| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.04 |
| Score | 0% | 61% |
The total water usage for a city is 50,000 gallons each day. Of that total, 25% is for personal use and 35% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 4,800 | |
| 5,000 | |
| 4,500 | |
| 2,000 |
35% of the water consumption is industrial use and 25% is personal use so (35% - 25%) = 10% more water is used for industrial purposes. 50,000 gallons are consumed daily so industry consumes \( \frac{10}{100} \) x 50,000 gallons = 5,000 gallons.
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 10% off." If Monty buys two shirts, each with a regular price of $45, how much money will he save?
| $20.25 | |
| $13.50 | |
| $18.00 | |
| $4.50 |
By buying two shirts, Monty will save $45 x \( \frac{10}{100} \) = \( \frac{$45 x 10}{100} \) = \( \frac{$450}{100} \) = $4.50 on the second shirt.
If \(\left|a\right| = 7\), which of the following best describes a?
a = -7 |
|
a = 7 |
|
a = 7 or a = -7 |
|
none of these is correct |
The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).
Cooks are needed to prepare for a large party. Each cook can bake either 5 large cakes or 16 small cakes per hour. The kitchen is available for 3 hours and 28 large cakes and 300 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?
| 8 | |
| 14 | |
| 9 | |
| 13 |
If a single cook can bake 5 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 5 x 3 = 15 large cakes during that time. 28 large cakes are needed for the party so \( \frac{28}{15} \) = 1\(\frac{13}{15}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 16 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 16 x 3 = 48 small cakes during that time. 300 small cakes are needed for the party so \( \frac{300}{48} \) = 6\(\frac{1}{4}\) 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 2 + 7 = 9 cooks.
Solve for \( \frac{5!}{6!} \)
| \( \frac{1}{4} \) | |
| \( \frac{1}{42} \) | |
| 336 | |
| \( \frac{1}{6} \) |
A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:
\( \frac{5!}{6!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6} \)
\( \frac{1}{6} \)