Sure, let's complete the statements step by step.
1. We start with the given conditions:
- The nominal diameter is 8.65 inches.
- The margin of error is 0.05 inch.
2. The equation to find the diameter [tex]\( d \)[/tex] of a new soccer ball reflects the condition that the difference between [tex]\( d \)[/tex] and the nominal diameter (8.65 inches) does not exceed the margin of error (0.05 inches). This can be written as:
[tex]\[
|d - 8.65| = 0.05
\][/tex]
3. Based on the condition given by the absolute value equation, the diameter [tex]\( d \)[/tex] can be either:
[tex]\[
d - 8.65 = 0.05 \quad \text{or} \quad d - 8.65 = -0.05
\][/tex]
4. Solving these equations for [tex]\( d \)[/tex] respectively:
[tex]\[
d = 8.65 + 0.05 \quad \text{and} \quad d = 8.65 - 0.05
\][/tex]
5. This gives us:
[tex]\[
d = 8.70 \quad \text{and} \quad d = 8.60
\][/tex]
6. Therefore, the minimum possible diameter of a soccer ball is 8.6 inches and the maximum possible diameter is 8.7 inches.
Let's fill in the blanks in the given statements:
The equation that can be used to find [tex]\( d \)[/tex], the diameter of a new soccer ball, is [tex]\( |d - 8.65| = 0.05 \)[/tex].
The minimum possible diameter of a soccer ball is 8.6 and the maximum possible diameter is 8.7 .
