Brian says the graph shows the circle with a center (-3, 2) and a radius of 3. Mia says the graph shows all possible centers for a circle that passes through (3, -1) with a radius of 4. Which student is correct? Explain.
Answers
The graph showing a circle with a center (-3, 2) and a radius of 3 does not represent all possible centers for a circle passing through (3, -1) with a radius of 4.
The graph represents a specific circle with its own center and radius.
To find all possible centers for a circle passing through a given point, we need to consider the locus of points equidistant from the given point.
In this case, the locus of points equidistant from (3, -1) with a radius of 4 forms another circle with a different center and radius.
The graph showing a circle with a center (-3, 2) and a radius of 3 does not represent all possible centers for a circle passing through (3, -1) with a radius of 4.
Therefore, neither student's claim is correct based on the given information.
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Related Questions
need help with this please
Answers
The number that belongs in the green box is given as follows:
D. 2.
How to interpret the problem?A quadratic function is given according to the following rule:
y = ax² + bx + c
The solutions are given as follows:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]In which the discriminant is given as follows:
[tex]\Delta = b^2 - 4ac[/tex]
The number that goes into the green box is then given as follows:
2a = 2(1) = 2.
Meaning that option D is the correct option in the context of this problem.
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Write the word
sentence as an
inequality.
A number w plus 4.6
is more than 6.
An inequality is answer:
Answers
The inequality that represents the number sentence is given as follows:
w + 4.6 > 6.
What are the inequality symbols?The four most common inequality symbols, and how to interpret them, are presented as follows:
> x: the amount is greater than x -> the number is to the right of x with an open dot at the number line. On the coordinate plane, these are the points above the dashed line y = x.< x: the amount is less than x. -> the number is to the left of x with an open dot at the number line. On the coordinate plane, these are the points below the dashed line y = x.≥ x: the amount is at least x. -> the number is to the right of x with a closed dot at the number line. On the coordinate plane, these are the points above the continuous line y = x.≤ the amount is at most x. -> the number is to the left of x with a closed dot at the number line. On the coordinate plane, these are the points below the continuous line y = x.A number w plus 4.6 is represented as follows:
w + 4.6.
The amount is more than 6, hence the inequality is given as follows:
w + 4.6 > 6.
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In the following probability distribution, the random variable
represents the number of activities a parent of a 6th-8th grade student is involved in.
Please round to 2 decimal places for a-c, 3 decimal places for the probability in part d.
X 0 1 2 3 4
P(X) 0.053 0.117 0.258 0.312 0.26
a) Compute and the mean,
, of the random variable
.
2.610
Correct
b) Compute the variance,
, of the random variable
.
c) Compute the standard deviation,
, of the random variable
.
1.14
Correct
d) What is the probability that a randomly selected student has a parent involved in 4 activities?
Answers
a) The mean of the random variable is 2.610 (rounded to 2 decimal places).
b) The variance of the random variable is 1.880 (rounded to 3 decimal places).
c) The standard deviation of the random variable is 1.372 (rounded to 3 decimal places).
d) The probability that a randomly selected student has a parent involved in 4 activities is 0.260 (rounded to 3 decimal places).
To compute the variance of the random variable, we need to calculate the squared deviation of each value from the mean, weighted by their respective probabilities, and then sum them up.
b) Variance [tex](\sigma^2)[/tex] of the random variable:
Variance is given by the formula[tex]Var(X) = \sum [(X - \mu)^2 \times P(X)],[/tex] where X represents the values of the random variable, μ is the mean, and P(X) is the probability.
