Question

An auto parts manufacturer throws out gaskets with weights that are more than 0.06 pounds away from the mean weight. The mean weight is 0.6 pounds. Write an inequality and solve the possible weights of the gaskets.

A) |W - 0.6| > 0.06; 0.54 ≤ W ≤ 0.66
B) |W - 0.6| < 0.06; 0.54 ≤ W ≤ 0.66
C) |W - 0.6| > 0.06; W < 0.54 or W > 0.66
D) |W - 0.6| < 0.06; W < 0.54 or W > 0.66

Answer 1

The correct inequality is |W - 0.6| > 0.06. The possible weights of the gaskets are 0.54 ≤ W ≤ 0.66.

Step-by-step explanation:

To write the inequality for the possible weights of the gaskets, we have to consider the mean weight and the acceptable range. The mean weight is 0.6 pounds. The gaskets that are thrown out are those with weights more than 0.06 pounds away from the mean. Since the weights can be both above and below the mean, we use the absolute value in the inequality. Therefore, the correct inequality is |W - 0.6| > 0.06.

To solve this inequality, we can split it into two separate inequalities:

W - 0.6 > 0.06 and W - 0.6 < -0.06

Solving the first inequality, we have:

W > 0.66

Solving the second inequality, we have:

W < 0.54

Combining the two inequalities, we get:

0.54 ≤ W ≤ 0.66

Therefore, the correct answer is option A) |W - 0.6| > 0.06; 0.54 ≤ W ≤ 0.66.