The start of an arithmetic sequence is shown below.
Work out the nth term
Work out the 30th term in this sequence.
4 - 13 - 22 - 31
Answers
Therefore , the solution of the given problem of arithmetic mean comes out to be a(30) = 265.
Define arithmetic mean.When all of the values in a set of data have the same unit of measurement, such as when all of the numbers are heights, miles, hours, etc., this technique is utilized. Take the numbers 4, 7, 9, and 10 as an illustration. The count of numerals is 4, and the sum of the numbers is 30. 30 divided by 4 equals 7.5, which is the numbers' arithmetic mean.
Here,
Given that there is a common difference between each word, this is an arithmetic sequence. In this instance, the following term is obtained by adding 9 to the phrase before it in the sequence.
Alternatively put,
=> an=a1+d(n−1)
.Arithmetic Sequence:
d=9
This is the formula of an arithmetic sequence.
=>an=a1+d(n−1)
Substitute in the values of
=> a1 =4 and
d=9
.=>an=4+9(n−1)
Simplify each term.
Tap for more steps...
an=4+9n−9
Subtract 9 from 4
an=9n−5
Thus 30th term :
=> a(30)=9(30)−5
=> a(30) = 265
Therefore , the solution of the given problem of arithmetic mean comes out to be a(30) = 265.
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Related Questions
Which of these is the absolute value parent function?
A. f(x) = x
OB. f(x) = 2ˣ
OC. f(x) = x²
OD. f(x) = Ixl
Answers
Option D) f(x) = |x|, is Correct.
What is parent function?
A parent function is a basic or fundamental function that serves as the starting point for a family or group of related functions. These functions can be obtained by applying a transformation to the parent function, such as shifting, stretching, or reflecting it.
The absolute value parent function is represented by the following function:
D. f(x) = |x|
The absolute value function is defined as |x| = x for x >= 0 and |x| = -x for x < 0. Graph of this function is a V-shape, and it's also known as "the absolute value of x" function. It is a reflection of the linear function f(x) = x across the x-axis and will always have a slope of 1 and a y-intercept of 0.
A. f(x) = x is a linear function, slope is 1 and y-intercept is 0, This is not absolute value function
B. f(x) = 2ˣ is the exponential function, and it is not an absolute value function
C. f(x) = x² is the quadratic function, it's a parabola opening upwards and not an absolute value function
D. f(x) = |x| is the absolute value function, V-shape and it's an example of the absolute value parent function.
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Which is equivalent to the ratio 35 : 100?
Answers
Answer: 7:20
Step-by-step explanation:
It seems like there are no options to choose from, but if that is one of the options, here's how:
You can simplify ratios by finding if there is a common multiple.
For 35 and 100, there is a common multiple of 5, so you can divide both sides by 5 to simplify the equation.
That leaves us with 7:20. Since one is a prime number, we can't simplify this further.
Answer:
The ratio equivalent to 35:100 is 7:20
Step-by-step explanation:
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
What is the Ratio?
The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here,
Given ratio,
= 35 / 100
= 5× 7 / 20 × 5
= 7 / 20
Michael's pumpkin farm sold 75 pumpkins on October 24 that day they made $600. What did Michael charge for each pumpkin?
Answers
Answer:
$8.
Step-by-step explanation:
right!!
How do you find the asymptotes and zeros of a function?
Answers
The process to find the asymptote and zeros of the function is explained below.
The term asymptote is referred as a horizontal/vertical/slant line to which the curve is very close to but the curve doesn't touch the asymptote.
Here we need to find the way to identify the asymptotes and zeros of a function.
The process of finding the asymptote is defined as,
If you want to find the horizontal asymptotes, then apply the limit x→∞ or x→ -∞.
Where as if you want to find the vertical asymptotes, then apply the limit y→∞ or y→ -∞.
Finally, if you want to find the slant asymptote, then divide the numerator by the denominator.
The process of finding the zero of the function is defined as the way to find the values of x where f(x) = 0.
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Write the equation of the line that passes through the points (6, 1) and
(6, -8). Put your answer in fully simplified point-slope form, unless it
is a vertical or horizontal line.
Answers
something noteworthy is that the x-coordinate is the same for each point, so Check the picture below.
What type of graph is absolute value?
Answers
On [0,∞] the function grows, whereas on [-∞, 0], it shrinks. f has absolute minimum value is 0, and it also has the same relative minimum value (0,0).
What does an absolute value graph look like?On the graph, you are able to see a "open circle" at it when x< 0. (0, 0).
