Let's solve the problem step by step.
### Step 1: Calculate the Food Percentage
The total pieces of food eaten by the three flocks are as follows:
- Flock X: 57 pieces of food
- Flock Y: 153 pieces of food
- Flock Z: 90 pieces of food
The total pieces of food eaten by all the flocks combined is 300 pieces.
To find the food percentage for each flock, we divide the number of pieces of food each flock ate by the total number of pieces of food, and then express it as a decimal:
- Flock X: [tex]\(\frac{57}{300}\)[/tex]
- Flock Y: [tex]\(\frac{153}{300}\)[/tex]
- Flock Z: [tex]\(\frac{90}{300}\)[/tex]
The values for the food percentage are:
- Flock X: 0.19
- Flock Y: 0.51
- Flock Z: 0.3
### Step 2: Calculate the Number of Birds in Each Flock for the 2nd Generation
The total number of birds is given as 30 birds.
To determine the number of birds in each flock for the 2nd generation, we multiply the food percentage for each flock by the total number of birds:
- Flock X: [tex]\(0.19 \times 30\)[/tex]
- Flock Y: [tex]\(0.51 \times 30\)[/tex]
- Flock Z: [tex]\(0.3 \times 30\)[/tex]
The calculated values for the number of birds in each flock for the 2nd generation are:
- Flock X: 5.7 birds
- Flock Y: 15.3 birds
- Flock Z: 9.0 birds
### Final Results
We can now update the table with these results:
[tex]\[
\begin{tabular}{|l|l|l|l|}
\hline Total Pieces of Food Eaten & Flock X & Flock Y & Flock Z \\
\hline Food Percentage $^*$ & 57 & 153 & 90 \\
\hline Simulated Number of Birds in Flock for 2nd Generation & \mathbf{5.7} & \mathbf{15.3} & \mathbf{9.0} \\
\hline
\end{tabular}
\][/tex]
Thus, after completing the calculations, we find that the simulated number of birds in each flock for the 2nd generation are 5.7 for Flock X, 15.3 for Flock Y, and 9.0 for Flock Z.
