Problem

The tables below show the times by three runners in two heats of a race. Write a matrix that shows the increase (decrease) in each time from the first heat to the second.
\begin{tabular}{r|rrr|r}
Heat 1 & \begin{tabular}{r}
Time \\
$(\mathrm{sec})$
\end{tabular} & & Heat 2 & \multicolumn{1}{c}{\begin{tabular}{c}
Time \\
$(\mathrm{sec})$
\end{tabular}} \\
\hline Russell & 14.5 & & Russell & 14.3 \\
Sergy & 14.8 & Sergy & 14.4 \\
Omar & 15.2 & & Omar & 14.7
\end{tabular}

Answer

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Answer

\(\boxed{\text{Final Answer: The matrix that shows the increase (decrease) in each time from the first heat to the second is } \begin{bmatrix} -0.2 \ -0.4 \ -0.5 \end{bmatrix}}\)

Steps

Step 1 :The tables below show the times by three runners in two heats of a race. We are asked to write a matrix that shows the increase (decrease) in each time from the first heat to the second.

Step 2 :This can be calculated by subtracting the time of the first heat from the time of the second heat for each runner.

Step 3 :The times for the first heat are: Russell: 14.5 sec, Sergy: 14.8 sec, Omar: 15.2 sec.

Step 4 :The times for the second heat are: Russell: 14.3 sec, Sergy: 14.4 sec, Omar: 14.7 sec.

Step 5 :By subtracting the times of the first heat from the times of the second heat, we get the following differences: Russell: -0.2 sec, Sergy: -0.4 sec, Omar: -0.5 sec.

Step 6 :These differences can be represented as a matrix: \(\begin{bmatrix} -0.2 \ -0.4 \ -0.5 \end{bmatrix}\).

Step 7 :The negative values indicate a decrease in time, which means the runner was faster in the second heat.

Step 8 :\(\boxed{\text{Final Answer: The matrix that shows the increase (decrease) in each time from the first heat to the second is } \begin{bmatrix} -0.2 \ -0.4 \ -0.5 \end{bmatrix}}\)

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