Answer:
After rounding the nearest tenth of a square foot, the surface area of the circular cylinder is 131.88 feet^2.
Step-by-step explanation:
To find surface area of a right circular cylinder we can use the formula,
A = 2πrh + 2πr^2
Here A is surface area,
π is mathematical constant ,
r is radius, and h is the height of the cylinder.
We have
r = 3 ft
h = 4 ft,
Now we put the values to find the surface area,
A = 2π × 3 × 4 + 2π ×3^2
A = 24π + 18π
A = 42π
A= 42×3.14 (we know π = 3.14 )
A = 131.88
After rounding the nearest tenth of a square foot, the surface area of the circular cylinder is 131.88 feet^2.
picture in the box findiing the average
-
[tex]\cfrac{6}{4+\sqrt{2}}\implies \cfrac{6}{4+\sqrt{2}}\cdot \cfrac{4-\sqrt{2}}{4-\sqrt{2}}\implies \cfrac{6(4-\sqrt{2})}{\underset{\textit{difference of squares}}{(4+\sqrt{2})(4-\sqrt{2})}} \implies \cfrac{6(4-\sqrt{2})}{(4)^2 - (\sqrt{2})^2} \\\\\\ \cfrac{6(4-\sqrt{2})}{16 - 2}\implies \cfrac{6(4-\sqrt{2})}{14}\implies \cfrac{3(4-\sqrt{2})}{7}\implies \cfrac{12-3\sqrt{2}}{7}[/tex]
The figure below is dilated by a factor of 4 centered at the origin. Plot the resulting image
The resulting image of the dilated figure has vertices at (-8, -4), (8, -8), and (4, 8).
What is dilation?Resizing an item uses a transformation called dilation. Dilation is used to enlarge or shorten the structures. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during dilatation.
To dilate the given figure by a factor of 4 centered at the origin, we need to multiply the coordinates of each vertex by 4.
The new coordinates of B will be:
x-coordinate: 4 x (-2) = -8
y-coordinate: 4 x (-1) = -4
So the new vertex B' is (-8, -4).
The new coordinates of C will be:
x-coordinate: 4 x (2) = 8
y-coordinate: 4 x (-2) = -8
So the new vertex C' is (8, -8).
The new coordinates of D will be:
x-coordinate: 4(1) = 4
y-coordinate: 4(2) = 8
So the new vertex D' is (4, 8).
Therefore, the image of the resultant figure is given in the image below.
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How long does it take jim to mow lawn alone?
The time Jim takes alone to mow the lawn is 10 hours.
How to find the number of hours Jim take to mow?Jim and Craig, working together can mow the lawn in 8 hours. Working alone, Craig take 4 times as long as Jim.
Therefore, the time it takes Jim to mow the lawn alone can be calculated as follows:
let
x = time use by Jim to mow the lawn
Therefore,
time Craig use to mow the lawn = 4x
Hence,
1 / 8 = 1 / 4x + 1 / x
1 / 8 = 1 + 4/ 4x
1 / 8 = 5 / 4x
cross multiply
4x = 40
x = 40 / 4
x = 10
Therefore,
time Jim takes alone to mow the lawn = 10 hours.
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Y = -6x + 2
Y = -6x - 8
Answer:
Flase, no real numbers (2+-8)
Step-by-step explanation:
First, you conjoined the equations (-6x+2=-6x-8). Then you conjoined the variables first, (-6x+6x=0). Now you have 2=-8, which is not true.
How many square feet of carpeting will Victoria need to buy?
Answer:
Below
Step-by-step explanation:
Rectangular area = L x W = 10 x 20 = 200 ft^2
PLUS triangular area = 1/2 b h = 1/2 * 10 * 10 = 50 ft^2
TOTAL = 250 ft^2
11) Scientists studied the growth rates of two types of the flu virus. The growth rate of the first virus is modeled by the equation y = P * 3 ^ x where P is the number of people initially infected with the virus in a given population. The growth rate of the second virus could be modeled by v = P * 9 ^ x The growth rate of the second virus could be expressed as P * 3 ^ k What is the value of k? Show the work that gives your solution method. y =
The value of k is given as follows:
k = 2x.
How to obtain the value of k?The exponential function that models the growth of the first virus is given as follows:
y = P(3)^x.
The exponential function that models the growth of the second virus is given as follows:
y = P(9)^x = P(3)^k.
We have that 9 is the second power of 3, hence we have that:
y = P(3²)^x = P(3)^k.
Applying the power of power rule, we have that:
y = P(3)^(2x) = P(3)^k.
Hence the value of k is given as follows:
k = 2x.
