To find the constant of proportionality for the ratio of robins to cardinals, follow these steps:
1. Understand the Concept: The constant of proportionality is the factor by which one quantity is multiplied to obtain the other quantity. In this case, it is the factor by which the number of cardinals is multiplied to obtain the number of robins.
2. Identify Pairs: Write down the pairs of cardinal and robin counts given in the table:
- Pair 1: Cardinals = 5, Robins = 15
- Pair 2: Cardinals = 6, Robins = 18
- Pair 3: Cardinals = 9, Robins = 27
- Pair 4: Cardinals = 10, Robins = 30
3. Calculate the Ratios: For each pair, divide the number of robins by the number of cardinals to find the constant of proportionality.
- For Pair 1:
[tex]\[
\text{Ratio} = \frac{\text{Robins 1}}{\text{Cardinals 1}} = \frac{15}{5} = 3.0
\][/tex]
- For Pair 2:
[tex]\[
\text{Ratio} = \frac{\text{Robins 2}}{\text{Cardinals 2}} = \frac{18}{6} = 3.0
\][/tex]
- For Pair 3:
[tex]\[
\text{Ratio} = \frac{\text{Robins 3}}{\text{Cardinals 3}} = \frac{27}{9} = 3.0
\][/tex]
- For Pair 4:
[tex]\[
\text{Ratio} = \frac{\text{Robins 4}}{\text{Cardinals 4}} = \frac{30}{10} = 3.0
\][/tex]
4. Summarize the Constant of Proportionality: From the calculations, you can observe that the ratio is consistent across all pairs of data. Each ratio equals 3.0. This consistent value implies that the constant of proportionality between the number of robins and the number of cardinals is 3.0.
Therefore, for the given data, the constant of proportionality for the ratio of robins to cardinals is [tex]\( \boxed{3.0} \)[/tex].
