Let's work through the question step-by-step to fill out the table. We have the total pieces of food eaten by each flock and the total pieces of food each flock ate. We are also given a percentage for Flock [tex]$Y$[/tex] and need to find the number of birds in the 3rd generation for each flock.
### Step 1: Calculate Food Percentage for Each Flock
- Food eaten by Flock [tex]$X$[/tex]: 32 pieces
- Food eaten by Flock [tex]$Y$[/tex]: 180 pieces
- Food eaten by Flock [tex]$Z$[/tex]: 88 pieces
- Total food eaten: 300 pieces
To find the food percentage for Flock [tex]$X$[/tex] and Flock [tex]$Z$[/tex], we divide the food eaten by the total food and multiply by 100:
#### Flock [tex]$X$[/tex]:
[tex]\[ \text{Food Percentage for Flock } X = \left(\frac{32}{300}\right) \times 100 = 10.67\% \][/tex]
#### Flock [tex]$Y$[/tex]:
We are given that the food percentage for Flock [tex]$Y$[/tex] is 8%, so we will use this directly for calculations.
#### Flock [tex]$Z$[/tex]:
[tex]\[ \text{Food Percentage for Flock } Z = \left(\frac{88}{300}\right) \times 100 = 29.33\% \][/tex]
### Step 2: Calculate Number of Birds in the 3rd Generation for Each Flock
We have a total of 30 birds. To find the number of birds in each flock for the 3rd generation, we multiply the food percentage by the total number of birds:
#### Flock [tex]$X$[/tex]:
[tex]\[ \text{Number of Birds } X = \left(\frac{10.67}{100}\right) \times 30 \approx 3.2 \][/tex]
#### Flock [tex]$Y$[/tex]:
[tex]\[ \text{Number of Birds } Y = \left(\frac{8}{100}\right) \times 30 = 2.4 \][/tex]
#### Flock [tex]$Z$[/tex]:
[tex]\[ \text{Number of Birds } Z = \left(\frac{29.33}{100}\right) \times 30 \approx 8.8 \][/tex]
### Summary of the Results:
Now that we have all the required calculations, let's fill in the table:
[tex]\[
\begin{array}{|l|l|l|l|}
\hline
& \text{Flock } X & \text{Flock } Y & \text{Flock } Z \\
\hline
\text{Total Pieces of Food Eaten} & 32 & 180 & 88 \\
\hline
\text{Food Percentage} & 10.67\% & 8\% & 29.33\% \\
\hline
\text{Simulated Number of Birds in Flock for 3rd Generation} & 3.2 & 2.4 & 8.8 \\
\hline
\end{array}
\][/tex]
These detailed steps demonstrate how to calculate the required food percentages and the simulated number of birds in each flock for the 3rd generation.
