| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.25 |
| Score | 0% | 65% |
What is the next number in this sequence: 1, 3, 7, 13, 21, __________ ?
| 40 | |
| 35 | |
| 31 | |
| 30 |
The equation for this sequence is:
an = an-1 + 2(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 + 2(6 - 1)
a6 = 21 + 2(5)
a6 = 31
A triathlon course includes a 400m swim, a 50.7km bike ride, and a 6.1km run. What is the total length of the race course?
| 57.2km | |
| 48km | |
| 54.5km | |
| 33.7km |
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 400 meters to kilometers, divide the distance by 1000 to get 0.4km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.4km + 50.7km + 6.1km
total distance = 57.2km
Simplify \( \sqrt{27} \)
| 5\( \sqrt{6} \) | |
| 3\( \sqrt{3} \) | |
| 6\( \sqrt{6} \) | |
| 4\( \sqrt{3} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{27} \)
\( \sqrt{9 \times 3} \)
\( \sqrt{3^2 \times 3} \)
3\( \sqrt{3} \)
How many hours does it take a car to travel 450 miles at an average speed of 50 miles per hour?
| 2 hours | |
| 9 hours | |
| 5 hours | |
| 6 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 = \( \frac{450mi}{50mph} \)
9 hours
Cooks are needed to prepare for a large party. Each cook can bake either 4 large cakes or 10 small cakes per hour. The kitchen is available for 3 hours and 27 large cakes and 100 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 | |
| 11 | |
| 6 |
If a single cook can bake 4 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 4 x 3 = 12 large cakes during that time. 27 large cakes are needed for the party so \( \frac{27}{12} \) = 2\(\frac{1}{4}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 10 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 10 x 3 = 30 small cakes during that time. 100 small cakes are needed for the party so \( \frac{100}{30} \) = 3\(\frac{1}{3}\) 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.