| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.89 |
| Score | 0% | 58% |
What is \( 7 \)\( \sqrt{80} \) + \( 5 \)\( \sqrt{5} \)
| 35\( \sqrt{400} \) | |
| 12\( \sqrt{16} \) | |
| 12\( \sqrt{80} \) | |
| 33\( \sqrt{5} \) |
To add these radicals together their radicands must be the same:
7\( \sqrt{80} \) + 5\( \sqrt{5} \)
7\( \sqrt{16 \times 5} \) + 5\( \sqrt{5} \)
7\( \sqrt{4^2 \times 5} \) + 5\( \sqrt{5} \)
(7)(4)\( \sqrt{5} \) + 5\( \sqrt{5} \)
28\( \sqrt{5} \) + 5\( \sqrt{5} \)
Now that the radicands are identical, you can add them together:
28\( \sqrt{5} \) + 5\( \sqrt{5} \)A triathlon course includes a 200m swim, a 40.2km bike ride, and a 10.3km run. What is the total length of the race course?
| 50.7km | |
| 58.9km | |
| 45.7km | |
| 60.7km |
To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 200 meters to kilometers, divide the distance by 1000 to get 0.2km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.2km + 40.2km + 10.3km
total distance = 50.7km
If all of a roofing company's 4 workers are required to staff 2 roofing crews, how many workers need to be added during the busy season in order to send 7 complete crews out on jobs?
| 10 | |
| 17 | |
| 19 | |
| 11 |
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 4 workers at the company now and that's enough to staff 2 crews so there are \( \frac{4}{2} \) = 2 workers on a crew. 7 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 7 x 2 = 14 total workers to staff the crews during the busy season. The company already employs 4 workers so they need to add 14 - 4 = 10 new staff for the busy season.
What is the next number in this sequence: 1, 4, 10, 19, 31, __________ ?
| 46 | |
| 54 | |
| 44 | |
| 38 |
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
What is \( \frac{3}{4} \) - \( \frac{3}{12} \)?
| \(\frac{1}{2}\) | |
| \( \frac{6}{12} \) | |
| 2 \( \frac{8}{12} \) | |
| 1 \( \frac{6}{14} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 4 and 12 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{3 x 3}{4 x 3} \) - \( \frac{3 x 1}{12 x 1} \)
\( \frac{9}{12} \) - \( \frac{3}{12} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{9 - 3}{12} \) = \( \frac{6}{12} \) = \(\frac{1}{2}\)