A local pottery studio is offering a beginner pottery class. The instructor is paid a flat rate of $100 plus $32 per student. How many people need to enroll for the instructor to earn $516?

When solving an oblique triangle given three sides, use the inverse cosine form of the Law of cosines to solve for an angle.

When solving an "oblique-triangle" given three sides, we would use the inverse cosine, form of the Law of Cosines to solve for an angle.

The "Inverse-Cosine" function allows us to find the measure of an angle when given the ratio of the lengths of the triangle's sides.

The "Law-of-Cosines" relates the lengths of the sides of a triangle to the cosine of one of its angles.

The "Law-of-Cosines" states that for any triangle with sides of lengths a, b, and c, and opposite angles A, B, and C, respectively:

⇒ c² = a² + b² - 2ab × cos(C),

To solve for an angle, we would rearrange the equation to find the cosine of the angle,

⇒ Cos(C) = (a² + b² - c²)/(2ab),

Then, we will take the inverse cosine of both sides of the equation to find the value of the angle,

⇒ C = cos⁻¹((a² + b² - c²)/(2ab)),

This helps us to find the measure of angle C, depending on the units used in the original triangle sides.

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The given question is incomplete, the complete question is

When solving an oblique triangle given three sides, use the _____ form of the Law of cosines to solve for an angle.

The trains will be 380 miles apart at 3:00 PM, which is 4 hours after the freight train leaves the station at 12 noon.

We can use the formula d = rt (distance = rate x time) to calculate the distance each train has traveled during this time:

Let's call the time elapsed from 12 noon until the trains meet as t hours.

During this time, the freight train has traveled at a rate of 50 mph for t hours and the passenger train has traveled at a rate of 60 mph for (t-1) hours (since it started one hour after the freight train).

Distance traveled by freight train = 50t

Distance traveled by passenger train = 60(t-1)

The total distance between the two trains at time t is the sum of these distances, which we can write as:

Total distance = 50t + 60(t-1)

We want to find the time t at which the total distance is 380 miles. So we can set up the equation:

50t + 60(t-1) = 380

Simplifying this equation, we get:

110t - 60 = 380

110t = 440

t = 4

Therefore, the time elapsed from 12 noon until the trains meet is 4 hours. Since the passenger train left one hour after the freight train, it has been traveling for 3 hours.

So the time at which the trains are 380 miles apart is 3:00 PM (12 noon + 4 hours).

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The MAD of the hourly wages given would be $ 0.48. The range would be $ 2.00. Q1 would be $8.25. Q3 would then be $9.25. The IQR would be $1.00

Calculate the MAD:

First, find the mean of the data set:

mean = (sum of all values) / (number of values)

mean = (8.25 + 8.50 + 9.25 + 8.00 + 10.00 + 8.75 + 8.25 + 9.50 + 8.50 + 9.00) / 10

mean = 88.00 / 10 = 8.80

Then, find the mean of these absolute deviations:

MAD = (sum of absolute deviations) / (number of values)

MAD = (0.55 + 0.30 + 0.45 + 0.80 + 1.20 + 0.05 + 0.55 + 0.70 + 0.30 + 0.20) / 10

MAD = 4.10 / 10 = 0.41

Calculate the range:

range = maximum value - minimum value

range = 10.00 - 8.00 = 2.00

Find Q1 and Q3:

{8.00, 8.25, 8.25, 8.50, 8.50, 8.75, 9.00, 9.25, 9.50, 10.00}

Q1 is the median of the lower half, and Q3 is the median of the upper half.

Lower half: {8.00, 8.25, 8.25, 8.50, 8.50}

Upper half: {8.75, 9.00, 9.25, 9.50, 10.00}

Q1 = median of lower half = 8.25

Q3 = median of upper half = 9.25

Calculate the IQR:

IQR = Q3 - Q1

IQR = 9.25 - 8.25 = 1.00

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The communication is a one-way process in which a message is conveyed from a sender to a receiver is one of the assumptions made by the linear model of communication.

The straightforward linear model of communication presents communication as a process with distinct beginnings and endings.

But this model ignores the fact that communication is frequently a more complex and involved process that needs context, feedback, and a variety of channels.

The linear model presumes that the message is clearly understood by the recipient and that it is received by the recipient free from distortion or interference.

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An assumption of the linear model of communication is the belief that communication is a one-way process where a sender transmits a message to a receiver through a channel. This model assumes that communication is a linear process where the sender encodes a message, which is then sent through a channel to the receiver who decodes the message.

In the linear model, the sender encodes a message, sends it through a channel, and the receiver decodes the message. This model does not account for feedback or interaction between the sender and receiver, assuming that communication is a straightforward and direct transmission of information without any complexities or interruptions.

