The Interquartile range IQR for the data set is 4.5.
What is the interquartile range(IQR)?
The interquartile range (IQR) is a measure of the dispersion of a set of numerical data. It is defined as the difference between the 75th and the 25th percentiles of the data and is a robust statistic, meaning that it is not greatly affected by outliers. The IQR is used to summarize the spread of a dataset and is often used in combination with box plots to visualize the distribution of the data.
To find the interquartile range (IQR) of a data set, you need to first find the 25th and 75th percentiles (also known as the first and third quartiles, Q1 and Q3, respectively).
The 25th percentile (Q1) is the value below which 25% of the data falls, and the 75th percentile (Q3) is the value below which 75% of the data falls.
Here's the calculation for the IQR of the data set: 0, 1, 1, 2, 3, 5, 6, 6, 8, 11:
Order the data in ascending order:
0, 1, 1, 2, 3, 5, 6, 6, 8, 11
Find the median (Q2), which is the middle value of the data:
3
Find Q1 and Q3:
Q1 = median of the first half of the data = 1.5
Q3 = median of the second half of the data = 6
Finally, calculate the IQR:
IQR = Q3 - Q1 = 6 - 1.5 = 4.5
So, the Interquartile range IQR for the data set is 4.5.
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Which representation shows what balloon Z resembles after each change occurs? The pressure is halved and the Kelvin temperature is halved. The balloon is placed in a hyperbaric chamber at a pressure of 2.5 atm.
Picture - 1 from left representation shows what balloon Z resembles after each change occurs when the pressure is halved and the Kelvin temperature is halved.
we have relation ,
PV= nRT , from ideal gas law
V = nRT /P
when P is halved P becomes P/2 and when T is halved it becomes T/2
V= nR ( T/2) / ( P/2)
= nRT
Thus volume is unchanged hence correct representation is same size balloon i.e middle
2) The pressure is 2.5 atm surrounding balloon. This makes balloon contract since pressure outside balloon is higher than pressure inside balloon.
Thus correct representation of change is smaller balloon i.e picture 1 from left
(The pictures are attached below )
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help pls asap due in 1 hour pls
Answer:
Subtract the amount of £1 coins from 50p coins:
256-172 = 84
84/3 coins = 28 people paid with 3 coins.
172 people paid using £1 coins
172 + 28 = 200 total people
percent who used 3 coins = 28/200 = 0.13 x 100 = 14% so the answer is 14%
a math test is worth 100 points and has 38 problems. Each problem is worth either 5 points or 2 points? How many problems of each point value are on the test?
there are ( ) five point problems
there are ( ) Two point problems
Answer: 30 2 point and 8 5 point
Step-by-step explanation: 30 times 2 = 60 8 times 5 = 40 60+40 = 100
2 WXYZ is translated 6 units to the left and
then reflected in the x-axis to create
W'X'Y'Z'.
Write an ordered pair to show the location
of each vertex of the transformed figure.
The coordinates of each vertex after the translation and reflection can be written as an ordered pair. The coordinates for W' are (6, 0), for X' are (0, 3), for Y' are (6, 6), and for Z' are (0, 9).
This means that point W' has been moved 6 units to the left, X' has been moved 6 units to the left and 3 units down, Y' has been moved 6 units to the left and 6 units down, and Z' has been moved 6 units to the left and 9 units down, and then all the points have been reflected across the x-axis. This transformation results in a figure that is the same size and shape as the original figure, but shifted and reflected across the x-axis.
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This is 7th grade math pls help
i dont know how to solve it but i got it right
The required systolic pressure will be lower when the patient takes the blood pressure medication at 7 a.m. between the interval of 7 a.m. to 9 a.m.
What is a piecewise function?A piecewise function is one that is constructed from pieces of different functions at different intervals.
Here,
A graph of the piecewise function is shown, from the graph it's clear that systolic pressure is low for the interval 5 < x < 9, such that the patient takes the medication at 7 A. M. So, corresponding to that required systolic pressure will be lower between 7 a.m. to 9 a.m.
Thus, the required systolic pressure will be lower when the patient takes the blood pressure medication at 7 a.m. is 7 a.m. to 9 a.m.
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determine if 4y=16x-24 is linear, why?
todd misread the recipe and added 3/5 of a teaspoon of salt to the bread dough the recipe called for 1/2 of a teaspoon how much extra salt was added
we have 15 voters and four alternatives, and the individual preference lists are as follows: voters 1-3: a d b c voters 4-5: b d a c voters 6-7: c d a b voters 8-9: a d c b voters 10-11: b d c a voters 12-13: c d b a voters 14-15: d b a c what choice or choices result from the plurality voting procedure?
