To determine the missing values in the table, we need to follow a few steps. Let’s go through them one by one:
1. Calculate the Food Percentage for each flock:
The food percentage can be found by dividing each flock's total food eaten by the total number of pieces of food and then multiplying by 100 to convert it to a percentage.
For Flock Y:
[tex]\[
\text{Food Percentage}_Y = \left(\frac{\text{Total Food Eaten by Flock Y}}{\text{Total Food}}\right) \times 100
= \left(\frac{153}{300}\right) \times 100
= 51\%
\][/tex]
For Flock Z:
[tex]\[
\text{Food Percentage}_Z = \left(\frac{\text{Total Food Eaten by Flock Z}}{\text{Total Food}}\right) \times 100
= \left(\frac{90}{300}\right) \times 100
= 30\%
\][/tex]
2. Calculate the Simulated Number of Birds in Flock for the 2nd Generation:
The simulated number of birds can be determined by multiplying the food percentage for each flock by the total number of birds and then converting the percentage to a decimal format.
For Flock Y:
[tex]\[
\text{Simulated Number of Birds}_Y = \left(\frac{\text{Food Percentage}_Y}{100}\right) \times \text{Total Birds}
= \left(\frac{51}{100}\right) \times 30
= 15.3
\][/tex]
For Flock Z:
[tex]\[
\text{Simulated Number of Birds}_Z = \left(\frac{\text{Food Percentage}_Z}{100}\right) \times \text{Total Birds}
= \left(\frac{30}{100}\right) \times 30
= 9.0
\][/tex]
Now, we can complete the table as follows:
[tex]\[
\begin{tabular}{|l|l|l|l|}
\cline { 2 - 4 } \multicolumn{1}{c|}{} & \text{Flock X} & \text{Flock Y} & \text{Flock Z} \\
\hline
\text{Total Pieces of Food Eaten} & 57 & 153 & 90 \\
\hline
\text{Food Percentage*} & & 51\% & 30\% \\
\hline
\text{Simulated Number of Birds in Flock for 2nd Generation} & & 15.3 & 9.0 \\
\hline
\end{tabular}
\][/tex]
By following these steps, we have determined the food percentages and the simulated number of birds for the second generation for Flock Y and Flock Z.