This is due to the fact that, as we've previously demonstrated, the points at y = x approaching (0, 0) as the x-values approach 0.Since x needs strictly be less than zero on only this stretch, the open circle being drawn in its place.When x ≥ 0, a point in (0, 0) is plugged in, thus "plugging" the hole shown by either open circle.Therefore, we get:On [0,∞] the function grows, whereas on [-∞, 0], it shrinks. Function f absolute minimum value is 0, and it also has the same relative minimum value (0,0).F has absolute minimum value is 0, and it also has the same relative minimum value (0, 0). F's highest relative value is zero.There consequently no absolute maximum value of f due to the graph's infinitely high y values.
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A box of 6 donuts has 3 plain donuts, 2 chocolate donuts, and 1 blueberry donut. Assume the plain donuts are identical, and the chocolate donuts are identical. How many visually distinct arrangements of the donuts are there?
Answers
If a box of 6 donuts has 3 plain donuts, 2 chocolate donuts, and 1 blueberry donut. The number of visually distinct arrangements of the donuts that are there is: 60.
How to find the number of visually distinct arrangements?Using this formula to find the number of visually distinct arrangements of the donut that are there.
Number visually distinct arrangements = Box of donuts!/ Plain donuts! × Chocolate donuts! × Blueberry donut!
Let plug in the formula
Number visually distinct arrangements = 6!/ 3! × 2! × 1!
Number visually distinct arrangements = 720/ 6 ×2 × 1
Number visually distinct arrangements = 720 /12
Number visually distinct arrangements = 60
Therefore the number of Number visually distinct arrangements is 12.
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1/4 - 7/1 (pls i nee answer)
Answers
Answer:3/4 is the answer
Step-by-step explanation:
Answer:(s)
1/4 - 7/1 = - 27/4
Decimal: - 6.75
Mixed number: - 6 3/4
Step-by-step explanation:
1/4 - 7/1 = - 27/4 or - 6.75 or - 6 3/4
LCM: 4, 1 = 4
Adjust Fraction Based On LCM:
1/4 - 28/4
Apply The Fraction Rule:
a/c - b/c = a - b/c
1 - 28/4
Subtract the numbers:
1 - 28 = - 27
= -27/4
Apply Fraction Rule:
- a/b = - a/b
Thus:
1/4 - 7/1 = - 27/4
Decimal: - 6.75
Mixed Number Form - 6 3/4
I hope that helps you!!!
please help it's for a test Which is an x-intercept of the graph of the function y=tan(x-5 pie/6)?
Answers
Answer:
5pie/6,0
Step-by-step explanation:
i graphed it
Lorraine prepared a 1.5-gallon pot filled with tomatoes to be canned in jars. Each jar will hold 1.5 quarts of tomatoes. If 1 gallon equals 4 quarts, how many jars
can Lorraine fill?
A.) 03 jars
B.)O4 jars
C.)05 jars
D.)O8 jars
Answers
If 1 gallon equals 4 quarts, Lorraine fill can 4 jars. Hence option B is the correct option.
What is the unit of an object?
The user can describe locations and dimensions in a wide range of various coordinate systems using unit objects. Every drawing is done in relation to a viewport, and the units determine the coordinate system to use there. "npc" is one example of a unit (coordinate system).
Given Lorraine filled a pot with tomatoes and the volume of the pot is 1.5 gallons.
She wants to fill the tomatoes in jars. The volume of the jar is 1.5 quarts.
1 gallon is equal to 4 quarts.
1.5 gallons is equal to 1.5 × 4 quarts = 6 quarts.
The number of jars that are filled with tomatoes is 6 quarts/ 1.5 quarts = 4.
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Which planets have surface features (e.g., mountains, canyons, volcanoes, etc.)?
Answers
Answer:
The answer is Terrestrial planets
highschool algebra:
combine like terms-
Answers
hope this helps :)
(NEED HELP ASAP!!)
What are the coordinates of the focus of the parabola?
A: (8, 6)
B: (-8, 6)
C: (-8, 2)
D: (8, 2)
Answers
Answer:
C: (-8, 2)
Step-by-step explanation:
Given parabola:
[tex]y=-\dfrac{1}{8}x^2-2x-4[/tex]
For the quadratic equation in the form y = ax² + bx + c, the x-value of the vertex is -b/2a.
