\begin{tabular}{|l|l|l|l|}
\cline {2-4}
\multicolumn{1}{c|}{} & Flock X & Flock Y & Flock Z \\
\hline
Total Pieces of Food Eaten & 57 & 153 & 90 \\
\hline
Food Percentage & & [tex]$\square \%$[/tex] & [tex]$\square$[/tex] \\
\hline
Simulated Number of Birds in Flock for 2nd Generation & & [tex]$\square$[/tex] & [tex]$\square$[/tex] \\
\hline
\end{tabular}

Divide each flock's total pieces of food by 300, the total number of pieces of food eaten.
Multiply the food percentage for each flock by the total number of birds (30).



Answer :

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.