A 30 foot by 24 foot carpet has a white center whose area is 432 square feet. The carpet also has a dark grey border and the top, bottom, and side parts of this border have the same width,
a.
Write an equation using the variable that would allow you to find the width of the border.
b.
Solve your equation to find the width of the border. Show your work. Include proper units in your
answer. Write your final answer in the shaded box.

a) (30 - 2x) * (24 - 2x) = 432

b) 3 inches

Step-by-step explanation:

Let's call the width of the border 'x'.

So the length of the white center is 30 - 2x, and the width is 24 - 2x.

Then, we have that the white center area is:

(30 - 2x) * (24 - 2x) = 432

720 - 108x + 4x2 = 432

4x2 - 108x + 288 = 0

x2 - 27x + 72 = 0

Using Bhaskara's formula to solve the quadratic equation, we have:

Delta = 27^2 - 288 = 441

sqrt(Delta) = 21

x1 = (27 + 21)/2 = 24 (Not a reasonable answer, as the length and width of the center area would be negative)

x2 = (27 - 21)/2 = 3

So the dark grey border has a width of 3 inches

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%