Answer:
1. $5
2. $38.4
Step-by-step explanation:
1) $5
2) 120/100 x 32 = $38.4
4x + y = 7
y = -4x + 7
using y = mx + b
b being your y intercept, (0,7)
Answer:
<em>x=25/16</em>
Step-by-step explanation:
<u>Approximate Roots of Functions:</u>
We are required to find the root of

Let's construct a function

Reducing:

The equation will have a solution when f(x)=0. We'll start from the approximate crossing point given in the graph (x=1.5)

We'll move up on x=1.52

We are closer to the solution, let's try some more up

This value x=1.54 is close enough to the solution of the original equation
From the options given,
is the closest to our solution

Answer:
The expected cost is 152
Step-by-step explanation:
Recall that since Y is uniformly distributed over the interval [1,5] we have the following probability density function for Y
if
and 0 othewise. (To check this is the pdf, check the definition of an uniform random variable)
Recall that, by definition

Also, we are given that
. Recall the following properties of the expected value. If X,Y are random variables, then

Then, using this property we have that
.
Thus, we must calculate E[Y] and E[Y^2].
Using the definition, we get that
![E[Y] = \int_{1}^{5}\frac{y}{4} dy =\frac{1}{4}\left\frac{y^2}{2}\right|_{1}^{5} = \frac{25}{8}-\frac{1}{8} = 3](https://tex.z-dn.net/?f=E%5BY%5D%20%3D%20%5Cint_%7B1%7D%5E%7B5%7D%5Cfrac%7By%7D%7B4%7D%20dy%20%3D%5Cfrac%7B1%7D%7B4%7D%5Cleft%5Cfrac%7By%5E2%7D%7B2%7D%5Cright%7C_%7B1%7D%5E%7B5%7D%20%3D%20%5Cfrac%7B25%7D%7B8%7D-%5Cfrac%7B1%7D%7B8%7D%20%3D%203)
![E[Y^2] = \int_{1}^{5}\frac{y^2}{4} dy =\frac{1}{4}\left\frac{y^3}{3}\right|_{1}^{5} = \frac{125}{12}-\frac{1}{12} = \frac{31}{3}](https://tex.z-dn.net/?f=E%5BY%5E2%5D%20%3D%20%5Cint_%7B1%7D%5E%7B5%7D%5Cfrac%7By%5E2%7D%7B4%7D%20dy%20%3D%5Cfrac%7B1%7D%7B4%7D%5Cleft%5Cfrac%7By%5E3%7D%7B3%7D%5Cright%7C_%7B1%7D%5E%7B5%7D%20%3D%20%5Cfrac%7B125%7D%7B12%7D-%5Cfrac%7B1%7D%7B12%7D%20%3D%20%5Cfrac%7B31%7D%7B3%7D)
Then
