Which statement is true?
1 answer:
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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
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
(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:
£59.25
Step-by-step explanation:
Hello!
To solve this problem, we must:
- Solve for the length of the fence (aka height)
- Find the area of the lawn (trapezoid)
- Find the number of cans needed
- Find the price of all the cans
Area of a trapezoid, and why the formula works:
A trapezoid is a quadrilateral with one set of parallel sides known as bases. The other two sides are known as the legs.
To find the area of a trapezoid, we use the formula:
This works because if we used the formula, we would be duplicating the trapezoid to form a rectangle with a side length of B1 + B2, and a height of h. Since the trapezoid is half of that, we divide by 2.
Solve for height:
The height is unknown but can be found using the Pythagorean Theorem.
The difference between the bases is the length of the bottom leg of the right triangle, and 17 is the hypotenuse.
Difference = 20 - 12 = 8
Hypotenuse = 17
- 8² + fence² = 17²
- 64 + fence² = 289
- 225 = fence²
- fence = 15
The height is 15
Solve for area:
Now we can solve for the area.
The area is 240
Cans:
The area of the lawn is 240 square meters. Each can cover 100 square meters.
- 240 ÷ 100 = 2.4
Since we can't use part of a can, we round up to three whole cans.
The price of 3 cans :
- 3 * 19.75
- 59.25
£59.25
The Pythagorean Theorem:
The Pythagorean theorem is a very common geometry formula used to find the length of the hypotenuse in a right triangle, given the lengths of the two other bases.
The formula is :
- a is a leg
- b is a leg
- c is the hypotenuse
Images attached for your reference
