the table shows the number of flowers in four bouquets and the total cost of each bouquet. what is the…

Explanation:

Step1: Recall correlation - coefficient formula

The formula for the correlation coefficient $r$ is $r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^{2}-(\sum x)^{2}][n\sum y^{2}-(\sum y)^{2}]}}$. Let $x$ be the number of flowers and $y$ be the total cost.

1. Calculate $\sum x$:
   • $x_1 = 8$, $x_2=12$, $x_3 = 6$, $x_4=20$. So, $\sum x=8 + 12+6 + 20=46$.
2. Calculate $\sum y$:
   • $y_1 = 12$, $y_2 = 40$, $y_3=15$, $y_4 = 20$. So, $\sum y=12 + 40+15 + 20=87$.
3. Calculate $\sum xy$:
   • $x_1y_1=8\times12 = 96$, $x_2y_2=12\times40 = 480$, $x_3y_3=6\times15 = 90$, $x_4y_4=20\times20 = 400$.
   • $\sum xy=96 + 480+90 + 400=1066$.
4. Calculate $\sum x^{2}$:
   • $x_1^{2}=8^{2}=64$, $x_2^{2}=12^{2}=144$, $x_3^{2}=6^{2}=36$, $x_4^{2}=20^{2}=400$.
   • $\sum x^{2}=64 + 144+36 + 400=644$.
5. Calculate $\sum y^{2}$:
   • $y_1^{2}=12^{2}=144$, $y_2^{2}=40^{2}=1600$, $y_3^{2}=15^{2}=225$, $y_4^{2}=20^{2}=400$.
   • $\sum y^{2}=144+1600 + 225+400=2369$.
   • Here, $n = 4$.

Step2: Substitute values into the formula

1. Calculate the numerator:
   • $n(\sum xy)-(\sum x)(\sum y)=4\times1066-46\times87=4264 - 4002=262$.
2. Calculate the first - part of the denominator:
   • $n\sum x^{2}-(\sum x)^{2}=4\times644-46^{2}=2576 - 2116 = 460$.
3. Calculate the second - part of the denominator:
   • $n\sum y^{2}-(\sum y)^{2}=4\times2369-87^{2}=9476 - 7569=1907$.
   • The denominator is $\sqrt{460\times1907}=\sqrt{877220}\approx936.6$.
   • $r=\frac{262}{936.6}\approx0.28$.

Answer:

0.28