| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.88 |
| Score | 0% | 58% |
What is 9\( \sqrt{8} \) x 2\( \sqrt{7} \)?
| 11\( \sqrt{56} \) | |
| 18\( \sqrt{15} \) | |
| 36\( \sqrt{14} \) | |
| 18\( \sqrt{8} \) |
To multiply terms with radicals, multiply the coefficients and radicands separately:
9\( \sqrt{8} \) x 2\( \sqrt{7} \)
(9 x 2)\( \sqrt{8 \times 7} \)
18\( \sqrt{56} \)
Now we need to simplify the radical:
18\( \sqrt{56} \)
18\( \sqrt{14 \times 4} \)
18\( \sqrt{14 \times 2^2} \)
(18)(2)\( \sqrt{14} \)
36\( \sqrt{14} \)
If all of a roofing company's 12 workers are required to staff 4 roofing crews, how many workers need to be added during the busy season in order to send 6 complete crews out on jobs?
| 2 | |
| 6 | |
| 10 | |
| 3 |
In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 12 workers at the company now and that's enough to staff 4 crews so there are \( \frac{12}{4} \) = 3 workers on a crew. 6 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 6 x 3 = 18 total workers to staff the crews during the busy season. The company already employs 12 workers so they need to add 18 - 12 = 6 new staff for the busy season.
How many 13-passenger vans will it take to drive all 83 members of the football team to an away game?
| 9 vans | |
| 13 vans | |
| 8 vans | |
| 7 vans |
Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:
vans = \( \frac{83}{13} \) = 6\(\frac{5}{13}\)
So, it will take 6 full vans and one partially full van to transport the entire team making a total of 7 vans.
Cooks are needed to prepare for a large party. Each cook can bake either 4 large cakes or 17 small cakes per hour. The kitchen is available for 4 hours and 36 large cakes and 210 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?
| 7 | |
| 13 | |
| 14 | |
| 10 |
If a single cook can bake 4 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 4 x 4 = 16 large cakes during that time. 36 large cakes are needed for the party so \( \frac{36}{16} \) = 2\(\frac{1}{4}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 17 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 17 x 4 = 68 small cakes during that time. 210 small cakes are needed for the party so \( \frac{210}{68} \) = 3\(\frac{3}{34}\) 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 3 + 4 = 7 cooks.
Roger loaned Latoya $1,200 at an annual interest rate of 3%. If no payments are made, what is the total amount owed at the end of the first year?
| $1,236 | |
| $1,284 | |
| $1,224 | |
| $1,272 |
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 $1,200
i = 0.03 x $1,200
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $1,200 + $36