The slopes of the secant line corresponding to the given intervals of t is 132.1, 116.3, 91.4 and 44.2 steps per minute.
To find the slope of a secant line between two points, we need to divide the difference in the y-values (number of steps) by the difference in the x-values (time in minutes).
For the interval from t = 0 to t = 10 minutes:
y1 = 3,288 steps
y2 = 4,609 steps
x1 = 0 minutes
x2 = 10 minutes
The slope of the secant line is:
(y2 - y1) / (x2 - x1) = (4,609 - 3,288) / (10 - 0)
= 1,321 / 10
= 132.1 steps per minute
For the interval from t = 10 to t = 20 minutes:
y1 = 4,609 steps
y2 = 5,772 steps
x1 = 10 minutes
x2 = 20 minutes
The slope of the secant line is:
(y2 - y1) / (x2 - x1) = (5,772 - 4,609) / (20 - 10)
= 1,163 / 10
= 116.3 steps per minute
Similarly, for interval t = 20 to t = 30 minutes
Slope = (6,686 - 5,772)/ (30 - 20) = 91.4 steps per minute
for interval t = 30 to t = 40 minutes
Slope = (7,128 - 6,686)/ (40 - 30) = 44.2 steps per minute
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A company's weekly profit in pesos is determined by the function P(×)=ײ( × + 100 ) ( × + 300 ) where × represent the number of branches it operates. How much profit does the company make in a week if it operates 10 branches
Patch traveled from his office to the seashore at a speed of 62 mph. He traveled the same route on his way back to the office, but on the return trip his speed was 66 mph. If, altogether, Patch spent a total of 4 hours on the road, how many hours did the trip to the seashore take? Round your answer to the nearest hundredth (two decimal places)
Answer:
1.03 hours
Step-by-step explanation:
Let x be the time taken to travel from office to seashore at 62mph
Distance traveled = speed x time = 62x miles
Since both trips together took 2 hours, the time taken for the same distance from seashore to office = 2 - x hours
At a speed of 66 mph, the distance traveled = 66(2-x) = 132 - 66x
Since the distances on each trip are equal:
62x = 132 - 66x
Add 66x to both sides => 62x + 66x = 132 =-66x + 66x
128x = 132
x = 132/128 = 1.03125 hours = 1.03 hours rounded to 2 decimal places
When air is pumped into an automobile tire, the pressure is inversely proportional to the volume. If the pressure is 35 pounds when the volume is 120 cubic inches, what is the pressure, in pounds, when the volume is 140 cubic inches?
The pressure in the tyre when the volume is 140 cubic inches will be 30 pounds.
What is Boyle's law?Boyle's law states that at a constant temperature, the pressure is inversely proportional to the volume. It means that the product of the pressure and the volume will remain constant for the given system.
Given that when air is pumped into an automobile tire, the pressure is inversely proportional to the volume. If the pressure is 35 pounds when the volume is 120 cubic inches.
The pressure will be calculated as:-
P₁V₁ = P₂V₂
( 35 x 120 ) = 140 x P₂
P₂ = ( 35 x 120 ) / 140
P₂ = 30 pounds
Therefore, when the volume is 140 cubic inches, the tire's pressure will be 30 pounds.
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for many medical tests, it is standard procedure to repeat the test when a positive signal is given. if repeated tests are independent, what is the probability that a man will test positive on two successive tests if he has the disease?
The probability that a man will test positive on two successive tests if he has the disease 81%.
In mathematical terms, probability can be represented as the ratio of the number of favorable outcomes to the number of possible outcomes. The formula for probability is as follows:
P(E) = n(E) / n(S)
Where:
P(E) is the probability of event E occurring
n(E) is the number of favorable outcomes for event E
n(S) is the number of possible outcomes in the sample space S
Let's assume the probability of a man testing positive for a disease if he has it is represented by the symbol "P".
If the tests are independent, meaning that the outcome of one test does not affect the outcome of the other, then the probability of a man testing positive on two successive tests can be calculated as the product of the probabilities of each individual test.
Therefore, the probability of a man testing positive on two successive tests if he has the disease is P * P, or P².
If the probability of a man testing positive for a disease if he has it is 90%, represented by P = 0.9, then the probability of him testing positive on two successive tests is 0.9 * 0.9 = 0.81, or 81%.
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There were 72 runners to start a race. In the first half of the race,1/
4
of them dropped out. In the second half of the race,2/3 of the remaining runners dropped out How many runners finished the race?
Step-by-step explanation:
First find 1/4 of 72 runners. To do this divide by 4.
