The demand function for the marginal revenue function is found as; p(x) = 0.02x² - 0.025x + 138.
Explain the term revenue function?The relationship between the demand function p(x) as well as the revenue function R(x) is given by the equation R(x)=xp(x), where x represents the quantity of units sold.In order to get the revenue function, we shall integrate the marginal revenue function R′(x).For the given question;
R′(x) = 0.06x² − 0.05x + 138
R(x) = ∫R′(x)dx
R(x) = ∫[0.06x² − 0.05x + 138] dx
R(x) = 0.06x³/3 - 0.05x²/2 + 138x + C
R(x) = 0.02x³ - 0.025x² + 138x + C
If R(0) = 0, revenue is 0.
Put x = 0.
0.02x³ - 0.025x² + 138x + C = 0
c = 0
Thus,
R(x) = 0.02x³ - 0.025x² + 138x
Factorizing the function,
R(x) = 0.02x³ - 0.025x² + 138x
R(x) = x(0.02x² - 0.025x + 138)
R(x) = xp(x) . Thus,
p(x) = 0.02x² - 0.025x + 138
Therefore, the demand function for the marginal revenue function is found as; p(x) = 0.02x² - 0.025x + 138.
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The ratio of the lengths of the sides of a right triangle is 1: √3:2. What is the sine of the triangle's
smallest angle?
Answer:
You're welcome. :)
Step-by-step explanation:
Hope you're able to understand it.
The number of vhs movie rentals has declined since the year 2000 due to the popularity of dvds, as the following table shows. The exponential regression equation was found to be where x represents the number of years since 2000. Use the regression equation to predict the number of vhs movies in 2011. Year 2000 2001 2002 2003 2004 2005 2006 vhs rentals (in millions) 10. 5 8. 1 6. 4 5. 2 4. 5 3. 8 3. 1 a. 1. 13 c. 0. 929 b. 1. 37 d. 3. 7 please select the best answer from the choices provided a b c d.
In 2011 we can predict there will be only 1.13 million VHS movie rentals.
What is regression equation?
A regression equation is utilized in details to figure out what relationship, if any, exists between sets of information. For instance, assuming that you measure a kid's level consistently you could find that they develop around 3 inches a year. That pattern (growing three inches a year) can be displayed with a regression equation.
According to question:
The remarkable relapse condition is the dramatic capability that best fits the arrangement of information and it is given in the structure:
y = a · bˣ
where:
a = beginning worth of the model
b = remarkable develop or rot
x = time elapsed all along
For our situation,
y = 9.92 · (0.8208)ˣ
where:
a = 9.92
b = 0.8208
Since 0 < b < 1 we have an outstanding rot, affirming that the quantity of VHS is diminishing with time.
We can then utilize this condition to gather the quantity of VHS motion pictures in 2011.
As something first, compute how long all along (2000) would pass:
x = 2011 - 2000 = 11
Presently, substitute this worth in the situation:
y = 9.92 · (0.8208)¹¹
= 1.13
Thus, number of vhs movies in 2011 is 1.13 million.
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RATIO AND PROPORTION
EXERCISE 12.1
1. There are 20 girls and 15 boys in a class.
(a) What is the ratio of number of girls to the number of boys?
(b) What is the ratio of number of girls to the total number of students in the class?
Salad 'n Scoops is a food truck that sells salads for $4 and scoops of ice cream for $2. On a hot July day, they had 118 customers and earned
$326. Let x be the number of scoops of ice cream sold and y be the number of salads sold that day. How many salads were sold that day?
45 be the number of scoops of ice cream sold and 73 be the number of salads sold that day.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Salad 'n Scoops is a food truck that sells salads for $4 and scoops of ice cream for $2
On a hot July day, they had 118 customers and earned $326.
Let x be the number of scoops of ice cream sold and y be the number of salads sold that day.
From the given information
4x+2y=$326...(1)
x+y=118
x=118-y..(2)
Substitute 2 in 1
4(118-y)+2y=326
472-4y+2y=326
472-2y=326
Subtract 472 on both sides
-2y=-146
Divide both sides by 2
y=73
Plug in y value in equation 2'
x+y=118
x+73=118
x=118-73
x=45
Hence, 45 be the number of scoops of ice cream sold and 73 be the number of salads sold that day.
