The two numbers whose difference is 86 and whose product is a minimum. The numbers are (43,-43) and therefore, the smaller number is -43 and largest number is 43.
Given :
Two numbers whose difference is 86 and whose product is a minimum.
To find : The numbers
Let the largest number be x,
and smallest number be y.
According to question,
Two numbers whose difference is 86.
i.e. x - y = 86 -----------------------------(1)
Product of two number is minimum.
i.e. xy = 86 -------------------------------- (2)
where P is minimum.
Now substitute x from (1) in (2),
x (x -86) = P
⇒ y(x) = x² - 86x = P ------------------------------ (3)
Differentiating Equation (3), we get:
y'(x) = 2x - 86
and y'(x) = 0
After subtracting we get:
2x - 86 = 0
⇒ x = 86 /2
⇒ x = 43
The vertex of the equation occur at x = 43.
Putting the value of x = 43 in equation (1) , we get:
48 - y = 86
⇒ -y = 86 - 48
⇒ y = -43
So, the value of y is - 43.
Therefore, the numbers are (43,-43).
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2x-7y=12 slope intercept form please help
Answer:
[tex]y=\frac{2}{7} x -\frac{12}{7}[/tex]
Marina needs to earn at least each month to cover her living expenses. Her income comes from a commission that she earns on everything she sells. What is the minimum amount she needs to sell in order to earn ?
Answer:
Step-by-step explanation:
Amount sold = $23000
Percentage rate = 15%
Total salary = Amount sold × Percentage rate = $23000 × (15 / 100) = $3450
Answer is $3450
What is the value of the expression 1/2 + 2/3 when b = -5?
-17/6
-1/6
23/6
I don't know.
Answer:
1st answer is correct
Step-by-step explanation:
[tex]\sf \frac{1}{2} +\frac{2b}{3}[/tex]
Given that,
b = -5
To find the value of the above expression, replace b with -5.
[tex]\sf \frac{1}{2} +\frac{2b}{3}\\\\\sf \frac{1}{2} +\frac{2*(-5)}{3}\\\\\sf \frac{1}{2} +\frac{-10}{3}[/tex]
Now, to solve the above fractions, you have to make the denominator the same.
For that, multiply both the numerator and denominator of (1/2) & (-10/3) by 3 & 2 respectively.
Let us solve it now.
[tex]\sf \frac{1}{2} +\frac{-10}{3}\\\\\sf \frac{1}{2} -\frac{10}{3}\\\\\sf \frac{1*3}{2*3} -\frac{10*2}{3*2}\\\\\sf\frac{3}{6} -\frac{20}{6} \\\\\sf\frac{-17}{6}[/tex]
29. The school that Lilly goes to is selling tickets to a drama performance. On the first day of ticket sales the
school sold 3 adult tickets and 1 child ticket for a total of $38. The school took in $104 on the second
day by selling 6 adult tickets and 4 child tickets. Find the price of an adult ticket and the price of a child
ticket.
Answer:
the price of an adult ticket is $8, and the price of a child ticket is $14.
Step-by-step explanation:
To find the price of an adult ticket and the price of a child ticket, we need to set up a system of equations. Let "A" represent the price of an adult ticket and "C" represent the price of a child ticket.
On the first day, the school sold 3 adult tickets and 1 child ticket for a total of $38, so we can set up the following equation to represent this information:
3A + C = 38
On the second day, the school took in $104 by selling 6 adult tickets and 4 child tickets, so we can set up the following equation to represent this information:
6A + 4C = 104
Now that we have our two equations, we can solve for the values of A and C. We can use the elimination method to solve this system of equations. To do this, we need to multiply one of the equations by a constant so that one of the variables has the same coefficient in both equations. We'll multiply the first equation by 2:
6A + 2C = 76
We can then subtract this equation from the second equation to eliminate the C term:
6A + 4C - 6A - 2C = 104 - 76
This simplifies to:
0A + 2C = 28
Dividing both sides by 2, we get:
C = 14
We can now substitute this value for C in one of our original equations and solve for A. We'll use the first equation:
3A + 14 = 38
Subtracting 14 from both sides, we get:
3A = 24
Dividing both sides by 3, we get:
A = 8
Therefore, the price of an adult ticket is $8, and the price of a child ticket is $14.
please help me!!!.....
