To determine the simulated number of birds in each flock for the 2nd generation, follow these detailed steps:
1. Determine the Total Pieces of Food Eaten by Each Flock:
Use the given food percentage values to find out the total pieces of food eaten by each flock. We'll assume the pieces of food eaten by each flock as [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] respectively.
2. Calculate the Proportion of Food Each Flock Ate:
The problem statement directs us to divide the total pieces of food eaten by each flock by 300 (the total number of pieces of food eaten).
[tex]\[
\text{Proportion for Flock X} = \frac{123}{300}
\][/tex]
[tex]\[
\text{Proportion for Flock Y} = \frac{99}{300}
\][/tex]
[tex]\[
\text{Proportion for Flock Z} = \frac{78}{300}
\][/tex]
3. Calculate the Simulated Number of Birds in Each Flock:
Next, we multiply the obtained proportion for each flock by the total number of birds, which is 30.
[tex]\[
\text{Number of Birds in Flock X} = \left(\frac{123}{300}\right) \times 30
\][/tex]
[tex]\[
\text{Number of Birds in Flock Y} = \left(\frac{99}{300}\right) \times 30
\][/tex]
[tex]\[
\text{Number of Birds in Flock Z} = \left(\frac{78}{300}\right) \times 30
\][/tex]
4. Simplify the Calculations:
Carrying out the multiplications:
[tex]\[
\text{Number of Birds in Flock X} = \left(\frac{123}{300}\right) \times 30 = \left(\frac{123 \times 30}{300}\right) = \left(\frac{3690}{300}\right) = 12.3
\][/tex]
[tex]\[
\text{Number of Birds in Flock Y} = \left(\frac{99}{300}\right) \times 30 = \left(\frac{99 \times 30}{300}\right) = \left(\frac{2970}{300}\right) = 9.9
\][/tex]
[tex]\[
\text{Number of Birds in Flock Z} = \left(\frac{78}{300}\right) \times 30 = \left(\frac{78 \times 30}{300}\right) = \left(\frac{2340}{300}\right) = 7.8
\][/tex]
Given these steps, the simulated number of birds in each flock for the second generation can be summarized as follows:
- Flock X: 12.3 birds
- Flock Y: 9.9 birds
- Flock Z: 7.8 birds
