On looking for a pattern in the given data set, the quadratic model best describes the data.
2nd option is correct.
A data model represents the type of relationship between the variables of a data set.
Data models are of four types, namely, Linear, Cubic, Quadratic and Exponential data models.
Given data is:
Distance Traveled Average Speed(miles per hour)
(miles)
1 7
2 6.3
3 5.67
4 5.103
A quadratic model is the best data model for the given data set.
The pattern observed in the given data set observes the properties of a quadratic function.
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Answer:
Exponential is the correct answer.
Step-by-step explanation:
Is f(x)= [tex]\sqrt{5-x^{2} }[/tex] a one to one function?
Answer:
No, it is not a one-to-one function.
Step-by-step explanation:
A one-to-one function means a value of y will only exist one value of x. This means that a value of y will only have one value of x.
An example of one-to-one function is an odd-degree polynomial such as linear function.
An example of non one-to-one function is a parabola since a value of y exists two values of x.
From the question, this function represents a graph of half circle with radius equal to [tex]\displaystyle{\sqrt{5}}[/tex]. (The graph has been attached below for visual reference.)
There's also a way to determine whether if a function is one-to-one or not. This can be done by drawing a horizontal line.
If a horizontal line and a graph have one common point then it's a one-to-one functionOtherwise (having more than one common points), a function is not a one-to-one.From the graph and a horizontal line, both have two common points. Therefore, the function is not a one-to-one function.
* The red graph represents the given function while blue graph is a horizontal line determining a one-to-one function or not *
three varieties of coffee -coffee A coffee B and coffee C are combined and roasted yield a 54 lb batch of coffee beans. twice as many pounds of coffee C which is retails for $10.39 per pound are needed as coffee a which sells for $15.21 per pound coffee b retails for $13.21 per pound. how many pounds of each coffee should be used in a blend that sells for $12.61 per pound?
8.9 pounds of coffee A, 27.3 pounds of coffee B and 17.8 pounds of coffee C are need to make a blend that sells for $12.61 per pound.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent coffee A, y represent coffee B and z represent coffee C, hence:
x + y + z = 54 (1)
Also:
2x = z (2)
And:
15.21x + 13.21y + 10.39z = 12.61(54) (3)
x = 8.9, y = 27.3 and z = 17.8
8.9 pounds of coffee A, 27.3 pounds of coffee B and 17.8 pounds of coffee C are need to make a blend that sells for $12.61 per pound.]
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Given h of x equals negative 2 times the square root of x minus 3 end root, which of the following statements describes h(x)?
The function h(x) is increasing on the interval (–∞, 3).
The function h(x) is increasing on the interval (–3, ∞).
The function h(x) is decreasing on the interval (–∞, 3).
The function h(x) is decreasing on the interval (3, ∞).
Answer:
The function h(x) is decreasing on the interval (3, ∞).
Step-by-step explanation:
Please take a look at the attached image.
You will see a graph of the given function h(x) = -2[tex]\sqrt{x-3}[/tex]. The function is decreasing.
The function starts at 3 and starts to go towards negative infinity on the x-axis. Therefore the function is decreasing on the interval (3, ∞).
Lisa is cutting a 14-inch piece of paper into 0.4-inch strips. How many strips of paper will she have when she is finished?
5.6
35
30
28
Answer:
take 14/0.4the multiply by ten both the denominator and .numerator then simplify by two your final answer will be 35
5 + 4 ⋅ ( 8 − 6 ) ^2
[tex]\boldsymbol{\sf{5+4\cdot(8-6)^{2} \ \ \longmapsto \ \ [Subtract \ 6 \ from \ 8.] }}[/tex]
[tex]\boldsymbol{\sf{5+4\cdot2^{2} }}[/tex]
Calculates 2 to the power of 2 and gets 4.
[tex]\boldsymbol{\sf{5+4\cdot4 \ \ \longmapsto \ \ [Multiply] }}[/tex]
[tex]\boldsymbol{\sf{5+16 \ \ \longmapsto \ \ [Add]}}[/tex]
[tex]\blue{\boxed{\boldsymbol{\sf{Answer \ \ \longmapsto \ \ 21}}}}[/tex]
Answer:
5+16x
Step-by-step explanation:
5+4x(8−6)
2
Subtract 6 from 8 to get 2.
5+4x×2
2
Calculate 2 to the power of 2 and get 4.
5+4x×4
Multiply 4 and 4 to get 16.
