Answer :
Sure, let's solve these two questions step-by-step!
1. Listing Correlation Coefficients from Weakest to Strongest:
Correlation coefficients range from -1 to 1, where:
- A coefficient of 1 indicates a perfect positive correlation.
- A coefficient of -1 indicates a perfect negative correlation.
- A coefficient of 0 indicates no correlation.
The strength of correlation is determined by the absolute value of the coefficient. So, we'll list the coefficients based on their absolute value from weakest to strongest:
- Given coefficients: 0.79, -0.43, 0.40, -0.82, 0.08
- Order based on strength (weakest to strongest):
- 0.08 (weakest)
- 0.40
- -0.43
- 0.79
- -0.82 (strongest)
2. Finding the Equation of a Line Perpendicular to a Given Line:
We want to find the equation of a line that is perpendicular to the line represented by the equation [tex]\( y = \frac{3}{5}x + 8 \)[/tex].
- Step 1: Identify the slope of the given line.
The slope of the line [tex]\( y = \frac{3}{5}x + 8 \)[/tex] is [tex]\(\frac{3}{5}\)[/tex].
- Step 2: Determine the perpendicular slope.
The slope of a line perpendicular to another line is the negative reciprocal of the original slope. Thus, the perpendicular slope is:
[tex]\[
-1 \div \left(\frac{3}{5}\right) = -\frac{5}{3}
\][/tex]
- Step 3: Write the equation in slope-intercept form.
Since we only need the slope for a line perpendicular, the equation in slope-intercept form, with an unspecified y-intercept, is:
[tex]\[
y = -\frac{5}{3}x + c
\][/tex]
Here, "c" can be any y-intercept since it wasn't specified in the problem.
Thus, the ordered correlation coefficients are [0.08, 0.4, -0.43, 0.79, -0.82] and the slope for the perpendicular line is [tex]\(-\frac{5}{3}\)[/tex].
1. Listing Correlation Coefficients from Weakest to Strongest:
Correlation coefficients range from -1 to 1, where:
- A coefficient of 1 indicates a perfect positive correlation.
- A coefficient of -1 indicates a perfect negative correlation.
- A coefficient of 0 indicates no correlation.
The strength of correlation is determined by the absolute value of the coefficient. So, we'll list the coefficients based on their absolute value from weakest to strongest:
- Given coefficients: 0.79, -0.43, 0.40, -0.82, 0.08
- Order based on strength (weakest to strongest):
- 0.08 (weakest)
- 0.40
- -0.43
- 0.79
- -0.82 (strongest)
2. Finding the Equation of a Line Perpendicular to a Given Line:
We want to find the equation of a line that is perpendicular to the line represented by the equation [tex]\( y = \frac{3}{5}x + 8 \)[/tex].
- Step 1: Identify the slope of the given line.
The slope of the line [tex]\( y = \frac{3}{5}x + 8 \)[/tex] is [tex]\(\frac{3}{5}\)[/tex].
- Step 2: Determine the perpendicular slope.
The slope of a line perpendicular to another line is the negative reciprocal of the original slope. Thus, the perpendicular slope is:
[tex]\[
-1 \div \left(\frac{3}{5}\right) = -\frac{5}{3}
\][/tex]
- Step 3: Write the equation in slope-intercept form.
Since we only need the slope for a line perpendicular, the equation in slope-intercept form, with an unspecified y-intercept, is:
[tex]\[
y = -\frac{5}{3}x + c
\][/tex]
Here, "c" can be any y-intercept since it wasn't specified in the problem.
Thus, the ordered correlation coefficients are [0.08, 0.4, -0.43, 0.79, -0.82] and the slope for the perpendicular line is [tex]\(-\frac{5}{3}\)[/tex].