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Find the volume V of the solid obtained by rotating the region bounded by the graphs of the given expressions about the specified line. y2 = x, x = 3y; about the y-axis V=
The volume, V of the solid obtained by rotating the region bounded by the graphs of the expressions, y² = x, x = 3y; about the y-axis is equals to the 162π/5 cubic units.
We have a region bounded by the graphs of two expressions. These expressios are y² = x, x = 3y. We have to calculate the volume of solid obtained by rotating the bounded region about the y-axis. First determine the intersection points of
y² = x, x = 3y.
=> x = 3y --(1)
=> y² = 3y
=> y² - 3y = 0
=> y( y - 3 ) = 0
=> y = 0 or y - 3 = 0
=> y = 0 , y = 3
from (1), x = 3y => x = 0, x = 9
Let the intersection points be O(0,0) and P(3,9). Now, the volume of rotating region or due to shaded region is
[tex]V = π\int_{0}^{3} (R² - r²) dy [/tex]
where R = 3y , r = y²
[tex]V = π\int_{0}^{3} [(3y)² - (y²)²]dy [/tex]
[tex]V = π \int_{0}^{3} (9y² - y⁴)dy [/tex]
[tex]V = π[ \frac{9y³}{3}- \frac{y⁵}{5} ]_{0}^{3} [/tex]
[tex]V = π[ \frac{9(3)³}{3}- \frac{{3}^{5} }{5} - 0- 0 ][/tex]
[tex]V = π(81 - \frac{243}{5} ) = \frac{162π}{5} [/tex]
Hence, the required volume is 162π/5 cubic units.
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if car traveling 40 mph takes 30 feet to stop, how many seconds will it take to stop? 
Answer:
To find the time it takes a car traveling at 40 mph to stop after covering a distance of 30 feet, we need to use the formula for distance, speed, and time, which is:
distance = speed * time
Rearranging the formula, we get:
time = distance / speed
Since the speed is in miles per hour (mph), we need to convert it to feet per second (fps). One mph is equivalent to 1.47 fps, so 40 mph is equivalent to 40 * 1.47 = 58.8 fps.
Now we can plug in the values for distance and speed into the formula:
time = 30 feet / 58.8 fps
time = 0.5104 seconds
Rounding to the nearest second, we get:
time = 0.51 seconds
So, it would take the car approximately 0.51 seconds to stop after traveling 40 mph.
Step-by-step explanation:
Charles and some friends ate at the Winterfield Café. Their bill was $50.00$ They paid $60.00. What percentage gratuity did they pay?
The percentage of gratuity paid is 20%.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Amount for the bill = $50
Amount paid = $60
The amount of gratuity.
= 60 - 50
= $10
Now,
The percentage of gratuity.
= 10/50 x 100
= 20%
Thus,
The percentage of gratuity is 20%.
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What is the range of this equation
This is college algebra
The range is the set of y-coordinates of the function.
As per graph we can see:
All positive values included as well as zero;There is one negative value, at y = - 2.Add all together to get the range:
y = - 2 and y ≥ 0As interval the range is:
y ∈ {-2} ∪ [0, + ∞)Use interval notation to write the intervals over which fis (a) increasing, (b) decreasing, and (c) constant.
y =f(x)
The intervals of each behavior of the function are given as follows:
a) Increasing: (-∞, -1).
b) Decreasing: (-1, 1).
c) Constant: (1, 3).
How to classify the function as increasing, decreasing or constant?The function is increasing when the graph moves right and up.The function is decreasing when the graph moves right and down.The function is constant when the graph of the function is an horizontal line.More can be learned about functions at https://brainly.com/question/24808124
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What is the surface area? 5 yd 10 yd 7 yd square yards
Based on the information, it can be inferred that the area of the figure is 310 yards²
How to calculate the surface area of this figure?To calculate the surface area of this figure we must find the area of all the faces of the figure:
5 * 10 = 5010 * 7 = 705 * 7 = 35Then we must multiply the area of each face by the number of faces with that area.
50 * 2 = 10070 * 2 = 14035 * 2 = 70Finally we must add the areas of the faces
100 + 140 + 70 = 310According to the above, the total surface area of this figure is 310 yards ²
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Shawn rounded a number to the nearest tenth and got 6.5 6 . 5 . When he rounded it to the nearest whole number, he got 6 6 . Which number could be the number he rounded?Shawn rounded a number to the nearest tenth and got 6.5 6 . 5 . When he rounded it to the nearest whole number, he got 6 6 . Which number could be the number he rounded?
The numbers could be:
6.45, 6.46, 6.47, 6.48, 6.49, 6.50, 6.51, 6.52, 6.53, and 6.54.