Therefore, the x-value of the vertex of the given parabola is:
[tex]\implies x=-\dfrac{b}{2a}=-\dfrac{-2}{2\left(-\frac{1}{8}\right)}=-8[/tex]
To find the y-value of the vertex, input x = -8 into the given equation:
[tex]\implies y=-\dfrac{1}{8}(-8)^2-2(-8)-4=4[/tex]
Therefore, the vertex (h, k) of the parabola is (-8, 4).
The focus of the parabola is (h, k+p) where:
(h, k) is the vertex[tex]p=\dfrac{1}{4a}[/tex]Therefore:
[tex]\implies \textsf{Focus}=\left(-8,4+\dfrac{1}{4\left(-\frac{1}{8}\right)}\right)=\left(-8,2)[/tex]
4x² - 20x = -21????????
Answers
Answer:
x=7/2
x=3/2
Step-by-step explanation:
Answer: ax^2+bx+c=0
(4x^2+20x+20=0)
Step-by-step explanation:
It may not make sense but...
Add -20 to both sides of the equation.
4x-20x=-20
Add -20 to both sides of the equation.
4x^2-20x+20=-20+20
Simplify the expression.
4x^2+20x+20=0
I hope this was what you were looking for. :) If not I'm still glad to help.
Mark purchased 3 hotdogs and 2 pretzels for $7.50. Mary’s purchased 2 hotdogs and 4 pretzels for $7. How much is each item
Answers
Answer:
Hotdog costs $2 and pretzel costs $0.75--------------------------
Let the cost of a hotdog be h and pretzel be p.
Set up equations as per question:
3h + 2p = 7.52h + 4p = 7Divide the second equation by 2, then subtract from the first one:
3h + 2p - 2h/2 - 4p/2 = 7.5 - 7/23h - h = 7.5 - 3.52h = 4h = 2Now find the value of p:
3*2 + 2p = 7.56 + 2p = 7.52p = 1.5p = 0.75Hotdog costs $2 and pretzel costs $0.75.
Compute the smallest base-10 positive integer greater than 5 that is a palindrome when written in both base 2 and 4.
Answers
The smallest base-10 positive integer greater than 5 that is a palindrome when written in both base 2 and 4 is 11.
To compute this, first convert 5 to binary and base-4:
5 in binary: 101
5 in base-4: 11
Since 11 is the same in both bases, the next number that would be a palindrome in both bases is 11.
To find the base 10 number of this palindrome, we convert 11 from binary and base-4 to base 10:
11 in binary: 1011
11 in base-4: 111
Therefore, the smallest base-10 positive integer greater than 5 that is a palindrome when written in both base 2 and 4 is 11.
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Simplify (4s^5t^-7/-2s^-2t^4). Write your answer using only positive exponents. Evaluate any numerical powers.
I'LL NAME YOU BRAINLIEST
please help!!
Answers
In positive exponents, the simplified form of the above polynomial is s⁷/t¹¹.
What is polynomial?A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive-integer powers of variables. x2 4x + 7 is an example of a polynomial with a single indeterminate x. A polynomial is an expression in mathematics that consists of variables (also known as indeterminates) and coefficients and includes only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
Here,
=4s⁵*t⁻⁷/-2s⁻²*-2t⁴
=s⁷/t¹¹
The simplified form of given polynomial is s⁷/t¹¹ in positive exponents.
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18
The table shows information about the numbers of points scored by 28 students in a quiz.
Number of points
0
1
2
3
4
5
(a) Find the modal number of points.
(b) Work out the total number of points scored.
Frequency
5
4
5
5
6
3
(1)
Answers
Consequently, this student's quiz results have a median, or "middle," value of 16.
Define median.When a dataset is ordered, the median value is the one that appears exactly in the middle of the dataset. The difference between the lowest and highest 50% of data is a measure of central tendency or average. Depending on whether you have an odd or even number of data points, the procedures for determining the median , mode change.
Here,
the median, or "middle" value in a data set. Your data must be in numerical order in order to calculate the median.
Exam results:
9, 13, 20, 15, 18, 17
Number the rows and columns.
9, 13, 15, 17, 18, 20
Calculate the "middle" value:
9, 13, 15, 17, 18, 20
If there are two middle values, put them together and divide by two.
15 + 17 = 32
32/2 = 16
Consequently, this student's quiz results have a median, or "middle," value of 16.
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Mike is saving money for a new bike that costs $180.00
If represents the amount of money he has saved so far, which expression represents the amount of money,in dollars, he still needs to save?
A
180+m180+m180+m
B
180−m180-m180−m
C
180×m180\times m180×m
D
180÷m180\div m180÷m
Answers
Answer: B
Step-by-step explanation:
B) 180−m180-m180−m
Determine whether the two expressions are equivalent. If so, tell what property is applied. If not, explain why.
