College Math Placement Practice Test

If the failure rate of a factory is 0.15%, how many functional gears would be produced from 8000 gears?

1. 7960 gears

2. 8000 gears

3. 7920 gears

4. 7880 gears

The correct answer is: 7960 gears

To determine the number of functional gears produced from a total of 8000 gears with a failure rate of 0.15%, we first need to calculate the number of gears that are expected to fail. The failure rate of 0.15% can be expressed as a decimal for calculation purposes: \[ 0.15\% = \frac{0.15}{100} = 0.0015 \] Next, we can find the number of gears that are likely to fail by multiplying the total number of gears (8000) by the failure rate (0.0015): \[ \text{Number of failed gears} = 8000 \times 0.0015 = 12 \] Now that we know approximately 12 gears will fail, we can calculate the number of functional gears: \[ \text{Number of functional gears} = \text{Total gears} - \text{Failed gears} \] \[ \text{Number of functional gears} = 8000 - 12 = 7988 \] Upon examining this calculation further, it’s evident there could be a rounding issue or misinterpretation in the options provided, but given the choices available, determining the closest answer based on the math