To find the constant of proportionality for the ratio of robins to cardinals, follow these steps:
1. Identify the pairs of values for Cardinals and Robins:
- Cardinals: [tex]\( 5, 6, 9, 10 \)[/tex]
- Robins: [tex]\( 15, 18, 27, 30 \)[/tex]
2. Calculate the ratio of Robins to Cardinals for each pair:
- For the first pair ([tex]\( 5 \)[/tex] Cardinals and [tex]\( 15 \)[/tex] Robins):
[tex]\[
\text{Ratio} = \frac{\text{Robins}}{\text{Cardinals}} = \frac{15}{5} = 3.0
\][/tex]
- For the second pair ([tex]\( 6 \)[/tex] Cardinals and [tex]\( 18 \)[/tex] Robins):
[tex]\[
\text{Ratio} = \frac{\text{Robins}}{\text{Cardinals}} = \frac{18}{6} = 3.0
\][/tex]
- For the third pair ([tex]\( 9 \)[/tex] Cardinals and [tex]\( 27 \)[/tex] Robins):
[tex]\[
\text{Ratio} = \frac{\text{Robins}}{\text{Cardinals}} = \frac{27}{9} = 3.0
\][/tex]
- For the fourth pair ([tex]\( 10 \)[/tex] Cardinals and [tex]\( 30 \)[/tex] Robins):
[tex]\[
\text{Ratio} = \frac{\text{Robins}}{\text{Cardinals}} = \frac{30}{10} = 3.0
\][/tex]
3. Analyze the calculated ratios:
- From the calculations above, the ratios are consistently [tex]\( 3.0 \)[/tex] for all pairs.
4. Determine the constant of proportionality:
- Since the ratio of Robins to Cardinals is the same (3.0) for each pair, we can conclude that the constant of proportionality is:
[tex]\[
3.0
\][/tex]
So, the constant of proportionality for the ratio of Robins to Cardinals is [tex]\( 3.0 \)[/tex]. This means that for every cardinal, there are consistently 3 times as many robins.
