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? \\(\bigcirc\\) \\(\longleftarrow\hspace{1.5cm}\bullet\hspace{0.5cm}\bullet\hspace{1.5cm}\longrightarrow\\) \\(17.5\quad17.75\quad18\quad18.25\quad18.5\\) \\(\bigcirc\\) \\(\longleftarrow\hspace{1.5cm}\diamond\hspace{0.5cm}\diamond\hspace{1.5cm}\longrightarrow\\) \\(17.5\quad17.75\quad18\quad18.25\quad18.5\\) \\(\bigcirc\\) \\(\longleftarrow\hspace{1.5cm}\bullet\hspace{0.5cm}\bullet\hspace{1.5cm}\longrightarrow\\) \\(17.5\quad17.75\quad18\quad18.25\quad18.5\\) \\(\bigcirc\\) \\(\longleftarrow\hspace{1.5cm}\diamond\hspace{0.5cm}\diamond\hspace{1.5cm}\longrightarrow\\) \\(17.5\quad17.75\quad18\quad18.25\quad18.5\\)

Explanation:

Step 1: Determine the acceptable weight range

The ideal weight is 18 ounces, and it can vary by \(\frac{1}{4}\) (which is 0.25) ounce. So the lower bound is \(18 - 0.25 = 17.75\) ounces, and the upper bound is \(18 + 0.25 = 18.25\) ounces. Boxes within \(17.75 \leq \text{weight} \leq 18.25\) can be sold as full.

Step 2: Identify the region for non - sellable boxes

Boxes that are overfilled or underfilled (cannot be sold as full) will have weights less than 17.75 ounces or greater than 18.25 ounces. On a number line, this is represented by two open intervals (since 17.75 and 18.25 are the boundaries of the sellable range, and we want values outside this range). The second graph has open circles at 17.75 and 18.25 and the shaded regions are to the left of 17.75 and to the right of 18.25, which represents weights less than 17.75 or greater than 18.25.

Answer:

The second graph (the one with open circles at 17.75 and 18.25 and shaded regions outside the interval from 17.75 to 18.25) represents the possible weights of boxes that are overfilled or underfilled and cannot be sold as full boxes. In the given options, if we assume the options are labeled as follows (from top to bottom):

1. First option (with closed circles at 17.75 and 18.25, shaded outside? No, the first has closed circles)
2. Second option (open circles at 17.75 and 18.25, shaded outside)
3. Third option (closed circles at 17.75 and 18.25, shaded inside - this is the sellable range)
4. Fourth option (open circles at 17.75 and 18.25, shaded inside - this is incorrect)

So the answer is the second option (the one with open diamonds at 17.75 and 18.25 and the shaded regions outside the 17.75 - 18.25 interval). If we use the option labels as per the original problem (assuming the second option in the list of four), the answer is the second graph. In the format of the options:

B. The graph with open circles (or diamonds) at 17.75 and 18.25 and shaded regions to the left of 17.75 and to the right of 18.25 (the second option in the given set of graphs)