There are 3 terms, 5x^2, -3x, and 2
Parallel lines have the same slope.
To compare the slopes of two different lines, you have to get
both equations into the form of
y = 'm' x + (a number) .
In that form, the 'm' is the slope of the line.
Notice that it's the number next to the 'x' .
The equation given in the question is y = 3 - 2 x .
Right away, they've done something to confuse you.
You always expect the 'x' term to be right after the 'equals' sign,
but here, they put it at the end. The slope of this line is the -2 .
Go through the choices, one at a time.
Look for another one with a slope of -2 .
Remember, rearrange the equation to read ' y = everything else ',
and then the slope is the number next to the 'x'.
Choice #4: y = 4x - 2 . The slope is 4 . That's not it.
Choice #3: y = 3 - 4x . The slope is -4 . That's not it.
Choice #2). 2x + 4y = 1
Subtract 2x from each side: 4y = 1 - 2x
Divide each side by 4 : y = 1/4 - 1/2 x .
The slope is -1/2. That's not it.
Choice #1). 4x + 2y = 5
Subtract 4x from each side: 2y = 5 - 4x
Divide each side by 2 : y = 5/2 - 2 x .
The slope is -2 .
This one is it.
This one is parallel to y = 3 - 2x ,
because they have the same slope.
Answer:
The standard deviation of the data set is 
.
Step-by-step explanation:
The Standard Deviation is a measure of how spread out numbers are. Its symbol is σ (the greek letter sigma)
To find the standard deviation of the following data set
we use the following formula
Step 1: Find the mean 
.
The mean of a data set is the sum of the terms divided by the total number of terms. Using math notation we have:
Step 2: Create the below table.
Step 3: Find the sum of numbers in the last column to get.
Step 4: Calculate σ using the above formula.
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.