What is place value?The place value of a number is given as:
Example:
1234.567
1 = thousand place value
2 = hundred place value
3 = tens place value
4 = ones place value
5 = tenths place value
6 = hundredths place value
7 = thousandths place value
We have,
Shawn rounded a number to the nearest tenth and got 6.5.
When he rounded it to the nearest whole number, he got 6.
Now,
The number = 6.45
Rounded to the nearest tenth = 6.5
Rounded to the nearest whole number = 6
The numbers can be 6.45, 6.46, 6.47, 6.48, 6.49, 6.50, 6.51, 6.52, 6.53, and 6.54.
Thus,
The possible numbers are:
6.45, 6.46, 6.47, 6.48, 6.49, 6.50, 6.51, 6.52, 6.53, and 6.54.
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Metalworking Twelve equally spaced holes are to be drilled in a metal strip 3414-in. long, with 2 in. remaining on each end. What is the distance, to the nearest hundredth of an inch, from center to center of two consecutive holes.
Based on the given data, the distance from center to center of two consecutive holes is approximately 25.83 inches.
Calculating Distance Between Equally Spaced Holes in MetalworkingTo solve this problem, we need to divide the length of the metal strip (excluding the 2 inches on each end) by the number of holes to be drilled, and that will give us the distance from center to center of two consecutive holes.
So the length of the metal strip available for the 12 holes is:
3414 - 2 - 2 = 3410 inches
Dividing this length by the number of holes gives us:
3410 ÷ 12 = 284.166666... inches
To find the distance from center to center of two consecutive holes, we need to divide this value by the number of spaces between the holes, which is 11 (since there are 12 holes, but only 11 spaces between them). So:
284.166666... ÷ 11 = 25.833333...
Rounding this to the nearest hundredth of an inch, we get:
25.83 inches (to the nearest hundredth)
Therefore, the distance from center to center of two consecutive holes is approximately 25.83 inches.
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A sprinter starts from rest, and accelerates at 1.87 m/s^2 over a distance of 14.0 m. What is a her final velocity?
Please Answer Quick!
The conditional probability P(B|F) of the two way table is; P(B|F) = 0.37 given that the students prefer to write with block letters, there is a 0.37 probability that they have fair dancing skills
How to find the conditional probability of a two-way table?Two-way tables are a way of sorting data so that the frequency of each category can be seen quickly and easily.
Conditional probability is defined as the possibility of an event or outcome happening, based on the existence of a previous event or outcome.
Now, from the given two way table,
B = the student prefers writing in block letters.
F = the student's dancing skills are fair.
Thus;
P(B|F) = 17/45
P(B|F) = 0.37
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parallelogram has vertices at (–9, –6), (–3, 12), and (9, 12). What could be the coordinates of the fourth vertex? Use the coordinate plane below. .
The coordinates of the fourth vertex D = (3,−1.5).
What property this parallelogram has?A parallelogram has the following property AB=DC
AB=OB−OA=(3,3)−(1,5)=(2,−2)
DC=OC−OD=(8,3)−(a,b)=(2,−2)
OD=OC−DC=(8,3)−(2,−2)=(6,5)
Turn them into vectors. Position vector of point d
should be 6,5
To get the 2nd point, just do AD=BC
BC=OC−OB=(8,3)−(3,3)=(5,0)
AD=OD−OA=(a,b)−(1,5)=(5,0)
OD=OA−AD=(1,5)−(5,0)=(−4,5)
As long as the shape has four sides and two of them are parallel, and you know the length, this should work. For instance, a trapezium where AB=2DC/2CD:
A=(0,0),B=(2,0),C=(2,−1.5),D=(a,b)
AB=(2,0)DC=(2,−1.5)−(a,b)=12(2,0)(a,b)=(1,−1.5)
OR
AB=(2,0)CD=(a,b)−(2,−1.5)=12(2,0)(a,b)=(3,−1.5)
Thus, The coordinates of the fourth vertex D = (3,−1.5).
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A shipping container will be used to transport several 40-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 25500 kilograms. Other shipments weighing 6400 kilograms have already been loaded into the container. Write and solve an inequality which can be used to determine x, the number of 40-kilogram crates that can be loaded into the shipping container.
If a shipping container will be used to transport several 40-kilogram crates across the country by rail. The inequality that can be used to determine x is: 40x≤ 25,500-6,400 and the number of 40-kilogram crates that can be loaded into the shipping container is: x=≤ 477.5.
What is inequality?