So
72/4=18
Now take 72 and subtract 18 to get 54
Next find 1/3 of 54 runners
54/3=18
Because it is 2/3 you need to multiply 18 by 2
So
18 x 2 = 36
So
54-36=18 runners that finished the race
If needed in fraction form
18/72
Now simplify
9/16 of the runners finished
Martin is walking from Antrim to Randalstown. Randalstown 13 miles Toome 94 miles Antrim 3½ miles (a) Work out the distance from Antrim to Randalstown.
The distance from Antrim to Randalstown is 6 5/6 miles.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, Martin is walking from Antrim to Randalstown.
Randalstown 3 1/3 miles, Toome is 9 1/4 miles Antrim 3 1/2 miles.
Therefore, the distance from Antrim to Randalstown is the sum of their distances which is,
= 3 1/3 + 3 1/2 miles.
= 10/3 + 7/2 miles.
= (20 + 21)/6 miles.
= 41/6 miles.
= 6 5/6 miles.
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Please help with this, im so confused
The required equivalent expression to the given expression is Lima invests $1000 in a mutual fund which gives her a return of 12% per year this situation can be modeled as y = 1000(1.2)ⁿ.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
An expression is given in the question that is,
[tex]Z(t) = 4000(12^{2t +2})[/tex]
We have to form a problem that represents the format of a function same as shown above.
Expression and problem is given as, Lima invests $1000 in a mutual fund which gives her a return of 12% per year this situation can be modeled as y = 1000(1.2)ⁿ.
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soooo umm I don't know?
Answer: The last option would be correct p= 75 + 5a. The reason being the last option is the right one is because the expression represents the additional points plus her original 75 she had on her homework assignments.
Adela paid $71.70 for 6 tickets at the skating rink. Calculate the unit rate per ticket.
$8.37
$11.95
$12.12
$65.70
In linear equation, the unit rate of tickets at the skating rink is; 11.95 per ticket.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
We have been given Adela paid $71.70 for 6 tickets at the skating rink.
We need to find the unit rate per ticket.
Total amount = 71.70
Number of tickets = 6
Unit rate = Total amount/ Number of tickets
Unit rate = 70.70/ 6
Unit rate = 11.95/1
Therefore, the unit rate of tickets at the skating rink is; 11.95 per ticket.
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Answer:B
Step-by-step explanation:
a dance class consists of 22 students, half of them are men and half of them are women. if 4 men and 4 women are to be chosen and then paired off, how many results are possible?
There exist 108,900 possible results.
Since there are 22 students in the class and half of them are men, there are 22/2 = 11 men. And since half of the students are women, there are 11 women.
When choosing 4 men and 4 women to pair off, the number of results possible is the number of combinations of 4 men from 11, which is C(11, 4), multiplied by the number of combinations of 4 women from 11, which is C(11, 4).
So, the number of results possible is C(11, 4) * C(11, 4) = 330 * 330 = 108900.
Therefore, there are 108,900 possible results.
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Janet is making chocolate chip cookies. One batch of chocolate chip cookies needs of a cup of sugar. Janet wants to make three batches of chocolate chip cookies.
Part A
How many total cups of sugar will Janet need to make three batches of chocolate chip cookies? Show your answer in lowest terms.
Part B:
Janet has 4 cups of sugar. How much sugar will she have left over after making three batches of chocolate chip cookies?
PART A) Janet needs only three cups of sugar to make three batches of chocolate chip cookies.
PART B) One cup of sugar will be left over after making three batches of cookies.
What is the unit price?
A unit price is the cost of a single object or unit of measurement, such as a pound, a kilogram, or a pint, and it is used to compare the prices of similar products offered in various weights and quantities. Selling more than one unit of the same product at a discount from its unit price is known as multiple pricing.
Given that Janet needs One cup of sugar to make one batch of chocolate chip cookies.
Part A:
Let The number of cups of sugar Janet needs to make three batches of cookies be 'x'.
Now,
1 batch/ 1 cup = 3 batch/ x cups
x= 3
Therefore, Janet needs only three cups of sugar to make three batches of chocolate chip cookies.
Part B:
Given that Janet has four cups of sugar.
From part A, we found that she only need three cups of sugar.
Available - Needed = Excess
4-3=1
So, one cup of sugar will be left over after making three batches of cookies.
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PLS HELP MEEEEEEEE PLS
The complex number z = 4√3 - i 4 has a norm 8 and a direction 330°. Its representation is in the image shown below.
How to graph a complex number and identify its norm and direction
In this question we find the definition of complex number in rectangular form, whose definition is shown below:
z = a + i b, where a, b are real numbers.