5+16x
Given u = 3i − 8j and v = −4i + 8j, what is u • v? 73 8 −76 −56
Explanation:
We're applying the dot product.
u dot v = 3*(-4) + (-8)*8
u dot v = -12 - 64
u dot v = -76
The idea is that we multiply the x coordinates together, and the y coordinates together separately. Afterward you add the products. The result of any dot product is a scalar value, aka a single number.
The dot product is useful in many applications. One of which is to determine if two vectors are orthogonal.
I need help with the questions in this photo
Part I: The correct formula is D. ((x₁ + x₂)/2, (y₁ + y₂)/2)
Part II: The midpoint of the segment with endpoints (-2, -1) and (0, 9) is (-1, 4)
Calculating the midpoint of a line segmentFrom the question, we are to determine the formula for calculating the midpoint of a segment
The midpoint of a segment can be determined by using the formula,
Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)
The correct formula is D. ((x₁ + x₂)/2, (y₁ + y₂)/2)
II. To determine the midpoint of the segment with endpoints (-2, -1) and (0, 9)
x₁ = -2
y₁ = -1
x₂ = 0
y₂ = 9
Putting the parameters into the formula,
Midpoint of the segment = ((-2 + 0)/2, (-1 + 9)/2)
Midpoint of the segment = (-2/2, 8/2)
Midpoint of the segment = (-1, 4)
Hence, the midpoint of the segment with endpoints (-2, -1) and (0, 9) is (-1, 4)
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In a sample of 198 observations, there were 80 positive outcomes. Find the margin of error for the 95% confidence interval used to estimate the population proportion.
Using the z-distribution, the margin of error for the 95% confidence interval used to estimate the population proportion is 0.0683 = 6.83%.
What is a confidence interval of proportions?
A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
For this problem, the parameters are given as follows:
[tex]n = 198, \pi = \frac{80}{198} = 0.404[/tex]
Hence the margin of error is:
[tex]M = 1.96\sqrt{\frac{0.404(0.596)}{198}} = 0.0683[/tex]
The margin of error for the 95% confidence interval used to estimate the population proportion is 0.0683 = 6.83%.
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Find the simple interest earned after 4 years on $2,250 invested at an interest rate of 5%.
simple interest= principal x time x rate/100
The length of a rectangular poster is 5 more inches than half its width. The area of the poster is 12 square inches. Solve for the dimensions (length and width) of the poster.
The dimensions (length and width) of the poster are 6 inches and 2 inches
How to determine the dimensions (length and width) of the poster?Represent the length with x and the width with y
From the question, we have the following parameters
x = 5 + 0.5y
Area, A = 12
The area of a rectangle is represented as:
A = xy
Substitute the known values in the above equation
(5 + 0.5y) * y = 12
Expand the bracket
5y + 0.5y^2 = 12
Multiply through by 2
10y + y^2 = 24
Rewrite as:
y^2 + 10y - 24 = 0
Expand
y^2 + 12y - 2y - 24 = 0
Factorize the expression
(y - 2)(y + 12) = 0
Solve for y
y = 2 or y = -12
The dimension cannot be negative.
So, we have
y = 2
Substitute y = 2 in x = 5 + 0.5y
x = 5 + 0.5 * 2
Evaluate
x = 6
Hence, the dimensions (length and width) of the poster are 6 inches and 2 inches
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Add (x^3 -2x^2+4) + (2x^3+x^2-2) express in standard form
Answer:
3x^3-x^2+0x+2Step-by-step explanation:
add both the equations then you will get
3x^3-x^2+2
but in the standard form there should be an x^1 term or x term since there is no term like that we write it as 0x
so the equation will be
3x^3-x^2+0x+2
An older person is 9 years older than four times the age of a younger person.the sum of their ages is 24.find their ages.
The age of the younger individual is 3 years, while the age of the older individual is 21 years.
Two distinct individuals' (or things') ages from the present to the past or future are often compared when resolving age-related concerns. The objective of these puzzles is often to ascertain the current age of each subject.
Let the younger person be x years of age.
The answer to the query is:
Age of senior = (4x + 9) years
Their combined ages are 24.
x+4x+9=24
5x=24-9
5x=15
x=15/5
x=3
Younger person's age is equal to x = 3 years.
Age of senior = 4x + 9 = 4(3) + 9 = 21 years
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Rabbits are known for being extremely prolific—having a high reproductive rate. The average gestation period for rabbits is about 28 days and they have an unusual reproductive system that permits a female rabbit to be pregnant with two litters at once. This is an adaptation that allows rabbits to survive in the wild where they have a high mortality rate—they’re a source of food for many species of predators! In situations where there are no natural predators, two adult rabbits could easily become 1000 in one year’s time. i. Using this information, construct an exponential model to predict the number of rabbits after “x” years if there are no natural predators. ii. If the rabbit population were left unchecked (no predators and an abundance of food), how many rabbits would there be at the end of 3 years?
