Three straight lines intersect at $O$, and ray $\overrightarrow{OD}$ divides $\angle COE$ into two angles of equal measure. The
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Answer:
Revenue , Cost and Profit Function
Step-by-step explanation:
Here we are given the Price/Demand Function as
P(x) = 253-2x
which means when the demand of Cat food is x units , the price will be fixed as 253-2x per unit.
Now let us revenue generated from this demand i.e. x units
Revenue = Demand * Price per unit
R(x) = x * (253-2x)
=
Now let us Evaluate the Cost Function
Cost = Variable cost + Fixed Cost
Variable cost = cost per unit * number of units
= 3*x
= 3x
Fixed Cost = 6972 as given in the problem.
Hence
Cost Function C(x) = 3x+6972
Let us now find the Profit Function
Profit = Revenue - Cost
P(x) = R(x) - C(x)
=
=
Now we have to find the quantity at which we attain break even point.
We know that at break even point
Profit = 0
Hence P(x) = 0
now we have to solve the above equation for x
Dividing both sides by -2 we get
Now we have to find the factors of 3486 whose sum is 125. Which comes out to be 42 and 83
Hence we now solve the above quadratic equation using splitting the middle term method .
Hence
Either (x-42) = 0 or (x-83) = 0 therefore
if x-42= 0 ; x=42
if x-83=0 ; x=83
Smallest of which is 42. Hence the number of units at which it attains the break even point is 42.
When the occurrence of one event say A does not affect the occurrence of another event say B, than the two events are said to be independent such that;
where, P(A) = probability of occurrence of event A
and P(B) = probability of occurrence of event B
(a).
Now, let event A = Sarah scores more than 175
and event B = Thomas scores more than 175
Thus, P(A)= Probability that Sarah scores more than 175 = 0.4
and P(B)= Probability that Thomas scores more than 175 = 0.2
Since, the scores are independent, thus the probability that both Sarah and Thomas scores more than 175 is,
Hence, the required probability is 0.08
(b).
When the occurrence of one event say A affects the occurrence of another event say B, than the two events are said to be dependent such that;
Now, let event A = Sarah scores more than 175
and event B = Thomas scores more than 175
Thus, P(A)= Probability that Sarah scores more than 175 = 0.4
P(B)= Probability that Thomas scores more than 175 = 0.2
and P(B|A) = Sarah scores more than Thomas given that Thomas scores more than 175 = 0.3
Thus, the required probability is calculated as follows;