Answer:
The demand curve is shown below, with the equation P = 50 - 1Qp. The supply curve is shown below, with the equation P = 40 + 1Qs. The point at the market equilibrium is shown with an asterisk, where the two curves intersect.
Demand Curve: 60- 50- * 40- 30- 20- 10- Price 0 2.5 5 10 7.5 Quantity 12.5 15 Q ON
Supply Curve: 60- 50- 40- * 30- 20- 10- Price 0 2.5 5 10 7.5 Quantity 12.5 15 Q ON
May someone please help me on this question? Thank you so much <33
Answer:
3 hours
Step-by-step explanation:
Graph the piecewise function. You must graph on your own and not use a web-based program to graph. f(x)={(1/3 x-1 if " x≤0 -1/2 x+6 if 0
The graph for the piecewise function f(x)={(1/3 x-1" if "x≤0 -1/2 x+6" if "0<x≤6 is attached in the solution.
What is a piecewise function?A piecewise function is a function that is defined on a sequence of intervals.
Given is a piecewise function f(x)={(1/3 x-1" if "x≤0 -1/2 x+6" if "0<x≤6
Plotting the graph for:
f(x)={(1/3 x-1" if "x≤0 -1/2 x+6" if "0<x≤6
From the graph, we conclude that:
The graph of the given piecewise function is a straight line with two segments.
The first segment, which lies between x = 0 and x = 6, has a slope of -1/2 and a y-intercept of 6.
The second segment, which lies between x = 0 and x = -∞, has a slope of 1/3 and a y-intercept of -1.
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Suppose I want to find an inverse to the function |cos x|. I intend to restrict the domain of the function to an interval whose left endpoint is x = 0 On which of the following intervals is |cos x| one-to one? Select one [0, pi/4] [0, pi/2] [0, pi] [0, 2 pi]
In the interval [0, π/2], the function is one-to-one or injective.
The functions which have one-to-one behaviour are called injective functions. An injective function is a function in which every horizontal line in the plane intersects the graph of f at most one point or we can say if f(x) = f(y) then x = y.
First, we need to draw the graph of y = |cos x|. The graph of y = |cos x| is attached.
We can see from the graph that the value of the function is 1 when x = 0 and the value of the function decreases till it takes 0 at x = π/2 and then the value of the function increases again.
In the option [0, π] and [0, 2π] the behaviour of the function is not injective.
In [0, π/4], the function is injective but [0, π/2] is the correct answer as it represents the largest interval starting from 0 on which this function is one-to-one.
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8÷4×(6+2 of 4)+32-2
[tex]8 \div 4 \times (6 + 2 of4) + 32 - 2[/tex]
Answer:
=94
Step-by-step explanation:
Hope itvhelps you↑↑
A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s2 for g. Use 1000 kg/m3 as the weight density of water. Assume that a = 4 m, b = 4 m, c = 18 m, and d = 3 m.)
W = __________ J
Answer:
Find the work required to pump the water out of the spout. (Use 9.8 m/s 2 for g. Use 1000 kg/m 3 as the weight density of water.
Step-by-step explanation:
Which decimal is greatest, .54, .504, or .45?
Answer:
The correct solution is .54
Step-by-step explanation:
Think about this like counting change.
0.54 is the largest amount. Next would be 0.504 (which in change would be close to 0.50 rounded down), lowest amount would be 0.45
a square has an perimeter of 56 ft what is the length of each side?
Answer:
14ft
Step-by-step explanation:
Perimeter of a square = 4s where s = side length
Here, we are given the perimeter, and we want to find the side length. To do so we plug in the perimeter and solve for s
Perimeter = 56
So 56 = 4s
==> divide both sides by 4
14 = s
A square with a perimeter of 56 feet has a side length of 14 feet
which of the following conclusions is best supported by the evidence above? regression 1 is a better fit because there appears to be a linear relationship between x and y. regression 2 is a better fit because there appears to be a linear relationship between x and y. regression 1 is a better fit because there appears to be a nonlinear relationship between x and y. regression 2 is a better fit because there appears to be a nonlinear relationship between x and
The correct option is (b) Regression 2 is a better fit because there appears to be a nonlinear relationship between x and y.
According to the above evidence, it is concluded that Regression 2 is better fit as, in the regression 2, the graph represents to be nonlinear relationship between x and y.
Since all the other concluded ones are not best describe the residential plot of given evidence, Hence, based on the evidence Regression 2 is better than the Regression 1 as it includes the nonlinear relationship between x and y that is exactly shown in the above evidence.
