Sure, let's go through the detailed steps necessary to complete the table.
1. Calculate food percentages:
To determine the food percentage eaten by each flock, we'll divide the total pieces of food eaten by each flock by the overall total number of food pieces (300), and then multiply by 100 to convert it to a percentage.
- For Flock X:
[tex]\[
\text{Percentage of food eaten by Flock X} = \left(\frac{147}{300}\right) \times 100 = 49\%
\][/tex]
- For Flock Y:
[tex]\[
\text{Percentage of food eaten by Flock Y} = \left(\frac{93}{300}\right) \times 100 = 31\%
\][/tex]
- For Flock Z:
[tex]\[
\text{Percentage of food eaten by Flock Z} = \left(\frac{60}{300}\right) \times 100 = 20\%
\][/tex]
2. Simulated number of birds in Flock for the 3rd Generation:
To find the number of birds in each flock for the 3rd generation, we'll multiply the food percentage for each flock by the total number of birds (30).
- For Flock X:
[tex]\[
\text{Number of birds in Flock X} = \left(\frac{49}{100}\right) \times 30 = 14.7
\][/tex]
- For Flock Y:
[tex]\[
\text{Number of birds in Flock Y} = \left(\frac{31}{100}\right) \times 30 = 9.3
\][/tex]
- For Flock Z:
[tex]\[
\text{Number of birds in Flock Z} = \left(\frac{20}{100}\right) \times 30 = 6.0
\][/tex]
Thus, filling in the table with these values:
[tex]\[
\begin{array}{|l|l|l|l|}
\hline
\multicolumn{1}{l|}{} & \text{Flock X} & \text{Flock Y} & \text{Flock Z} \\
\hline
\text{Total Pieces of Food Eaten} & 147 & 93 & 60 \\
\hline
\text{Food Percentage} & 49\% & 31\% & 20\% \\
\hline
\text{Simulated Number of Birds in Flock for 3rd Generation} & 14.7 & 9.3 & 6.0 \\
\hline
\end{array}
\][/tex]
This completes the table with detailed, step-by-step calculations.
