A) Demand function
price (x) demand (D(x))
4 540
3.50 810
D - 540 810 - 540
----------- = -----------------
x - 4 3.50 - 4
D - 540
----------- = - 540
x - 4
D - 540 = - 540(x - 4)
D = -540x + 2160 + 540
D = 2700 - 540x
D(x) = 2700 - 540x
Revenue function, R(x)
R(x) = price * demand = x * D(x)
R(x) = x* (2700 - 540x) = 2700x - 540x^2
b) Profit, P(x)
profit = revenue - cost
P(x) = R(x) - 30
P(x) = [2700x - 540x^2] - 30
P(x) = 2700x - 540x^2 - 30
Largest possible profit => vertex of the parabola
vertex of 2700x - 540x^2 - 30
When you calculate the vertex you find x = 5 /2
=> P(x) = 3345
Answer: you should charge a log-on fee of $2.5 to have the largest profit, which is $3345.
Answer:
The correct option is 1.
Step-by-step explanation:
It is given that the Brian, Kelsey, and Geoff each have a remote-controlled car. They simultaneously started their cars and drove them in a straight line away from a motion sensor.
It means they are travelling at a constant rate.
Slope formula:

From the given table it is clear that the of Brian's car from the sensor is 34 at 1 sec and 38 at 3 sec. The rate of change is

It means the Brian's car traveled at the rate of 2 cm per sec.
From the given table it is clear that the of Brian's car from the sensor is 27 at 1 sec and 31 at 3 sec. The rate of change is

It means the Kelsey's car traveled at the rate of 2 cm per sec.
From the given table it is clear that the of Brian's car from the sensor is 27 at 1 sec and 33 at 3 sec. The rate of change is

It means the Geoff's car traveled at the rate of 3 cm per sec.
Since Brian's and Geoff's car traveled at the same rate, therefore option 1 is correct.
24, since 54-30 is 24, and 30+24 is 54.
Answer:
1/4
Step-by-step explanation:
the numerator is 12 because there are 12 possible outcomes. The numerator is 3 because there are 3 numbers in this set that are greater than 9. You get 3/12 which then simplifies to 1/4
F = 
express the equation with F on the left side
3F - 24 = s ( add 24 to both sides )
3F = s + 24 ( divide both sides by 3 )
F = 