| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.05 |
| Score | 0% | 61% |
Cooks are needed to prepare for a large party. Each cook can bake either 5 large cakes or 16 small cakes per hour. The kitchen is available for 4 hours and 30 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?
| 10 | |
| 9 | |
| 14 | |
| 7 |
If a single cook can bake 5 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 5 x 4 = 20 large cakes during that time. 30 large cakes are needed for the party so \( \frac{30}{20} \) = 1\(\frac{1}{2}\) 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 4 hours, a single cook can bake 16 x 4 = 64 small cakes during that time. 460 small cakes are needed for the party so \( \frac{460}{64} \) = 7\(\frac{3}{16}\) 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 2 + 8 = 10 cooks.
What is the next number in this sequence: 1, 4, 10, 19, 31, __________ ?
| 51 | |
| 38 | |
| 46 | |
| 39 |
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 \( \frac{3}{5} \) + \( \frac{9}{7} \)?
| 1 \( \frac{3}{35} \) | |
| 1\(\frac{31}{35}\) | |
| \( \frac{3}{35} \) | |
| 1 \( \frac{7}{35} \) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [35, 70] making 35 the smallest multiple 5 and 7 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{3 x 7}{5 x 7} \) + \( \frac{9 x 5}{7 x 5} \)
\( \frac{21}{35} \) + \( \frac{45}{35} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{21 + 45}{35} \) = \( \frac{66}{35} \) = 1\(\frac{31}{35}\)
Convert c-3 to remove the negative exponent.
| \( \frac{-1}{-3c} \) | |
| \( \frac{1}{c^3} \) | |
| \( \frac{-1}{-3c^{3}} \) | |
| \( \frac{1}{c^{-3}} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
A triathlon course includes a 200m swim, a 30.2km bike ride, and a 18.200000000000003km run. What is the total length of the race course?
| 36.6km | |
| 48.6km | |
| 31.8km | |
| 41.1km |
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 + 30.2km + 18.200000000000003km
total distance = 48.6km