A carpet cleaning business has 100 customers when they charge $125 for a cleaning. Research shows that every $5 reduction in price attracts another 20 customers. What price should the business implement to maximize its revenue?
a $75
b $100
c $120
d $90
The linear relationship is c(p) = -4p + b. Then the price that maximizes revenue is $75.
What is the linear system?It is a system of an equation in which the highest power of the variable is always 1.
A carpet cleaning business has 100 customers when they charge $125 for cleaning.
Research shows that every $5 reduction in price attracts another 20 customers.
Since a $5 decrease in price increases customers by 20, we can say that we have two options.
(120, 100) and (120, 120) from these we can find the slope or rate of change of customers as a function of price.
[tex]\rm m = \dfrac{20}{-5}\\\\ m = -4[/tex]
Then we have
[tex]\rm c(p ) = -4 p +b[/tex]
Now, we can use (125, 100) to solve for b
100 = -4(125) + b
b = 600
So our number of customers as a function of price is
[tex]\rm c(p) = 600 - 4p[/tex]
Revenue will simply be the number of customers times the price charged per customer will be
[tex]\rm r(p) = 600 p -4p^2[/tex]
We can find a price that creates maximum revenue by finding when the derivative is equal to zero.
[tex]\rm \dfrac{dr}{dp} = 600 - 8p\\\\[/tex]
WE know that for maximum,
[tex]\rm \dfrac{dr}{dp} = 0\\\\0 = 600 - 8p\\\\p = 75[/tex]
So, the price that maximizes revenue is $75.
More about the linear system link is given below.
The length of a rectangle is twice its width. if the area of the rectangle is 162 cm2 , find its perimeter.
Choose the correct simplification of (6x4y2z3)(3x4y3z5).
18x16y6z15
18x8y5z8
9x8y5z8
9x16y6z15
Answer:
18 x 8y 5z 8 witch is answer choice B
Step-by-step explanation:
What is the equation in point-slope form of the line passing through (0, 5) and (−2, 11)? y − 5 = −3(x + 2) y − 5 = 3(x + 2) y − 11 = −3(x − 2) y − 11 = −3(x + 2)
Hello : let A(0,5) B(-2,11)
the slope is : (YB - YA)/(XB -XA)
(11-5)/(-2-0) = 6/(-2)
the slope is : -3
Answer: [tex]y-11=-3(x+2)[/tex]
Step-by-step explanation:
Given points : (0, 5) and (−2, 11)
Slope of the line passing through given points .
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{11-5}{-2-0}=\frac{6}{-2}=-3[/tex]
Thus, slope of line passing through given points m=-3
We know that the equation of a line passing through points [tex](x_0,y_0)[/tex] with slope 'm' is [tex](y-y_0)=m(x-x_0)[/tex]
Thus, equation of a line passing through (−2, 11) with slope m=-3 will be
[tex](y-11)=(-3)(x-(-2))\\\Rightarrow\ y-11=-3(x+2)[/tex]
Hence, the equation of line is [tex]y-11=-3(x+2)[/tex]
what is the range of f(x)=log0.6x
Compare 9 ⋅ 104 to 3 ⋅ 102.
9 ⋅ 104 is 3 times larger than 3 ⋅ 102.
9 ⋅ 104 is 30 times larger than 3 ⋅ 102.
9 ⋅ 104 is 300 times larger than 3 ⋅ 102.
9 ⋅ 104 is 3,000 times larger than 3 ⋅ 102.
Answer:
9×10⁴ is 300 times greater than 3×10²
Step-by-step explanation:
guy above me's work. thanks to him we get this answer :)
If the tangent line to y = f(x) at (7, 4) passes through the point (0, 3), find f(7) and f '(7).
Final answer:
To find f(7) and f'(7) of y = f(x) given a point on the tangent line passing through another point.
Explanation:
Given:
Equation of tangent line to y = f(x) at (7, 4) passes through (0, 3).
To find:
f(7) and f'(7).
The line through the midpoint of and perpendicular to the segment joining points (1, 0) and (5, -2). The answe is x_ _= something
Two lines are perpendicular. if one line has a slope of 0, what is the slope of the other line?