Answer: 52 degrees
Step-by-step explanation:
angles stay the same even when the size is decreased. they are similar so the angle is the same. while line ab might be 2 units, and line de might be 1, the angle would stay the same.
Last year, Elsa opened an investment account with$5400 . At the end of the year, the amount in the account had increased by 6.5%. How much is this increase in dollars? How much money was in her account at the end of last year? Increase in amount and Year-end amount
Answer:
Here you go
Step-by-step explanation:
The increase in amount is $351.00 ($5400 x 0.065 = $351). The amount in the account at the end of the year was $5751.00 ($5400 + $351 = $5751).
Given the function h (x) = -10x + 5, find the corresponding range values when the domain is {-1,2,4]
-35
35
000000
15
- 15
25
-25
W
The range of the function f(x) = 5 -10x for domain {-1, 2, 4} is { 15, -15, -35}
What is Domain and Range of a function ?A function's domain and range are its constituent parts. Range, Domain, and Function. A is the domain and B is the co-domain if a function f: A B exists that maps every element of A to an element in B. 'b', where (a,b) R, provides the representation of an element 'a' under a relation R. The collection of photos is the function's range. In general, a function's domain and range are denoted as follows:
Domain(f) = {x ∈ R} and range(f)={f(x) : x ∈ domain(f)}
"All the values" that are input into a function are referred to as the domain of a function. The collection of all potential inputs for a function is its domain. Think of this box as the f(x) = 2x function. The domain is only the collection of natural numbers when the input values are x = 1,2,3,4,..., and the values that are returned are referred to as the range. However, f(x) = 2x is often defined for all real values of x, and as a result, its domain is the set of all real numbers, which is represented by (-∞, ∞). The general formulae for determining the domain of various types of functions are listed below. The set of all real numbers, or R, is used here.
The collection of all a function's outputs is its range. Example: Let's have a look at the function f: A->B, where f(x) = 2x and A and B each represent a "collection of natural numbers." The domain in this instance is A, and the co-domain is B. The range then appears as the function's output. Set of even natural numbers is the range. The components of the co-domain that are mapped are known as the pictures, while the elements of the domain are known as pre-images. The set of all pictures of the domain's elements in this case serves as the function's range, as does the set of all of its outputs.
Domain of the function x = {-1,2,4}
The function is f(x) = 5 - 10x
range when x = -1
f(x) = 5 - 10*(-1) = 15
when x = 2
f(x) = 5 - 10* 2 = -15
and x= 4
f(x) = 5 - 10*4 = -35
The range of the function for domain {-1, 2, 4} is { 15, -15, -35}.
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The range of the function f(x) = 5 -10x for domain {-1, 2, 4} is { 15, -15, -35}
What is Domain and Range of a function ?
The domain of a function is the set of all possible inputs for the function. It is the set of all x-values which will make the function "work", and will output real y-values. The range of a function is the set of all possible outputs of the function. It is the set of all y-values which can be produced by the function for the given set of x-values. In other words, it is the set of values that result when the function is applied to all the elements of the domain. In order for a function to be defined, both the domain and the range must be specified.
Domain of the function x = {-1,2,4}
The function is f(x) = 5 - 10x
range when x = -1
f(x) = 5 - 10*(-1) = 15
when x = 2
f(x) = 5 - 10* 2 = -15
and x= 4
f(x) = 5 - 10*4 = -35
The range of the function for domain {-1, 2, 4} is { 15, -15, -35}.
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there are about 10,000 taste buds on a human tongue. write this number in scientific notation
Answer:
I guess 1*10^4 is the answer. Not sure.