( 8 + 27) + 52 and 8 + (27 + 52)
Which one is correct
yes, it uses the Commutative Property
yes, it uses the Identity Property
yes, it uses the Associative Property
no they are not equivalent
Answers
Answer:
yes, it uses the Associative Property
Step-by-step explanation:
The two expressions (8 + 27) + 52 and 8 + (27 + 52) are equivalent because they both equal 87. This is an example of the Associative Property of Addition which states that the order of the terms within an expression can be changed without changing the result.
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otal deposit for Problems 5 through 19.
Currency
Tens Fives Ones Half Dollars Quarters Dimes Nickels Pennies Checks Total
$96.23 $
6.51
63 874.56
85
123.65
347.98
134.97
0
43.44
5
168.14
31
777.50
154 123.19
12 11
32
9
40
54
75
32
8
7
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13
10
12
1
16
67
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8
15
23
74
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9
6
7
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27
11
9
40
15
13
7
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3
13
34
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Coins
18
32
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15. Jess Norton stopped at an ATM location to deposit 2 one hundred-dollar
bills and checks for $474.85 and $321.15. He received $50.00 in cash.
16. Olive Baker, Spirit club treasurer, deposits the club's receipts. She has 4
checks for $10.00 each, 12 for $7.50, and cash consisting of six 20-dollar
bills, five 10-dollar bills, and 18 one-dollar bills.
17. Cyndi Winer deposits three checks for $425.22, $883.99, and $57.05. She
also deposits cash of 45 one-dollar bills, 15 five-dollar bills, and 12 ten-
dollar bills. The change deposited includes 28 quarters, 16 dimes, 19
nickels, and 65 pennies. She would like to receive $60.00 in cash.
18. Elias Rubio deposits three checks for $598.20, $2,274.26, and $3,248.79.
His cash consists of 75 one-dollar bills, 78 five-dollar bills, 33 ten-dollar
bills, 80 quarters, 32 dimes, 95 nickels, and 5 pennies. He would like to
receive $40.00 in cash.
Answers
The total cost of Jess Norton is $995.85 and the total cost of Olive Baker is $678 .
What is total cost ?
The total cost formula is used to total up the variable and constant expenses associated with providing commodities. Total cost = (Average Fixed Cost x Average Variable Cost) x Units Produced is the formula.
In economics, total cost is the total of all expenses a company incurs to produce a particular level of output.
The average cost, or the typical sum of money required to create a unit, can be determined using the cost function. The average cost function is A(x)=C(x)x, where x > 0 and C is the constant. Calculating the average cost per unit requires dividing the total cost by the quantity of units produced.
For Jees Norton,2 one hundred dollar bills = 2 x $100
= $200
Total deposits = 2 one hundred dollar bills + Checks
= $200 + $474.85 + $321
= $995.85
For Olive Baker,
Checks amount = $100 x 4
= $400
12 for $7.5
= 12 x $7.5
= $90
Six 20-dollar bills = 6 x $20
= $120
Five 10-dollar bills = 5 x $10
= $50
Eighteen 1-dollar bills = 18 x $1
= $18
Total deposits = $400 + $90 + $120 + $50 + $18
= $678
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108% of 75.5 is what number
Answers
Answer:
81.54
Step-by-step explanation:
% of a # = (% * #)/100
% = 108
# = 75.5
(108 * 75.5)/100
8,154/100
81.54
OR
% of a # = (%/100) * #
% = 108
# = 75.5
(108/100) * 75.5 = 1.08 * 75.5
81.54
What is the horizontal line on a graph?
Answers
The horizontal line of the graph is known as x axis,
The term graph in math is defined as the visual representation of data or the function in math.
Here we have to find the definition for the horizontal line on a graph.
Here we know that the straight line that is mapped from left to right and it is parallel to the X-axis in the plane coordinate system.
On the other hand, we all also know that the straight line that does not make any intercept on the X-axis and it can have an intercept on Y-axis is called horizontal line.
And we all also know that the straight line that is parallel to the x-axis and where all the points on the line have the same y-coordinate and basically all horizontal lines are parallel to each other.
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What is a 1 million sided shape called?
Answers
A one million sided shape called as Megagon.
We know that a polygon is noting but a closed two-dimensional figure which is enclosed by line segments.
These line segments are known as sides.
A polygon has at least three straight sides and angles.