An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.
here, we have,
Inequality
x is the integer
First step is to formulate the inequality
40x≤ 25,500-6,400
Now let determine the x by using the inequality
40x≤ 25,500-6,400
40x≤19,100
x=≤19,100/40
x=≤ 477.5
Therefore If a shipping container will be used to transport several 40-kilogram crates across the country by rail. The inequality that can be used to determine x is: 40x≤ 25,500-6,400 and the number of 40-kilogram crates that can be loaded into the shipping container is: x=≤ 477.5.
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Maria's abuela gave her $2000.00 for her quinceañera under the condition that she had to deposit it in a savings account for 42 months. How much interest will she have if the account earns 7.8% per annum simple interest?
Answer:
$ 546.00
Step-by-step explanation:
Simple Interest = P x r x t
where t = number of years
r = interest rate per year as a decimal
P = amount invested(deposit)
We are given that r = 7.8% per year = 7,8/100 = 0.078
However, since this is the yearly interest, the monthly interest = 0.078/12
The time period is 42 months
Initial deposit = $2,000
Therefore interest
I = 2000x (0.078/12) x 42 = $ 546.00
Does anyone know the reasoning for B
Answer:because angles in a triangle add up to 180 degrees.
Step-by-step explanation:
A=40
C=30
So 180-40-30=110
Please I just need help so badly asap Please
Answer:
- It is a parallelogram
Step-by-step explanation:
- The interior angle sum of a quadrilateral is 360°
Considering the four angles;
[tex]{ \tt{m \angle A + m \angle B + m \angle C + m \angle D = 360 \degree}} \\ \\ { \tt{(x + 12) + \{2(x + 3) \} + ( \frac{3}{2} x - 15) + ( \frac{7}{3} x - 12) = 360}} \\ \\ { \tt{(x + 2x + \frac{3}{2}x + \frac{7}{3}x) + (12 + 6 - 15 - 12) = 360 }} \\ \\ { \tt{ \frac{41}{6} x - 9 = 360}} \\ \\ { \tt{ \frac{41}{6}x = 369 }} \\ \\ { \tt{41x = 2214}} \\ \\ { \tt{x = 54}}[/tex]
- Therefore, substitute in x and find the angles.
[tex] { \tt{m \angle A = (x + 12) = (54 + 12) = 66 \degree}} \\ \\ { \tt{m \angle B = 2(x + 3) = 2(54 + 3) = 114 \degree}} \\ \\ { \tt{m \angle C = ( \frac{3}{2}x - 15) = \{( \frac{3}{2} \times 54) - 15 \} = 66 \degree }} \\ \\ { \tt{m \angle D = ( \frac{7}{3}x - 12) = \{( \frac{7}{3} \times 54) - 12 \} = 114 \degree }}[/tex]
What is the solution to the system of equations?
{2x−3y=−5
{3x+y=−2
The solution to the system of equations is x = -1 and y = 1.
What is system of equations?A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."
The system of equation is given as:
2x - 3y = -5 .........(1)
3x + y = -2 ........(2)
Equation 2 can be written as:
y = -2 - 3x
Substituting the value of y in equation 1 we have:
2x - 3(-2 - 3x) = -5
2x + 6 + 9x = -5
11x + 6 = -5
11x = -5 -6
11x = -11
x = -1
Substituting the value of x in equation 2 we have:
3x + y = -2
3(-1) + y = -2
-3 + y = -2
y = -2 + 3
y = 1
Hence, the solution to the system of equations is x = -1 and y = 1.
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Please help me with this question please
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
The pair of opposite angles formed by two intersecting straight lines are known as Vertical Angles.
In the given figure, there are two pairs of vertical angles~
That are :
[tex]\qquad \sf \dashrightarrow \: \angle1 \: \: and \: \: \angle3[/tex]
and
[tex]\qquad \sf \dashrightarrow \: \angle2 \: \: and \: \: \angle4[/tex]
Also, vertical opposite angles are equal in measure.
Answers for this photo?
The slope for:
1 = 1/2 (Option E)
2 = 2 (Option C)
3 = -1/2 (Option H)
4 = -2 (Option A)
What is slope in Maths?The slope or gradient of a line in mathematics is a quantity that specifies both the direction and the steepness of the line.
The formula for slope (m) is given as:
m = Rise/Run = y2-y1/x2-x1
(x1,y1) = Coordinates of the first point in the line
(x2,y2) = Coordinates of the second point in the line.