Answer:
1 * 10⁴
Step-by-step explanation:
10,000 = 10 * 10 * 10 * 10 = 1 * 10⁴
The triangular base of a prism is a right triangle of sides a and b = 2a. The height h of the prism is equal to 10 mm and its volume is equal to 40 mm3, find the lengths of the sides a and b of the triangle.
A prism having a triangular base is a right triangle of sides a and b = 2a.
The lengths of side "a" is 3.464 mm.
The length of side "b" is 6.928 mm.
Volume of the Triangular Prism:
A triangular prism is an object in three dimensional space with a triangular base and three other triangles connected to it. A triangular prism has four corners, and the distance from the base to the diagonal vertex is called the height of the triangular prism.
It is given by the multiplication of the area of the base to the height of the prism.
V = (Area × height of prism)/3
=> V = Ah/3
we have given that,
Base of prism is right angle triangle with sides "a" and "b" such that b = 2a ---(1)
Height of prism (h) = 10mm
Volume (V) = 40mm³
the Area of triangluar base = 1/2 × base× height of triangular base
A = (1/2)a ×b
=> A = (1/2)a × 2a = a²
Volume of prism (V) = a²×h/3 = 40
=> a²×10/3 = 40
=> a² = 120/10 = 12
=> a = √12 = 2√3
=> a = 2(1.732) = 3.464
from equation (1) , b = 2a = 2(3.464)
=> b = 6.928
So, the lengths of sides of triangle are
a= 3.464 and b = 6.928
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Rightround is a firm that manufactures record players. Suppose rightround sells its record players to online retailers for $342 each and requires those online retailers to charge at least $362 to shoppers for each record player.
False. All economists do not believe that predatory pricing is a profitable business strategy.
What does "predatory pricing" mean?
A dominant company will often use predatory pricing as a deliberate strategy to drive out rivals by setting exceptionally cheap prices or supplying products for less than the company would otherwise have to spend on manufacturing (often equated for practical purposes with average variable costs).
Predatory pricing, sometimes referred to as undercutting, is a pricing strategy in which a good or service is offered at an extremely low cost with the goal of driving out rivals or establishing barriers to entry for potential new competitors.
If a competitor was selling a TV for $100 and you were offering the same TV for $80, you would be using predatory pricing.
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The ratio of roses to lilles in a garden is 3 to 2 what percentage of the gardens flowers are roses
Answer:
To find the percentage of roses in the garden, we first need to determine the total number of flowers in the garden. We can do this by adding the number of roses and lilies, and then multiplying that number by the ratio of roses to lilies. For example, if there are 3 roses and 2 lilies in the garden, the total number of flowers would be 5 (3 + 2 = 5). To determine the percentage of roses, we would then divide the number of roses by the total number of flowers, and multiply by 100. In this case, the percentage of roses would be 60% (3 / 5 * 100 = 60).
students who study for 7 hours over the course of a week will perform better than students who cram for 7 hours the night before the exam. the dependent variable in this hypothesis is:
The dependent variable in this hypothesis is test performance.
What is a dependent variable?
In mathematical modelling, statistical modelling, and experimental sciences, there are dependent and independent variables. Dependent variables get their name because, during an experiment, one‘s values are examined under the assumption as well as demand that they are dependent on the value of another variable due to some law or rule (for example, a mathematical function). In the context of the experiment in question, independent variables are those that are not thought to be depending on other variables. Time, space, specific gravity, mass, fluid flow rate and previous values of certain observed value of interest (such as the size of the human population) are examples of common independent variables that can be used to forecast future value systems (the dependent variable).
The outcome of this hypothesis is the dependent variable.
Hence, the dependent variable in this hypothesis is test performance.
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Pls help a girl out
The statement that best describes how income levels have changed in the United States is given as follows:
C. High-income earners are making more, but most people have only seen limited gains.
How to obtain the correct statement?Recently, in the entire world, an especially in the United States, inflation has been a problem, and thus people's income has not followed the pattern, staying mostly stagnant while inflation happens. This has happened even though the economy has improved from the 2008 global crisis.