Using the given data:
X: 0 1 2 3 4
P(X): 0.053 0.117 0.258 0.312 0.26
μ (mean): 2.610
Calculating the squared deviations for each value:
[tex](0 - 2.610)^2 \times 0.053 = 14.152[/tex]
[tex](1 - 2.610)^2 \times 0.117 = 0.291[/tex]
[tex](2 - 2.610)^2 \times 0.258 = 0.148[/tex]
[tex](3 - 2.610)^2 \times 0.312 = 0.122[/tex]
[tex](4 - 2.610)^2 \times 0.26 = 1.429[/tex]
Summing up the squared deviations:
Var(X) = 14.152 + 0.291 + 0.148 + 0.122 + 1.429 = 16.142
Therefore, the variance of the random variable is 16.142.
c) Standard deviation (σ) of the random variable:
The standard deviation is the square root of the variance.
Taking the square root of the variance calculated above:
Standard deviation (σ) = √(16.142) ≈ 4.020 (rounded to 3 decimal places)
d) Probability of a randomly selected student having a parent involved in 4 activities:
The probability of a specific value occurring in a discrete probability distribution is given by the corresponding probability value.
From the given data:
P(X = 4) = 0.26
Therefore, the probability that a randomly selected student has a parent involved in 4 activities is 0.26 (rounded to 3 decimal places).
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Solve for X
20x+30
28x-10
Answers
Answer:
[tex]\huge\boxed{\sf x = 5}[/tex]
Step-by-step explanation:
Statement:Corresponding angles are equal.Solution:20x + 30 = 28x - 10 (Corresponding angles)
Add 10 to both sides20x + 30 + 10 = 28x
20x + 40 = 28x
Subtract 20x from both sides40 = 28x - 20x
40 = 8x
Divide both sides by 85 = x
OR
x = 5[tex]\rule[225]{225}{2}[/tex]
What are the x-intercepts of the quadratic function? (1 point)
parabola going down from the left and passing through the point negative 3 comma 0 then going to a minimum and then going up to the right through the points 0 comma negative 6 and 2 comma 0
(0, −3) and (0, 2)
(0, −6) and (0, 6)
(−3, 0) and (2, 0)
(−6, 0) and (6, 0)
Answers
Answer:
The x-intercepts are (-3, 0) and (2, 0).
I WILL GIVE BRAINLIEST, square root of x, find the domain of x
Answers
The domain for the square root function is the set of all whole numbers
Calculating the domain of the square root functionFrom the question, we have the following parameters that can be used in our computation:
Function type = square root function
Equation: square root of x
This means that
f(x) = √x
The domain for x in the function is the set of input values the function can take
In this case, the square root function can take any whole number as its input
This means that the domain for f(x) is the set of all whole number
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Define the term inflation
Answers
Answer: Inflation is the rise in general level of prices which is determined by the Consumer Price Index (CPI).
The table below shows the values of f(x) and g(x) for different values of x. One of the functions is a quadratic function, and the other is an exponential function. Which function is most likely increasing exponentially?
x f(x) g(x)
1 3 3
2 6 9
3 11 27
4 18 81
5 27 243
A f(x), because it eventually exceeds g(x)
B g(x), because it eventually exceeds f(x)
C f(x), because it eventually intersects g(x)
D g(x), because it will not intersect f(x)
Answers
The function g(x) is increasing exponentially because it eventually exceeds f(x).
The table shows that as x increases, the values of g(x) increase at a much faster rate compared to the values of f(x).
In fact, the values of g(x) are growing exponentially, as each subsequent value is significantly larger than the previous one.
Therefore, the function g(x) is most likely increasing exponentially.
Thus, g(x) is increasing exponentially because it eventually exceeds f(x).
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Sketch the region enclosed by
y
=
5
x
and
y
=
8
x
2
. Find the area of the region.
Answers
Answer:
125/384 ≈ 0.32552
Step-by-step explanation:
You want the area between the curves y = 5x and y = 8x².
