Answer:
a) 98.522
b) 0.881
c) The correlation coefficient and co-variance shows that there is positive association between marks and study time. The correlation coefficient suggest that there is strong positive association between marks and study time.
Step-by-step explanation:
a.
As the mentioned in the given instruction the co-variance is first computed in excel by using only add/Sum, subtract, multiply, divide functions.
Marks y Time spent x y-ybar x-xbar (y-ybar)(x-xbar)
77 40 5.1 1.3 6.63
63 42 -8.9 3.3 -29.37
79 37 7.1 -1.7 -12.07
86 47 14.1 8.3 117.03
51 25 -20.9 -13.7 286.33
78 44 6.1 5.3 32.33
83 41 11.1 2.3 25.53
90 48 18.1 9.3 168.33
65 35 -6.9 -3.7 25.53
47 28 -24.9 -10.7 266.43
![Covariance=\frac{sum[(y-ybar)(x-xbar)]}{n-1}](https://tex.z-dn.net/?f=Covariance%3D%5Cfrac%7Bsum%5B%28y-ybar%29%28x-xbar%29%5D%7D%7Bn-1%7D)
Co-variance=886.7/(10-1)
Co-variance=886.7/9
Co-variance=98.5222
The co-variance computed using excel function COVARIANCE.S(B1:B11,A1:A11) where B1:B11 contains Time x column and A1:A11 contains Marks y column. The resulted co-variance is 98.52222.
b)
The correlation coefficient is computed as
![Correlation coefficient=r=\frac{sum[(y-ybar)(x-xbar)]}{\sqrt{sum[(x-xbar)]^2sum[(y-ybar)]^2} }](https://tex.z-dn.net/?f=Correlation%20coefficient%3Dr%3D%5Cfrac%7Bsum%5B%28y-ybar%29%28x-xbar%29%5D%7D%7B%5Csqrt%7Bsum%5B%28x-xbar%29%5D%5E2sum%5B%28y-ybar%29%5D%5E2%7D%20%7D)
(y-ybar)^2 (x-xbar)^2
26.01 1.69
79.21 10.89
50.41 2.89
198.81 68.89
436.81 187.69
37.21 28.09
123.21 5.29
327.61 86.49
47.61 13.69
620.01 114.49
sum(y-ybar)^2=1946.9
sum(x-xbar)^2=520.1




The correlation coefficient computed using excel function CORREL(A1:A11,B1:B11) where B1:B11 contains Time x column and A1:A11 contains Marks y column. The resulted correlation coefficient is 0.881.
c)
The correlation coefficient and co-variance shows that there is positive association between marks and study time. The correlation coefficient suggest that there is strong positive association between marks and study time. It means that as the study time increases the marks of student also increases and if the study time decreases the marks of student also decreases.
The excel file is attached on which all the related work is done.
Answer:
3/2 x-5
Step-by-step explanation:
<span>To get the bigger number, divide by 2 the sum of the given sum of the numbers and their difference. In this case-
(226 + 200)/2 = 426/2 = 213.
To get the smaller number, divide by 2 the difference of the given sum of the numbers and their difference. In this case -
(226 - 200)/2 = 26/2 =13.
The two numbers are 213 and 13.
The bigger number is 213</span>
Answer:
27/2
Step-by-step explanation:
Given
Vertices (0, 0), (3, 0), and (0, 3)
Since the base of the equilateral in the plane perpendicular to the x-axis goes from the x-axis to the line y = 3 - x.
So, the length of each side of the triangle is (3-x)
Calculating the area;
Area = ½bh
Where b = base = 3 - x
height is calculated as;
h² = (3-x)² + (½(3-x))² --- from Pythagoras
h² = 9 - 6x + x² + (3/2 - ½x)²
Let h² = 0
0 = 9 - 6x + x² + (9/4 - 6/4x + ¼x²)
0 = 9 + 9/4 - 6x - 6/4 + x² + ¼x²
0 = 45/4 - 30x/4 + 5x²/4
0. = 5x²/4 - 30x/4 + 45/4
0 = 5x² - 15x/4 - 15x/4 + 45/4
0 = 5x(x/4-¾) - 15(x/4 - ¾)
0 = (5x - 15)(x/4 - ¾)
5x = 15 or x/4 = 3/4
x = 3 or x = 3
So, h = 3
Area = ½bh
Area = ½ * (3-x) * 3
Area = ½(9-3x)
Volume= Integral of ½(9-3x) {3,0}
V = 9/2 - 3x/2 {3,0}
V = 9x/2 - 3x²/4 {3,0}
V = 9(3)/2 - 3(3)²/4
V = 27/2 - 27/4
V = 27/2