| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.36 |
| Score | 0% | 67% |
If all of a roofing company's 6 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?
| 17 | |
| 7 | |
| 15 | |
| 6 |
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 6 workers at the company now and that's enough to staff 2 crews so there are \( \frac{6}{2} \) = 3 workers on a crew. 7 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 7 x 3 = 21 total workers to staff the crews during the busy season. The company already employs 6 workers so they need to add 21 - 6 = 15 new staff for the busy season.
How many hours does it take a car to travel 40 miles at an average speed of 20 miles per hour?
| 1 hour | |
| 2 hours | |
| 4 hours | |
| 8 hours |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Solving for time:
time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{40mi}{20mph} \)
2 hours
Simplify \( \frac{40}{72} \).
| \( \frac{5}{9} \) | |
| \( \frac{7}{17} \) | |
| \( \frac{3}{10} \) | |
| \( \frac{3}{7} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40] and the factors of 72 are [1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72]. They share 4 factors [1, 2, 4, 8] making 8 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{40}{72} \) = \( \frac{\frac{40}{8}}{\frac{72}{8}} \) = \( \frac{5}{9} \)
If the ratio of home fans to visiting fans in a crowd is 3:1 and all 32,000 seats in a stadium are filled, how many home fans are in attendance?
| 30,667 | |
| 23,250 | |
| 39,167 | |
| 24,000 |
A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:
32,000 fans x \( \frac{3}{4} \) = \( \frac{96000}{4} \) = 24,000 fans.
What is the next number in this sequence: 1, 5, 13, 25, 41, __________ ?
| 66 | |
| 65 | |
| 61 | |
| 67 |
The equation for this sequence is:
an = an-1 + 4(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 + 4(6 - 1)
a6 = 41 + 4(5)
a6 = 61