Answered

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The table shows the number of flowers in four bouquets and the total cost of each bouquet.

Cost of Bouquets
\begin{tabular}{|c|c|}
\hline
Number of flowers in the bouquet & Total cost \\
\hline
8 & \[tex]$12 \\
\hline
12 & \$[/tex]40 \\
\hline
6 & \[tex]$15 \\
\hline
20 & \$[/tex]20 \\
\hline
\end{tabular}

What is the correlation coefficient for the data in the table?

A. [tex]$-0.57$[/tex]
B. [tex]$-0.28$[/tex]
C. 0.28
D. 0.57

Sagot :

GinnyAnsweridn
To find the correlation coefficient for the data in the table, follow these steps:

### Step 1: Understand the Data
We have two sets of values:
1. Number of flowers in the bouquet: [tex]\([8, 12, 6, 20]\)[/tex]
2. Total cost of each bouquet: [tex]\([12, 40, 15, 20]\)[/tex]

### Step 2: Interpret Correlation Coefficient
The correlation coefficient measures the degree to which two variables are linearly related. It ranges from -1 to 1, where:
- [tex]\(1\)[/tex] indicates a perfect positive linear relationship,
- [tex]\(-1\)[/tex] indicates a perfect negative linear relationship,
- [tex]\(0\)[/tex] indicates no linear relationship.

### Step 3: Calculate the Correlation Coefficient
Based on the data provided and the calculations, the result for the correlation coefficient between the number of flowers and the total cost is approximately [tex]\(0.28\)[/tex].

This means there is a weak positive linear relationship between the number of flowers in the bouquet and the total cost.

### Step 4: Select the Correct Answer
Given the choices:
- [tex]\(-0.57\)[/tex]
- [tex]\(-0.28\)[/tex]
- [tex]\(0.28\)[/tex]
- [tex]\(0.57\)[/tex]

The correct answer is [tex]\(0.28\)[/tex].

This value shows that as the number of flowers increases, the total cost tends to increase to some extent, but the relationship is not very strong.
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