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Which equation is a point slope form equation for line AB? Responses y−2=−2(x+2) y−2=−2(x+6) y−2=2(x+2)
The equation in point slope form will be -
y - 2 = 2(x - 3).
What is the general equation of a Straight line?
The general equation of a straight line is -
y = mx + c[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.Other possible equations of lines are -
(y - y₁) = m(x - x₁) {Point - slope form}(y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁) {Two point - slope form}x/a + y/b = 1 {intercept form}x cos(β) + y sin(β) = L {Normal form}We have some equations of line as given in the question.
The point slope form is -
(y - y₁) = m(x - x₁)
The points are -
(3, 2) and (5, 6)
So -
m = (6 - 2)/(5 - 3)
m = 4/2
m = 2
Equation will be -
y - 2 = 2(x - 3)
Therefore, the equation in point slope form will be -
y - 2 = 2(x - 3)
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What is the slope of a line parallel to the line whose equation is
8x-6y=-24
The slope of a line parallel to the line 8x - 6y = -24 is 4/3.
What is slope of a line parallel to the line whose equation is given?The slope-intercept formula is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the equation of the line.
8x - 6y = -24
First, rewrite in slope-intercept form.
8x - 6y = -24
Solve for y
8x + 24 = 6y
6y = 8x + 24
y = (8/6)x + 24/6
y = (4/3) + 4
Now, from the slope-intercept form;
y = mx + b
Where m is the slope
Slope of the line y = (4/3) + 4 will be
m = 4/3
All line parallel to the line y = (4/3) + 4 must have the same slope.
Hence, the slope of a parallel line to the line y = (4/3) + 4 will be;
m_parallel = 4/3
Therefore, the slope of the parallel line is 4/3.
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2/3 x=27
PLEASE HELPPPP ASAPPP
Answer:
81/2 is answer.......2/3× 81/ 2 = 27
Answer:
x=40.5
Step-by-step explanation:
2/3x=27
x3. x3
2x=81
/2 /2
x=40.5
hopes this helps please mark brainliest
Morgan ha 6 pack of eraer. Each pack of eraer ha x eraer in it. After Avery give her 3 more eraer, he ha a total of 27 eraer. A. Model the ituation with an equation. B. Find a olution to your equation from part (a)
c. Interpret the olution in the context of the problem
The equation that represents the model is 6x + 3 = 27, the solution of the equation is x = 4
Total number of pack of eraser = 6
Number of eraser in one pack = x
Number of erasers in 6 pack = 6x
Add 3 more erasers
Total number of erasers = 6x + 3
Total number of erasers = 27
Then the equation that represents the model will be
6x + 3 = 27
Solve the equation
6x = 27 - 3
Subtract the numbers
6x = 24
x = 24/6
Divide the numbers
x = 4
Therefore, the equation is 6x + 3 = 27, and the solution of the equation x = 4
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Literal Equations
help asap !!
Answer:
Step-by-step explanation:
7y = -3x + 7
y = -3/7x + 1
The point (6,9) is shown on the graph. Write an equation that represent this situation, where Y represent the amount of water, in cups, and X represents the number of lemons
The equation that represents the situation will be y = 1.5x.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
From the graph, the y-intercept of the line is zero. Then the equation is given as,
y = mx
The line is passing through (6, 9), then we have
9 = 6m
m = 9 / 6
m = 1.5
Then the equation that represents the situation will be y = 1.5x.
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Please answer this question I dont get it
21.8 cm is length of rectangle .
What is the name of the rectangle shape?
A rectangle may also be referred to as an equiangular quadrilateral. This is so because a rectangle is a quadrilateral (4-sided form) with parallel sides that are equal to one another and corners with 90o angles on each side.
An equiangular quadrilateral is another name for a rectangle shape because all of the angles are 90 degrees.
