To solve this problem, we will follow the given instructions step by step, calculating the percentage of food each flock has eaten and using these percentages to determine the simulated number of birds in each flock for the second generation.
### Step-by-Step Solution:
1. Calculate the percentage of food eaten by each flock:
- Flock X:
- Percentage of food: [tex]\( \frac{123}{300} \approx 0.41 \)[/tex]
- Flock Y:
- Percentage of food: [tex]\( \frac{99}{300} \approx 0.33 \)[/tex]
- Flock Z:
- Percentage of food: [tex]\( \frac{78}{300} \approx 0.26 \)[/tex]
This means:
- Flock X ate 41% of the total food.
- Flock Y ate 33% of the total food.
- Flock Z ate 26% of the total food.
2. Calculate the number of birds in each flock for the second generation:
- Total number of birds = 30
Using the percentages calculated in the previous step:
- Number of birds in Flock X:
- Percentage of food [tex]\( \times \)[/tex] Total number of birds
- [tex]\( 0.41 \times 30 \approx 12.30 \)[/tex]
- Number of birds in Flock Y:
- Percentage of food [tex]\( \times \)[/tex] Total number of birds
- [tex]\( 0.33 \times 30 = 9.90 \)[/tex]
- Number of birds in Flock Z:
- Percentage of food [tex]\( \times \)[/tex] Total number of birds
- [tex]\( 0.26 \times 30 \approx 7.80 \)[/tex]
### Final Answer:
- Flock X:
- Percentage of Food: [tex]\( \approx 0.41 \)[/tex]
- Simulated Number of Birds in 2nd Generation: [tex]\( \approx 12.30 \)[/tex]
- Flock Y:
- Percentage of Food: [tex]\( \approx 0.33 \)[/tex]
- Simulated Number of Birds in 2nd Generation: [tex]\( 9.90 \)[/tex]
- Flock Z:
- Percentage of Food: [tex]\( \approx 0.26 \)[/tex]
- Simulated Number of Birds in 2nd Generation: [tex]\( \approx 7.80 \)[/tex]
To summarize, the food percentages are approximately 0.41 for Flock X, 0.33 for Flock Y, and 0.26 for Flock Z, leading to 12.30 birds in Flock X, 9.90 birds in Flock Y, and 7.80 birds in Flock Z for the second generation.
