Sure, let's solve this step-by-step.
### Step 1: Calculate the Food Percentage for Each Flock
To find the percentage of food eaten by each flock, you need to divide the total pieces of food each flock ate by the total pieces of food (300 pieces).
For Flock [tex]$X$[/tex]:
[tex]\[ \text{Food Percentage X} = \frac{123}{300} \approx 0.41 \][/tex]
For Flock [tex]$Y$[/tex]:
[tex]\[ \text{Food Percentage Y} = \frac{99}{300} \approx 0.33 \][/tex]
For Flock [tex]$Z$[/tex]:
[tex]\[ \text{Food Percentage Z} = \frac{78}{300} \approx 0.26 \][/tex]
### Step 2: Calculate the Simulated Number of Birds in Each Flock for the 2nd Generation
To find the number of birds in each flock for the 2nd generation, multiply the food percentage for each flock by the total number of birds (30 birds).
For Flock [tex]$X$[/tex]:
[tex]\[ \text{Birds in Flock X} = 0.41 \times 30 \approx 12.3 \][/tex]
For Flock [tex]$Y$[/tex]:
[tex]\[ \text{Birds in Flock Y} = 0.33 \times 30 \approx 9.9 \][/tex]
For Flock [tex]$Z$[/tex]:
[tex]\[ \text{Birds in Flock Z} = 0.26 \times 30 \approx 7.8 \][/tex]
### Summary of Results
Here are the calculated values for the food percentage and simulated number of birds in each flock for the 2nd generation:
[tex]\[
\begin{array}{|l|c|c|c|}
\cline{2-4}
& \text{Flock X} & \text{Flock Y} & \text{Flock Z} \\
\hline
\text{Total Pieces of Food Eaten} & 123 & 99 & 78 \\
\hline
\text{Food Percentage} & 0.41 & 0.33 & 0.26 \\
\hline
\text{Simulated Number of Birds in Flock for 2nd Generation} & 12.3 & 9.9 & 7.8 \\
\hline
\end{array}
\][/tex]
This approach allows us to see how the food consumption by each flock impacts the population in the next generation.