L=5+6W
156 = 2L + 2w
2(5+6W) + 2W = 156
10+ 12W +2W =50
14W = 40
W = 40/14
W = 2.8 CM
W =5 cm
L= 5+6( 2.8 ) = 21.8 cm
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What set of key points can she use to graph the equation
The vertex of the graph for the given equation is (-1, -8).
What is differentiation?The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) = (f(x + h) - f(x)) /(x + h - x).
Its geometrical aspect is the slope of the tangent at a given point.
The given equation is y = 2x² + 4x - 6.
The vertex is a point at the graph where the slope becomes zero. It can be found by equating the differentiation of the equation to zero as below,
y = 2x² + 4x - 6
=> y' = 4x + 4 = 0
=> x = -1
At x = -1 the value of y can be found as,
y = 2 × -1² + 4 × -1 - 6
= 2 - 4 - 6
= -8
Thus, the vertex is given as (-1, -8) which is only valid for option (b).
Hence, the key points to be used by sandy to draw the graph are x-intercept (1, 0), y-intercept (-3, 0) and vertex (-1, -8).
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during his college basketball season, jeff made 646 baskets out of 1360 attempts. what was his shooting percentage? round to the nearest whole percent.
Answer: I think its 10%
Step-by-step explanation: I hope that helps
Are the lines C and D parallel? (The figure may not be drawn to scale). Giving brainliest for whoever answers correctly
1. Yes
2.no
3. Can’t be determined
Explain what the solution means in the context of the word problem. 8x + 10 ≤ 53
Answer:
8x ≤ 53 - 10
8x ≤ 43
x ≤ 43/8
X is smaller or equal to 43/8 (5.375)
What is the value of Y?
(Please help me with this question.)
Answer:
x = 8
y = 36
Step-by-step explanation:
The triangle shown in the image is an isosceles triangle.
We can find the value of x using the above mentioned information:
∠B = ∠A
5x = 40 divide both sides by 5
x = 8
The sum of interior angles in a triangle is equal to 180°.
Since ∠B and ∠C are both 40°:
40 + 40 + 3y - 8 = 180 add/subtract like terms
72 + 3y = 180 subtract 73 from both sides
3y = 108 divide both sides by 3
y = 36
Select all ordered pair(s) that satisfies the function h(x)=x+3.
2
(0, -2)
(-4,-3)
(-5,-4) (-2,0)
(1,4)
(3,0)
(3,7)
(0, 3)
Answer:
I think its these:
(0,3)
(1,4)
(2,5)
Step-by-step explanation:
Which equation represents a vertical line? *
A. y =2x
B. x = 2
C. y = 3
D. y = -x
Answer:
x = 2
Step-by-step explanation:
X is the vertical edge
x=2
Answer: x = 2
Step-by-step explanation:
The slope of a vertical line is undefined, so the equation of a vertical line is x = a
In this problem, the only choice that represents a vertical line is x = 2 (where a = 2)
In order to make a pecific hade of green paint a paint mixe 1/2 of a gallon of blue paint with 4/5 of a gallon of yellow piant how many gallon of each color ate needed to make 26 total gallon of thi color
To make 26 gallons of the shade of green paint, 13 gallons of blue paint is needed.To make 26 gallons of the shade of green paint, 20.8 gallons of yellow paint is needed.
What is meant by multiplication?Finding the product of two or more integers is done mathematically through the action of multiplication. It entails adding a number, known as the , known as the multiplier. For instance, adding three to itself four times produces the result of multiplying three by four, which is twelve. In other ways, repeated addition may be expressed using the abbreviation "multiplication." It is frequently used to calculate the overall worth of a set of paint, such as the cost of numerous products in a shopping cart. Finding the area of a rectangle or the volume of a cube are two more more difficult mathematical procedures that employ it.
How to solve?
To make 26 gallons of the shade of green paint, 1/2 * 26 = 13 gallons of blue paint is needed.
To make 26 gallons of the shade of green paint, 4/5 * 26 = 20.8 gallons of yellow paint is needed.
