Assume that the sales of a certain appliance dealer are approximated by a linear function. Suppose that sales were $14,500 in 19
1 answer:
A linear function has the form : f(x)=ax+b
we are given that
f(0)=a*0+b=b is <span>$14,500.
so the sales in the first year were </span>$14,500.
f(1) gives the sales in the second year (year 83)
f(2) gives the sales in the third year (year 84)
.
.
f(5) gives the sales in the sixths year (year 87)
the slope of the line, a, is given by :
thus,
S=ax+b=10,200x+<span>14,500
</span>
Answer: S=10,200x+14,500
we are given that
f(0)=a*0+b=b is <span>$14,500.
so the sales in the first year were </span>$14,500.
f(1) gives the sales in the second year (year 83)
f(2) gives the sales in the third year (year 84)
.
.
f(5) gives the sales in the sixths year (year 87)
the slope of the line, a, is given by :
thus,
S=ax+b=10,200x+<span>14,500
</span>
Answer: S=10,200x+14,500
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Answer:
a) Data given: 42 36 48 51 39 39 42 36 48 33 39 42 45
b) 44.1, 37.8, 50.4, 53.55, 40.95, 44.1, 37.8, 50.4 ,34.65, 40.95, 44.1, 47.25
c) 3.5, 3, 4, 4.25, 3.25, 3.25, 3.5, 3, 4, 2.75, 3.25, 3.5, 3.75
d) As we can see, the average of part b is 1.05 times the average of part a (1.05 * 41.538 = 43.615) and the average of part c is equal to the average obtained in part a divided by 12 (41.538 / 12 = 3.462).
And that happens because we create linear transformations for the parts b and c and the linear transformation affects the mean.
And you have the same interpretation for the deviation, it is affected by the linear transformation as the mean.
Step-by-step explanation:
For this case we can use the following formulas for the mean and standard deviation:
Part a
Data given: 42 36 48 51 39 39 42 36 48 33 39 42 45
And if we calculate the mean we got:
Part b
For this case we know that each value present a 5% of rise so we just need to multiply each value bu 1.05 and we have this new dataset:
44.1, 37.8, 50.4, 53.55, 40.95, 44.1, 37.8, 50.4 ,34.65, 40.95, 44.1, 47.25
And if we calculate the new mean and deviation we got:
Part c
The new dataset would be each value divided by 12 so we have:
3.5, 3, 4, 4.25, 3.25, 3.25, 3.5, 3, 4, 2.75, 3.25, 3.5, 3.75
And the new mean and deviation would be:
Part d
As we can see, the average of part b is 1.05 times the average of part a (1.05 * 41.538 = 43.615) and the average of part c is equal to the average obtained in part a divided by 12 (41.538 / 12 = 3,462).
And that happens because we create linear transformations for the parts b and c and the linear transformation affects the mean.
And you have the same interpretation for the deviation, it is affected by the linear transformation as the mean.