Part A:
3.14 X (4)^2 X 3/3
= 50.26548246
14.6 is the constant because no matter how many hours she will work (that number could change) it will always be a linear growth of 14.6.
If <em>X</em> is uniformly distributed on the interval (0, 12), then its PDF is

or simply

and the zero-elsewhere case is assumed.
Whether you include 0 and 12 in the domain is irrelevant, since the probability that <em>X</em> = 0 or <em>X</em> = 12 are both zero.
<span>The definition of quadratic function is given by:
</span>

<span>
So the problem asks for two conditions:
<em>1. Write the quadratic function in factored form.
</em>
<em>2. The vertex has an x-coordinate of 3.</em>
Then the equation (1) must be written as follows:
</span>

<span>
To satisfy the two conditions:
So we are free to choose the value of one root, say:

Thus:
Finally,
the answer is:

The graph of this function is shown in the figure below.</span>
An angle bisector is a line or ray that divides an angle in half