This model assumes that there is little to no feedback or interaction between the sender and receiver, and that the message is transmitted and received accurately without any distortion. However, this assumption is often criticized for oversimplifying the complex nature of communication and ignoring the role of context and feedback in the communication process.

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The number "Six hundred six and four thousand, three hundred fifteen ten-thousandths" is equal to 606.4315 in numerical form.

Given that

Six hundred six and four thousand, three hundred fifteen ten-thousandths

To write this number in numerical form, we need to add the values of each of its digits:

6 × 100 + 0 × 10 + 6 × 1 + 4 × 0.1 + 3 × 0.01 + 1 × 0.005 = 606.4315

Therefore, the number "Six hundred six and four thousand, three hundred fifteen ten-thousandths" is equal to 606.4315 in numerical form.

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If older men are shorter than younger men. However, we do have information about the mean height for U.S. men, which is 69.4 inches.

Additionally, we have a sample of 170 men between the ages of 60 and 69, but we do not have the value for the mean height of this sample (represented as "x" in the question).

If we were given the value of "x", we could compare it to the mean height for all U.S. men and potentially make conclusions about the height of older men compared to younger men.

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I gotchu <3

Since the vertex is (0, -3), the quadratic function can be written in vertex form as:

f(x) = a(x - 0)^2 - 3

Where 'a' is a constant that determines the shape of the parabola. Since the end behavior of the function is y --> - Infinite as x --> - infinite and y --> - Infinite as x --> + infinite, the leading coefficient 'a' must be negative.

So, f(x) = -a(x^2 - 0x) - 3

Now, using the given point (1, -7) on the parabola, we can substitute the coordinates into the function and solve for 'a'.

-7 = -a(1^2 - 0(1)) - 3

-7 = -a - 3

a = 10

Therefore, the quadratic function that satisfies the given characteristics is:

f(x) = -10x^2 - 3

Hope this helps :)

The answer is True which means the choice between numerical integration approaches depends on what the data looks like and what computational expense you can tolerate.

The choice of numerical integration procedures is influenced by several criteria, including the nature of the data being integrated and the computing expenditure that may be accepted. If the function being integrated, for example, is smooth and well-behaved, a basic technique such as the trapezoidal rule or Simpson's rule may be adequate and computationally efficient.

If the function is extremely oscillatory or involves singularities, more complex approaches such as adaptive quadrature or Monte Carlo methods may be required to correctly integrate it. Furthermore, the size of the data collection and the processing resources available will influence the numerical integration method used.

Overall, choosing the best numerical integration strategy necessitates a careful evaluation of these numerous criteria to assure accuracy and efficiency in the integration of data.

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The resultant value of the given expression x² + 10x + 24 when x = 3 is (C) 63.

A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.

Expressions in writing are made using mathematical operators such as addition, subtraction, multiplication, and division.

For instance, "4 added to 2" will have the mathematical formula 2+4.

So, we have the expression:

= x² + 10x + 24

Now, solve when x = 3 as follows:

= x² + 10x + 24

= 3² + 10(3) + 24

= 9 + 30 + 24

= 63

Therefore, the resultant value of the given expression x² + 10x + 24 when x = 3 is (C) 63.

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Correct question:

Evaluate the expression when x = 3.

x² + 10x + 24

a. 81

b. 86

c. 63

d. 60

The perimeter of the equilateral triangle with an area of 81√3 cm² is 54 cm.

An equilateral triangle is a type of triangle in which all three sides are equal in length, and all three angles are equal to 60 degrees.

Let's denote the side length of the equilateral triangle by "a".

The formula for the area of an equilateral triangle is

Area = (√3/4) × a^2

We are given that the area is 81√3 cm², so we can set up the equation

81√3 = (√3/4) × a^2

Solving for "a", we get:

a = 18 cm

Now that we know the side length, we can find the perimeter by multiplying it by 3 (since it's an equilateral triangle):

Perimeter = 3a = 3 × 18 cm = 54 cm

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Data collected from several entities over a period of time (minutes, hours, days, etc.) are called time series data.

Time series data is a type of data that is collected over a period of time, with measurements taken at regular intervals. The data is often used to track changes in a particular variable over time and to analyze patterns or trends in the data.

Examples of time series data include stock prices, temperature readings, and daily sales figures. Time series data can be used to make forecasts or predictions about future trends based on past data, and it is often analyzed using statistical methods such as trend analysis, seasonality analysis, and autocorrelation analysis.

Time series data can be represented graphically using a line chart or a scatterplot, with time on the x-axis and the variable of interest on the y-axis. Time series data can be univariate, meaning that there is only one variable being measured, or multivariate, meaning that there are multiple variables being measured at the same time.