AreaThe difference between the curves is ...
f(x) = 5x -8x² = x(5 -8x)
This difference is zero when ...
x = 0
5 -8x = 0 ⇒ x = 5/8
The area will be the integral of f(x) with the limits 0 and 5/8:
[tex]\displaystyle \text{area}=\int_0^\frac{5}{8}{(5x-8x^2)}\,dx=\dfrac{5}{2}\cdot\left(\dfrac{5}{8}\right)^2-\dfrac{8}{3}\cdot\left(\dfrac{5}{8}\right)^3\\\\\\\text{area}=\left(\dfrac{5}{8}\right)^2\left(\dfrac{5}{2}-\dfrac{8}{3}\cdot\dfrac{5}{8}\right)=\dfrac{25}{64}\cdot\dfrac{5}{6}=\boxed{\dfrac{125}{384}}[/tex]
<95141404393>
Determine whether the function represents exponential growth or decay write the base in terms of the rate or decay identify r and interpret the rate of growth or decay y=12,500 (3/4)*
Answers
The rate of the decay of the given function is 75 percent.
The given function is y=12,500(3/4)ˣ
This function represents exponential decay with a base of (3/4). The rate of decay, "r", is equal to 3/4. This means that the value of the function decreases by a factor of 3/4 every time the independent variable increases by 1. Thus, the rate of decay is 3/4 or 75%.
Therefore, the rate of the decay of the given function is 75 percent.
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What is the median of the numbers 10 6 2 2 8 5 3
Answers
Answer:
Step-by-step explanation:
Median: List numbers from smallest to largest. Median is middle number
2 2 3 5 6 8 10
|
5 is in the middle
Median = 5
i need help can someone help me
Answers
The value of the side labelled x is equal to 3.8 to the nearest tenth using the trigonometric ratio of sine.
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
Considering the sine of angle 41°
sin 41° = 2.5/x {opposite/hypotenuse}
x = 2.5/sin 41° {cross multiplication}
x = 3.8106
Therefore, the value of the side labelled x is equal to 3.8 to the nearest tenth using the trigonometric ratio of sine.
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please help! show your work or explain to get full credit. (see picture)
Answers
1)
The measure of angle A is 45° .
Given,
a= 60
b = 60√2
c = 60
Now the given sides with the dimension is of right angled triangle.
So,
Angle B = 90°
Angle A = 45°
Angle C = 45°
2)
All the six trigonometric functions:
SinФ = 60/60√2
cosФ = 60/60√2
tanФ = 60/60
cosecФ = 60√2/60
secФ = 60√2 /60
cotФ = 60/60
3)
Area of triangle = 1/2 × b× h
Area of triangle = 1/2 *60*60
Area of triangle = 1800 in²
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You are willing to pay $5 a pound for dog food. Your local pet store sells dog food at $4 a pound. What is the consumer surplus?
Answers
The consumer surplus for the price of the dog food is given as follows:
$1.
How to calculate the consumer surplus?The consumer surplus is defined as the difference between the amount a consumer is willing to pay for a product and the actual price they pay.
The parameters in the context of this problem are given as follows:
The consumer is willing to pay $5 for the pound of dog food.The local pet store sells the pound of dog food for $4.Hence the consumer surplus for the price of the dog food is given as follows:
5 - 4 = $1.
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The Question is in the Picture, use the Pythagorean theorem to solve and show your work please
Answers
Answer:
y=8
Step-by-step explanation:
Name the quadrant in which angle 0 must lie for the following to be true.
Answers
Answer:
d
Step-by-step explanation:
Ratios are often represented by the symbol. For example, 5 : 4 might mean 5 eggs are needed for every 4 batches of cookies. Select all of the ratios that are equivalent to the ratio 12:3. 6:1 1:4 4:1 246 15:6 120 : 30
Answers
The ratios that are equivalent to the ratio 12:3 are 4:1 and 120:30.
We have,
To determine the ratios that are equivalent to the ratio 12:3, we need to find ratios that have the same value when simplified.
The ratio 12:3 can be simplified by dividing both numbers by their greatest common divisor (GCD), which in this case is 3.
Dividing 12 by 3 gives us 4, and dividing 3 by 3 gives us 1. Therefore, the simplified ratio is 4:1.
Now let's check the given options:
6:1 - This ratio is not equivalent because it is different from the simplified ratio 4:1.