(i) The exponential growth model to predict the number of rabbits after 'x' years is [tex]A = 2e^{6.21460809842x}[/tex].
(ii) The number of rabbits at the end of 3 years will be 250000000.
A continuous exponential growth function is of the form [tex]A = Pe^{rt}[/tex], where A is the final amount, which was initially P, growing continuously at the rate of r, after a time of t years.
In the question, we are asked to construct an exponential model to predict the number of rabbits after 'x' years.
We assume the exponential growth model to be a continuous model, of the form [tex]A = Pe^{rt}[/tex], where A is the final amount of rabbits, which was initially P, growing continuously at the rate of r, after a time of t years.
The initial quantity of rabbits, P = 2.
Time, t = x years.
Substituting the values, we get:
[tex]A = 2e^{rx}[/tex] ... (i)
We have been told that after 1 year, the number of rabbits was 1000.
Thus, substituting A = 1000, and x = 1, we get:
[tex]1000 = 2e^{r*1}\\\Rightarrow 1000 = 2e^r\\\Rightarrow e^r = 1000/2 = 500[/tex]
Taking log on both sides, we get:
[tex]log_ee^r = log_e500\\\Rightarrow rlog_ee = log_e500\\\Rightarrow r = 6.21460809842[/tex]
Thus, the rate of growth, r = 6.21460809842.
Substituting r = 6.21460809842 in (i), we get:
[tex]A = 2e^{6.21460809842x}[/tex], which is the required model.
To find the number of rabbits at the end of 3 years, we put x = 3, in the above equation to get:
[tex]A = 2e^{6.21460809842*3}\\\Rightarrow A = 2e^{18.6438242953}\\\Rightarrow A = 2*125000000\\\Rightarrow A =250000000[/tex]
Thus, there would be 250000000 rabbits at the end of 3 years.
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(5.01 LC) A square is shown below. which expression can be used to find the area, in square units, of the Shaded triangle in the Square?
(answer options are in picture)
The expression can be used to find the area, in square units, of the Shaded triangle in the Square is 1/2 ( 4 · 4 ) .
What is the area of a square?The area of a square can be calculated as the square of the sides of a given figure.
The area of a square = side x side
where s = side length.
If a diagonal is drawn to create 2 halves, then area of each half is 8.
So, The area of a square = 1/2 ( 4 · 4 ) = 16.
If a square has a side length of 4, then the area of the square is 16.
The expression can be used to find the area, in square units, of the Shaded triangle in the Square is 1/2 ( 4 · 4 ) .
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You purchase a very basic cell phone plan that charges $24.99 a month. This plan allows for data usage but that will cost you $5 for every GB you use in a month. Write an equation below in slope-intercept form that models this situation.
The equation of this given condition in the intercept form would be
y = 5x + 24.99
The slope-intercept is the most “popular” form of a straight line. Many students find this useful because of its simplicity. One can easily describe the characteristics of the straight line even without seeing its graph because the slope and y-intercept can easily be identified or read off from this form.
The linear equation written in the form
y = mx + b
is in slope-intercept form where: m is the slope, and b is the y-intercept.
In the given question the slope of the equation is 5 as $5 is charged for every GB used while $24.99 would be the intercept.
Thus the equation of this given condition in the intercept form would be
y = 5x + 24.99
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On parallelogram ABC∧
mΔA=42 mΔB=___ mΔC___ mΔD=___
The measures of the remaining angles of the parallelogram are m ∠ B = 138°, m ∠ C = 42° and m ∠ D = 138°
How to determine the measure of missing angles in a parallelogram by geometric theorems
In this problem we know the measure of an angle and we should find the values of the three remaining angles. According to Euclidean geometry, the sum of internal angles in a parallelogram equals 360° and there exists the following property between each pair of angles:
m ∠ A = m ∠ Cm ∠ B = m ∠ Dm ∠ A + m ∠ B = m ∠ B + m ∠ C = m ∠ C + m ∠ D = m ∠ A + m ∠ D = 180°Then, the measures of the missing angles are, respectively:
m ∠ B = 180° - m ∠ A
m ∠ B = 180° - 42°
m ∠ B = 138°
m ∠ D = 138°
m ∠ C = 42°
Remark
The statement is poorly formatted, presents typing mistakes and image is missing, correct form is shown below:
On parallelogram ABCD, m ∠ A = 42, m ∠ B = ____, m ∠ C = _____, m ∠ D = _____
A representation of the parallelogram is shown in the image attached below.
