Answer :
Sure, let's walk through the solution to this problem step-by-step. The table has data for three flocks (X, Y, and Z) with the total pieces of food they have eaten. We need to fill out the missing information: the food percentage and the simulated number of birds in each flock for the second generation.
### Step-by-Step Solution
1. Calculate the Food Percentage for Each Flock:
The food percentage for each flock is calculated by dividing the number of pieces of food eaten by that flock by the total number of pieces of food eaten (300), then multiplying by 100 to get the percentage.
- Flock X:
[tex]\[ \text{Food Percentage}_{X} = \left(\frac{123}{300}\right) \times 100 \][/tex]
[tex]\[ \text{Food Percentage}_{X} = 41.0\% \][/tex]
- Flock Y:
[tex]\[ \text{Food Percentage}_{Y} = \left(\frac{99}{300}\right) \times 100 \][/tex]
[tex]\[ \text{Food Percentage}_{Y} = 33.0\% \][/tex]
- Flock Z:
[tex]\[ \text{Food Percentage}_{Z} = \left(\frac{78}{300}\right) \times 100 \][/tex]
[tex]\[ \text{Food Percentage}_{Z} = 26.0\% \][/tex]
2. Calculate the Simulated Number of Birds in Each Flock for the 2nd Generation:
Multiply the food percentage for each flock by the total number of birds (30) and divide by 100 to simulate the number of birds in each flock for the second generation.
- Flock X:
[tex]\[ \text{Simulated Birds}_{X} = \left(\frac{41.0}{100}\right) \times 30 \][/tex]
[tex]\[ \text{Simulated Birds}_{X} = 12.3 \][/tex]
- Flock Y:
[tex]\[ \text{Simulated Birds}_{Y} = \left(\frac{33.0}{100}\right) \times 30 \][/tex]
[tex]\[ \text{Simulated Birds}_{Y} = 9.9 \][/tex]
- Flock Z:
[tex]\[ \text{Simulated Birds}_{Z} = \left(\frac{26.0}{100}\right) \times 30 \][/tex]
[tex]\[ \text{Simulated Birds}_{Z} = 7.8 \][/tex]
### Completed Table
Using the above calculations, we can now fill in the missing values in the provided table.
[tex]\[ \begin{array}{|c|c|c|c|} \hline & \text{Flock X} & \text{Flock Y} & \text{Flock Z} \\ \hline \text{Total Pieces of Food Eaten} & 123 & 99 & 78 \\ \hline \text{Food Percentage} & 41.0\% & 33.0\% & 26.0\% \\ \hline \text{Simulated Number of Birds in Flock for 2nd Generation} & 12.3 & 9.9 & 7.8 \\ \hline \end{array} \][/tex]
This table summarizes the food percentages and the projected bird populations for the second generation based on the given information.
### Step-by-Step Solution
1. Calculate the Food Percentage for Each Flock:
The food percentage for each flock is calculated by dividing the number of pieces of food eaten by that flock by the total number of pieces of food eaten (300), then multiplying by 100 to get the percentage.
- Flock X:
[tex]\[ \text{Food Percentage}_{X} = \left(\frac{123}{300}\right) \times 100 \][/tex]
[tex]\[ \text{Food Percentage}_{X} = 41.0\% \][/tex]
- Flock Y:
[tex]\[ \text{Food Percentage}_{Y} = \left(\frac{99}{300}\right) \times 100 \][/tex]
[tex]\[ \text{Food Percentage}_{Y} = 33.0\% \][/tex]
- Flock Z:
[tex]\[ \text{Food Percentage}_{Z} = \left(\frac{78}{300}\right) \times 100 \][/tex]
[tex]\[ \text{Food Percentage}_{Z} = 26.0\% \][/tex]
2. Calculate the Simulated Number of Birds in Each Flock for the 2nd Generation:
Multiply the food percentage for each flock by the total number of birds (30) and divide by 100 to simulate the number of birds in each flock for the second generation.
- Flock X:
[tex]\[ \text{Simulated Birds}_{X} = \left(\frac{41.0}{100}\right) \times 30 \][/tex]
[tex]\[ \text{Simulated Birds}_{X} = 12.3 \][/tex]
- Flock Y:
[tex]\[ \text{Simulated Birds}_{Y} = \left(\frac{33.0}{100}\right) \times 30 \][/tex]
[tex]\[ \text{Simulated Birds}_{Y} = 9.9 \][/tex]
- Flock Z:
[tex]\[ \text{Simulated Birds}_{Z} = \left(\frac{26.0}{100}\right) \times 30 \][/tex]
[tex]\[ \text{Simulated Birds}_{Z} = 7.8 \][/tex]
### Completed Table
Using the above calculations, we can now fill in the missing values in the provided table.
[tex]\[ \begin{array}{|c|c|c|c|} \hline & \text{Flock X} & \text{Flock Y} & \text{Flock Z} \\ \hline \text{Total Pieces of Food Eaten} & 123 & 99 & 78 \\ \hline \text{Food Percentage} & 41.0\% & 33.0\% & 26.0\% \\ \hline \text{Simulated Number of Birds in Flock for 2nd Generation} & 12.3 & 9.9 & 7.8 \\ \hline \end{array} \][/tex]
This table summarizes the food percentages and the projected bird populations for the second generation based on the given information.
