Sure! Let's fill in the table and provide a detailed step-by-step solution for the given problem:
1. Given Data:
- Total pieces of food eaten by all flocks = 300
- Pieces of food eaten by Flock X = 147
- Pieces of food eaten by Flock Y = 93
- Pieces of food eaten by Flock Z = 60
- Total number of birds = 30
2. Calculate the Food Percentage for Each Flock:
- For Flock X:
[tex]\[
\text{Food Percentage for Flock X} = \frac{\text{Pieces of food eaten by Flock X}}{\text{Total pieces of food eaten}} = \frac{147}{300} = 0.49
\][/tex]
- For Flock Y:
[tex]\[
\text{Food Percentage for Flock Y} = \frac{\text{Pieces of food eaten by Flock Y}}{\text{Total pieces of food eaten}} = \frac{93}{300} = 0.31
\][/tex]
- For Flock Z:
[tex]\[
\text{Food Percentage for Flock Z} = \frac{\text{Pieces of food eaten by Flock Z}}{\text{Total pieces of food eaten}} = \frac{60}{300} = 0.20
\][/tex]
3. Calculate the Simulated Number of Birds in Each Flock for 3rd Generation:
- For Flock X:
[tex]\[
\text{Number of Birds in Flock X} = \text{Food Percentage for Flock X} \times \text{Total number of birds} = 0.49 \times 30 = 14.7
\][/tex]
- For Flock Y:
[tex]\[
\text{Number of Birds in Flock Y} = \text{Food Percentage for Flock Y} \times \text{Total number of birds} = 0.31 \times 30 = 9.3
\][/tex]
- For Flock Z:
[tex]\[
\text{Number of Birds in Flock Z} = \text{Food Percentage for Flock Z} \times \text{Total number of birds} = 0.20 \times 30 = 6.0
\][/tex]
Now, let's fill in the table with these results:
[tex]\[
\begin{tabular}{|l|l|l|l|}
\cline { 2 - 4 } & \text{Flock X} & \text{Flock Y} & \text{Flock Z} \\
\hline \begin{tabular}{l}
\text{Total Pieces of Food Eaten} \\
\text{(from previous page)}
\end{tabular} & 147 & 93 & 60 \\
\hline \text{Food Percentage} & 0.49 & 0.31 & 0.20 \\
\hline \begin{tabular}{l}
\text{Simulated Number of Birds in} \\
\text{Flock for 3rd Generation}
\end{tabular} & 14.7 & 9.3 & 6.0 \\
\hline
\end{tabular}
\][/tex]
By following the steps outlined above, we have calculated the food percentages and the simulated number of birds for each flock for the 3rd generation successfully.
