| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.18 |
| Score | 0% | 64% |
What is 4c4 + 3c4?
| -c-4 | |
| c-4 | |
| 7c16 | |
| 7c4 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:
4c4 + 3c4
(4 + 3)c4
7c4
Cooks are needed to prepare for a large party. Each cook can bake either 4 large cakes or 11 small cakes per hour. The kitchen is available for 3 hours and 31 large cakes and 170 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?
| 13 | |
| 5 | |
| 15 | |
| 9 |
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. 31 large cakes are needed for the party so \( \frac{31}{12} \) = 2\(\frac{7}{12}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 11 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 11 x 3 = 33 small cakes during that time. 170 small cakes are needed for the party so \( \frac{170}{33} \) = 5\(\frac{5}{33}\) 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 + 6 = 9 cooks.
The total water usage for a city is 20,000 gallons each day. Of that total, 32% is for personal use and 46% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 2,800 | |
| 4,400 | |
| 3,300 | |
| 2,850 |
46% of the water consumption is industrial use and 32% is personal use so (46% - 32%) = 14% more water is used for industrial purposes. 20,000 gallons are consumed daily so industry consumes \( \frac{14}{100} \) x 20,000 gallons = 2,800 gallons.
Find the average of the following numbers: 17, 9, 16, 10.
| 15 | |
| 13 | |
| 17 | |
| 16 |
To find the average of these 4 numbers add them together then divide by 4:
\( \frac{17 + 9 + 16 + 10}{4} \) = \( \frac{52}{4} \) = 13
Simplify \( \frac{40}{76} \).
| \( \frac{2}{3} \) | |
| \( \frac{10}{17} \) | |
| \( \frac{10}{19} \) | |
| \( \frac{1}{2} \) |
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 76 are [1, 2, 4, 19, 38, 76]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{40}{76} \) = \( \frac{\frac{40}{4}}{\frac{76}{4}} \) = \( \frac{10}{19} \)