| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.74 |
| Score | 0% | 55% |
Which of these numbers is a factor of 32?
| 2 | |
| 33 | |
| 26 | |
| 1 |
The factors of a number are all positive integers that divide evenly into the number. The factors of 32 are 1, 2, 4, 8, 16, 32.
Convert 9,433,000 to scientific notation.
| 94.33 x 105 | |
| 9.433 x 10-6 | |
| 9.433 x 107 | |
| 9.433 x 106 |
A number in scientific notation has the format 0.000 x 10exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:
9,433,000 in scientific notation is 9.433 x 106
Cooks are needed to prepare for a large party. Each cook can bake either 2 large cakes or 15 small cakes per hour. The kitchen is available for 4 hours and 37 large cakes and 200 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 | |
| 7 | |
| 15 |
If a single cook can bake 2 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 2 x 4 = 8 large cakes during that time. 37 large cakes are needed for the party so \( \frac{37}{8} \) = 4\(\frac{5}{8}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 15 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 15 x 4 = 60 small cakes during that time. 200 small cakes are needed for the party so \( \frac{200}{60} \) = 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 5 + 4 = 9 cooks.
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 7 to 2 and the ratio of baseball to basketball cards is 7 to 1, what is the ratio of football to basketball cards?
| 9:8 | |
| 5:1 | |
| 49:2 | |
| 5:8 |
The ratio of football cards to baseball cards is 7:2 and the ratio of baseball cards to basketball cards is 7:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 49:14 and the ratio of baseball cards to basketball cards as 14:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 49:14, 14:2 which reduces to 49:2.
A machine in a factory has an error rate of 8 parts per 100. The machine normally runs 24 hours a day and produces 9 parts per hour. Yesterday the machine was shut down for 8 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 132.5 | |
| 119.7 | |
| 145.6 | |
| 116.4 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{8}{100} \) x 9 = \( \frac{8 \times 9}{100} \) = \( \frac{72}{100} \) = 0.72 errors per hour
So, in an average hour, the machine will produce 9 - 0.72 = 8.28 error free parts.
The machine ran for 24 - 8 = 16 hours yesterday so you would expect that 16 x 8.28 = 132.5 error free parts were produced yesterday.