Probability A survey of a college freshment class has determined that the mean height of females in the class is 64 inches,with
a standard deviation of 3.2 inches.
(a) Assuming the data can be modeled by a normal probability density function,find a model for these data.h
(b) Use a graphing utility to graph the model.Be sure to choose an appropriate viewing window.
(c) Find the derivative of the model.
(d) Show that f ' > 0 for x < µ and f' < 0 for x > µ.
(a) Assuming the data can be modeled by a normal probability density function,find a model for these data.h
(b) Use a graphing utility to graph the model.Be sure to choose an appropriate viewing window.
(c) Find the derivative of the model.
(d) Show that f ' > 0 for x < µ and f' < 0 for x > µ.
1 answer:
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Answer:
We know that:
Price of a taco = $4
Price of a burrito = $6.50
x = number of tacos sold
y = number of burritos sold.
We must have that:
x + y ≤ 150 (Because she only has supplies to make 150 tacos or burritos, but she can sell less than that)
And also we know that she must sell at least $780, then:
x*$4 + y*$6.50 ≥ $780
Now we found the system of inequalities:
x + y ≤ 150
x*$4 + y*$6.50 ≥ $780
To solve it graphically, we just need to find each one of the region solutions for each equation, and the intersection of these regions will be the solution for the system.
To graph them may be easier to write them as lines, you can do it as follows:
y ≤ 150 - x
y ≥ ($780 - x*$4)/$6.50
in the first equation, we will shade the area below the line, and in the second equation, we will shade the area above the line.
You can see the image below.
Where the accepted solutions are the ones in the darker part, and we only restrict this to positive values of x (because of how we defined the variable x)
Then looking at the image, we can see that one solution can be the point
x = 20, y = 120