Where:
a - Real componentb - Imaginary componentGraphically speaking, the real component is associated to the horizontal axis of Cartesian plane and the imaginary component is associated to the vertical axis of that plane. The norm (r) and direction (θ) of the complex number are, respectively:
Norm
r = √(a² + b²)
Direction
θ = tan⁻¹ (b / a)
The norm and the direction of the complex number are, respectively:
r = √[(4√3)² + (- 4)²]
r = 8
θ = tan⁻¹ [(- 4) / (4√3)]
θ ≈ 330°
Lastly, we represent the complex number with the help of a graphing tool.
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Que pongo?rápido porfiii
Answer:
4xy + 2xy - 3xy +5xz - yz
4xy - 3xy + 2xy + 5xz - yz
1xy+2xy + 5xz - yz
3xy + 5 xz - yz
Please help I have a learning disailty and this is due today.PLEASE PLEASE I DONT KNOW THE ANSWER AND SOOOOOOOOOOOO NEED THIS I WILL DO ANYTHING YOU WANT MARK YOU ASK A QUESTION SO YOU GET THE POINTS PLEASE I JUST REALLY NEED HELP.
Start at hexagon A. After you solve the expression find the answer in blue on the edge on the hexagon. The answer will lead you to your next hexagon.
Continue along the maze path until you reach the hexagon with an S in the flower. This is where you will finish.
To answer the questions below, type the letter in each hexagon that you solved along the maze in the order they were answered.
You do not need to include the starting hexagon (of A) or the end hexagon (of S). These are already written in the order below.
Use only capital letters when typing in the hexagon letter
Starting hexagon A
Second hexagon solved ______________________
Third hexagon solved____________________________
Fourth hexagon solved________________________________
A mathematical description of hexagon is given above.
What is a polygon?In geometry, a polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.
The bounded plane region, the bounding circuit, or the two together, may be called a polygon.
The segments of a polygonal circuit are called its edges or sides.
Given is hexagon.
In geometry, a hexagon is a six-sided polygon creating the outline of a cube. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°.
A regular hexagon is defined as a hexagon that is both equilateral and equiangular. It is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle).
Therefore, a mathematical description of hexagon is given above.
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According to Cavalieri's principle, when the height and diameter of a cylinder are equal to the diameter of a sphere, which statement is true about the volume of the sphere?
Responses
A The volume of half of the sphere is 34
the volume of the cylinder.The volume of half of the sphere is 3 4 the volume of the cylinder.
B The volume of half of the sphere is 23
the volume of the cylinder.The volume of half of the sphere is 2 3 the volume of the cylinder.
C The volume of half of the sphere is 43
the volume of the cylinder.The volume of half of the sphere is 4 3 the volume of the cylinder.
D The volume of half of the sphere is 13
the volume of the cylinder.The volume of half of the sphere is 1 3 the volume of the cylinder.
The correct statement regarding the volumes is given as follows:
B. The volume of half the sphere is 2/3 the volume of the cylinder.
How to obtain the volumes?The volume of a cylinder of radius r and height h is given by the equation presented as follows:
V = πr²h.
The volume of a sphere of radius r is given by the equation presented as follows:
V = 4πr³/3
The diameter is twice the radius, however they have the same unit, hence we can keep using the radius for the formulas.
If the diameter and the radius of the cylinder are equal to the height, the volume is given as follows:
V = πr² x r = πr³.
Hence the volume of the sphere is of 4/3 the volume of the cylinder, hence the volume of half the sphere is 2/3 the volume of the cylinder, meaning that option B is correct.
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Which is the better buy? (18 points)
7-pack of T-shirts for $23.02
8-pack of T-shirts for $26.72
Answer: 7 Pack
Step-by-step explanation: Divide each price by the number of shirts :)
Find the equation of the line parallel to 8x+5y=1 passing through the point (1,−3)
The equation of the line parallel to 8x+5y=1 passing through the point (1,−3)
is y = (-8/5)x - (7/5).
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The equation of the line is y = m(1)x + c
Now,
The equation of the line parallel to 8x+5y=1 passes through the point (1, -3).
This means,
8x + 5y = 1
5y = - 8x + 1
y = (-8/5)x + 1/5
This is in the form of y = m(2)x + c
m(2) = (-8/5)
Now,
Since the line is parallel.
m(1) = m(2) = (-8/5)
So,
y = (-8/5)x + c
Now,
(1, -3) = (x, y)
-3 = (-8/5) x 1 + c
c = -3 + 8/5
c = (-15 + 8) / 5
c = -7/5
So,
y = (-8/5)x - (7/5)
Thus,
The equation of the line is y = (-8/5)x - (7/5).