1) The points are:
x1= -2
y1 = 2
x2 =2
y2 = 4
m = (4 - 2) / (2 - (-2))
m = 2 / 4
m = 1/2
Thus, Δy/Δx = 1/2
2) The points are:
x1= -1
y1 = -12
x2 =5
yx = 0
m = (y2 - y1) / (x2 - x1)
Substituting the given values, we get:
m = (0 - (-12)) / (5 - (-1))
m = 12 / 6
m = 2
Thus, Δy/Δx = 2
3) Where the points are:
x1= 2
y1 = -6
x2 = - 4
y2 = -3
Substituting the given values, we get:
m = (-3 - (-6)) / (-4 - 2)
m = 3 / (-6)
m = -1/2
Thus, Δy/Δx = -1/2
4) Where the points are:
x1= 0
y1 = 3
x2 = 1.5
y2 = 0
Substituting the given values, we get:
m = (0 - 3) / (1.5 - 0)
m = -3 / 1.5
m = -2
Thus, Δy/Δx = -2
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A positive integer is 3 less than another. If the sum of the reciprocal of the smaller and
twice the reciprocal of the larger is 9/10 then find the two integer
Let's call the smaller integer "x". Then the larger integer would be "x + 3".
The sum of the reciprocal of the smaller integer and twice the reciprocal of the larger integer is 9/10, so we can write that as:
1/x + 2/(x + 3) = 9/10
Expanding and simplifying the right side:
1/x + 2/(x + 3) = 9/10
(x + 6)/(x * (x + 3)) = 9/10
10(x + 6) = 9x * (x + 3)
10x + 60 = 9x^2 + 27x
9x^2 - 83x + 60 = 0
Now we have a quadratic equation that we can solve using the quadratic formula or by factoring. Since the coefficients are integers, we can try factoring:
(3x - 20)(3x - 3) = 0
So either 3x - 20 = 0 or 3x - 3 = 0, which means either x = 20/3 or x = 3. Since x must be a positive integer, the only solution is x = 3.
So the two integers are 3 and 3 + 3 = 6.
HURRRRRRYYYYYYYYYYYYYYYYYYYYYYYY Drag numbers to show which are closest to ‐1
and ‐1/4
on the number line.
The number that is closest to -1 is -0.82 while the number that is closest to -1/4 is -0.28.
What are the closest numbers?In order to obtain the numbers that are close to a given number, we need to place the numbers side by side for a better understanding. For instance, the number 3 is closer to number 1 while the number 9 is closer to number 10.
Given the number line above, we can arrive at the conclusion that -0.82 is closer to -1 because by approximating the decimal, we will arrive at figure 1. Also, the number, -0.28 is closer to -1/4 or - 0.25 when converted to decimal.
Options;
A. -0.28
B. -0.82
C. -4/5
D. -1/5
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4232852 round off yo the nearest 1000
Answer:
4,233,000
Step-by-step explanation:
4,232,000 4,4232,852 4,233,000
4,4232,852 is between 4,232,000 and 4,233,000. It is closer to 4,233,000.
The rule is to look a the digit in the hundreds' place. That number is 8. If the digit in the hundreds' place is 5 or larger, you round up.
Write a rule for each graph below and explain it step by step
1) the rule for the graph is y=3x+3
2) the rule for the graph is y=4x+10
What is slope ?
A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
1) slope, m = change in y/change in x = 3/1 = 3
y-intercept = b = 3
A line's slope intercept form is y=mx+b
Thus, the rule for the graph is y=3x+3
2) slope, m = change in y/change in x = 4/1 = 4
y-intercept = b = 10
A line's slope intercept form is y=mx+b
Thus, the rule for the graph is y=4x+10
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Multiple step Fnd the value of X.
8)
(X-745)
560 4x0
(3x+2)
36
The value of x in the diagrams are 14 and 99 respectively
How to determine the valuesNote the following points;
Corresponding angles are equal Sum of angles at a point is equivalent to 360 degreesFrom the information given in the diagram
56 degrees and 4x degrees are corresponding
Then,
4x = 56
Make 'x' the subject
x = 14
From the second image
Add the angles and equate to 360 degrees, we have;
3x + 2 + 36 + x - 74 = 360
collect like terms
4x = 360 + 36
4x = 396
Make 'x' the subject
x = 99
Hence, the values are 14 and 99
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The rate in the portion formula is not always expressed with a percent symbol?
That's correct. The rate in the portion formula can be expressed as a decimal, fraction, or percentage, depending on the context and what is most convenient for the problem being solved.
What is the proportional and ratio formula?How do you calculate ratio and proportion? Ans: The ratio formula is written as a: b a/b for any two numbers. Contrarily, the percentage formula is written as a:b::c:da:b::c:da:b=cd.
What does a ratio example look like?An equation in which two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls) 1 out of 4 are boys, and 3/ 4 are girls.
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