The complete question is:
We have 15 voters and four alternatives, and the individual preference lists are as follows:
Voters 1-3: a d b c
Voters 4-5: b d a c
Voters 6-7: c d a b
Voters 8-9: a d c b
Voters 10-11: b d c a
Voters 12-13: c d b a
Voters 14-15: d b a c
1) The plurality voting procedure? - Voters 1-3: a d b c
2) The Condorcet procedure? - Voters 8-9: a d c b
3) The Hare (instant runoff) system? - Voters 4-5: b d a c
4) The Borda count procedure? - Voters 8-9: a d c b
5) Sequential pairwise voting with agenda bdac? - Voters 8-9: a d c b
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What i (1 x ) (3 x 1) (5 x ) (3 x ) in word form?
A. One and three hundred fifty-three thouandth
B. Thirteen and fifty-three hundredth
C. One hundred three and fifty-three thouandth
D. One hundred three and five hundred three thouandth
Word form One hundred three and five hundred three thouandth
How do you write the number in word form? Word form means expressing numbers by spelling them out in words. ⇒ Expanded form means expressing according to place value. This is a little trickier because you have to. think about how much is in each place: ones, tens, hundreds, etc.To write a given number in word form, identify the largest place value, write each number as we would in the ones place based on hundreds, tens, and ones, then write which period the digits fit into, whether it be millions, thousands, etc., but excluding the ones. Repeat this process from left to right100 in words is written as One hundred or simply Hundred. The name of the number 100 in English is “HundredTo learn more about number in word form refers to:
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How do you find the regression line on a calculator?
You have to put the value of the variables in the given column. Then press the button to calculate to find the regression line.
What is the regression line?
The linear equation that best fits the points is linear regression.
There are various methods for selecting the best-fitting line, with ordinary least squares being the most popular (OLS). The dependent variable (Y) and the independent variables are related according to linear regression (X).
Based on the independent variables, the linear regression model calculates the dependent variable (DV) (IV, predictors).
Select the type of regression line
Step 1: First make the column
Step 2: Then input the value of the variables.
Step 3: Press shift + 0 to get the menu option.
Step 4: from the menu select regression line number.
Step 5: Get the equation of the regression line.
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The regression line can be calculated by finding the slope and intercept. The equation of the regression line is y = slope * x + intercept.
Explanation:
To calculate the regression line, we need to find the slope and intercept of the line. Let's denote the independent variable as x and the dependent variable as y. The given data can be represented as a set of (x, y) pairs:
(x1, y1), (x2, y2), ..., (xn, yn)
To calculate the slope, we need to calculate the following sums:
Σxy: the sum of the products of x and y valuesΣx: the sum of the x valuesΣy: the sum of the y valuesΣx^2: the sum of the squared x valuesUsing these sums, the slope can be calculated as:
slope = (nΣxy - ΣxΣy) / (nΣx^2 - (Σx)^2)
Next, we can calculate the intercept using the following formula:
intercept = (Σy - slopeΣx) / n
Once we have the slope and intercept, we can write the equation of the regression line as:
y = slope * x + intercept
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your cat gives birth to six kittens. three are black, two are grey and one is white. what percentage of the kittens are black?
50% of the kittens are black in colour.
Total number of kittens = 6
Out of these, 3 are black, 2 are grey, and 1 is white.
The Latin word "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions with a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.
A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.
Now, percentage of kittens that are black:
(Total number of Black Kittens/Total number of kittens) x 100 %
= 3/6 x 100 % = 50%
Therefore, 50% of the kittens are black in colour.
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Find the derivative of y with respect to x if y=e^-14x
Given that the function of ex is ex, the derivative of y with respect to x is -14e-14x.
The rate of a function's change with regard to one of its variables is known as the derivative. The derivative of y with respect to x in the case of y=e-14x is the rate at which y varies as x changes. The derivative is the derivative of ex, which is ex because derivative the function is e-14x. Simply multiplying ex by the coefficient of x, which is -14, yields the derivative of y with respect to x. Consequently, derivative -14e-14x is the derivative of y with respect to x. Accordingly, y will drop by 14e-14x units for every unit increase in x.
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the probility of alvins mother will server rice with dinner is 0.78 the probilty that she will server carrots is with dinner is 0.30
The probability of both rice and carrots being served with dinner is 23.4%.