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Question 3(Multiple Choice Worth 5 points)
(Systems of Linear Equations MC)
Which point is a solution to the system of linear equations?
y = -x + 4
x - 3y = 12?
O (0, 3)
O (1, 2)
O (6, -2)
O (4,-4)
Answer:
(6, -2)
Step-by-step explanation:
The only option that satisfies both equations is (6, -2).
What number is equivalent to
7 x 1,000,000,000 + 5 x 1,000,000 + 9 x
10,000+ 9 x 100 + 7 x 1?
A. 75,997
B. 759,971
C. 7,509,907
D. 7,005,090,907
Answer:
D
Step-by-step explanation:
7 x 1,000,000,000 + 5 x 1,000,000 + 9 x 10,000+ 9 x 100 + 7 x 1
=7,000,000,000
+ 5,000,000
+ 90,000
+ 900
+ 7
answer is D
10. Communicate and Justify Jane interpreted
the mean of the given data set, 8.48, as
meaning half the cats weighed less than
8.48 pounds and half weighed more. What
was Jane's error? Explain.
Jane's error was that she assumed that the mean of the data set would represent a midpoint, where half of the cats weighed more and half weighed less.
What informs the assertion?This is not necessarily the case, as the mean is only an average of the data set and does not necessarily represent any particular point within the data set. For example, if the data set was composed of 8 cats that all weighed 8.48 pounds, then the mean would be 8.48, but none of the cats would weigh less than 8.48 pounds.
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Find the probability of taking out the king from a well shuffled pack of 52 cards
Answer:
1/13
Step-by-step explanation:
There are 52 cards in a deck, there are 4 suits and a king in each suit.
That makes 4 kings in a deck of cards.
P(king) = number of kings/ total cards
= 4/52 = 1/13
Answer:
1/13
Step-by-step explanation:
in 52 cards there was 4king
so ＝4/52
simplify ＝1/13
What’s two fifteen divided by nine
Answer:
23.8888888889 that's the answer
Answer:
215/9=23.8888888889
Step-by-step explanation:
10 in
12 in
10 in
3 in
Step-by-step explanation:
10in×10in×3in×3in×12in=2172
substitution, pls help!
By using the substitution method, the solution to the given system of equations include the following:
x = -9.
y = 36.
How to solve this system of equations?In order to solve the given system of equations, we would apply the substitution method. From the information provided in the image attached above, we have the following system of equations:
y = -2x + 18 .......equation 1.
y = -4x .......equation 2.
By using the substitution method to substitute equation 1 into equation 2, we have the following:
-2x + 18 = -4x
By re-arranging and collecting like terms, we have the following:
-4x + 2x = 18
-2x = 18
x = -18/2
x = -9
For the value of y, we have the following:
y = -4x
y = -4(-9)
y = 36.
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If investments double every 9 years and you
start with a $600 investment, how much
money would you have after 27 years?
First, complete the equation:
Future Amount = [?](1+
↑
initial amount
growth rate
Xtime
periods
After 27 years, you would have $4800 in the account.
What is Exponential Growth?An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases over time.
y = a(1+r)ˣ,
where a is the initial population and r is the rate in decimals and x is the time period.
Given:
Investment double every 9 years,
and you start with $600 investment.
So, by the exponential growth function,
y = 600(1+r)ˣ,
To find the growth rate:
1200 = 600(1 + r)⁹
r = 1.08006
So, the equation is,
y = 600(1+0.8006)ˣ
After 27 years,
y = 600 x 8
y = $4800
Therefore, $4800 is the required amount.
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Discussion: Quadratic Functions
Consider a quadratic function in forms of f(x) = ax^2 + bx + c. How many real zeros can it have? How many complex zeros can it have? How does each case relate to its graph?
To find its zeros you can use two different methods. What are they? When would it be appropriate to use one method over the other?
1. There are two real zeros, one real zero, or two complex conjugate zeros, depending on the discriminant of the quadratic formula, which is b² - 4ac.
2. This formula gives the two zeros of the quadratic function. You can use the quadratic formula when factoring is not possible or not easy to do.
Quadratic FunctionsA quadratic function in the form of f(x) = ax² + bx + c can have either two real zeros, one real zero, or two complex conjugate zeros, depending on the discriminant of the quadratic formula, which is b² - 4ac.
If the discriminant is positive, meaning b² - 4ac > 0, then the quadratic function has two real zeros, since the quadratic formula gives two distinct real roots. The graph of the function will intersect the x-axis at two distinct points.