However, high-income earners are making more, as the number of millionaires and billionaires increase, increasing the gap between high and low income earners. Thus option C is the correct option.
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Find the perimeter and area of the figure.
Which of the following is the correct classification of AMNP if m/M = 37° and m/P = 106° ?
A Right
B Isosceles
C Acute
D Scalene
Answer:
B Isosceles
Step-by-step explanation:
You want to know the classification of ∆MNP when ∠M = 37° and ∠P = 106°.
Third angleThe third angle of the triangle can be found using the fact that the sum of angles is 180°.
∠N = 180° -37° -106° = 37°
This tells us angles M and N have the same measure (37°), so ...
the triangle is isosceles.
What are the 5 infinitives?
The five types of infinitives are full infinitives, bare infinitives, split infinitives, continuous infinitives , and perfect continuous infinitive.
Explanation:
Types of infinitives:
Five types of infinitives are as follow:
Full infinitives : Add 'to' Infront of the verb to complete the the situation.Bare infinitives: here " to" get omitted from the sentence.Split infinitives : Here adjectives slides between infinitives marker.To hear : full infinitives changes to split infinitives : to slowly hear.
Continuous infinitives: Action going for certain period of required time.Example : to be missing
Perfect continuous infinitives: prior to a time :Example : to have seen
Therefore, there are are five types of infinitives .
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please i need help fast!!!
Answer:c
Step-by-step explanation:
bert and ernie each have a well-shuffled standard deck of 52 cards. they each draw one card from their own deck. compute the probability that: bert and ernie both draw a heart.
The probability that Bert and Ernie both draw a heart = (1/4)²
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
Probability = (Number of possible outcomes)/(Total number of outcomes)
Bert:
Probability of drawing a heart = 1/4
Ernie:
Probability of drawing a heart = 1/4
The probability that Bert and Ernie both draw a heart = 1/4 * 1/4 = (1/4)²
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PLEASE HELP ME WITH MY MATH HOMEWORK
ill give you brainliest
Answer: [tex]H = -16s(s-6)[/tex]
Work Shown:
[tex]H = -16s^2+96s\\\\H = -16s*s+16s*6\\\\H = -16s(s-6)\\\\[/tex]
The answer can be confirmed by using the distributive rule to multiply -16s by each term inside the parenthesis. You should get [tex]-16s^2+96s[/tex] after distributing.
Meteorologists in Texas want to increase the amount of rain delivered by thunderheads by seeding the clouds. Without seeding, thunderheads produce, on average, 300 acrefeet. The meteorologists randomly selected 29 clouds which they seeded with silver iodide to test their theory that average acrefeet is more.
What conclusion can they reach based on the above output when they set the significance level to be 0.10?
a.The data does not provided statistical evidence that the average acrefeet from seeded clouds is more than 300.
b.The data does provide statistical evidence that the average acrefeet from seeded clouds is more than 300.
c.The data does not provided statistical evidence that the sample average acrefeet from seeded clouds is more than 300.
d.Two of the above are correct.
e.We can not draw conclusions based on the above statistical output because the conditions are not met due to the extreme outliers.
Conclusion can they reach based on the above output when they set the significance level to be 0.10 is that we can not draw conclusions based on the above statistical output because the conditions are not met due to the extreme outliers.
Define meteorologists.A person with specific training in meteorology applies scientific principles to describe, comprehend, observe, or forecast atmospheric occurrences on earth and/or how the atmosphere impacts the planet's surface and life are meteorologists.
Given,
Meteorologists in Texas want to increase the amount of rain delivered by thunderheads by seeding the clouds. Without seeding, thunderheads produce, on average, 300 acrefeet. The meteorologists randomly selected 29 clouds which they seeded with silver iodide to test their theory that average acrefeet is more.
Conclusion can they reach based on the above output when they set the significance level to be 0.10 is,
e. We can not draw conclusions based on the above statistical output because the conditions are not met due to the extreme outliers.
