2 | |
| 72 m2 | |
| 162 m2 | |
| 18 m2 |
The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 18 meters so the equation becomes: 2w + 2h = 18.
Putting these two equations together and solving for width (w):
2w + 2h = 18
w + h = \( \frac{18}{2} \)
w + h = 9
w = 9 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 9 - 2w
3w = 9
w = \( \frac{9}{3} \)
w = 3
Since h = 2w that makes h = (2 x 3) = 6 and the area = h x w = 3 x 6 = 18 m2
What is \( 2 \)\( \sqrt{20} \) - \( 5 \)\( \sqrt{5} \)
| -3\( \sqrt{20} \) | |
| 10\( \sqrt{5} \) | |
| -3\( \sqrt{21} \) | |
| -1\( \sqrt{5} \) |
To subtract these radicals together their radicands must be the same:
2\( \sqrt{20} \) - 5\( \sqrt{5} \)
2\( \sqrt{4 \times 5} \) - 5\( \sqrt{5} \)
2\( \sqrt{2^2 \times 5} \) - 5\( \sqrt{5} \)
(2)(2)\( \sqrt{5} \) - 5\( \sqrt{5} \)
4\( \sqrt{5} \) - 5\( \sqrt{5} \)
Now that the radicands are identical, you can subtract them:
4\( \sqrt{5} \) - 5\( \sqrt{5} \)