If the discriminant is zero, meaning b² - 4ac = 0, then the quadratic function has one real zero with a multiplicity of two, which means the graph will touch the x-axis at one point but not cross it.
If the discriminant is negative, meaning b² - 4ac < 0, then the quadratic function has two complex conjugate zeros. The graph will not intersect the x-axis, but it will have a minimum or maximum point called the vertex.
To find the zeros of a quadratic function, you can use two different methods: factoring and the quadratic formula.
Factoring is an efficient method if the quadratic expression can be factored easily. For example, if the expression is in the form of x² + 5x + 6, it can be factored as (x + 2)(x + 3), and the zeros are x = -2 and x = -3.
The quadratic formula is another method to find the zeros of a quadratic function. This formula can be used for any quadratic expression, regardless of whether it can be factored or not. The quadratic formula is:
x = (-b ± √(b² - 4ac)) / 2a
This formula gives the two zeros of the quadratic function. You can use the quadratic formula when factoring is not possible or not easy to do.
In general, factoring is quicker and simpler when it is possible, but the quadratic formula is always reliable and will give the zeros in any case.
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If a member is increased by 88,the result is 155. What is the number?
Answer:67
Step-by-step explanation:
88-155=67
HELP pls will mark you the brainliest
We can acquire a number of kites of 6 kites for a total price of $ 30 in both stores (Kites-R-Fun, Windy Kites).
What is the solution to a system of linear equations formed by two lines
In this problem we find the case of two lines being represented on Cartesian plane, both have a point of intersection that represents the solution to the system. Each line represents a price function for a kite model sold in a store, where the horizontal axis represents the number of kites and the vertical axis represents the total cost.
According to the given figures, we can acquired a number of kites of 6 kites at a total price of $ 30 in both stores.
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Saul makes trail mix with peanuts, raisins, and pretzels. The ratio of cups of raisins to cups of peanuts is 1 to 6. The ratio of cups of pretzels to cups of raisins is 3 to 1. Decide if each statement describing the trail mix is true or false. Choose True or False for each statement.
1.) "Saul uses 6 times as many cups of peanuts as cups
of raisins."
2.) "Saul uses 3 times as many cups of raisins as cups
of pretzels."
3.) "The ratio of cups of peanuts to cups of pretzels is 3 : 6."
4.) "Saul uses 2 times as many cups of peanuts as cups
of pretzels."
The following statements describing the trail mix;
1.) "Saul uses 6 times as many cups of peanuts as cups of raisins."True
2.) "Saul uses 3 times as many cups of raisins as cups of pretzels."False
3.) "The ratio of cups of peanuts to cups of pretzels is 3 : 6."False
4.) "Saul uses 2 times as many cups of peanuts as cups of pretzels."False
Which statement is true or false?The ratio of cups of raisins to cups of peanuts is 1 to 6.
The ratio of cups of pretzels to cups of raisins is 3 to 1.
Check all that applies;
1.) "Saul uses 6 times as many cups of peanuts as cups of raisins."
True
2.) "Saul uses 3 times as many cups of raisins as cups of pretzels."
False
3.) "The ratio of cups of peanuts to cups of pretzels is 3 : 6."
False
ratio of cups of peanuts to cups of pretzels = 6 : 3
4.) "Saul uses 2 times as many cups of peanuts as cups of pretzels."
False
Hence, the statement can be true if the ratio is correct.
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England and Scotland both produce scones and sweaters. Suppose that an English worker can produce 40 scones per hour or 1 sweater per hour. Suppose that a Scottish worker can produce 20 scones per hour or 2 sweaters per hour. _____________ workers have an absolute advantage in producing scones, _______________ workers have an absolute advantage in producing sweaters.
English workers have an absolute advantage in producing scones, Scottish workers have an absolute advantage in producing sweaters.
How to get workers with absolute advantage?English workers have an absolute advantage in producing scones as they can produce 40 scones per hour,
while Scottish workers can only produce 20 scones per hour. On the other hand, Scottish workers have an absolute advantage in producing sweaters as they can produce 2 sweaters per hour, while English workers can only produce 1 sweater per hour.
Absolute advantage refers to the ability of a country or individual to produce a good or service more efficiently than another country or individual.
This means that the country or individual with the absolute advantage is able to produce the same good or service with fewer resources or in less time. In this case, each country has an absolute advantage in producing one of the goods, scones or sweaters.
Thus,English workers have an absolute advantage in producing scones, Scottish workers have an absolute advantage in producing sweaters.
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