| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.76 |
| Score | 0% | 55% |
If the ratio of home fans to visiting fans in a crowd is 4:1 and all 33,000 seats in a stadium are filled, how many home fans are in attendance?
| 33,600 | |
| 24,667 | |
| 32,667 | |
| 26,400 |
A ratio of 4:1 means that there are 4 home fans for every one visiting fan. So, of every 5 fans, 4 are home fans and \( \frac{4}{5} \) of every fan in the stadium is a home fan:
33,000 fans x \( \frac{4}{5} \) = \( \frac{132000}{5} \) = 26,400 fans.
Which of the following statements about exponents is false?
all of these are false |
|
b0 = 1 |
|
b1 = b |
|
b1 = 1 |
A number with an exponent (be) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b1 = b) and a base with an exponent of 0 equals 1 ( (b0 = 1).
| 5.4 | |
| 2.0 | |
| 1 | |
| 6.0 |
1
What is (a4)4?
| 4a4 | |
| a16 | |
| a8 | |
| a0 |
To raise a term with an exponent to another exponent, retain the base and multiply the exponents:
(a4)4A machine in a factory has an error rate of 9 parts per 100. The machine normally runs 24 hours a day and produces 7 parts per hour. Yesterday the machine was shut down for 2 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 140.1 | |
| 98.9 | |
| 100.1 | |
| 100.8 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{9}{100} \) x 7 = \( \frac{9 \times 7}{100} \) = \( \frac{63}{100} \) = 0.63 errors per hour
So, in an average hour, the machine will produce 7 - 0.63 = 6.37 error free parts.
The machine ran for 24 - 2 = 22 hours yesterday so you would expect that 22 x 6.37 = 140.1 error free parts were produced yesterday.