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Simplify. ‒36 ÷ (27 ÷ 3 ∙ 2)
The simplified value of expression -36/(27/3*2) is -8.
Given an expression -36/(27/3*2).
We are required to find the simplified value of given expression. To simplify the expression we need to use addition,subtraction,multiplication, division, brackets, etc. We can say that we have to use BODMAS in order to find the simplified value of expression.
Expression is combination of numbers, symbols, coefficients, determinants, indeterminants, fraction,algebraic operations,etc. usually not found in equal to form.
The given expression :
=-36/(27/3*2) (Multiplying 3 and 2 first)
=-36/(27/6)
=(-36*2)/9 (Invert the fraction given in denominator)
=-72/9 (Multiplying -36 to 2)
=-8
Hence the simplified value of expression -36/(27/3*2) is -8.
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Find the intercepts of y=−7x+3
Answer:
X-intercepts:
[tex] (\frac{3}{7} ,0)[/tex]
Y-intercepts:(0,3)
Step-by-step explanation:
Hello!
given expression
[tex]y = - 7x + 3[/tex]
x-intercept is the point on the graph where y=0
solve
[tex] - 7x + 3 = 0 \\ - 7x = - 3 \\ x = \frac{3}{7} [/tex]
Thus, x-intercept
[tex]( \frac{3}{7} ,0)[/tex]
y-intercept is the point on the graph where x=0
solve
[tex]y = - 7(0) + 3 \\ y = 0 + 3 \\ y = 3[/tex]
Thus, y-intercept (0,3)
Hope it helps!
the perimeter of a rectangle if 24 inches. the rectangle is enlarged so that each side is twice as long as the original. what effect does this enlargement have on the perimeter?
The perimeter becomes double when each side is twice as long as the original.
According to the statement
we have given that the perimeter of a rectangle is 24 inches. and we have to find that the what effect does this enlargement have on the perimeter.
So, For this purpose, we know that the
A rectangle is a parallelogram all of whose angles are right angles especially : one with adjacent sides of unequal length.
The formula to find the perimeter of rectangle is 2(L + B)
And we the length is goes to increased by double then the perimeter will also goes to double.
Because perimeter is directly proportional to the length and breadth of rectangle.
So, The perimeter becomes double when each side is twice as long as the original.
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What is the distance from (-1,-14) and (-2,-6)?
Answer:
d = [tex]\sqrt{65}[/tex]
Step-by-step explanation:
The distance between two points is found by
d = [tex]\sqrt{( x2-x1)^2 + ( y2-y1)^2}[/tex] where (x1,y1) and (x2,y2) are the two points
d = [tex]\sqrt{(-2 - -1)^2+(-6 - -14)^2 }[/tex]
d =[tex]\sqrt{( -2+1)^2 + (-6+14)^2}\\[/tex]
d = [tex]\sqrt{(-1)^2 +( 8)^2 }[/tex]
d = [tex]\sqrt{1+64}[/tex]
d = [tex]\sqrt{65}[/tex]
Find the x-intercept.
x + 3
X-2
y =
([?], [_])
Answer: 1
Step-by-step explanation: It's subtraction and add ion look at the right side
Ian is playing video games. For every 11 enemies he defeats, he gets 6 points. If he has 24 points at the end of the game, how many enemies has Ian defeated?
Hi
if he has 24 point he scored 24/ 6 = 4 times
As he score points every 11 ennemies,
He had : 4*11= 44 ennemies.
Someone please help me with this question! How can I prove it?
Answer:
TS=QV
Step-by-step explanation:
To prove SAS congruence, you need to prove that two lines and the angle between them are all respectively equal.
In the diagrams we already have RS=WV and ∠RST=∠WVQ, so it follows that we need to prove that TS=QV.
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
For triangles to be congruent by SAS congruency criteria, one angle and the two adjacent sides to the angle should be equal to corresponding angle and it's adjacent aides of another triangle.
And we have already been given the angle and one of the side. so the third side that need to be equal in both side to pe proved congruent are :
TS = QV[tex] \qquad \large \sf {Conclusion} : [/tex]
Correct option is 1(5+2g)exp5 for g=-2
help pls
The value of the expression when g = -2 is -1
How to simplify the expressionGiven the expression;
(5+2g)exp5
(5+2g)^5
For g = -2
Let's substitute the value of g in the expression
= ( 5 + 2 ( -2) ) ^5
Expand the bracket
= ( 5 - 4) ^ 5
Find the difference
= (-1) ^5
= -1
Thus, the value of the expression when g = -2 is -1
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Find g(x), where g(x) is the translation 2 units left and 13 units up of f(x)=–7x+7.
