Answer:
a) 
b) 
Step-by-step explanation:
By definition, we have that the change rate of salt in the tank is  , where
, where  is the rate of salt entering and
 is the rate of salt entering and  is the rate of salt going outside.
 is the rate of salt going outside.
Then we have,  , and
, and

So we obtain.   , then
, then
 , and using the integrating factor
, and using the integrating factor  , therefore
, therefore   , we get
, we get    , after integrating both sides
, after integrating both sides  , therefore
, therefore  , to find
, to find  we know that the tank initially contains a salt concentration of 10 g/L, that means the initial conditions
 we know that the tank initially contains a salt concentration of 10 g/L, that means the initial conditions  , so
, so 

Finally we can write an expression for the amount of salt in the tank at any time t, it is 
b) The tank will overflow due Rin>Rout, at a rate of  , due we have 500 L to overflow
, due we have 500 L to overflow  , so we can evualuate the expression of a)
, so we can evualuate the expression of a)  , is the salt concentration when the tank overflows
, is the salt concentration when the tank overflows
 
 
        
             
        
        
        
17x +x to the second power
        
             
        
        
        
the x and y values makes both equations true
Explanation
a linear system is the set of 2 linear equations.
Step 1
the solution to a linear system is the coordiante where the line intersect, this coordiante satisfies both equations, then
the x and y values makes both equations true
 
        
             
        
        
        
Answer:
Probability that a randomly selected firm will earn less than 100 million dollars is 0.8413.
Step-by-step explanation:
We are given that the mean income of firms in the industry for a year is 95 million dollars with a standard deviation of 5 million dollars. Also, incomes for the industry are distributed normally.
<em>Let X = incomes for the industry</em>
So, X ~ N( )
)
Now, the z score probability distribution is given by;
          Z =  ~ N(0,1)
 ~ N(0,1)
where,  = mean income of firms in the industry = 95 million dollars
 = mean income of firms in the industry = 95 million dollars
              = standard deviation = 5 million dollars
 = standard deviation = 5 million dollars
So, probability that a randomly selected firm will earn less than 100 million dollars is given by = P(X < 100 million dollars)
     P(X < 100) = P(  <
 <  ) = P(Z < 1) = 0.8413   {using z table]
 ) = P(Z < 1) = 0.8413   {using z table]
                                                      
Therefore, probability that a randomly selected firm will earn less than 100 million dollars is 0.8413.