Let's solve the problem step-by-step.
### Step 1: Calculate the Food Percentage for Each Flock
To find the percentage of food eaten by each flock, divide the number of pieces of food they ate by the total number of pieces of food (300) and then multiply by 100 to convert it to a percentage.
Flock X:
[tex]\[
\text{Percentage for Flock X} = \left(\frac{32}{300}\right) \times 100
\][/tex]
Flock Y:
[tex]\[
\text{Percentage for Flock Y} = \left(\frac{180}{300}\right) \times 100
\][/tex]
Flock Z:
[tex]\[
\text{Percentage for Flock Z} = \left(\frac{88}{300}\right) \times 100
\][/tex]
Using these calculations, the food percentages are:
- Flock X: 10.6667%
- Flock Y: 60.0000%
- Flock Z: 29.3333%
### Step 2: Simulated Number of Birds in Each Flock for the 3rd Generation
To find the number of birds in each flock for the 3rd generation, multiply the food percentage for each flock by the total number of birds (30).
Flock X:
[tex]\[
\text{Birds in Flock X} = \left(\frac{10.6667}{100}\right) \times 30
\][/tex]
Flock Y:
[tex]\[
\text{Birds in Flock Y} = \left(\frac{60.0000}{100}\right) \times 30
\][/tex]
Flock Z:
[tex]\[
\text{Birds in Flock Z} = \left(\frac{29.3333}{100}\right) \times 30
\][/tex]
Using these calculations, the number of birds in each flock for the 3rd generation are:
- Flock X: 3.2 birds
- Flock Y: 18.0 birds
- Flock Z: 8.8 birds
### Final Solution
We'll fill in the table with the calculated percentages and the number of birds:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline & Flock X & Flock Y & Flock Z \\
\hline Total Pieces of Food Eaten & 32 & 180 & 88 \\
\hline Food Percentage ${ }^{\star}$ & 10.6667\% & 60.0000\% & 29.3333\% \\
\hline Simulated Number of Birds in Flock for 3rd Generation ${ }^{ }$ & 3.2 & 18.0 & 8.8 \\
\hline
\end{tabular}
\][/tex]
This detailed solution steps through how to calculate the food percentages and the simulated number of birds for each flock.