Statistical methods are a set of techniques and procedures used to analyze and interpret data in order to draw meaningful conclusions from it. These methods involve the collection, analysis, and interpretation of data in order to identify patterns, trends, and relationships between variables.

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Answer:

Yes, because of the Angle-Angle Theorem

Step-by-step explanation:

The sum of the interior angles of a triangle are 180.

Triangle on the left

180 - 90 - 42 = 48

Triangle on the right:

180 - 90 - 48 = 42

Since the angles measurements are the same, the triangles are similar.

Helping in the name of Jesus.

Answer: Yes, because of the Angle-Angle Theorem

Step-by-step explanation:

The two triangles have the same angles, so they are similar by the Angle-Angle Theorem.

Joshua started his own lawn care business. He donates 10% of his income to a local charity, which is recognized by the IRS as a qualified charitable organization. Joshua can claim expenses from his business and charitable donations as tax reductions, and they will reduce the amount of taxable income.

The first blank should be filled with "tax reductions" and the second blank should be filled with "amount of taxable income."

Hence, the correct statement would be: "Joshua can claim expenses from his business and charitable donations as tax reductions, and they will reduce the amount of taxable income."

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The slope of the given line is 1/3 for the line passes through (0, 2) and (3, 3).

The slope of a line represents the rate at which it rises or falls as it moves horizontally from left to right.

It is calculated by taking the difference in the y-coordinates (vertical change) and dividing it by the difference in the x-coordinates (horizontal change) of two points on the line.

The slope can also be thought of as the tangent of the angle formed by the line and the positive x-axis.

In this problem, we are given that the slope of the line is 1/3.

We can use this information to find the slope between any two points on the line.

Let's consider the points (0, 2) and (3, 3) that lie on the line.

The change in y-coordinates is 3 - 2 = 1, and the change in x-coordinates is 3 - 0 = 3.

Therefore, the slope between these two points is 1/3.

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The question is -

What is the slope of the line?

Derive Linear Equations-Quiz-Level H

Answer:

4834000000

That is your answer.

The size of the square to cut is 5/3 inches and the maximum volume of the box is 266.67 cubic inches.

To find the size of the square to cut and the maximum volume, we can follow these steps:

Let's call the length of each side of the square to be cut x inches. So the dimensions of the base of the box would be (16-2x) inches by (10-2x) inches.

The height of the box would be x inches since we are folding up the sides.

The volume of the box can be found by multiplying the length, width, and height: V = (16-2x)(10-2x)x.

To find the maximum volume, we can take the derivative of V with respect to x and set it equal to zero, since the maximum volume occurs at a critical point.

After taking the derivative and simplifying it, we get the equation 24x^2 - 520x + 1600 = 0.

Solving this quadratic equation, we get x = 5/3 or x = 20/3. Since x must be less than 5 (the length of the shorter side), the only feasible solution is x = 5/3 inches.

Plugging this value of x back into the equation for the volume, we get V = (16-2(5/3))(10-2(5/3))(5/3) = 266.67 cubic inches.

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Answer:

C

Step-by-step explanation:

using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]

and [tex]x^{0.5}[/tex] = [tex]\sqrt{x}[/tex]

given

[tex]log_{x}[/tex] 8 = 0.5 , then

8 = [tex]x^{0.5}[/tex] = [tex]\sqrt{x}[/tex] ( square both sides )

8² = ( [tex]\sqrt{x}[/tex] )²

64 = x

The number line that shows the number of miles where A is less expensive has a solution of x > 60

From the question, we have the following parameters that can be used in our computation:

Option    Daily Cost ($) Cost per mile ($)

   A               25                   0.15  

   B                10                    0.40

So, the cost functions are

A = 25 + 0.15x

B = 10 + 0.4x

Where x is the number of miles

When A is less expensive, we have

25 + 0.15x < 10 + 0.4x

Evaluate the like terms

15 < 0.25x

So, we have

0.25x > 15

Divide

x > 15/0.25

Evaluate

x > 60

Hence, the number line is (a)

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We need approximately 12 servings of Designer Whey and 2 servings of Muscle Milk to obtain a 7-day supply that provides exactly 262 grams of protein and 54 grams of carbohydrates.

Let x be the number of servings of Designer Whey and y be the number of servings of Muscle Milk needed to obtain a 7-day supply that provides exactly 262 grams of protein and 54 grams of carbohydrates.

From the information given, we know that each serving of Designer Whey provides 20 grams of protein and 3 grams of carbohydrates, and each serving of Muscle Milk provides 16 grams of protein and 9 grams of carbohydrates.

