To determine the range of rejected bags, we need to understand the acceptable weight range for the candy bags and then derive the ranges that fall outside this acceptance range.
1. Determine the accepted weight range:
- Each bag is advertised as weighing 500 grams.
- A bag must weigh within 5.3 grams of this advertised weight to be accepted.
2. Calculate the lower and upper limits of the accepted range:
- Lower limit: Subtract 5.3 grams from 500 grams.
[tex]\[
500 - 5.3 = 494.7 \text{ grams}
\][/tex]
- Upper limit: Add 5.3 grams to 500 grams.
[tex]\[
500 + 5.3 = 505.3 \text{ grams}
\][/tex]
3. Identify the accepted range:
- The accepted weight range for the bags is from 494.7 grams to 505.3 grams, inclusive.
4. Determine the range of rejected bags:
- The bags that do not fall within this range will be rejected. Specifically:
- Bags weighing less than 494.7 grams will be rejected.
- Bags weighing more than 505.3 grams will also be rejected.
- Combining these two conditions gives us the range of rejected weights.
Thus, the range of rejected bags is:
[tex]\[ x < 494.7 \quad \text{or} \quad x > 505.3 \][/tex]
Given the options, the correct range for the rejected bags is:
[tex]\[ x < 494.7 \quad \text{and} \quad x > 505.3 \][/tex]
So, the correct choice is:
[tex]\[ x < 494.7 \quad \text{and} \quad x > 505.3 \][/tex]
