Twelve points are spaced evenly around a circle, lettered from a to l. let n be the total number of isosceles triangles, including equilateral triangles, that can be constructed from three of these points. a different orientation of the same lengths counts as a different triangle, because a different combination of points form the vertices. what is the value of n?

  N = 52

Step-by-step explanation:

We assume that a 1-5-9 equilateral triangle is indistinguishable from a 5-9-1 equilateral triangle, so only count it once.

There are 5 isosceles triangles that can be created using each lettered vertex as the apex. Of those, 1 is equilateral, so there are 4×12 non-equilateral isosceles triangles that can be formed.

There are 4 unique equilateral triangles, so the total number is ...

  N = 4×12 + 4 = 52

Expected rate of return is 10.3%

Step-by-step explanation:

CAPM calculate the expected return by using the risk free rate market premium and beta of investment. It helps to decided the additional investment in a well diversified portfolio.

Formula of CAPM to calculate the rate of return

Rate of Return = Risk free rate + beta ( Risk premium )

Rate of Return = 4% + 0.7 ( 9% )

Rate of Return = 4% + 0.7 ( 9% )

Rate of Return = 10.3%