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