The probability of Alvin's mother serving rice with dinner can be expressed using the formula P(Rice) = 0.78. This means that the probability of Alvin's mother serving rice with dinner is 78%. The probability of Alvin's mother serving carrots with dinner can be expressed using the formula P(Carrots) = 0.30. This means that the probability of Alvin's mother serving carrots with dinner is 30%. To calculate the combined probability of both rice and carrots being served with dinner, we can use the formula P(Rice and Carrots) = P(Rice) * P(Carrots) = 0.78 * 0.30 = 0.2340. This means that the probability of both rice and carrots being served with dinner is 23.4%.
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Let C R2 be the circle with radius 6 centered at the origin. Let F : R2 → R2 be the vector field defined by F(x, y) = (7x, 1 1). Find the flux of F coming out of the circle through the curve C.
The flux of F coming out of the circle C is 126π.
The flux of a vector field, F, out of a surface, S, is given by the formula
Flux = ∮F • n ds,
where n is a unit normal vector to the surface S.
In this case, the surface S is the circle C with radius 6 centered at the origin and the vector field F is given by F(x, y) = (7x, 11). We can use Green's Theorem to find the flux from the circle C. The equation for the circle is x2 + y2 = 36. Differentiating this equation with respect to x and y gives us the unit normal vector, n = (x/6, y/6).
Plugging these values into the flux formula, we get
Flux = ∮F • n ds = ∮ (7x, 11) • (x/6, y/6) ds
= ∮ 7x2/6 + 11y/6 ds
= (7/6) ∮ (x2 + y2) ds
= (7/6) * Area of C
= (7/6) * π * 36
= 126π.
Therefore, the flux of F coming out of the circle C is 126π.
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John, scores 35 more than triple the amount of points and Amy. If Amy, scores 25 point, how many points does Giannis John score?
John scored 110 points in total.
What is an equation?A equation is used to equate two expressions. For example -
4x + 4 = 7
Given is that John, scores 35 more than triple the amount of points than Amy. Amy scores 25 points.
The total points scored by john would be -
{p} = 3{a} + 35 .... Eq { 1 }
{p} = 3 x 25 + 35
{p} = 110 points
Therefore, John scored 110 points in total.
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identify the property of 3x·-4=1
The addition property and division properties are used to solve the expression.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ 3x - 4 = 1
Now, We can solve as;
⇒ 3x - 4 = 1
Add 4 both side,
⇒ 3x - 4 + 4 = 1 + 4
⇒ 3x = 5
Divide by 3;
⇒ x = 5/3
Thus, The addition property and division properties are used to solve the expression.
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A car traveled a ditance of 600. 15 km in 7. 5 hour. How many kilometer did the car travel per hour on the average?
The car traveled 80.02 kilometer per hour on the average
What is velocity?It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).
The formula and procedure we will use to solve this problem is:
v= x/t
Where:
x = distancet = timev = velocityInformation about the problem:
x = 600.15 kmt = 7.5 hv = ?Applying the velocity formula we have:
v = x/t
v = 600.15 km / 7.5 h
v = 80.02 km/h
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A health club charges a $20 one-time sign-up fee and a monthly membership fee of $54 per month. Find the rate of change.
The rate of change for a health club is, 24.
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
We have to given that;
A health club charges a $20 one-time sign-up fee and a monthly membership fee of $54 per month.
Hence, The equation to represents that the health club charges,
⇒ y = 24x + 54
Since, The general form of the slope - intercept equation is :
⇒ y = mx + c
Where, m = slope = rate of change in y per change in x
Therefore, By comparing the expressions, the slope of the cost function given is 24.
Hence, The rate of change = 24
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Three large cones hang from the ceiling in an office building in front of a bank of windows. The height of each cone is 12 feet and the circumference of the base of each cone is 8π feet. The base and 70% of the lateral surface of each cone is painted red, and the rest of each cone is painted black.
What is the total surface area painted black? Use π≈3.14.
Enter your answer, rounded to the nearest tenth, in the box.
ft²
The area of the cone that was painted black is given by 47.66 ft²
What is the area and volume of a right circular cone?For a right circular cone of radius 'r', height 'h', and slant height 'l', we have; Curved surface area of the right circular cone = π r l. The total surface area of a right circular cone = π(r + l) r. The volume of a right circular cone = 1/3π r2 h.