What are the possible values of x in x2 + 3x + 3 = 0?
What is the remainder of (x3 - 6x2 - 9x + 3) ÷ (x - 3) A. -25 B. -52 C. -51 D. -17
the correct answer in C. -51 hope this helps you
Which line is parallel to the line y=12x+5 and passes through the point (-2, 1)?
The equation of the line parallel to y=12x+5 that passes through the point (-2, 1) is y=12x+25.
Since the two lines are parallel, they will have the same slope. The slope of the given line is the coefficient of x, which is 12. Therefore, the line we are looking for also has a slope of 12.
To find the equation of the new line, we'll use the point-slope form of a line equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point.
Substituting the given point and the slope into this form we get:
y - 1 = 12(x + 2)
Expanding and simplifying this, we have:
y - 1 = 12x + 24
Finally, adding 1 to both sides to solve for y, we get:
y = 12x + 25, which is the equation of the line that is parallel to y=12x+5 and passes through the point (-2, 1).
Write an inequality for the situation.
all real numbers y that are less than –3 or greater than 18
A) y < –3 or y < 18
B) y < 18 or y > –3
C) –3 < y < 18
D) y < –3 or y > 18
points (0,0) and (3,3) lie on line k what is the slope of the line that is perpendicular to k
Solve by taking square roots: x^2 - 40 = 9
2, -4, 8, -16, . . . find the next two numbers in the pattern and describe the pattern.
On Mars, if you hit a baseball, the height of the ball at time "t" would be modelled by the quadratic function h=-1.85t^2+20t+1, where t is in seconds and h is in metres. When will the ball hit the ground?
Tony is four years younger than his brother josh, and two years older than his sister cindy. tony also has a twin brother, evan. all the ages of the children totaled together is 66. how old is tony?
To solve this problem, let us assign the variables. Let us say that:
x = age of Tony = which also the age of his twin brother Evan
x + 4 = age of Josh (since tony is 4 years younger, then josh must be 4 years older)
x – 2 = age of Cindy (since tony is 2 years older, then cindy must be 2 years younger)
There are a total of 4 children, therefore:
x + x + x + 4 + x – 2 = 66
4 x + 2 = 66
4 x = 64
x = 16
Therefore Tony is 16 years old.
To find Tony's age, we can set up an equation using the information given and solve for x. After solving the equation, we find that Tony is 16 years old.
Explanation:To solve this problem, we can assign variables to each person's age. Let's say Tony is x years old. Since Tony is four years younger than Josh, Josh's age can be represented as x + 4. Since Tony is two years older than Cindy, Cindy's age can be represented as x - 2. Since Tony has a twin brother, Evan, we can assign Evan's age as x as well.
According to the information provided, the sum of all their ages is 66, so we can set up the equation: x + (x + 4) + (x - 2) + x = 66. Simplifying the equation, we get 4x + 2 = 66. By subtracting 2 from both sides and dividing by 4, we find that x = 16.
Therefore, Tony is 16 years old.
Which law would you use to simplify the expression (p/q)^3
Answer:
B. Power of quotient.
Step-by-step explanation:
We have been given an expression [tex](\frac{p}{q} )^3[/tex] and we are asked to choose the correct rule to simplify our given expression.
Since our given expression is a fraction raised to 3rd power. Power of a quotient rule states when a quotient is raised to an exponent, then the exponent is distributed to both numerator and denominator of the quotient.
Using power of a quotient rule, we will get,
[tex](\frac{p}{q} )^3=\frac{p^3}{q^3}[/tex]
Therefore, we can simplify our given expression using power of a quotient and option B is the correct choice.
The power of quotients is the law that would be used to simplify the expression.
What is the power of quotients?This is a mathematical rule that states that the power of a quotient is the same thing as the quotient that is gotten.
Given that the numerator p and the denominator q are raised to to the power expressed in the question separately.
The division is calculated after this has done
Read more on the power of quotient here:
https://brainly.com/question/2141690
In the above figure, AE = 2, CE = 3, and DE = 4. What is the length of BE?
