| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.69 |
| Score | 0% | 54% |
The total water usage for a city is 25,000 gallons each day. Of that total, 21% 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?
| 5,000 | |
| 9,000 | |
| 4,250 | |
| 12,800 |
38% of the water consumption is industrial use and 21% is personal use so (38% - 21%) = 17% more water is used for industrial purposes. 25,000 gallons are consumed daily so industry consumes \( \frac{17}{100} \) x 25,000 gallons = 4,250 gallons.
Cooks are needed to prepare for a large party. Each cook can bake either 3 large cakes or 15 small cakes per hour. The kitchen is available for 2 hours and 37 large cakes and 160 small cakes need to be baked.
How many cooks are required to bake the required number of cakes during the time the kitchen is available?
| 29 | |
| 13 | |
| 6 | |
| 55 |
If a single cook can bake 3 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 3 x 2 = 6 large cakes during that time. 37 large cakes are needed for the party so \( \frac{37}{6} \) = 6\(\frac{1}{6}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 15 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 15 x 2 = 30 small cakes during that time. 160 small cakes are needed for the party so \( \frac{160}{30} \) = 5\(\frac{1}{3}\) cooks are needed to bake the required number of small cakes.
Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 7 + 6 = 13 cooks.
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 3 to 2 and the ratio of baseball to basketball cards is 3 to 1, what is the ratio of football to basketball cards?
| 9:4 | |
| 9:2 | |
| 1:1 | |
| 9:6 |
The ratio of football cards to baseball cards is 3:2 and the ratio of baseball cards to basketball cards is 3:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 9:6 and the ratio of baseball cards to basketball cards as 6:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 9:6, 6:2 which reduces to 9:2.
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?
| 8 m2 | |
| 32 m2 | |
| 2 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 8a3 - 4a3?
| -4a3 | |
| 12a9 | |
| 4a3 | |
| -4a-3 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:
8a3 - 4a3
(8 - 4)a3
4a3