Question:
Which of the following conclusions is best supported by the evidence above?
a) Regression 1 is a better fit because there appears to be a nonlinear relationship between x and y.
b) Regression 2 is a better fit because there appears to be a nonlinear relationship between x and y.
c) Regression 1 is a better fit because there appears to be a linear relationship between x and y.
d)Regression 2 is a better fit because there appears to be a linear relationship between x and y
e) There is a negative correlation between x and y.
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Choose the correct Set-builder form for the following set written in Roster form: { -4,− 3 , − 2 , − 1 , 0 , 1 }
The correct Set-builder form for the following set written in Roster form { -4,− 3 , − 2 , − 1 , 0 , 1 } is,
⇒ {x ∈ Z | - 4 ≤ x ≤ 1}
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The set is,
⇒ { -4,− 3 , − 2 , − 1 , 0 , 1 }
Now, The correct Set-builder form for the following set written in Roster form { -4,− 3 , − 2 , − 1 , 0 , 1 } is,
⇒ {x ∈ Z | - 4 ≤ x ≤ 1}
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phil bikes a distance of x miles at a rate of 15 miles per hour. how many hours did the trip take?
Answer:
Below
Step-by-step explanation:
The equation you need to remember is:
rate X time = distance re-arrange to
time = distance / rate sub in the numbers given to get
time = x / 15 hours
A B C Total
Male 5 15 20 40
Female 2 14 16 32
Total 7 29 36 72
If one student is chosen at random from those who took the test,
Find the probability that the student was female GIVEN they got a 'B'.
Round answer 4 places after the decimal if needed.
The probability that the student was female GIVEN they got a 'B' is 0.194.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
A B C Total
Male 5 15 20 40
Female 2 14 16 32
Total 7 29 36 72
We have to find the probability that the student was female GIVEN they got a 'B'
P(Female ∩ B) = 14/72 = 0.1944
Hence, the probability that the student was female GIVEN they got a 'B' is 0.194.
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Simplify the following ratio
a) 75m : 125cm
please help!
determine if ST is parallel to PR
Answer:
Step-by-step explanation:
Picture?
You didn’t give enough info. Are you able to provide more information? Or a picture?
A country's census lists the population of the country as 244 million in 1990, 287 million in 2000, and 324 million in 2010. Fit a second-degree polynomial passing through these three points. (Let the year 2000 be x = 0 and let p(x) represent the population in millions.)
A second-degree polynomial can be used to fit the three data points by finding the coefficients of the polynomial that pass through the three given points. The general form of a second-degree polynomial is:
p(x) = ax^2 + bx + c
We can use the three data points to solve for the coefficients a, b, and c. Let's use the year 2000 as the reference point and set x = 0. Then, we have:
p(0) = c = 287 million (at x = 0, the population is 287 million)
Next, let's use the data point for 1990, which is 244 million. The year 1990 is 10 years before 2000, so x = -10. Substituting these values into the polynomial, we have:
p(-10) = a * (-10)^2 + b * (-10) + c = 244 million
Solving for a and b using the two equations above, we have:
a = (244 - 287 + 10b) / 100
c = 287
Substituting these values back into the polynomial, we have:
p(x) = (244 - 287 + 10b) / 100 * x^2 + bx + 287
Finally, let's use the data point for 2010, which is 324 million. The year 2010 is 10 years after 2000, so x = 10. Substituting these values into the polynomial, we have:
p(10) = (244 - 287 + 10b) / 100 * 10^2 + b * 10 + 287 = 324 million
Solving for b, we have:
b = (324 - 244 + 287) / 10 - (244 - 287) / 100 * 10^2 = 37
Therefore, the final form of the second-degree polynomial that passes through the three data points is:
p(x) = (244 - 287 + 10 * 37) / 100 * x^2 + 37x + 287 = 7x^2 + 37x + 287
This polynomial can be used to estimate the population of the country for any year close to 1990, 2000, or 2010.
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Please help me with this question.
The value of the given indefinite integral is[tex]=\frac{1}{2}\ln \left|x^2+6x+45\right|-\frac{3}{2}\arctan \left(\frac{1}{6}\left(x+3\right)\right)+C[/tex]
What are indefinite integrals?An integral which is not having any upper and lower limit is known as an indefinite integral. Mathematically, if F(x) is any anti-derivative of f(x) then the most general antiderivative of f(x) is called an indefinite integral and denoted, ∫f(x) dx = F(x) + C.