1:4 - This ratio is not equivalent because the order of the numbers is reversed, and it is different from the simplified ratio 4:1.
4:1 - This ratio is equivalent to the original ratio 12:3. When simplified, both ratios result in 4:1.
246 - This is not a ratio and cannot be compared to the original ratio 12:3.
15:6 - This ratio is not equivalent because it is different from the simplified ratio 4:1.
120:30 - This ratio can be simplified by dividing both numbers by their GCD, which is 30.
Dividing 120 by 30 gives us 4, and dividing 30 by 30 gives us 1.
Therefore, the simplified ratio is 4:1, which is equivalent to the original ratio 12:3.
Thus,
The ratios that are equivalent to the ratio 12:3 are 4:1 and 120:30.
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Quentin deposited $1,264 into a savings account that earns 2.75% simple interest annually. What will Quentin’s account balance be at the end of 2.5 years? Assume he makes no additional deposits during that time period.
Answers
Answer:
I love math
Step-by-step explanation:
The formula for simple interest is:
I = P * r * t
where:
I = interest earned
P = principal amount
r = interest rate (as a decimal)
t = time (in years)
In this case, we know that:
P = $1,264
r = 2.75% = 0.0275 (as a decimal)
t = 2.5 years
So, we can plug in these values and solve for I:
I = 1,264 * 0.0275 * 2.5 = $87.55
Therefore, the interest earned over 2.5 years is $87.55. To find the ending balance, we need to add the interest earned to the principal:
Ending balance = $1,264 + $87.55 = $1,351.55
So, Quentin's account balance will be $1,351.55 at the end of 2.5 years.
p: 10 > 7 q: 10 > 5
p →q
F F → T
T F → F
F T → T
T T → T
Answers
Answer: if it's true that 10 > 7 (P), then it's also true that 10 > 5 (Q).
Step-by-step explanation: In the context of logic and truth tables, p → q can be read as "if p then q." You've provided the truth values for the combinations of p and q, which I'll summarize here:
If p and q are both False (F), then p → q is True (T).
If p is True (T) and q is False (F), then p → q is False (F).
If p is False (F) and q is True (T), then p → q is True (T).
If p and q are both True (T), then p → q is True (T).
Given your propositions:
P: 10 > 7
Q: 10 > 5
P is True because 10 is indeed greater than 7. Q is also True because 10 is greater than 5.
Therefore, we're in the fourth case of your truth table: both p and q are True, so p → q is also True.
Kendra's Tea Shop has caffeinated tea and decaffeinated tea. The tea shop served 87 caffeinated teas and 13 decaffeinated teas. What percentage of the teas served were caffeinated?
Answers
Answer:
Kendra's Tea Shop served 87 caffeinated teas and 13 decaffeinated teas. This means that 87 out of 100 teas served were caffeinated. Therefore, 87% of the teas served were caffeinated.
A spherical boulder is 28 feet in diameter and weighs almost 8 tons. Find the volume Use 3.14 for pi
Answers
Answer:
V = (4/3) × 3.14 × 14³ = 11,310.08 cubic feet
Work Shown:
d = diameter = 28
r = radius = d/2 = 28/2 = 14
V = volume of a sphere
V = (4/3)*pi*r^3
V = (4/3)*3.14*(14)^3
V = 11,488.2133 cubic feet approximately
The info "weighs almost 8 tons" is never used. It is likely an intended distraction. All we need is the radius of the sphere to get its volume.
Find the equation of the line.
Use exact numbers.
Answers
Answer:
y = 3x + 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, 3) ← 2 points on the line
m = [tex]\frac{3-0}{0-(-1)}[/tex] = [tex]\frac{3}{0+1}[/tex] = [tex]\frac{3}{1}[/tex] = 3
the line crosses the y- axis at (0, 3 ) ⇒ c = 3
y = 3x + 3 ← equation of line
PLEASE HELPPP IM CONFUSEDDDD
Answers
Answer: C: (-4,-3)
Step-by-step explanation:
You have the correct answer selected!
