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Sagot :
To solve the given problem, we need to fill in the table by calculating the food percentage for each flock and then determining the simulated number of birds for each flock in the 3rd generation.
### Step-by-Step Solution
1. Calculate the Food Percentage for Each Flock
The formula to calculate the food percentage for each flock is:
[tex]\[ \text{Food Percentage} = \frac{\text{Total Pieces of Food Eaten by the Flock}}{\text{Total Pieces of Food Eaten by All Flocks}} \][/tex]
Given:
- Total pieces of food eaten by all flocks = 300
- Total pieces of food eaten by Flock X = 32
- Total pieces of food eaten by Flock Y = 180
- Total pieces of food eaten by Flock Z = 88
Food percentage for Flock X:
[tex]\[ \text{Food Percentage}_\text{X} = \frac{32}{300} = 0.10666666666666667 \][/tex]
Food percentage for Flock Y:
[tex]\[ \text{Food Percentage}_\text{Y} = \frac{180}{300} = 0.6 \][/tex]
Food percentage for Flock Z:
[tex]\[ \text{Food Percentage}_\text{Z} = \frac{88}{300} = 0.29333333333333333 \][/tex]
2. Calculate the Simulated Number of Birds for Each Flock in the 3rd Generation
The formula to calculate the simulated number of birds for each flock is:
[tex]\[ \text{Simulated Number of Birds} = \text{Food Percentage} \times \text{Total Number of Birds} \][/tex]
Given:
- Total number of birds = 30
Simulated number of birds for Flock X:
[tex]\[ \text{Birds}_\text{X} = 0.10666666666666667 \times 30 = 3.2 \][/tex]
Simulated number of birds for Flock Y:
[tex]\[ \text{Birds}_\text{Y} = 0.6 \times 30 = 18.0 \][/tex]
Simulated number of birds for Flock Z:
[tex]\[ \text{Birds}_\text{Z} = 0.29333333333333333 \times 30 = 8.8 \][/tex]
3. Fill in the Table
[tex]\[ \begin{tabular}{|l|l|l|l|} \cline { 2 - 4 } \multicolumn{1}{c|}{} & Flock X & Flock Y & Flock Z \\ \hline Total Pieces of Food Eaten & 32 & 180 & 88 \\ \hline Food Percentage & 0.10666666666666667 & 0.6 & 0.29333333333333333 \\ \hline Simulated Number of Birds in Flock for 3rd Generation & 3.2 & 18.0 & 8.8 \\ \hline \end{tabular} \][/tex]
That completes the detailed solution for the question.
### Step-by-Step Solution
1. Calculate the Food Percentage for Each Flock
The formula to calculate the food percentage for each flock is:
[tex]\[ \text{Food Percentage} = \frac{\text{Total Pieces of Food Eaten by the Flock}}{\text{Total Pieces of Food Eaten by All Flocks}} \][/tex]
Given:
- Total pieces of food eaten by all flocks = 300
- Total pieces of food eaten by Flock X = 32
- Total pieces of food eaten by Flock Y = 180
- Total pieces of food eaten by Flock Z = 88
Food percentage for Flock X:
[tex]\[ \text{Food Percentage}_\text{X} = \frac{32}{300} = 0.10666666666666667 \][/tex]
Food percentage for Flock Y:
[tex]\[ \text{Food Percentage}_\text{Y} = \frac{180}{300} = 0.6 \][/tex]
Food percentage for Flock Z:
[tex]\[ \text{Food Percentage}_\text{Z} = \frac{88}{300} = 0.29333333333333333 \][/tex]
2. Calculate the Simulated Number of Birds for Each Flock in the 3rd Generation
The formula to calculate the simulated number of birds for each flock is:
[tex]\[ \text{Simulated Number of Birds} = \text{Food Percentage} \times \text{Total Number of Birds} \][/tex]
Given:
- Total number of birds = 30
Simulated number of birds for Flock X:
[tex]\[ \text{Birds}_\text{X} = 0.10666666666666667 \times 30 = 3.2 \][/tex]
Simulated number of birds for Flock Y:
[tex]\[ \text{Birds}_\text{Y} = 0.6 \times 30 = 18.0 \][/tex]
Simulated number of birds for Flock Z:
[tex]\[ \text{Birds}_\text{Z} = 0.29333333333333333 \times 30 = 8.8 \][/tex]
3. Fill in the Table
[tex]\[ \begin{tabular}{|l|l|l|l|} \cline { 2 - 4 } \multicolumn{1}{c|}{} & Flock X & Flock Y & Flock Z \\ \hline Total Pieces of Food Eaten & 32 & 180 & 88 \\ \hline Food Percentage & 0.10666666666666667 & 0.6 & 0.29333333333333333 \\ \hline Simulated Number of Birds in Flock for 3rd Generation & 3.2 & 18.0 & 8.8 \\ \hline \end{tabular} \][/tex]
That completes the detailed solution for the question.
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