Transform M to the standard normally distributed random variable Z via
where and
are the mean and standard deviation for
, respectively. Then
What is the volume of the following rectangular prism?
2 answers:
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Step 1
Find the perimeter of rectangle ABDE
we know that
the perimeter of rectangle is equal to
In this problem
substitute
Step 2
Find the perimeter of triangle BCD
we know that
the perimeter of triangle is equal to
In this problem we have
Applying the Pythagoras theorem
substitute
Find the ratio of the perimeter of rectangle ABDE to the perimeter of triangle BCD
we have
the perimeter of rectangle is equal to
the perimeter of the triangle is
so
the ratio is equal to
therefore
<u>the answer Part 1) is the option B</u>
Step 3
Find the area of polygon ABCDE
we know that
The area of polygon is equal to the sum of the area of rectangle plus the area of triangle
Area of rectangle is equal to
Area of the triangle is equal to
the height h of the triangle is equal to
substitute
The area of polygon is
therefore
<u>the answer part 2) is the option C</u>