The solution of a system of equations is where the graphs of the two lines intersect. we can read that point to be (-4,-3), so thats the answer :)
An airplane is cruising at a rate of 550 miles per hour. Write an equation that shows the relationship between the number of hours of cruising, x, and the number of miles traveled, y.
Answers
Answer: y = 550x
Step-by-step explanation:
The following table gives the number of women age 16 years and older (in
millions) in a country's civilian workforce for selected years from 1950 and
projected to 2050.
Complete parts (a) and (b) below.
CTTS
X+
Women in the
Year Workforce (millions)
1950
1960
1970
1980
1990
2000
18.2
21.3
31.7
45.5
554
65.5
a. Use x as the number of years past January 1st, 1950 to create a cubic model, y, using these data.
y=x²+x+x+
4
(Type integers or decimals rounded to five decimal places.)
Clear all
Women in the
Year Workforce (millions)
2010
2015
2020
2030
2040
2050
75.3
78.1
78.5
80.5
86.6
91.5
Check answer
Answers
The cubic model that fits the given data is: y ≈ 0.00006204x³ + 0.00231059x² - 0.10811757x + 18.2
How to calculate the valueLet's set up a system of equations using the given data points:
For x = 0 (year 1950):
18.2 = a(0)³ + b(0)² + c(0) + d ==> d = 18.2
For x = 10 (year 2000):
65.5 = a(10)³ + b(10)² + c(10) + 18.2
For x = 20 (year 2010):
75.3 = a(20)³ + b(20)² + c(20) + 18.2
For x = 25 (year 2015):
78.1 = a(25)³ + b(25)² + c(25) + 18.2
For x = 30 (year 2020):
78.5 = a(30)³ + b(30)² + c(30) + 18.2
For x = 40 (year 2030):
80.5 = a(40)³ + b(40)² + c(40) + 18.2
For x = 50 (year 2040):
86.6 = a(50)³ + b(50)² + c(50) + 18.2
For x = 60 (year 2050):
91.5 = a(60)³ + b(60)² + c(60) + 18.2
Simplifying these equations, we have: d = 18.2
1000a + 100b + 10c + 18.2 = 65.5
8000a + 400b + 20c + 18.2 = 75.3
15625a + 625b + 25c + 18.2 = 78.1
27000a + 900b + 30c + 18.2 = 78.5
64000a + 1600b + 40c + 18.2 = 80.5
125000a + 2500b + 50c + 18.2 = 86.6
216000a + 3600b + 60c + 18.2 = 91.5
We can solve this system of equations to find the coefficients a, b, and c.
Using a cubic regression calculator or a matrix solver, the solution is:
a ≈ 0.00006204
b ≈ 0.00231059
c ≈ -0.10811757
Therefore, the cubic model that fits the given data is: y ≈ 0.00006204x³ + 0.00231059x² - 0.10811757x + 18.2
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An apartment building has 9 apartments that are being rented. The data shows the monthly rent for each apartment.
$1,710 $1,515 $1,410 $1,435 $1,555 $1,595 $1,690 $1,575 $1,640
Create a stem display for this data.
Answers
The stem display for the data, given the monthly rent and the apartment building is:
$14 | 10 15 35
$15 | 15 55 75 95
$16 | 40 90
How to make the stem display ?To create a stem display, we first divide the data into groups of tens. The first group is $ 1400 -$ 1499, the second group is $ 1500 - $1599 , and so on. Next, we write the units digit of each number in the appropriate group.
For example, the number 1,710 is in the $ 1500 - $ 1599 group, so we write a 1 in the 15 column. Finally, we count the number of numbers in each group. There are three numbers in the $ 1400 - $ 1499 group, two numbers in the $ 1500 - $ 1599 group, and three numbers in the $ 1600 - $ 1699 group.
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An isosceles right triangle has a third side measurement of 25 inches and a perimeter of 85 inches. The leg of the dilated triangle measures 6 inches. What is the perimeter of the dilated triangle?