Given is an indefinite integral, [tex]\int \frac{x-6}{\left(x+3\right)^2+36}dx[/tex]
Solving,
Applying u-subsituition,
[tex]=\int \frac{u-9}{u^2+36}du[/tex]
Expanding,
[tex]=\int \frac{u}{u^2+36}du-\int \frac{9}{u^2+36}du[/tex]
Since, [tex]\int \frac{u}{u^2+36}du = \frac{1}{2} ln|u^2+36|[/tex]
And,
[tex]\int \frac{9}{u^2+36}du = \frac{3}{2} tan^-^1(\frac{u}{6} )[/tex]
Therefore,
[tex]=\int \frac{u}{u^2+36}du-\int \frac{9}{u^2+36}du[/tex] [tex]=\frac{1}{2}\ln \left|u^2+36\right|-\frac{3}{2}\arctan \left(\frac{u}{6}\right)[/tex]
Substitute u = x+3
[tex]=\frac{1}{2}\ln \left|\left(x+3\right)^2+36\right|-\frac{3}{2}\arctan \left(\frac{x+3}{6}\right)[/tex]
[tex]=\frac{1}{2}\ln \left|x^2+6x+45\right|-\frac{3}{2}\arctan \left(\frac{1}{6}\left(x+3\right)\right)[/tex]
Add constant c,
[tex]=\frac{1}{2}\ln \left|x^2+6x+45\right|-\frac{3}{2}\arctan \left(\frac{1}{6}\left(x+3\right)\right)+C[/tex]
Hence, the value of the given indefinite integral is
[tex]=\frac{1}{2}\ln \left|x^2+6x+45\right|-\frac{3}{2}\arctan \left(\frac{1}{6}\left(x+3\right)\right)+C[/tex]
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solve 10 + x ≥ 14. then graph the solution.
Answer:
x ≥ 4
Step-by-step explanation:
Just treat the equation like you would a regular algebraic equation.
10 + x ≥ 14
10 + x - 10 ≥ 14 - 10
x ≥ 4
As for graphing it, I'm not really sure if you want a proper graph or a number line.
For a number line, put a closed dot on a 4
[100 points] A force of 6 lb is required to hold a spring stretched 2 in. beyond its natural length. How much work W is done in stretching it from its natural length to 4 in. beyond its natural length?
W = ___________ ft-lb
Answer:
its 48 lb·in.
I'll give you an example and plug in the numbers:
Given:
6 lb is needed to stretch 4 inches beyond natural length.
Need work done to stretch same string from natural length to 8 inches.
Solution:
string stiffness, K
= Force / stretched distance
= 6 lb / 4 inches
= 1.5 lb/inch
Work done on a string of stiffness K
= (Kx^2)/2 lb-in
= 1.5 lb/in *(8 in)^2)/2
= 48 lb-in.
Two cyclists leave towns 255 kilometers apart at the same time and travel toward each other. One cyclist travels 7 kmh slower than the other. If they meet in 5 hours, what is the rate of each cyclist?
Check the picture below.
r = rate of the faster cyclist
r - 7 = rate of the slower cyclist
we know they both met 5 hours later, so the time each one has been cycling has been 5 hours for each.
let's say the faster cyclist on those 5 hours covered "k" kilometers, that means the slower one cover the slack, namely "255 - k" kilometers.
[tex]{\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{Km s}{distance}&\stackrel{km/h}{rate}&\stackrel{hour}{time}\\ \cline{2-4}&\\ \textit{faster cyclist}&k&r&5\\ \textit{slower cyclist}&255-k&r-7&5 \end{array}\hspace{5em} \begin{cases} k=(r)(5)\\\\ 255-k=(r-7)(5) \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{k=5r}\hspace{5em}\stackrel{\textit{substituting on the 2nd equation}}{255-(5r) = (r-7)(5)} \\\\\\ 255-5r=5r-35\implies 255=10r-35\implies 290=10r \\\\\\ \cfrac{290}{10}=r\implies 29=r\hspace{5em}\stackrel{\textit{faster cyclist}}{\text{\LARGE 29}~\frac{km}{h}}\hspace{5em}\stackrel{\textit{slower cyclist}}{\text{\LARGE 22}~\frac{km}{h}}[/tex]
At an amusement park, the straight water slide is 42m long and drops 20m. What angle does the slide ma with the horizontal?
The angle formed 28.42 degree between the slide and the drop.
What is Trigonometry?The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).
Given:
length of water slide is 42m. (Hypotenuse)
and length of drop = 20 m (Perpendicular)
Using Trigonometry
sin [tex]\theta[/tex] = P/ H
sin [tex]\theta[/tex] = 20 / 42
sin [tex]\theta[/tex] = 10 /21
sin [tex]\theta[/tex] = 0.476
[tex]\theta[/tex] = [tex]sin ^{-1[/tex] (0.476)
[tex]\theta[/tex] = 28.42 degree.
