Question

the weight of a box of cereal can vary by \\(\frac{1}{4}\\) of an ounce and still be sold as a full box. each box is supposed to contain 18 ounces of cereal. which graph represents the possible weights of boxes that are overfilled or underfilled and cannot be sold as full boxes?\
\\(\boldsymbol{\circ}\\) \\(\longleftarrow\\) \\(\boldsymbol{17.5}\\) \\(\boldsymbol{17.75}\\) \\(\boldsymbol{18}\\) \\(\boldsymbol{18.25}\\) \\(\boldsymbol{18.5}\\) \\(\boldsymbol{\longrightarrow}\\)\
\\(\boldsymbol{\circ}\\) \\(\longleftarrow\\) \\(\boldsymbol{17.5}\\) \\(\boldsymbol{17.75}\\) \\(\boldsymbol{18}\\) \\(\boldsymbol{18.25}\\) \\(\boldsymbol{18.5}\\) \\(\boldsymbol{\longrightarrow}\\)\
\\(\boldsymbol{\circ}\\) \\(\longleftarrow\\) \\(\boldsymbol{17.5}\\) \\(\boldsymbol{17.75}\\) \\(\boldsymbol{18}\\) \\(\boldsymbol{18.25}\\) \\(\boldsymbol{18.5}\\) \\(\boldsymbol{\longrightarrow}\\)\
\\(\boldsymbol{\circ}\\) \\(\longleftarrow\\) \\(\boldsymbol{17.5}\\) \\(\boldsymbol{17.75}\\) \\(\boldsymbol{18}\\) \\(\boldsymbol{18.25}\\) \\(\boldsymbol{18.5}\\) \\(\boldsymbol{\longrightarrow}\\)

Explanation:

Step1: Determine the acceptable weight range

The target weight is 18 ounces, and the variation allowed is $\frac{1}{4}$ (0.25) ounce. So the acceptable range is $18 - 0.25 \leq x \leq 18 + 0.25$, which simplifies to $17.75 \leq x \leq 18.25$.

Step2: Identify overfilled/underfilled weights

Boxes that are overfilled or underfilled lie outside this range. So we need weights $x < 17.75$ or $x > 18.25$.

Step3: Analyze the number lines

• Open circles (not filled) represent values not included. For the ranges $x < 17.75$ and $x > 18.25$, we use open circles at 17.75 and 18.25 (since those values are the boundaries of the acceptable range and not part of the over/underfilled).
• The fourth option (with open circles at 17.75 and 18.25, and arrows pointing left from 17.75 and right from 18.25) matches $x < 17.75$ or $x > 18.25$.

Answer:

The fourth graph (with open circles at 17.75 and 18.25, and arrows for \( x < 17.75 \) and \( x > 18.25 \))