X=5
Y=8
Z=8
3x+2y-z=23 --> z=-23+2y+3x
Y=8
Substitute for -2y+4z=16
-2(8)+4(-23+2(8)+3x)=16
-16-28+12x=16
-44+12x=16
12x=60
X=5
Substitute known y and x values into z=-23+2y+3x
Z=-23+2(8)+3(5)
Z=-23+16+15
Z=8
        
             
        
        
        
The standard form for an equation is y=mx+b. You find the slope by using the formula of rise over run. This means that for problem 6 you first look to see if its positive or negative slope. The slope is positive if the line is going uphill and if its going downhill its negative. The slope would be negative for number 6 because it is going downhill. Then for the actualy slope you would start with rise. So you look at the point (0,1) and go up 3 until you hit the line of the other point and run over 2. So your slope would be -3/2.
        
             
        
        
        
Answer:
a) 
And we can use the probability mass function and we got:
 
  
 
  
 
  
And adding we got:

b)  
  
c) ![P(X>3) = 1-P(X \leq 3) = 1- [P(X=0)+P(X=1)+P(X=2)+P(X=3)]](https://tex.z-dn.net/?f=P%28X%3E3%29%20%3D%201-P%28X%20%5Cleq%203%29%20%3D%201-%20%5BP%28X%3D0%29%2BP%28X%3D1%29%2BP%28X%3D2%29%2BP%28X%3D3%29%5D%20)
 
  
 
  


And replacing we got:
![P(X>3) = 1-[0.0115+0.0576+0.1369+0.2054]= 1-0.4114= 0.5886](https://tex.z-dn.net/?f=%20P%28X%3E3%29%20%3D%201-%5B0.0115%2B0.0576%2B0.1369%2B0.2054%5D%3D%201-0.4114%3D%200.5886)
d) 
Step-by-step explanation:
Previous concepts  
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".  
Solution to the problem  
Let X the random variable of interest, on this case we now that:  
 
  
The probability mass function for the Binomial distribution is given as:  
 
  
Where (nCx) means combinatory and it's given by this formula:  
 
  
Part a
We want this probability:

And we can use the probability mass function and we got:
 
  
 
  
 
  
And adding we got:

Part b
We want this probability:

And using the probability mass function we got:
 
  
Part c
We want this probability:

We can use the complement rule and we got:
![P(X>3) = 1-P(X \leq 3) = 1- [P(X=0)+P(X=1)+P(X=2)+P(X=3)]](https://tex.z-dn.net/?f=P%28X%3E3%29%20%3D%201-P%28X%20%5Cleq%203%29%20%3D%201-%20%5BP%28X%3D0%29%2BP%28X%3D1%29%2BP%28X%3D2%29%2BP%28X%3D3%29%5D%20)
 
  
 
  


And replacing we got:
![P(X>3) = 1-[0.0115+0.0576+0.1369+0.2054]= 1-0.4114= 0.5886](https://tex.z-dn.net/?f=%20P%28X%3E3%29%20%3D%201-%5B0.0115%2B0.0576%2B0.1369%2B0.2054%5D%3D%201-0.4114%3D%200.5886)
Part d
The expected value is given by:

And replacing we got:

 
        
             
        
        
        
12 x 16 = 192. So, the room is 192 square feet.