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0.796 divided by 9.95
Answer:
0.08
Step-by-step explanation:
Geometry HL question. Statements and proofs.
The proof that shows that ΔPRS ≅ ΔQSR by HL congruence theorem is explained below.
How to Prove that two Triangles are Congruent by HL?The HL congruence theorem can be used to prove that two triangles are congruent to each other if we can show that the two triangles are right triangles that have a pair of corresponding congruent legs, and a pair of congruent hypotenuse.
The proof for stating that triangles PRS and QSR are congruent is given below.
Statement Reasons
1. QS ≅ PR, PS ⊥ RS, QR ⊥ RS 1. Given
2. <RSP and <SRQ are right angles 2. Definition of perpendicular
3. SR ≅ RS 3. Reflexive property of congruency
4. ΔPRS ≅ ΔQSR 4. HL
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Two dice are rolled. What is the probability that the sum of the numbers rolled is either 2 or 5? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answer: first lowest: 1/3 second lowest:2/6
Step-by-step explanation:
Which tatement are true? Select all that apply. A) The equation |-x - 4| = 8 will have two olution. B) The equation 3. 4|0. 5x - 42. 1| = -20. 6 will have one olution. C) The equation |1/2x - 3/4| = 0 will have no olution. D) The equation |2x - 10| = -20 will have two olution. E) The equation |0. 5x - 0. 75| 4. 6 = 0. 25 will have no olution. F) The equation |1/8x - 1| = 5 will have infinitely many olution
The true statement is option (A) The equation |-x - 4| = 8 will have two solution
Consider each statement
All the statements are absolute value equation
Part A
|-x-4| = 8
We can write it in two way
-x - 4 = 8
- x = 12
x = -12
Then,
-(-x-4) = 8
x+4 = 8
x = 4
It has two solution
Part B
3. 4|0. 5x - 42. 1| = -20. 6
Divide both side by 3.4
|0.5x - 42.1| = -103/17
Absolute value cannot be negative
The equation has no solution
Part C
|1/2x - 3/4| = 0
1/2x - 3/4 = 0
1/2x = 3/4
x = 3/4 ÷ 1/2
x = 3/2
The equation has one solution
Part D
|2x - 10| = -20
Absolute value cannot be negative
This equation has no solution
Part E
|0. 5x - 0. 75| 4. 6 = 0. 25
Divide both side by 4.6
|0.5x - 0.75| = 5/92
The equation divided into two
0.5x - 0.75 = 5/92
x = 37/23
0.5x - 0.75 = -5/92
x = 32/23
The equation has two solution
Part F
|1/8x - 1| = 5
1/8x - 1 = 5
x = 48
1/8x - 1 = -5
x = -32
The equation has two solution
Therefore, the equation |-x - 4| = 8 will have two solution is true
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edges 1. at the world tic-tac-toe championship, each player must play against 7 other players. new games start every hour. how many hours will the tournament take?
Each game starts every hour then 28 games will be occurred in 28 hours and therefore the tournament will take 28 hours for completion.
Given, there are total 8 players playing the tournament of world tic-tac-toe championship.
Also, new game start each hour.
We have to find the number of hours the tournament will take to complete.
Total games occurred be,
we will use the concept of A.P. to find the total number of games
First player will play with 7 players, second player will play with 6 players and so on.
Total games = 8/2[14 + 7×(-1)]
Total games = 4×7
Total games = 28
Now, if each game start every hour then 28 games will occurred in 28 hours and therefore the tournament will take 28 hours for completion.
Hence, the tournament will take 28 hours for completion.
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coffee is draining from a conical filter into a cylindrical coffeepot at the rate of 10 in3/min. (a) how fast is the level in the pot rising when the coffee in the cone is 5 in deep?
The level in the pot rising when the coffee in the cone is 5 in deep is 0.35 in/min.