Given here: The height of the cone is 12 feet and circumference of the base of the cone is 8π
We know the base of the cross section is always a circle.
Thus we have
2πr=8π
2r=8
r=4
Now slant height of the cone is given using the pythagoraes theorem as follows
l=[tex]\sqrt{4^2+12^2}[/tex]
=12.65 feet
Thus lateral surface area of the cone is L= πrl
=3.14×4×12.65
=158.884 ft²
Now we can infer from the question that 30% of the lateral surface area is painted black thus
Area painted black is = 30%×158.884
=0.3×158.884
=47.66 ft²
Hence, The area of the cone that was painted black is given by 47.66 ft²
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Answer: 47.7
Step-by-step explanation:i took the quiz the guy on top is wrong
Name all chords that are drawn in Circle C
The name of all the chords that are drawn in Circle C are; SU, UV and TW.
How to Identify Circle Chords?The chord of a circle is a term that is defined as the line segment joining any two points on the circumference of the circle.
Looking at the image and comparing with the definition of chords above, we can say that the chords will be SU, UV and TW. This is because they join two points on the circumference of the given circle with center C
We further see that the segment CV is only the radius of the circle.
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Please help! Solve for x
The value of the variable 'x' will be 40.50. Then the correct option is D.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
The triangle ΔPQS is similar to the triangle ΔRQS. Then the equation is given as,
x / 45 = 18 / 20
x / 45 = 0.90
x = 40.5
The value of the variable 'x' will be 40.50. Then the correct option is D.
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1 - 8p= -6p - 7
tthanks
Answer: 7/15
Step-by-step explanation:
8p + 7 = -6p
15p = 7
p = 7/15
[tex] \: [/tex]
[tex]\large \frak{- 8p + 6p = - 7 - 1}[/tex][tex] \: [/tex]
[tex]\large \frak{- 2p = - 8}[/tex][tex] \: [/tex]
[tex] \large \frak{p = \cancel \frac { - 8}{ - 2} }[/tex][tex] \: [/tex]
[tex] \boxed{\underline{\large {\frak{\red{ \: p = 4 \: }}}}}[/tex][tex] \: [/tex]
━━━━━━━━━━━━━━━━━━━━━━━━━━
hope it helps! :)
Find the horizontal and vertical asymptotes of the curve. You may want to use a graphing calculator (or computer) to check your work by graphing the curve and estimating the asymptotes. (Enter your answers as comma-separated lists. If an answer does not exist, enter DNE.)
y = X3 - x / x² – 3x + 2 X = y =
The horizontal asymptote is y = X, and the vertical asymptotes are x = 2 and x = 1.
What do you mean by curve?A curve is a continuous, smooth, and often repeating shape in the plane or in space. It is a geometric object that can be described mathematically by an equation or a set of points.
In mathematics, curves are used to model real-world phenomena and to study geometric and mathematical properties. For example, curves can be used to describe the shape of objects, the path of moving objects, or the graph of a mathematical function.
There are many types of curves, including lines, circles, ellipses, parabolas, hyperbolas, and spirals, among others. Each type of curve has unique properties and characteristics, and they are studied and used in different ways in different fields of mathematics and science.
The horizontal asymptotes are found by examining the degree of the numerator and denominator when x approaches infinity or negative infinity.
Since the numerator is of degree 3 and the denominator is of degree 2, the horizontal asymptote is y = X3 - x / x² – 3x + 2 = X.
For the vertical asymptotes, we look for the values of x that make the denominator equal to zero and the numerator either equal to zero or undefined.
The denominator x² – 3x + 2 = 0 has roots at x = 1 and x = 2.
At x = 1, the numerator x³ - x = 0, so the function has a hole at x = 1 and y = 0.
At x = 2, the function is undefined, so x = 2 is a vertical asymptote.
Thus, the horizontal asymptote is y = X, and the vertical asymptotes are x = 2 and x = 1.
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Which equation can be used to solve for the measure of
angle ABC?
[Not drawn to scale)
O tan(x) = 36
O tan(x) =
O since) –
sin(x) = 10. 3
Using relations in a right- triangle, the equation can be used to break for the measure of angle ABC is tan x = 2.4/10
The relations in a right triangle are given as follows
The sine of an angle is given by the length of the contrary side to the angle divided by the length of the hypotenuse.
The cosine of an angle is given by the length of the conterminous side to the angle divided by the length of the hypotenuse.
The digression of an angle is given by the length of the contrary side to the angle divided by the length of the conterminous side to the angle.
