a) The total monthly cost is the sum of the fixed cost and the variable cost. If q represents the number of cones sold in a month, the monthly cost c(q) is given by
c(q) = 300 + 0.25q
b) If q cones are sold for $1.25 each, the revenue is given by
r(q) = 1.25q
c) Profit is the difference between revenue and cost.
p(q) = r(q) - c(q)
p(q) = 1.00q - 300 . . . . . . slope-intercept form
d) The equation in part (c) is already in slope-intercept form.
q - p = 300 . . . . . . . . . . . . standard form
The slope is the profit contribution from the sale of one cone ($1 per cone).
The intercept is the profit (loss) that results if no cones are sold.
e) With a suitable graphing program either form of the equation can be graphed simply by entering it into the program.
Slope-intercept form. Plot the intercept (-300) and draw a line with the appropriate slope (1).
Standard form. It is convenient to actually or virtually convert the equation to intercept form and draw a line through the points (0, -300) and (300, 0) where q is on the horizontal axis.
f) Of the three equations created, we presume the one of interest is the profit equation. Its domain is all non-negative values of q. Its range is all values of p that are -300 or more.
g) The x-intercept identified in part (e) is (300, 0). You need to sell 300 cones to break even.
h) Profit numbers are
425 cones: $125 profit
550 cones: $250 profit
700 cones: $400 profit
Answer: h(x)
Explanation:
1) f(x) is not a function because there is an ambiguity for x = 4.
x = 4 belongs to both intervals - 2 ≤ x ≤ 4 and x ≥ 4
Then you find two different possible images for x: 0 and -(2)^2 = - 4.
That makes that f(x) be not a function.
2) similar thing happens with g(x)
as per the given relation the value of g(x) for x = 2 is 4 and 4+1 = 5. Which makes that g(x) be not a function.
3) j(x) is not a function because the image of x = -4 is -3(-4) = 12 and 3.
4) h(x) is a function, because there is not any ambiguity in its definition, for every x in its domain there is only one image h(x).
Answer:
Options D & E are independent
Step-by-step explanation:
For any of the options to be independent, they have to be mutually exclusive i.e A ∩ B = 0
A) A ∩ B = {1, 2, 3}. They are not mutually exclusive and so they are not independent.
B) A ∩ B = {3}. They are not mutually exclusive and so they are not independent.
C) A ∩ B = {8}. They are not mutually exclusive and so they are not independent.
D) A ∩ B = 0. They are mutually exclusive and thus they are independent.
E) A ∩ B = 0. They are mutually exclusive and thus they are independent.
Answer :
It is D because you have to subtract 4.73 from both sides in order to isolate the y by itself and get the answer which is 3.27
Step-by-step explanation:
A. 3.25 or 3 1/4
B. 2
C. .25 or 1/4
D. -.75 or -3/4
E. -2.25 or -2 1/4
F. -3.75 or -3 3/4