Here the variables are the height of the coffee in the filter hf , the radius of the top of the coffee in the filter rf , and the height of the coffee in the pot hp:
We allowed Vp to represent the volume of coffee in the pot. We are interested in the instant when
hf = 5 in and dVp/dt = 10 in³/min.
The question is dhp/dt =? when dVp/dt = 10 in³/min and hf = 5 in
We need to relate hp to the other variables. In the pot (idealized as a cylinder), we have the volume Vp as Vp = π(3)²hp = 9πhp in³(since the volume of a cylinder of radius r and height h is V = πr²h).
Differentiation of Vp with respect to time gives dVp/dt = 9πhp/dt or
dhp/dt = (1/9π).(dVp/dt)
When dVp/dt = 10 in³/min and hf = 5 in, we have
dhp/ dt = 1/9π(10)
= 10/9π in/min
dhp/ dt ≈ 0.35 in/min (notice that the answer here is independent of hf ).
Hence, the level in the pot rising when the coffee in the cone is 5 in deep is 0.35 in/min.
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The point (2, -3) is the midpoint of segment JK . Point K is located at (-6, -3). What is the length of segment JK ?
Answer:
16
Step-by-step explanation:
The distance from the midpoint to [tex]K[/tex] is [tex]|-6-2|=8[/tex].
By definition, this is half the length of [tex]\overline{JK}[/tex], meaning [tex]JK=16[/tex].
What is surface area of any figure?
Surface area of any figure is the area that the outer surface of any figure covers.
If we look at the different figures we find that these figures if placed somewhere or if we need to cover the figures with some kind of material then in order to find the the dimensions of the material we will need to find out the area that the overall surface of the figure will cover. This will reduce the time and complication of the calculations of every part of the shape. For example, If there is a need to find the surface area of the cylinder then we use the formula for its curved surface area as
S = 2πrh where r is the radius and h is the height of cylinder
Also, the total surface area will be expressed as
T = 2πr(r + h) where r is the radius and h is the height.
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-4x² + x - 7 = y
2x + 8 = -y ( solve by elimination )
A technique for solving an equation system is elimination.
What is elimination method ?Elimination is a method of solving a system of equations. In elimination, the goal is to eliminate one of the variables by adding and subtracting equations in order to create an equation with a single variable. This equation can then be solved for the single variable. For example, given the system of equations 2x + 8 = -y and 4x² + x - 7 = y, we can use elimination to solve for the variables x and y. To do this, we first need to multiply the first equation by -4, giving us -8x - 32 = 4y. We then add the two equations together, which gives us 4x² + 9x - 39 = 0. This equation can be solved using the quadratic formula, which gives us x = -3. To solve for y, we can plug x = -3 into either of the original equations. Plugging this value into the first equation gives us 2(-3) + 8 = -y, which simplifies to -6 + 8 = -y, and therefore y = 2. This method of using elimination to solve a system of equations can be used to solve any system of equations with two variables.2x + 8 = -y
-4x² + x - 7 = -y
Subtracting 2x + 8 from both sides:
-4x² - x + 15 = 0
(4x - 5)(x + 3) = 0
4x - 5 = 0
x = 5/4
x + 3 = 0
x = -3
Solutions:
x = 5/4 and x = -3
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Write an inequality for the statement:
negative three eighths is at most the product of a number and negative five sevenths
A negative 3 over 8 ≤ negative 5 over 7w
B negative 5 over 7 ≤ negative 3 over 8w
C negative 5 over 7 ≥ negative 3 over 8w
D negative 3 over 8 ≥ negative 5 over 7w
The inequality for the statement negative three eighths is at most the product of a number and negative five sevenths is negative 3 over 8 ≤ negative 5 over 7w which is option A.
What is inequality?inequality, In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
negative three eighths = -3/8
negative five sevenths = -5/7
At most for inequality symbol = [tex]\leq[/tex]
mathematically
-3/8 [tex]\leq[/tex] -5/7w
which is negative 3 over 8 ≤ negative 5 over 7w
In conclusion the inequality for the statement is negative 3 over 8 ≤ negative 5 over 7w
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