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The table shows the number of games a chess player won in professional competitions, based on the number of games played.

\begin{tabular}{|c|c|c|c|c|c|}
\hline Games Played [tex]$( x )$[/tex] & 10 & 15 & 20 & 25 & 30 \\
\hline Games Won [tex]$( y )$[/tex] & 4 & 10 & 16 & 21 & 25 \\
\hline
\end{tabular}

The line of best fit for the situation is: [select from options]

If the chess player plays 40 games in the next competition, the expected number of games won would be approximately: [select from options]

Sagot :

GinnyAnswer
To find the line of best fit and the expected number of games won when the chess player plays 40 games, follow these steps:

### Step 1: Construct the Data Points
You have the following data points from the table:
- Games Played [tex]$(x)$[/tex]: 10, 15, 20, 25, 30
- Games Won [tex]$(y)$[/tex]: 4, 10, 16, 21, 25

### Step 2: Perform Linear Regression
To determine the line of best fit, a linear regression analysis is conducted, which finds the relationship in the form \( y = mx + c \). Here:
- \( m \) represents the slope of the line.
- \( c \) represents the y-intercept.

The result from the analysis gives us:
- \( m = 1.06 \)
- \( c = -6.00 \)

So, the equation of the line of best fit is:
[tex]\[ y = 1.06x - 6.00 \][/tex]

### Step 3: Predict the Number of Games Won for 40 Games Played
To find the expected number of games won when the player plays 40 games, substitute \( x = 40 \) into the equation of the line of best fit:
[tex]\[ y = 1.06(40) - 6.00 \][/tex]

Calculating this:
[tex]\[ y = 42.4 - 6.00 \][/tex]
[tex]\[ y = 36.4 \][/tex]

Thus, if the chess player plays 40 games in the next competition, the expected number of games won would be approximately 36.40.

### Final Answer:
The line of best fit for the situation is \( y = 1.06x - 6.00 \).
If the chess player plays 40 games in the next competition, the expected number of games won would be approximately 36.4.
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