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Which data table indicates a positive linear association between the hours worked and the daily wages of waiters in a restaurant?

A. table B
\begin{tabular}{|c|c|}
\hline Hours Worked & Daily Wage (\[tex]$) \\
\hline 9 & 45 \\
\hline 8 & 40 \\
\hline 7 & 45 \\
\hline 6 & 40 \\
\hline
\end{tabular}

B. table C
\begin{tabular}{|c|c|}
\hline Hours Worked & Daily Wage (\$[/tex]) \\
\hline 9 & 45 \\
\hline 8 & 45 \\
\hline 7 & 45 \\
\hline 6 & 45 \\
\hline
\end{tabular}

C. table D
\begin{tabular}{|c|c|}
\hline Hours Worked & Daily Wage (\$) \\
\hline 6 & 30 \\
\hline 7 & 35 \\
\hline 8 & 40 \\
\hline 9 & 45 \\
\hline
\end{tabular}



Answer :

GinnyAnswer
To determine which data table indicates a positive linear association between the hours worked and the daily wages of waiters, we need to examine each table and see if there is a pattern of increasing wages with increasing hours worked.

Let's analyze the data tables provided:

Table B:
[tex]\[ \begin{array}{|c|c|} \hline \text{Hours Worked} & \text{Daily Wage (\$)} \\ \hline 9 & 45 \\ \hline 8 & 40 \\ \hline 7 & 45 \\ \hline 6 & 40 \\ \hline \end{array} \][/tex]
- For 9 hours worked, the wage is \[tex]$45. - For 8 hours worked, the wage is \$[/tex]40.
- For 7 hours worked, the wage is \[tex]$45. - For 6 hours worked, the wage is \$[/tex]40.

In Table B, we notice that the daily wage does not consistently increase as the hours worked increase. Hence, Table B does not show a positive linear association.

Table C:
[tex]\[ \begin{array}{|c|c|} \hline \text{Hours Worked} & \text{Daily Wage (\$)} \\ \hline 9 & 45 \\ \hline 8 & 45 \\ \hline 7 & 45 \\ \hline 6 & 45 \\ \hline \end{array} \][/tex]
- For 9 hours worked, the wage is \[tex]$45. - For 8 hours worked, the wage is \$[/tex]45.
- For 7 hours worked, the wage is \[tex]$45. - For 6 hours worked, the wage is \$[/tex]45.

In Table C, the daily wage remains constant regardless of the hours worked, meaning there is no variability in wages. Therefore, Table C does not indicate a positive linear association.

Table D:
[tex]\[ \begin{array}{|c|c|} \hline \text{Hours Worked} & \text{Daily Wage (\$)} \\ \hline 6 & 30 \\ \hline 7 & 35 \\ \hline 8 & 40 \\ \hline 9 & 45 \\ \hline \end{array} \][/tex]
- For 6 hours worked, the wage is \[tex]$30. - For 7 hours worked, the wage is \$[/tex]35.
- For 8 hours worked, the wage is \[tex]$40. - For 9 hours worked, the wage is \$[/tex]45.

In Table D, we observe that as the hours worked increase, the daily wage also increases consistently. Therefore, Table D shows a positive linear association.

By reviewing each table, we find that Table D indicates a positive linear association between the hours worked and the daily wages of waiters.

Hence, the correct answer is:
D. Table D.

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