Polygons are classified mainly into four categories. Regular polygon, Irregular polygon, Convex polygon and Concave polygon
We know that a polygon with n sides is called n-gon.
For n = 1000000, i.e., a polygon with one million sides is called as Megagon.
A number of edges and vertices = 1000000
And the internal angle of megagon is about 179.99 degrees.
Therefore, a shape with 1 million sides is known as a Megagon
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Find the derivative of the function. y = arctan √[(1 − x) /(1 + x)]
y' = ?
Answers
The derivative of the function y = [tex]tan^{-1}[/tex] √[(1 - x)/(1 + x)] is given by
y' = -1/[(1 + x)²× √[(1 - x)/(1 + x)]].
To find the derivative, we use the chain rule. The derivative of the outermost function, arctan, is
1/[1 + (√[(1 - x)/(1 + x)])²], and the derivative of the innermost function, the square root, is
-1/2×(1 - x)/[[tex](1+x)^{3/2}[/tex])]. Multiplying these two derivatives together gives us the final result.
1/[1 + (√[(1 - x)/(1 + x)])²]×-1/2×(1 - x)/[[tex](1+x)^{3/2}[/tex])]
=-1/[(1 + x)²× √[(1 - x)/(1 + x)]].
When we take the derivative of a function, we are essentially finding the slope of the tangent line of a function at a given point. This derivative will tell us the rate at which y changes with respect to x. The derivative of the function y = [tex]tan^{-1}[/tex] √[(1 - x)/(1 + x)] is a negative value, which means that as x increases, y decreases. Therefore, this function has a negative slope.
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What is the opposite inverse of 4?
Answers
4 is the additive inverse of -4.
OR
The opposite of 4 is -4, or negative four.
Now, According to the question:
Opposite numbers:-
Every number has an opposite. In fact, every number has two opposites: the additive inverse and the reciprocal—or multiplicative inverse. Don't be intimidated by these technical-sounding names, though. Finding a number's opposites is actually pretty straightforward.
If a number is added to its additive inverse, the sum of both the numbers becomes zero.
For any given number, the additive inverse is a number or a value which when added to the original number results in zero.
Mathematically: a + (-a) = 0
So here, 'a' and '-a' are the additive inverses of each other.
Therefore, for 4, the additive inverse is 4 = -4
Thus, 4 is the additive inverse of -4.
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What are the three types of algorithms?
Answers
The three types of algorithms are Brute Force algorithm, Greedy algorithm and Recursive algorithm.
What is Brute Force algorithm?As a very general approach to problem solving and an algorithmic paradigm, brute-force search or exhaustive search entails iteratively listing all potential candidates for the solution and determining if each one satisfies the problem's statement.
In order to find the divisors of a natural number n, a brute-force algorithm would count all integers from 1 to n & determine whether each one divides n without leaving a remainder.
A brute-force method might look at all possible configurations of 8 pieces on the 64-square chessboard and determine whether each queen piece may engage in mutually exclusive attacks for each configuration for the eight queens puzzle.
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In a circle, an angle measuring 5. 5 radians intercepts an arc of length 8. 4. Find the
radius of the circle to the nearest 10th.
Answers
The circle's radius is equal to 3.659 or 3.7.
What is Radius?A circle's or a sphere's radius is the length of the line between the center and the edge.
From the center of the circle or sphere to any point on its perimeter, the radius' length is constant.
Its diameter is halved by its length.
A line segment from a circle's or sphere's center to its perimeter or boundary is known as the radius in geometry. I
t is a crucial component of spheres and circles and is frequently abbreviated as "r."
When discussing multiple radiuses at once, the plural form of radius is "radii." the longest line connecting any points on the opposite side of a circle or sphere.
Hence, The circle's radius is equal to 3.659 or 3.7.
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N(t) = 8950 times (0.7)^2t
Answers
Answer: t = 0
Step-by-step explanation:
Expand 8950×0.7²: 4385.5t
8950(0.7) ²t
8950×0.49t = 4385.5t
N(t) = 4385.5t
N(t) - 4385.5t=0
Factor N(t) - 4385.5t: t (N - 4385.5)
t (N - 4385.5) =0
t=0
Use the quadratic formula to find the solutions to the equation y = 5x² - 9x + 3.
What are the zeros of the equation?
Answers
On solving the provided question, we can say that the quadratic equation is y = 5x² - 9x + 3 this quadratic equation can not factorized further
What is quadratic equation?A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.
the quadratic equation is
y = 5x² - 9x + 3
this quadratic equation can not factorized further
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