Answer:
Step-by-step explanation:
Given
6 rolls of a die;
Required
Determine the possible sequence of rolls
From the question, we understand that there were three possible outcomes when the die was rolled;
The outcomes are either of the following faces: 1, 2 and 3
Total Number of rolls = 6
Possible number of outcomes = 3
The possible sequence of rolls is then calculated by dividing the factorial of the above parameters as follows;
Hence, there are 120 possible sequence.
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.
It is given in the question that,
Line QS bisects angle PQR. Solve for x and find the measure of angle PQR.
And
Since QS bisects angle PQR, therefore
Substituting the values, we will get