To determine the fraction that represents the model, we first analyze the total number of parts and how many are shaded.
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Total heptagons: There are 5 heptagons. Each heptagon is divided into 7 equal parts, so the total number of parts is: \[ 5 \times 7 = 35 \text{ parts} \]
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Shaded parts: The first four heptagons are completely shaded. Since each heptagon has 7 parts, the number of parts shaded in the first four heptagons is: \[ 4 \times 7 = 28 \text{ shaded parts} \] Additionally, the last heptagon has 4 parts shaded, so we add that to the shaded parts: \[ 28 + 4 = 32 \text{ shaded parts} \]
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Fraction of shaded parts: The fraction representing the shaded parts out of the total parts is: \[ \frac{32 \text{ shaded parts}}{35 \text{ total parts}} = \frac{32}{35} \]
None of the provided responses exactly match \(\frac{32}{35}\), but among the listed options, there is one response that can be translated.
The closest response that represents the situation is:
- \(28 \frac{4}{7}\) (This can be interpreted as \(28 + \frac{4}{7}\)).
However, this isn't an exact fraction but rather a mixed number.
Based on the analysis, the fraction that correctly reflects the model you’ve described is \(\frac{32}{35}\), but it seems there might be an error in the provided response options.
The best interpretation based on the provided options, in this case, would lead to the selection of \(28 \frac{4}{7}\) as it includes the similar number of parts being referenced, but one should note that \(28 \frac{4}{7}\) simplifies differently from the calculated fraction \(\frac{32}{35}\).
It's important to ensure that the options provided actually correlate to the analysis done to avoid any miscalculations or misunderstandings.