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Georgia [21]
3 years ago
14

The manager of a grocery store wants to determine the average amount of money spent at his store as it compares to the average d

ollar amount spent at his competitor's store. At the end of the day, he reviews the amounts of the last 15 grocery orders. The amounts rounded to the nearest dollar are:
41, 38, 19, 30, 21, 53, 34, 34, 37, 29, 50, 43, 57, 28, 50
He then visits the store of his competitor and surveys the first 15 people leaving the store with groceries. The amounts he records, also rounded to the nearest dollar, are:
86, 15, 75, 40, 51, 60, 27, 45, 112, 7, 65, 31, 18, 27, 69
What is the average amount of money spent at each store to the nearest cent?
For which store is the mean a better representation of the data? In two or more complete sentences, explain your answer.
Mathematics
1 answer:
LUCKY_DIMON [66]3 years ago
3 0
<span> Mean is $37.60 The mean is an excellent representation of the data, because the variability is so small. Both stores have medians close to the means, but the IQR is much less for the first store.</span>
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These are the cost and revenue functions for a line of trumpets sold at a music store:
Maslowich

Answer:

168 trumpets for $1702

Step-by-step explanation:

Profit is the measure to be maximized.  We are given revenue and cost relationships as a function of units, x (trumpets).  Profit is the difference:

Profit = Revenue[R(x)] - Cost[C(x)]

Profit = (76x – 0.25x^2) - (-7.75x + 5,312.5)

Profit = 76x - 0.25x^2 + 7.75x - 5,312.5

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Profit = - 0.25x^2 + 83.75x - 5312.5

At this point we can find the trumpets needed for maximum profit by either of two approaches:  algebraic and graphing.  I'll do both.

<u>Mathematically</u>

The first derivative will give us the slope of this function for any value of x.  The maximum will have a slope of zero (the curve changes direction at that point).  Take the first derivative and set that equal to 0 and solve for x.

First derivative:

d(Profit)/dx = - 2(0.25x) + 83.75

d(Profit)/dx = - 0.50x + 83.75

0 = - 0.50x + 83.75

0.50x = 83.75

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Plot the profit function and look for the maximum.  The graph is attached.  The maximum is 167.5 trumpets.

Round up or down to get a whole trumpet.  I'll go up:  168 trumpets.

<u>Maximum Profit</u>

Solve the profit equation for 168 trumpets:

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Profit = - 0.25(168)^2 + 83.75(168) - 5312.5

<u>Profit = $1702</u>

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