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Nikki gathered data about the length of time she spent listening to the radio and the number of commercials she heard. She organized the data in a scatter plot, where [tex]$x$[/tex] represents the minutes spent listening and [tex]$y$[/tex] represents the number of commercials. Then she used the graphing tool to find the equation of the line of best fit:

[tex]\[ y = 0.338x - 1.387 \][/tex]

Based on the line of best fit, for approximately how many minutes will Nikki need to listen to the radio to hear 20 commercials?

A. 10
B. 55
C. 63
D. 72



Answer :

GinnyAnswer
To determine the number of minutes Nikki will need to listen to the radio to hear 20 commercials, we will use the given line of best fit equation:

[tex]\[ y = 0.338x - 1.387 \][/tex]

Here, [tex]\( y \)[/tex] represents the number of commercials and [tex]\( x \)[/tex] represents the number of minutes spent listening. We are given [tex]\( y = 20 \)[/tex] and need to solve for [tex]\( x \)[/tex].

Start by substituting [tex]\( y = 20 \)[/tex] into the equation:

[tex]\[ 20 = 0.338x - 1.387 \][/tex]

Next, isolate [tex]\( x \)[/tex] by following these steps:

1. Add 1.387 to both sides of the equation to eliminate the constant term on the right-hand side:
[tex]\[ 20 + 1.387 = 0.338x \][/tex]
[tex]\[ 21.387 = 0.338x \][/tex]

2. Divide both sides by 0.338 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{21.387}{0.338} \][/tex]

By calculating this division, we find that:
[tex]\[ x \approx 63.275 \][/tex]

Therefore, Nikki will need to listen to the radio for approximately 63 minutes to hear 20 commercials.

The correct answer is:
C. 63

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