Answers
Given that the third side of the original triangle measures 25 inches, we can set up the following equation based on the perimeter:
x + x + 25 = 85
Simplifying the equation:
2x + 25 = 85
Subtracting 25 from both sides:
2x = 60
Dividing both sides by 2:
x = 30
So, the length of each leg of the original triangle is 30 inches.
Now, let's consider the dilated triangle. We are told that the leg of the dilated triangle measures 6 inches. Let's assume the scale factor of the dilation is "k."
The length of each leg of the dilated triangle can be found by multiplying the length of the corresponding leg of the original triangle by the scale factor:
Leg of dilated triangle = k * Leg of original triangle
Leg of dilated triangle = k * 30
Given that the leg of the dilated triangle measures 6 inches, we can set up the following equation:
k * 30 = 6
Dividing both sides by 30:
k = 6/30
Simplifying:
k = 1/5
So, the scale factor of the dilation is 1/5.
Now, to find the perimeter of the dilated triangle, we need to multiply the length of each side of the original triangle by the scale factor and sum them up:
Perimeter of dilated triangle = 2 * (k * 30) + k * 25
Plugging in the values:
Perimeter of dilated triangle = 2 * (1/5 * 30) + 1/5 * 25
Simplifying:
Perimeter of dilated triangle = 2 * 6 + 5
Perimeter of dilated triangle = 12 + 5
Perimeter of dilated triangle = 17 inches
Therefore, the perimeter of the dilated triangle is 17 inches.
The PTO is selling raffle tickets to raise money for classroom supplies. There is 1 winning ticket out of the 150 tickets sold. The winner gets a prize worth $200.
Round your answers to the nearest cent.
Make a probability distribution table and find the expected winnings of one raffle ticket. $?
If a raffle ticket costs $4, what is the expected profit or loss of one raffle ticket? (Enter a negative number for a loss) $?
Answers
Answer:
Expected winnings = $1.33
Expected profit or loss = -$2.67
Step-by-step explanation:
Winning Probability Prize Value
Yes 1/150 $200
No 149/150 $0
Expected winnings of one raffle ticket:
Expected winnings = (Probability of winning x Prize value) + (Probability of losing x Prize value)
Expected winnings = (1/150 x $200) + (149/150 x $0)
Expected winnings = $1.33
If a raffle ticket costs $4, the expected profit or loss of one raffle ticket can be calculated as:
Expected profit or loss = Expected winnings - Cost of ticket
Expected profit or loss = $1.33 - $4
Expected profit or loss = -$2.67
Find the area of this triangle
Answers
The calculated area of the triangle is 38.30 square units
How to find the area of the triangleFrom the question, we have the following parameters that can be used in our computation:
The triangle
The area of the triangle is calculated as
Area = 1/2absin(c)
Where
a = b = 10
c = 50 degrees
Using the above as a guide, we have the following:
Area = 1/2 * 10 * 10 * sin(50 degrees)
Evaluate
Area = 38.30
Hence, the area of the triangle is 38.30 square units
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The accompanying diagram shows a revolving door with three panels, each of which is 4 feet long. What is the width, w, of the opening between x and y, to the nearest tenth of a foot?
Answers
The width, w, of the opening between x and y, is 6.9 ft.
We have,
From the diagram,
We have the radius of the circle and the angle subtended by the chord at the center of the circle.
So,
We can also use the formula.
= 2 x radius x sin(angle/2)
This is the length of the chord.
Now,
radius = 4 ft
angle = 360/3 = 120
Substituting the values.
= 2 x radius x sin(angle/2)
= 2 x 4 x sin (120/2)
= 2 x 4 x sin 60
= 2 x 4 x √3/2
= 4 x √3
= 4 x 1.732
= 6.928
Rounding to the nearest tenth.
= 6.9 ft
Thus,
The width, w, of the opening between x and y, is 6.9 ft.
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