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?

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Absolute Value Inequalities", "Number Line Representation" ], "new_concepts": [], "current_concepts": [ "Absolute Value Inequalities", "Number Line Representation", "Compound Inequalities" ] } ## Define acceptable weight range Using the *Absolute Value Inequalities* knowledge point $$ \begin{aligned} &\text{Target weight} = 18\text{ oz}\ &\text{Allowed variation} = \frac{1}{4}\text{ oz} = 0.25\text{ oz}\ &|w - 18| \le 0.25 \iff 17.75 \le w \le 18.25 \end{aligned} $$ ## Determine unacceptable weight range Using the *Absolute Value Inequalities* knowledge point $$ \begin{aligned} &\text{Unacceptable weights cannot be sold.}\ &w < 17.75 \quad \text{or} \quad w > 18.25 \end{aligned} $$ ## Identify graphical representation Using the *Number Line Representation* knowledge point $$ \begin{aligned} &\text{Strict inequalities } (<, >) \implies \text{open circles.}\ &\text{Open circles at } 17.75 \text{ and } 18.25.\ &\text{Shading goes outward to } -\infty \text{ and } +\infty. \end{aligned} $$

(A) Outward-pointing rays starting from closed circles at 17.75 and 18.25

(B) Outward-pointing rays starting from open circles at 17.75 and 18.25

(C) A shaded segment between closed circles at 17.75 and 18.25

(D) A shaded segment between open circles at 17.75 and 18.25

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Absolute Value Inequalities" ] }

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Define acceptable weight range

Determine unacceptable weight range

Identify graphical representation

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