You need to hang seven pictures in a straight line. In how many ways may
his be accomplished?

The seven pictures can be hanged in 5040 ways in a straight line.

Step-by-step explanation:

It is given that, there are seven pictures that are to be hanged in a straight line in many ways.

The seven pictures can be arranged in several ways which can be found using the factorial.

Since there are 7 different pictures, the number of ways it can be arranged is 7 factorial ⇒ 7!

if we are filling the 7 pictures at a time, we have seven options to fill the first position.

And then, there are 6 options to fill the second position and followed by the third position which as 5 options to filled and it continues till the seventh position which will have only 1 option to be filled.

Therefore, it is calculated as :

⇒  7! = 7×6×5×4×3×2×1

⇒ 5040 ways.

The seven pictures are hanged in 5040 ways.

required rate of return = 0.166 = 16.6%

step-by-step explanation:

under the capital asset pricing model (capm), the required or expected rate of return for a particular security or asset is given using the formula:

required rate of return = risk-free rate + beta*(market risk premium)

we are given that;

risk-free rate = 4% = 0.04

beta = 1.4

market risk premium = 9% = 0.09

we simply plug these values into the above formula;

required rate of return = 0.04 + 1.4*(0.09)

required rate of return = 0.04 + 0.126

required rate of return = 0.166 = 16.6%