The manager of Hudson Auto Repair wants to advertise one price for an engine tune-up, with parts included. Before he decides the price to advertise, he needs a good estimate of the average cost of tune-up parts. A sample of 20 customer invoices for tune-ups has been taken and the costs of parts, rounded to the nearest dollar, are listed below. 91
78
93
57
75
52
99
80
105
62
104
74
62
68
97
73
77
65
80
109
Provide a 90% confidence interval estimate of the mean cost of parts per tune-up for all of the tune-ups performed at Hudson Auto Repair.

x = -2

y = 848

step-by-step explanation:

plug in the numbers

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204

multiplication is multiplication.   it might feel harder depending on what level of math you are in, but generally it will be the same old stuff, while implementing some new concepts and methods of solving work.