Let's go through the steps to fill out the table and calculate the missing values.
### Table Provided:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline
& \text{Flock X} & \text{Flock Y} & \text{Flock Z} \\
\hline
\text{Total Pieces of Food Eaten} & 32 & 180 & 88 \\
\hline
\text{Food Percentage}\ [{ }^x] & \square \% & \square \% & \square\% \\
\hline
\text{Simulated Number of Birds in Flock for 3rd Generation} [{ }^{\star *}] & \square & \square & \square \\
\hline
\end{array}
\][/tex]
### Step-by-Step Solution:
1. Food Percentage Calculation
First, we calculate the percentage of food eaten by each flock.
- For Flock X:
[tex]\[
\text{Food Percentage}\ [{ }^x] = \left(\frac{32}{300}\right) \times 100 = 10.67\%
\][/tex]
- For Flock Y:
[tex]\[
\text{Food Percentage}\ [{ }^x] = \left(\frac{180}{300}\right) \times 100 = 60.00\%
\][/tex]
- For Flock Z:
[tex]\[
\text{Food Percentage}\ [{ }^x] = \left(\frac{88}{300}\right) \times 100 = 29.33\%
\][/tex]
2. Simulated Number of Birds Calculation
Next, we multiply the food percentage for each flock by the total number of birds (30) to estimate the number of birds in the 3rd generation.
- For Flock X:
[tex]\[
\text{Simulated Number of Birds}\ [{ }^{\star *}] = \left(\frac{10.67}{100}\right) \times 30 = 3.20
\][/tex]
- For Flock Y:
[tex]\[
\text{Simulated Number of Birds}\ [{ }^{\star *}] = \left(\frac{60.00}{100}\right) \times 30 = 18.00
\][/tex]
- For Flock Z:
[tex]\[
\text{Simulated Number of Birds}\ [{ }^{\star *}] = \left(\frac{29.33}{100}\right) \times 30 = 8.80
\][/tex]
### Completed Table:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline
& \text{Flock X} & \text{Flock Y} & \text{Flock Z} \\
\hline
\text{Total Pieces of Food Eaten} & 32 & 180 & 88 \\
\hline
\text{Food Percentage}\ [{ }^x] & 10.67\% & 60.00\% & 29.33\% \\
\hline
\text{Simulated Number of Birds in Flock for 3rd Generation} [{ }^{\star *}] & 3.20 & 18.00 & 8.80 \\
\hline
\end{array}
\][/tex]
By following these steps, we've determined the food percentage and the simulated number of birds for each flock based on their food consumption.