Answer:
its 6 i think
Explanation:
if you have the choices 6, 8, 12, 5.. then 6 is ur answer. why?
well u do CE x DE = AE x BE
(3)(4)= (2)(BE)
12=2x
12÷2= 6
State two reasons why including the p-value is prudent when you are reporting the results of a hypothesis test.
Which number line represents the solution set for the inequality 2x – 6 ≥ 6(x – 2) + 8?
what way do you shade in
Answer:
x < = -1/2 or -0.5
Step-by-step explanation:
that's the answer
To make bread dough, a baker mixes flour, eggs, yeast and salt by weight in pounds in the ratio of 11:9:3:2, respectively. how many pounds of yeast are required to make 20 pounds of bread dough?
Find the value of X.
the minute hand of a clock is 9.5cm long, How far does the tip of the hand travel in one day?
The graph below shows a line segment PQ: graph of line PQ going through ordered pairs negative 1, 3 and 2, negative 3 Which of the following equations best represents the line segment PQ?A: y = −3x + 2B: y = −2x + 1C: y = −3x − 2D: y = −2x − 1
Answer:
y = -2x + 1. The answer is B.
Step-by-step explanation:
Describe the graph of the function.y = |x – 4| – 7
We are given a function as:
[tex]y=|x-4|-7[/tex]
We know that this function is a transformation of the parent function y=|x| i.e. the modulus function.
The rule that holds in this transformation is:
It is a translation of the parent function 4 units to the right and 7 units down.
Also, the graph of the function is attached to the answer.
Solve the system using elimination. y – x = 13 7y + x = 11
The graph shows the functions f(x), p(x), and g(x): Graph of function g of x is y is equal to 1 plus the quantity 1.5 raised to the power of x. The straight line f of x joins ordered pairs 4, 1 and 2, negative 3 and is extended on both sides. The straight line p of x joins the ordered pairs 0, 2 and 1, negative 5 and is extended on both sides. Courtesy of Texas Instruments Part A: What is the solution to the pair of equations represented by p(x) and f(x)? (3 points) Part B: Write any two solutions for f(x). (3 points) Part C: What is the solution to the equation p(x) = g(x)? Justify your answer. (4 points)
Part A: Intersection at [tex]\((-13/4, -83/4)\)[/tex].
Part B: Two solutions for [tex]\( f(x) \): (0, -11) and (5, 14).[/tex]
Part C: Solve [tex]\( p(x) = g(x) \)[/tex] graphically for the Point of intersection
Part A: Solution to the Pair of Equations (p(x) and f(x)):
The solution to the pair of equations represented by [tex]\( p(x) \) and \( f(x) \)[/tex]is the point of intersection. From the information provided, it seems that the intersection point is [tex]\((-13/4, -83/4)\).[/tex]
Part B: Two Solutions for [tex]\( f(x) \)[/tex]:
1. [tex]\( (0, -11) \)[/tex]
2. [tex]\( (5, 14) \)[/tex]
Part C: Solution to [tex]\( p(x) = g(x) \)[/tex]:
To find the solution to [tex]\( p(x) = g(x) \), set \( p(x) = 7x + 2 \)[/tex] equal to [tex]\( g(x) = 1 + 1.5^x \). Solve for \( x \)[/tex] to determine the point of intersection between [tex]\( p(x) \) and \( g(x) \)[/tex]. The solution to this equation provides the [tex]\( x \)[/tex] coordinate, and substituting it into either [tex]\( p(x) \) or \( g(x) \)[/tex] gives the [tex]\( y \)[/tex] coordinate. The justification lies in the graphical intersection of the functions.
Note: It's essential to examine the graph for precise details, as visual inspection can help confirm the solutions.
For such more questions on point of intersection
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Which person in the high rise building is closest to the street level?Moira is in her doctor’s office on the fourth floor.Geoffrey is in the elevator between the second and third floors.Sandy is in the laundry room on the –2 basement floor.Hasim is leaving the parking garage and is currently between –1 and –2 levels.
Answer
Hasim is the closest... I just took the test