Let's go through the values step-by-step:
1. Total Pieces of Food Eaten by Each Flock:
- Flock [tex]\(X\)[/tex] = 32 pieces
- Flock [tex]\(Y\)[/tex] = 180 pieces
- Flock [tex]\(Z\)[/tex] = 88 pieces
2. Calculate the Total Food:
- The total pieces of food eaten by all flocks is [tex]\(32 + 180 + 88 = 300\)[/tex] pieces.
3. Calculate Food Percentage for Each Flock:
- For Flock [tex]\(X\)[/tex]:
[tex]\[
\text{Food Percentage of } X = \frac{32}{300} = 0.1067 \quad (10.67\%)
\][/tex]
- For Flock [tex]\(Y\)[/tex]:
[tex]\[
\text{Food Percentage of } Y = \frac{180}{300} = 0.6 \quad (60\%)
\][/tex]
- For Flock [tex]\(Z\)[/tex]:
[tex]\[
\text{Food Percentage of } Z = \frac{88}{300} = 0.2933 \quad (29.33\%)
\][/tex]
4. Simulate the Number of Birds for Each Flock in the 3rd Generation:
- The total number of birds is 30.
- For Flock [tex]\(Y\)[/tex]:
[tex]\[
\text{Number of Birds in } Y = 0.6 \times 30 = 18.0 \text{ birds}
\][/tex]
- For Flock [tex]\(Z\)[/tex]:
[tex]\[
\text{Number of Birds in } Z = 0.2933 \times 30 \approx 8.8 \text{ birds}
\][/tex]
To summarize, the completed table looks like this:
[tex]\[
\begin{tabular}{|l|l|l|l|}
\cline{2-4}
& \text{Flock} \, X & \text{Flock} \, Y & \text{Flock} \, Z \\
\hline
\text{Total Pieces of Food Eaten} & 32 & 180 & 88 \\
\hline
\text{Food Percentage} & 0.1067 & 0.6 & 0.2933 \\
\hline
\text{Simulated Number of Birds in Flock for 3rd Generation} & & 18.0 & 8.8 \\
\hline
\end{tabular}
\][/tex]
Thus, we've calculated the food percentages and the simulated number of birds for the third generation for each flock.
