<span>The correct answer is 2x</span>²<span>-16x+30.
Explanation<span>:
(p*q)(x) is a composition of the two functions p(x) and q(x); it is the same as p(q(x)). We replace every x in p(x) with our value of q(x), x-3:
instead of 2x</span></span>²<span><span>, we have 2(x-3)</span></span>²<span><span>, and instead of -4x, we have -4(x-3).
This gives us 2(x-3)</span></span>²<span><span>-4(x-3). This is the same as 2(x-3)(x-3)-4(x-3).
Multiplying, we have
2(x*x-3*x-3*x-3(-3))-(4*x-4*3)
=2(x</span></span>²<span><span>-3x-3x+9)-(4x-12)
=2(x</span></span>²<span><span>-6x+9)-4x+12.
Using the distributive property gives us
2*x</span></span>²<span><span>-2*6x+2*9-4x+12
=2x</span></span>²<span><span>-12x+19-4x+12.
Combine like terms, and we have 2x</span></span>²<span><span>-16x+30.</span></span>
9x-6-13x=94
-4x-6=94
-4x=100
x= -25
We are given the following variables:
μ = the sample mean = 152 pounds
σ = the standard deviation = 26 pounds
x = the sample value we want to test = 180 pounds
n = the sample size = unknown
MOE = margin of error = 4% = 0.04
Confidence level = 96%
The first thing we can do is to find for the value of z
using the formula:
z = (x – μ) / σ
z = (180 – 152) / 26
z = 1.0769 = 1.08
Since we are looking for the people who weigh more than
180 pounds, therefore this is a right tailed z test. The p value is:
p = 0.1401
Then we can use the formula below to solve for n:
n = z^2 * p * (1 – p) / (MOE)^2
n = 1.08^2 * 0.1401 * (1 – 0.1401) / (0.04)^2
n = 87.82 = 88
Therefore around 88 people must be surveyed.
