<span> The difference between the observed </span>value<span> of the dependent variable (y) and the predicted </span>value<span> (ŷ) is called the </span>residual<span> (e). When x is equal to 3, the value of y from the best fit line would be 0.8. Therefore, the residual would be -1 - 0.8 = -1.8. Option A is the correct answer.</span>
The interquartile range<span> (</span>IQR<span>) is a measure of variability, based on dividing a </span>data set<span>into quartiles. Quartiles divide a rank-ordered </span>data set<span> into four equal parts. The values that divide each part are called the first, second, and third quartiles; and they are denoted by Q1, Q2, and Q3, respectively.</span>
For this problem, I think there is no need for the details of 12 inches width and 4 inches length. This is because an equation is already given. It was clearly specified that A as a function of θ represents the area of the opening. Then, we are asked to find exactly that: the area of opening. Moreover, the value of θ was also given. Therefore, I am quite sure that the initial details given are for the purpose of red herring only.
So, all we have to do is substitute θ=45° to the function given.
A = 16 sin 45° ⋅ (cos 45° + 1)
The angle 45° is a special angle in trigonometry. So, it would be easy to remember trigonometric functions of this angle. Sine of 45° is equal to √2/2 while cosine of 45° is also √2/2.
A = 16(√2/2) ⋅ (√2/2 + 1)
A = 8+8√2
A = 19.31 square inches
15 x .30 = 4.50 discount 15-4.50= 10.50
10.50 x .40 = 4.20
Final cost of shirt 10.50-4.20 = $6.30
