To fill in the missing information in the table, we'll follow the steps outlined in the notes provided.
### Step 1: Calculate the food percentage for each flock
We start by dividing the number of pieces of food eaten by each flock by the total number of pieces of food (300), then convert this fraction to a percentage by multiplying by 100.
1. Flock [tex]$X$[/tex]:
[tex]\[
\text{Food Percentage for Flock } X = \left(\frac{32}{300}\right) \times 100 = 10.67\%
\][/tex]
2. Flock [tex]$Y$[/tex]:
[tex]\[
\text{Food Percentage for Flock } Y = \left(\frac{180}{300}\right) \times 100 = 60.00\%
\][/tex]
3. Flock [tex]$Z$[/tex]:
[tex]\[
\text{Food Percentage for Flock } Z = \left(\frac{88}{300}\right) \times 100 = 29.33\%
\][/tex]
### Step 2: Calculate the number of birds in each flock for the 3rd generation
To find the number of birds in each flock, multiply the food percentage by the total number of birds (30).
1. Flock [tex]$X$[/tex]:
[tex]\[
\text{Number of Birds in Flock } X = \left(10.67\% \times 30\right) = 3.2
\][/tex]
2. Flock [tex]$Y$[/tex]:
[tex]\[
\text{Number of Birds in Flock } Y = \left(60.00\% \times 30\right) = 18.0
\][/tex]
3. Flock [tex]$Z$[/tex]:
[tex]\[
\text{Number of Birds in Flock } Z = \left(29.33\% \times 30\right) = 8.8
\][/tex]
Let's update the table with our calculations:
[tex]\[
\begin{tabular}{|l|l|l|l|}
\cline { 2 - 4 } \multicolumn{1}{c|}{} & Flock $X$ & Flock $Y$ & Flock Z \\
\hline Total Pieces of Food Eaten & 32 & 180 & 88 \\
\hline Food Percentage * & 10.67\% & 60.00\% & 29.33\% \\
\hline Simulated Number of Birds in Flock for 3rd Generation & 3.2 & 18.0 & 8.8 \\
\hline
\end{tabular}
\][/tex]
In summary, by calculating the food percentage and then the corresponding number of birds, we filled out the table with the correct values.
