Amount = 252 / 0.72
= 350
<u>Solution-</u>
We know that,
<em>Residual value = Given value - Predicted value</em>
The table for residual values is shown below,
Plotting a graph, by taking the residual values on ordinate and values of given x on abscissa, a random pattern is obtained where the points are evenly distributed about x-axis.
We know that,
<em>If the points in a residual plot are randomly dispersed around the horizontal or x-axis, a linear regression model is appropriate for the data. Otherwise, a non-linear model is more appropriate.</em>
As, in this case the points are distributed randomly around x-axis, so the residual plot show that the line of regression is best fit for the data set.
Answer:
![\sec(x)=\frac{1}{\sqrt{1-m^2}}](https://tex.z-dn.net/?f=%5Csec%28x%29%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B1-m%5E2%7D%7D)
Step-by-step explanation:
We know that:
![\sin(-x)=-m](https://tex.z-dn.net/?f=%5Csin%28-x%29%3D-m)
First, since sine is an odd function, we can move the negative outside:
![=-\sin(x)=-m](https://tex.z-dn.net/?f=%3D-%5Csin%28x%29%3D-m)
Divide both sides by -1:
![\sin(x)=m](https://tex.z-dn.net/?f=%5Csin%28x%29%3Dm)
We will now use the Pythagorean Identity:
![\cos^2(x)+\sin^2(x)=1](https://tex.z-dn.net/?f=%5Ccos%5E2%28x%29%2B%5Csin%5E2%28x%29%3D1)
Substitute m for sine:
![\cos^2(x)+m^2=1](https://tex.z-dn.net/?f=%5Ccos%5E2%28x%29%2Bm%5E2%3D1)
Solve for cosine:
![\cos^2(x)=1-m^2](https://tex.z-dn.net/?f=%5Ccos%5E2%28x%29%3D1-m%5E2)
Take the square root of both sides:
![\cos(x)=\pm\sqrt{1-m^2}](https://tex.z-dn.net/?f=%5Ccos%28x%29%3D%5Cpm%5Csqrt%7B1-m%5E2%7D)
Since x is an acute angle, cosine will always be positive. Thus:
![\cos(x)=\sqrt{1-m^2}](https://tex.z-dn.net/?f=%5Ccos%28x%29%3D%5Csqrt%7B1-m%5E2%7D)
Take the reciprocal of both sides. Hence:
![\frac{1}{\cos(x)}=\sec(x)=\frac{1}{\sqrt{1-m^2}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5Ccos%28x%29%7D%3D%5Csec%28x%29%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B1-m%5E2%7D%7D)
Answer: 850
Step-by-step explanation:
34 x 25 = 850
Answer:
y = -1/3x + 5
Step-by-step explanation:
Perpendicular lines have <u>negative reciprocal slopes</u>. This means that if you multiply the slopes of both linear equations, the product will be -1.
Given the linear equation, y = 3x - 2, and the point (0, 5):
The negative reciprocal of the slope (m) = 3 is -1/3. Hence, we can assume that the slope of the other line must be -1/3.
Next, using the slope of the other line (m = -1/3) and the given point, (0, 5), we'll substitute these values into the slope-intercept form, y = mx + b, to solve for the y-intercept (b):
y = mx + b
5 = -1/3(0) + b
5 = 0 + b
5 = b
The y-intercept (b) of the other line is 5.
Therefore, the linear equation of the line perpendicular to y = 3x - 2 is:
y = -1/3x + 5
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