For angle Alphabet = x, we've that
The length of the contrary side is of2.4 cm.
The length of the conterminous side is of 10 cm.
Hence, the equation is tan x = 2.4/10.
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Solve for x :
[tex] \frak{ \large{4x + 5 = 2x - \frac{6}{2} }}[/tex]
ty
The diameter of a cone's circular base measures 6 inches, and the slant height of the cone is 8 inches
What is the approximate surface area of the cone?
94.2 in²
103.6 in²
131.9 in²
257.5 in²
The surface area of a cone is 103.6 in².
Option B is the correct answer.
What is a cone?It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.
We have,
Cone:
Diamter = 6 in
Radius = 3 in
Slant height.
s = 8 in
Now,
The surface area of a cone.
= πrs + πr²
= πr (s + r)
= 3.14 x 3 (8 + 3)
= 3.14 x 3 x 11
= 103.62 in²
Thus,
103.62 in² is the surface area of a cone.
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yy x cos y da, d is bounded by y 0, y x 2, x 1
First, we need to set up the bounds for the integral. The lower and upper limits of the integral are x = 1 and y = x2, respectively. The integral ∫x1 [cos(x2)dx] is equal to -2/3.
Next, we can substitute the upper limit of the integral into the integrand to get:
∫x1 [cos(x2)dx]
Then, we can use integration by parts to solve the integral. We let u = cos(x2) and dv = dx. This gives us:
du = -2x sin(x2) dx
and
v = x
This gives us:
∫x1 [cos(x2)dx] = x cos(x2) - ∫x1 [-2x sin(x2)dx]
Now, we can solve the second integral. We let u = x2 and dv = -2 sin(x2)dx. This gives us:
du = 2x dx
and
v = -cos(x2)
This gives us:
∫x1 [-2x sin(x2)dx] = -x2 cos(x2) - ∫x1 [2x dx]
Finally, we can solve the last integral. We let u = x and dv = 2 dx. This gives us:
du = dx
and
v = x2
This gives us:
∫x1 [2x dx] = x3 + c
where c is the constant of integration.
Putting it all together, we get that
∫x1 [cos(x2)dx] = x cos(x2) - x2 cos(x2) - x3 - c
Substituting in the limits of the integral, we get that
∫x1 [cos(x2)dx] = 1 - x2 - x3 - c
Since the lower limit of the integral is x = 1, we have that
∫x1 [cos(x2)dx] = -x2 - x3 - c
Substituting in the upper limit of the integral, we get that
∫x1 [cos(x2)dx] = -1 - x2 - x
The integral ∫x1 [cos(x2)dx] is equal to -2/3.
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Which type of transformation is described by (x,y) → (-x, y)?
a reflection across the y-axis
a rotation of 90° about the origin
a dilation of scale factor - 1
a rotation of 180° about the origin
Answer:
Reflection across the x-axis.
Step-by-step explanation:
Use squared paper and plot some coordinate points.
For example: (2,3) and (−3,−2) and reflect them in the x-axis. You should obtain the following results.
(2,−3) and (−3,2) respectively.
(Note that the x-coordinate remains unchanged, while the y-coordinate is the negative of the original point.In general this can be expressed as: Under reflection in the x-axis (x,y)→(x,−y))
Binomial Distribution - Algebra 2B
A local bakery sells the freshest bread in town. In fact, 65% of customers who come into this store buy bread. What is the probability that at least 3 customers out of the first 6 will buy bread?
So the probability that at least 3 customers out of the first 6 will buy bread is 0.7929 or about 79.29%.
To determine the appropriate probability, we may utilise the binomial distribution's cumulative distribution function (CDF). The likelihood that the number of successful occurrences in a specified number of independent trials is less than or equal to a specific value is given by the binomial distribution's CDF.
Let X represent the proportion of the first 6 clients who purchase bread. Then, X has a binomial distribution with n = 6 and p = 0.65 as its parameters. One less than the likelihood that fewer than three consumers will purchase bread results in the chance that at least three will:
P(X >= 3) = 1 - P(X < 3)
Using a cumulative distribution function of the binomial distribution, we can calculate P(X < 3) as:
P(X < 3) = CDF(2, n=6, p=0.65)
Using a binomial calculator or a programming library that implements the CDF of the binomial distribution, we find that P(X < 3) = 0.2071. Therefore, the desired probability is:
P(X >= 3) = 1 - P(X < 3) = 1 - 0.2071 = 0.7929
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