Answer:
N(x) = 40 - 2x
P(x) = -2x² + 52 x - 240
maximum profit = 13
Step-by-step explanation:
given data 
feeder cost = $6
average sell = 20 per week
price = $10 each
solution
we consider here price per feeder = x 
and profit per feeder  id here formula   = x - 6 
so that here
total profit will be
P (x)  = ( x - 6 ) Nx
here N(x) is number of feeders sold at price =  x
so formula for N (x)  is here 
N(x) = 20 - 2 ( x - 10 )    
N(x) = 40 - 2x
so that 
P(x) = (x-6) ( 40 - 2x) 
P(x) = -2x² + 52 x - 240
since here 
a = -2
b = 52
c = -240 
a < 0
so quadratic function have maximum value of c -  
 
so it will be 
maximum value = -240 -  
 
maximum value = 98
so here maximum profit attained at 
x = 
x = 
x = 13
maximum profit = 13
 
        
             
        
        
        
(1) See below for a diagram. Basically, the distance on the ground from the person to the building (34 ft) is adjacent to the angle of elevation (74 degrees) and the height of the building (labeled h in the diagram) is the side opposite the angle. Since we are dealing with opposite and adjacent we use the tangent of the angle and tan = opp/adj
Specifically, 


<span class="_wysihtml5-temp-placeholder"></span>

 feet.
Please be sure your calculator is set to degrees (not radians) when you do this problem.
(2) Here since P & Q are complimentary it means that their sum is 90 degrees. Since this is a right triangle that means that the remaining angle (R) must be the right angle. See below for a diagram. 
sin = opp/hyp. As the sin Q =  9/41 this means that 9 is the length of the side opposite Q (the side PR) and 41 is the length of the hypotenuse. This makes the remaining side (QR) 40 in length.
cos = adj/hyp. If we focus on angle P the side adjacent (next to) is 9 and the hypotenuse is 41. Thus the cos of P = 9/41.
You could have also realized that if P & Q are complimentary the sin P = cos Q and the cos P = sin Q. We were not asked about tangent but it is also the case that tan P = cot Q and cot P = tan Q.
 
        
        
        
A relation is (also) a function if every input x is mapped to a unique output y.
In terms of graphical representation, this implies that a graph represents a function if there doesn't exist a vertical line that intersects the graph more than once. So:
- The first graph is exactly a vertical line, so it's not a function.
- The second graph represents the function y=x, so it's a function: you can see that every possible vertical line crosses the graph only once.
- The third graph is not a function, because you can draw vertical lines that cross the graph twice.
- Similarly, in the fourth graph you can draw vertical lines that cross the graph twice
- The fifth graph is a function, because every vertical line crosses the graph once
- The last graph is a function, although discontinuous, for the same reason.
 
        
                    
             
        
        
        
To get the probability that at least 8 of the words on the test are words that students know we need to do the following calculations.
<span>=[C(16,8)*C(10,2) + C(16,9)*C(10,1) + C(16,10)*C(10,0)] / C(26,10)
</span>
=0.132