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-10x - 5 = -51
solve for the variable please
Answer:
-10x = -51 + 5
-10x = -46
x=-46/-10
x=46/10
x=4.6
Answer:
x=23/5
Step-by-step explanation:
-10x-5=-51
-10x=-51+5
-10x=-46
10x=46
x=46/10
x=23/5
7x^(2 )+5x +4
what is the constant term?
what is the degree of the expression?
write down the coefficient of the second term
calculate the value of the expression 7x²+5x+4 if x = -1
In given expression constant term is 4, degree of expression is 2, coefficient of second term is 5 and at x=-1 value of expression is 6.
What is constant term and degree of expression?The highest or greatest power of a variable in a polynomial equation is referred to as the degree of the polynomial.
The degree denotes the polynomial's highest exponential power.
A term in an equation with a fixed value that is unaffected by variations in the variable.
A constant is typically represented as c to reflect a fixed value when written as a variable.
The usage of the word "variable" in this terminology may be perplexing, but all it really implies is that c is a variable that may stand in for any fixed value.
Given: p(x)=7x²+5x+4
(a) Constant term is coefficient of [tex]x^{0}[/tex].
So constant term in given equation is 4.
(b) Degree of expression is highest power of x in the expression. For our expression we have two as our highest power.
So, degree of expression is 2.
(c) Coefficient of second term is 5.
(d) On substituting value of x as -1, we get
7× (-1)² +5(-1) +4 = 7-5+4 = 6
So, value of expression at x=-1 is 6.
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100 Points , MAX. Please help I dont have a lot of time, assignment goes due tonight.
I will give brainliest.
Answer:pt 1). Oliver is correct
pt 2). The volumes are the same
yw
i need help past due
Answer:
1:2
1 to 2
These are the other notations for 1/2
Let f be a differentiable function with f(1) = 2, f'(1) = 3, f(-4)= -3, and
f'(-4)= 4. Let the function g(x) = f(2x - 6). Write the equation of the line
tangent to the graph of g at the point where x = 1.
The equation of the line tangent to the graph of g at the point where x = 1 y + 10x + 44 =0.
What is line tangent?
A line that touches a curve at one point is said to be tangent. A point of tangency is the location where a curve and a line intersect. Y = mx + b is the slope-intercept formula for a line, where m is the line's slope. The straight line that "just touches" the curve at a particular location is referred to as the tangent line to a plane curve in geometry. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.
Given g(x)=f(2x)
Differentiate it on both side with respect to x.
[tex]\begin{aligned}& \frac{d g(x)}{d x}=2 * \frac{d f(2 x)}{d x} \\& \frac{d g(-1)}{d x}=2 * \frac{d f(-8)}{d x}=-5^* 2=-10\end{aligned}[/tex]
Slope =-10
Here x coordinate = -4
g(-4)=f(-8)=-4 = y coordinate
Thus point of tangency on function g is (-4,-4)
Thus equation of tangent is
y + 4= -10(x+4)
y + 10x + 44 =0
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Answer:
y = 8x -11
Step-by-step explanation:
You want the equation of the line tangent to g(x) = f(2x-6) at x=1, where f is a differentiable function with f(1) = 2, f(-4) = -3, f'(1) = 3, f'(-4) = 4.
Tangent lineThe equation of the tangent line at x=1 can be written ...
y = g'(1)(x -1) +g(1)
The necessary function values are ...
g(1) = f(2·1 -6) = f(-4) = -3
and
g'(x) = f'(2x -6)·(2x -6)' = 2f'(2x -6)
g'(1) = 2f'(2·1 -6) = 2f'(-4) = 8
Then the equation of the line is ...
y = 8(x -1) +(-3) = 8x -8 -3
y = 8x -11 . . . . . . tangent to g(x) at x=1
__
Additional comment
The minimum polynomial function f(x) that can have the desired values and derivatives is a cubic. The attached graph shows g(x) and the tangent at x=1 using that cubic for f(x).
Estima.
162÷4.1≈
porfavoor
Answer:
39.512195122
Step-by-step explanation:
You divide 162 by 4.1, you can use a calculator to help solve. If needed to be rounded it is 40
A plane leaves Charlotte at 9:00 AM and flies north at 400 knots. At the same time, another plane flies south from Charlotte as 250 knots. How long is it before they are 1000 nautical miles apart?