Hence, the angle is 28.42 degree.
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investigate whether the set of whole numbers, the set of integers, and the set of rational numbers are closed under each of the four basic operations. drag and drop yes or no into each box to show whether the set of polynomials in one variable is closed under the four basic operations. then complete the statement that explains whether polynomials are like whole numbers, integers, or rational numbers with respect to closure.
The set of whole numbers, the set of integers, and the set of rational numbers are closed under each of the four basic operations.
Whole numbers:
Addition: Yes
Subtraction: No (e.g. 5 - 7 = -2)
Multiplication: Yes
Division: No (e.g. 4 ÷ 2/3 is not a whole number)
Integers:
Addition: Yes
Subtraction: Yes
Multiplication: Yes
Division: No (e.g. 4 ÷ 1/2 is not an integer)
Rational numbers:
Addition: Yes
Subtraction: Yes
Multiplication: Yes
Division: Yes (provided the denominator is non-zero)
Polynomials:
Addition: Yes
Subtraction: Yes
Multiplication: Yes
Division: No (in general, polynomials cannot be divided by other polynomials)
Polynomials are like rational numbers with respect to closure under addition, subtraction, and multiplication.
However, they are not closed under division like rational numbers.
A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x.
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Tanis has contracted for an oil delivery price of $3.95 per gallon. His tank holds 210 gallons. If Tanis has six fill-ups during the winter, what will be his total cost?
The total cost of the six fill-ups during winter is $4977.
Word problems in mathematics.Word problems are mathematical problems expressed with words that involve the interpretation of mathematical variables and the usage of the appropriate arithmetic operations to solve them.
From the given information;
If the price per gallon is $3.95 and a tank can hold 210 gallons. Then, the price for a single full tank is $3.95 × 210 = $829.5
In addition to that, if Tanis has six fill-ups tanks during the winter, his total cost would be:
= $829.5 × 6
= $4977
Therefore, we can conclude that the total cost of the six fill-ups during winter is $4977.
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The number of households in the U.S. that own homes is 79.4 million, or 63.5% of all households. Find the total number of households to the nearest hundredth of a million.
Answer:
125 million
Step-by-step explanation:
[tex]79.4 \times \frac{100}{63.5} = 125.03[/tex]
Please help me I don't know
the answer be quick
Answer:
5:2 is the answer of that question.
help me please I really don't get this and I have sooo many questions about this stuff >_
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{(\dfrac{7}{8})^4}[/tex]
[tex]\mathsf{= \dfrac{7}{8}\times\dfrac{7}{8}\times\dfrac{7}{8}\times\dfrac{7}{8}}[/tex]
[tex]\mathsf{= \dfrac{7\times7\times7\times7}{8\times8\times8\times8}}[/tex]
[tex]\mathsf{= \dfrac{49\times49}{64\times64}}[/tex]
[tex]\mathsf{= \dfrac{2,401}{4,096}}[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
[tex]\huge\boxed{\mathsf{\dfrac{2,401}{4,096}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
The market for cast iron marble urns has the supply and demand functions below.
Supply: p = 15 + 0.1q
Demand: p= √650- 5q
(a) Find the point of equilibrium for this market.
(b) Find the Consumers' surplus for this market.
(c) Find the Producers' surplus for this market.
By applying supply and demand concept, it can be concluded that:
a. Point of equilibrium for this market will be reached when p = 20 and q = 50
b. Consumers' surplus for this market when -150 < q < 50
c. Producers' surplus for this market when 50 < q < 130
Demand is the number of goods purchased or requested in the market at a certain price and time, while supply is the number of goods sold or offered in the market at a certain price and time.
Point of equilibrium will be reached when supply and demand are in balance.
We have the following supply and demand functions:
Supply: p = 15 + 0.1q
Demand: p= √(650- 5q)
A. The point of equilibrium occurs when supply and demand are in balance:
15 + 0.1q = √(650- 5q)
(15 + 0.1q)² = 650 - 5q
225 + 3q + 0.01q² = 650 - 5q
0.01q² + 3q + 5q + 225 - 650 = 0
0.01q² + 8q - 425 = 0
q² + 800q - 42500 = 0
q² + 800q + 160000 - 202500 = 0
(q + 400)² - 202500 = 0
(q + 400)² = 202500
q + 400 = 450
q = 50
As we know q, we can calculate the p:
p = 15 + 0.1q
= 15 + 0.1 * 50
= 20
B. The Consumers' surplus when demand > supply:
√(650- 5q) > 15 + 0.1q ⇔ q < 50
which implies:
√(650- 5q) > 0 ⇔ q < 130
15 + 0.1q > 0 ⇔ q > -150
So, the Consumers' surplus for this market when -150 < q < 50
C. The Producers' surplus when supply > demand:
15 + 0.1q > √(650- 5q) ⇔ q > 50
which implies:
√(650- 5q) > 0 ⇔ q < 130
15 + 0.1q > 0 ⇔ q > -150
So, the Producers' surplus for this market when 50 < q < 130
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Do the segments connecting points A, B, and C form a right triangle? Show work that leads to your answer. Round to the nearest tenths place if necessary.
