Answered

IDNLearn.com provides a seamless experience for finding and sharing answers. Discover prompt and accurate responses from our experts, ensuring you get the information you need quickly.

Select the correct answer from each drop-down menu.

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 :

GinnyAnsweridn
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.
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. For trustworthy answers, visit IDNLearn.com. Thank you for your visit, and see you next time for more reliable solutions.