They took 1.53 hrs long before they are 1000 nautical miles apart.
What is the distance?
Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.
Here, we have
A plane leaves Charlotte at 9:00 AM and flies north at 400 knots. At the same time, another plane flies south from Charlotte at 250 knots
The speeds are added when going in opposite directions = 400 + 250knots = 650 knots
We apply here distance formula,
Distance = rate × time
t = d/r
= 1000/650 hours
= 1.53 hours
Hence, they took 1.53 hrs long before they are 1000 nautical miles apart.
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Add −3.7+ [tex]\frac{1}{4}[/tex] Write your answer as a decimal to the nearest hundredth.
Answer:
Step-by-step explanation:
-3.45
1. How long did it take Alex to get his first friends house
2.How long did he stay at his first friends house
3. how long did it take Alec to ride his bike from his first friends house to his second friend's house
4.how much longer did alec stay at his first friends house than at his second friend's house
5. in which parts of the graph is alec riding his bike towards his home
6. in which parts of the graph is alec traveling the fastest
7. how long was alec away from his house
From the given 2D graph:
1. It took 20 minutes for Alec to get to his first friend's house.
2. Alec stayed for 40 minutes at his first friend's house.
3. It took 10 minutes for Alec to ride his bike from his first friend's house to his second friend's house.
What is a 2D graph?
In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.
4. Alec stayed for 10 minutes longer at his first friend's house than at his second friend's house.
5. In part E of the graph Alec is riding his bike toward his home.
6. In part A of the graph Alec is traveling the fastest.
7. Alec was away from his house for 115 minutes.
1. From the given graph we can observe that part A of the graph is the time taken by Alec to reach his first friend's house which is 20 minutes.
2. From the given graph we can observe that part B of the graph is the time that Alec stayed at his first friend's house.
3. From the given graph we can observe that part C of the graph is the time that Alec took to ride his bike from his first friend's house to his second friend's house.
4. Alec stayed at his first friend's home for 40 minutes, and he stayed at his second friend's home for 30 minutes, therefore Alec stayed for 10 minutes longer at his first friend's house than at his second friend's house.
5. In part E of the graph Alec is riding his bike toward his home.
6. In part A of the graph Alec is traveling the fastest.
7. Alec was away from his house for part(A+B+C+D+E)=20+40+10+30+15=115 minutes.
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Write the y = mx + b equation of the line passing through points (5, 18) and (8, 9).
The equation of the line passing through points (5, 18) and (8, 9) will be y = - 3x + 33.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The points are given below.
(5, 18) and (8, 9)
The points (5, 18) and (8, 9) will satisfy the equation y = mx + c, then the equations are given as,
18 = 5m + c ...1
9 = 8m + c ...2
From equations 1 and 2, then we have
18 - 9 = 5m - 8m
3m = - 9
m = -3
Then the value of 'c' is given as,
9 = 8(-3) + c
9 = - 24 + c
c = 33
The equation is written as y = -3x + 33.
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An isosceles triangle has a perimeter of 23 meters. The base of the triangle is 7 meters.
Write an equation to represent the other lengths, X, of the triangle.
An equation to represent the other lengths, X, of the triangle is 2X+7=23.
What is meant by an isosceles triangle?An isosceles triangle is one that has two equal-length sides in geometry. The term "equilateral triangle" can refer to a shape with either exactly two sides that are the same length or at least two sides that are the same length, with the latter definition containing the equilateral triangle as an exception. The faces of bipyramids and a few Catalan solids are examples of isosceles triangles, as are the isosceles right triangle, the golden triangle, and others.
Isosceles triangles have been the subject of mathematical research since the time of the Babylonians and the Egyptians.
Given,
Perimeter of an isosceles triangle=23 meters
The base of a triangle=7 meters
P=2X+b
2X+7=23
Therefore, an equation to represent the other lengths, X, of the triangle is 2X+7=23.
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