Answer:
[tex]g(x)=-7x+6[/tex]
Step-by-step explanation:
Translations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
Parent function:
[tex]f(x)=-7x+7[/tex]
Translation of 2 units left:
[tex]\implies f(x+2)=-7(x+2)+7[/tex]
Translation of 13 units up:
[tex]\implies f(x+2)+13=-7(x+2)+7+13[/tex]
Simplifying:
[tex]\implies g(x)=-7(x+2)+7+13[/tex]
[tex]\implies g(x)=-7x-14+7+13[/tex]
[tex]\implies g(x)=-7x+6[/tex]
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) The following scatterplot shows the percentage of the vote a candidate received in the 2016 senatorial elections
according to the voter's income level based on an exit poll of voters conducted by a news agency. The income
levels 1-8 correspond to the following income classes:
1 = Under $15,000; 2 = $15-30,000; 3 = $30-50,000; 4 = $50-75,000; 5 = $75-100,000;
6 = $100-150,000; 7 = $150-200,000; 8 = $200,000 or more.
Use the election scatterplot to the find the critical values corresponding to a 0.01 significance level used to test
the null hypothesis of ρs = 0.
A) -0.881 and 0.881
B) -0.881
C) -0.738 and 0.738
D) 0.881
The critical values corresponding to a 0.01 significance level used to test the null hypothesis of ρs = 0 is (a) -0.881 and 0.881
How to determine the critical values corresponding to a 0.01 significance level?The scatter plot of the election is added as an attachment
From the scatter plot, we have the following highlights
Number of paired observations, n = 8Significance level = 0.01Start by calculating the degrees of freedom (df) using
df =n - 2
Substitute the known values in the above equation
df = 8 - 2
Evaluate the difference
df = 6
Using the critical value table;
At a degree of freedom of 6 and significance level of 0.01, the critical value is
z = 0.834
From the list of given options, 0.834 is between -0.881 and 0.881
Hence, the critical values corresponding to a 0.01 significance level used to test the null hypothesis of ρs = 0 is (a) -0.881 and 0.881
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find the value of a x 7 when a=6
Answer:
=> 42 ..
Step-by-step explanation:
Given : a = 6
=> a × 7
=> 6 × 7
=> 42
thank you for helping
Answer: TRS is congruent to CSE
Step-by-step explanation:
You can find congruent angles by locating the ones with the same number of lines. You want to start with the angles in the order of TRS.
Angle T has 1 line, so is congruent to C, which also has 1 line.
Angle R has 2 lines, so is congruent to S, which also has 2 lines.
Angle S has 3 lines, so is congruent to E, which also has 3 lines.
You want to keep these in the same order, so TRS, in the order of 1-2-3 lines, is congruent to CSE, also in the order of 1-2-3 lines (aka congruency markings).
Which table of values represents a function?
x y
-3 10
4 4
-5 -3
4 4
x y
2 8
6 9
6 3
5 7
x y
1 2
1 4
1 6
1 8
x y
5 2
-3 2
2 2
1 7
The table in the list of tables that represent an actual function is the first table i.e.
x y
-3 10
4 4
-5 -3
4 4
How to determine the table of values represents a function?The table of values is given as:
Table 1
x y
-3 10
4 4
-5 -3
4 4
Table 2
x y
2 8
6 9
6 3
5 7
Table 3
x y
1 2
1 4
1 6
1 8
Table 4
x y
5 2
-3 2
2 2
1 7
For a table to represent a function, each of the x value on the table must correspond to exactly one y value
i.e.
x1 = y1
x2 = y2
And so on
Using the above highlights, the table that represents a function is table 1
Hence, the table in the list of tables that represent an actual function is the first table i.e.
x y
-3 10
4 4
-5 -3
4 4
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How is the Gauss-Jordan elimination method different from the Gaussian elimination method?
The Gauss-Jordan elimination method different from the Gaussian elimination method in that unlike the Gauss-Jordan approach, which reduces the matrix to a diagonal matrix, the Gauss elimination method reduces the matrix to an upper-triangular matrix.
What is the Gauss-Jordan elimination method?
Gauss-Jordan Elimination is a technique that may be used to discover the inverse of any invertible matrix as well as to resolve systems of linear equations.
It is based on the following three basic row operations that one may apply to a matrix: Two of the rows should be switched around. Multiply a nonzero scalar by one of the rows.
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