| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.66 |
| Score | 0% | 53% |
What is \( 6 \)\( \sqrt{75} \) - \( 5 \)\( \sqrt{3} \)
| 30\( \sqrt{25} \) | |
| 25\( \sqrt{3} \) | |
| \( \sqrt{3} \) | |
| 30\( \sqrt{75} \) |
To subtract these radicals together their radicands must be the same:
6\( \sqrt{75} \) - 5\( \sqrt{3} \)
6\( \sqrt{25 \times 3} \) - 5\( \sqrt{3} \)
6\( \sqrt{5^2 \times 3} \) - 5\( \sqrt{3} \)
(6)(5)\( \sqrt{3} \) - 5\( \sqrt{3} \)
30\( \sqrt{3} \) - 5\( \sqrt{3} \)
Now that the radicands are identical, you can subtract them:
30\( \sqrt{3} \) - 5\( \sqrt{3} \)The total water usage for a city is 25,000 gallons each day. Of that total, 34% is for personal use and 65% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 1,300 | |
| 12,000 | |
| 7,750 | |
| 6,500 |
65% of the water consumption is industrial use and 34% is personal use so (65% - 34%) = 31% more water is used for industrial purposes. 25,000 gallons are consumed daily so industry consumes \( \frac{31}{100} \) x 25,000 gallons = 7,750 gallons.
A tiger in a zoo has consumed 60 pounds of food in 5 days. If the tiger continues to eat at the same rate, in how many more days will its total food consumtion be 120 pounds?
| 5 | |
| 4 | |
| 32 | |
| 3 |
If the tiger has consumed 60 pounds of food in 5 days that's \( \frac{60}{5} \) = 12 pounds of food per day. The tiger needs to consume 120 - 60 = 60 more pounds of food to reach 120 pounds total. At 12 pounds of food per day that's \( \frac{60}{12} \) = 5 more days.
Damon loaned Frank $100 at an annual interest rate of 9%. If no payments are made, what is the interest owed on this loan at the end of the first year?
| $8 | |
| $9 | |
| $36 | |
| $56 |
The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:
interest = annual interest rate x loan amount
i = (\( \frac{6}{100} \)) x $100
i = 0.09 x $100
i = $9
Cooks are needed to prepare for a large party. Each cook can bake either 3 large cakes or 16 small cakes per hour. The kitchen is available for 2 hours and 21 large cakes and 460 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?
| 13 | |
| 19 | |
| 14 | |
| 15 |
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. 21 large cakes are needed for the party so \( \frac{21}{6} \) = 3\(\frac{1}{2}\) 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 2 hours, a single cook can bake 16 x 2 = 32 small cakes during that time. 460 small cakes are needed for the party so \( \frac{460}{32} \) = 14\(\frac{3}{8}\) 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 4 + 15 = 19 cooks.