To solve this question, we need to follow a series of steps to both calculate the food percentage for each flock and then use those percentages to determine the simulated number of birds in each flock for the 2nd generation.
Here’s the detailed step-by-step solution:
### Step 1: Calculate the Food Percentage for Each Flock
The food percentage for each flock is found by dividing the total pieces of food eaten by that flock by the total number of pieces of food eaten (300).
For Flock X:
[tex]\[ \text{Food Percentage for Flock X} = \frac{57}{300} = 0.19 \][/tex]
For Flock Y:
[tex]\[ \text{Food Percentage for Flock Y} = \frac{153}{300} = 0.51 \][/tex]
For Flock Z:
[tex]\[ \text{Food Percentage for Flock Z} = \frac{90}{300} = 0.30 \][/tex]
### Step 2: Simulated Number of Birds in Flock for the 2nd Generation
Now, we use the food percentages to calculate the simulated number of birds in each flock for the 2nd generation. We multiply the food percentage by the total number of birds (30).
For Flock X:
[tex]\[ \text{Birds in Flock X for 2nd Generation} = 0.19 \times 30 = 5.7 \text{ birds} \][/tex]
For Flock Y:
[tex]\[ \text{Birds in Flock Y for 2nd Generation} = 0.51 \times 30 = 15.3 \text{ birds} \][/tex]
For Flock Z:
[tex]\[ \text{Birds in Flock Z for 2nd Generation} = 0.30 \times 30 = 9.0 \text{ birds} \][/tex]
### Final Solution
Here are the results summarized in the table format:
[tex]\[
\begin{tabular}{|l|l|l|l|}
\cline{2-4}
\multicolumn{1}{l|}{Total Pieces of Food Eaten} & Flock X & Flock Y & Flock Z \\
\hline
Food Percentage * & 0.19 & 0.51 & 0.30 \\
\hline
Simulated Number of Birds in Flock for 2nd Generation & 5.7 & 15.3 & 9.0 \\
\hline
\end{tabular}
\][/tex]
Calculation: Each flock's total pieces of food divided by 300, the total number of pieces of food eaten.
* Calculation: The food percentage for each flock multiplied by the total number of birds (30).
These percentages and simulated bird counts tell us how food consumption by each flock relates to their population in the next generation.
