To determine the range within which the actual weight of the object lies, given that the measured weight is [tex]\( 155.2 \)[/tex] lbs and it may vary from the actual weight by at most [tex]\( 0.4 \)[/tex] lbs, follow these steps:
1. Identify the measured weight and the deviation:
- Measured weight: [tex]\( 155.2 \)[/tex] lbs
- Deviation: [tex]\( 0.4 \)[/tex] lbs
2. Calculate the lower bound of the actual weight:
- Subtract the deviation from the measured weight:
[tex]\[
155.2 - 0.4 = 154.8
\][/tex]
3. Calculate the upper bound of the actual weight:
- Add the deviation to the measured weight:
[tex]\[
155.2 + 0.4 = 155.6
\][/tex]
4. Establish the range of the actual weight:
- The actual weight can be as low as [tex]\( 154.8 \)[/tex] lbs or as high as [tex]\( 155.6 \)[/tex] lbs.
Therefore, based on the calculations, the range of actual weights of the object is:
[tex]\[
154.8 \leq x \leq 155.6
\][/tex]
Given the options provided:
A. [tex]\( x \leq 154.8 \)[/tex] or [tex]\( x \geq 155.6 \)[/tex]
B. [tex]\( 154.8 \leq x \leq 155.6 \)[/tex]
C. [tex]\( 154.8 \geq x \geq 155.6 \)[/tex]
D. [tex]\( 154.8 \geq x \leq 155.6 \)[/tex]
The correct answer is:
B. [tex]\( 154.8 \leq x \leq 155.6 \)[/tex]
