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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*I am assuming that the hexagons in all questions are regular and the triangle in (24) is equilateral*
(21)
Area of a Regular Hexagon: square units
(22)
Similar to (21)
Area = square units
(23)
For this case, we will have to consider the relation between the side and inradius of the hexagon. Since, a hexagon is basically a combination of six equilateral triangles, the inradius of the hexagon is basically the altitude of one of the six equilateral triangles. The relation between altitude of an equilateral triangle and its side is given by:
Hence, area of the hexagon will be: square units
(24)
Given is the inradius of an equilateral triangle.
Substituting the value of inradius and calculating the length of the side of the equilateral triangle:
Side = 16 units
Area of equilateral triangle = square units