To compare the two classes, the Coefficient of Variation (COV) can be used. The formula for COV is this:
C = s / x
where s is the standard deviation and x is the mean
For the first class:
C1 = 10.2 / 75.5
C1 = 0.1351 (13.51%)
For the second class:
C2 = 22.5 / 75.5
C2 = 0.2980 (29.80%)
The COV is a test of homogeneity. Looking at the values, the first class has more students having a grade closer to the average than the second class.
The equation line passing through a point is understood to be parallel to the x-axis. In this case, the equation should be expressed as y = b where b is any number. Since y = 14 in the point (1,14), the equation of horizontal line passing through this point is y = 14.
The increase in miles would be 11 miles
Answer:
The width and length of rectangle is 12.728 m
Step-by-step explanation:
Let the length of the rectangle = L
let the width of the rectangle = W
The subjective function is given by;
F(p) = 2(L + W)
F = 2L + 2W
Area of the rectangle is given by;
A = LW
LW = 162 ft²
L = 162 / W
Substitute in the value of L into subjective function;
![f = 2l + 2w\\\\f = 2(\frac{162}{w} )+2w\\\\f = \frac{324}{w} + 2w\\\\\frac{df}{dw} = \frac{-324}{w^2} +2\\\\](https://tex.z-dn.net/?f=f%20%3D%202l%20%2B%202w%5C%5C%5C%5Cf%20%3D%202%28%5Cfrac%7B162%7D%7Bw%7D%20%29%2B2w%5C%5C%5C%5Cf%20%3D%20%5Cfrac%7B324%7D%7Bw%7D%20%2B%202w%5C%5C%5C%5C%5Cfrac%7Bdf%7D%7Bdw%7D%20%3D%20%5Cfrac%7B-324%7D%7Bw%5E2%7D%20%2B2%5C%5C%5C%5C)
Take the second derivative of the function, to check if it will given a minimum perimeter
![\frac{d^2f}{dw^2}= \frac{648}{w^3} \\\\Thus, \frac{d^2f}{dw^2}>0, \ since,\frac{648}{w^3} >0 \ (minimum \ function \ verified)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%5E2f%7D%7Bdw%5E2%7D%3D%20%5Cfrac%7B648%7D%7Bw%5E3%7D%20%5C%5C%5C%5CThus%2C%20%5Cfrac%7Bd%5E2f%7D%7Bdw%5E2%7D%3E0%2C%20%5C%20since%2C%5Cfrac%7B648%7D%7Bw%5E3%7D%20%3E0%20%5C%20%28minimum%20%5C%20function%20%5C%20verified%29)
Determine the critical points of the first derivative;
df/dw = 0
![\frac{-324}{w^2} +2 = 0\\\\-324 + 2w^2=0\\\\2w^2 = 324\\\\w^2 = \frac{324}{2} \\\\w^2 = 162\\\\w= \sqrt{162}\\\\w = 12.728 \ m](https://tex.z-dn.net/?f=%5Cfrac%7B-324%7D%7Bw%5E2%7D%20%2B2%20%3D%200%5C%5C%5C%5C-324%20%2B%202w%5E2%3D0%5C%5C%5C%5C2w%5E2%20%3D%20324%5C%5C%5C%5Cw%5E2%20%3D%20%5Cfrac%7B324%7D%7B2%7D%20%5C%5C%5C%5Cw%5E2%20%3D%20162%5C%5C%5C%5Cw%3D%20%5Csqrt%7B162%7D%5C%5C%5C%5Cw%20%3D%2012.728%20%5C%20m)
L = 162 / 12.728
L = 12.728 m
Therefore, the width and length of rectangle is 12.728 m
Answer:
$341 the selling price
Step-by-step explanation:
Cost $620
$620-45% ($279 profit)
$620-$279=$341 should be the selling price