A= -2,2
B=6,2
C=0,6
Step-by-step explanation:
we need to calculate the distances between the points as the side lengths of the triangle.
these side lengths must satisfy the Pythagoras principle :
c² = a² + b²
with c being the Hypotenuse (side opposite of the 90° angle) and the longest of the 3 sides, a and b being the legs.
the distance between 2 points is again calculated via Pythagoras, as the coordinate differences (= the legs) with the distance as Hypotenuse create right-angled triangles.
this is then caked the distance formula, but it is all Pythagoras again.
AB² = (xB - xA)² + (yB - yA)² = (6 - -2)² + (2 - 2)² =
= 8² + 0² = 8²
AB = 8
AC² = (0 - -2)² + (6 - 2)² = 2² + 4² = 4 + 16 = 20
AC = sqrt(20)
BC² = (0 - 6)² + (6 - 2)² = (-6)² + 4² = 36 + 16 = 52
BC = sqrt(52)
as sqrt(20) is a little bit more than 4, and sqrt(52) is a little bit more than 7, 8 is the longest side and Hypotenuse.
if this is a right-angled triangle, then
8² = sqrt(20)² + sqrt(52)²
must be true.
but
64 = 20 + 52 = 72
is wrong.
so, the segments do not form a right-angled triangle.
During the time interval 4 St ≤ 8, the rate at which the number of wolves in a forest is changing, in wolves per week, can be modeled by the function
E(t) = 31 cos(0.11t?), where t is measured in weeks.
What is the rate at which the number of wolves in the
forest is changing at timet = 7? You may use a
calculator and round to the nearest thousandth. Indicate units of measure.
For the function E(t) = 31 cos (0.11t), the rate at which the number of wolves in the forest is changing at time t = 7 is 22.2549.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The function to model the rate at which the number of wolves in a forest is changing is E(t) = 31 cos (0.11t)
Here t is the time measured in weeks.
The time value is given as t = 7
Substitute the value of t in the equation -
E(t) = 31 cos (0.11t)
Apply the arithmetic operation of multiplication -
E(7) = 31 cos (0.11 × 7)
E(7) = 31 cos (0.77)
E(7) = 31 × 0.7179
E(7) = 22.2549
Therefore, the rate value is obtained as 22.2549.
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The doctor orders 1000 mL D5RL to run at 100 ml/hr. How long will this IV infusion run?
This IV infusion will run for ____ hours.
(Round your answer to the nearest whole number.)
Answer: The IV infusion will run for 10 hours.
To find out, you divide the total volume of fluid (1000 mL) by the rate of infusion (100 mL/hr):
1000 mL / 100 mL/hr = 10 hours.
Rounding to the nearest whole number, the IV infusion will run for 10 hours.
Step-by-step explanation:
Answer:
The doctor orders 1000 mL of fluid to run at a rate of 100 mL per hour. To find out how long this IV infusion will run, divide the total volume of fluid by the flow rate:
1000 mL / 100 mL/hr = 10 hours
So, the IV infusion will run for 10 hours.
Scale Factor: 2; Center: (-2, 1)
Answer:
Brhaaliarwoiagsajaidgsiuaaidywlx
he radius of a circle is tripled. Which of the following describes the effect of this change on the area? The area is multiplied by 1/9 . The area is multiplied by 9. The area is multiplied by 3. The area is multiplied by 1/3.
Tripling the radius of a circle results in a nine-fold increase in its area.
The radius of a circle is a critical component in determining its size. Tripling the radius of a circle means that the size of the circle has increased three times its original size.
The area of a circle can be calculated using the formula
=> A = πr²,
where A represents the area of the circle, π is Pi, and r is the radius. When the radius of a circle is tripled, the value of r becomes 3 times its original value, meaning the formula becomes
=> A = π(3r)² = π * 9r² = 9πr².
Therefore, the new area of the circle is nine times the original area of the circle.
Complete Question:
The radius of a circle is tripled. Which of the following describes the effect of this change on the area?
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