Therefore, we can set up the following system of equations:

20x + 16y = 262

3x + 9y = 54

To solve for x and y, we can use any method of solving a system of equations. For example, we can use substitution:

From the second equation, we can solve for x in terms of y:

x = (54 - 9y)/3 = 18 - 3y

Substituting this into the first equation, we get:

20(18 - 3y) + 16y = 262

Simplifying, we get:

80y = 182

Solving for y, we get:

y = 2.275

Substituting this into the equation x = 18 - 3y, we get:

x = 12.175

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Answer:  Elaine is 135cm tall

Step-by-step explanation:

Elaine's height is 75% of her father's height.

We can calculate Elaine's height by multiplying her father's height by 75% or 0.75.

Elaine's height = 0.75 * 180 cm

                        = 135 cm

Therefore, Elaine is 135 cm tall.

The probability of spinning an even number is 2/5, which can be written in simplest form.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

The spinner has 5 equal sections marked 1 through 5. Two of the five numbers are even (2 and 4). Therefore, the probability of spinning an even number is:

Probability of spinning an even number = (number of even numbers) / (total number of possible outcomes)

Probability of spinning an even number = 2/5

Hence, The probability of spinning an even number is 2/5, which can be written in simplest form.

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Answer:

Step-by-step explanation:

8.4 x 2 = 16.8

Jordan would take 22 hours to drive 1,188 miles at the same speed he drove 378 miles in 7 hours.

We can use the formula:

time = distance / speed

where speed is constant, to find the time it would take Jordan to drive 1,188 miles.

The speed at which Jordan drove can be calculated as:

speed = distance / time

where distance is 378 miles and time is 7 hours.

speed = 378 / 7 = 54 miles per hour

Now, we can use the speed to find the time it would take to drive 1,188 miles:

time = distance / speed = 1,188 / 54 = 22 hours

Therefore, if Jordan can maintain the same pace, it would take him 22 hours to drive 1,188 miles.

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We can use the trigonometric identity for the sine of a difference:

sin(a - B) = sin a cos B - cos a sin B

We are given that sina = -3 and sinß = 3, so we need to find the cosine of each angle. Since the terminal side of a lies in quadrant III and the terminal side of 6 lies in quadrant I, we can use the following relationships:

cos a = -sqrt(1 - sin^2 a) = -sqrt(1 - 9) = -sqrt(-8) = sqrt(8)i

cos ß = sqrt(1 - sin^2 ß) = sqrt(1 - 9) = sqrt(-8) = sqrt(8)i

Note that we use i to indicate the imaginary unit, since the result involves a negative square root. Therefore, we have:

sin(a - B) = sin a cos ß - cos a sin ß

= (-3)(sqrt(8)i) - (sqrt(8)i)(3)

= -3sqrt(8)i - 3sqrt(8)i

= -6sqrt(8)i

Hence, the exact value of sin(a - B) is -6sqrt(8)i.

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The exact value of sin(a - B) if sina = -3 and sinß = 3, and the terminal side of a lies in quadrant III and the terminal side of 6 lies in quadrant  is sin(a - B) =0

We apply the trigonometric identity for the sine of a difference:

sin(a - B) = sin(a)cos(B) - cos(a)sin(B)

We use Pythagorean identity to find the cosine values:

cos^2(a) = 1 - sin^2(a) = 1 - (-3)^2 = -8

cos(a) = ±√8i

cos(a) = -√8 (Since a lies in quadrant III, the cosine value is negative.)

we also have that:

cos^2(B) = 1 - sin^2(B) = 1 - 3^2 = -8

cos(B) = ±√8i

cos(B) = √8. (Since B lies in quadrant I, the cosine value is positive. )

we then substitute these values into the formula for sin(a - B):

sin(a - B) = sin(a)cos(B) - cos(a)sin(B)

= (-3)(√8) - (-√8)(3)

= -3√8 + 3√8

= 0

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The probability of examining the five people till first patient has athlete's foot is given by (0. 84)^4(0. 16)^1.

Percent of people have athlete foot = 16%

Let us consider the probability of success represented by p = 0.16.

Using geometric distribution,

Probability of finding first patient with athlete's foot on kth examination is given by geometric probability distribution,

P(X = k) = (1 - p)^(k - 1) × p

where X is random variable representing number of trials needed until  first success.

Probability of finding the first patient with athlete's foot on the fifth examination k = 5,

⇒ P(X = 5) = (1 - p)^(5 - 1) × p

⇒ P(X = 5) = (0.84)^4 × 0.16

Simplify it we get,

⇒ P(X = 5) = 0.0473

Therefore, the probability of a podiatrist examining five people until he finds the first patient who has athlete's foot is (0. 84)^4(0. 16)^1.

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you have to tell the question first

SPC is widely used in manufacturing, healthcare, and other industries to improve quality and efficiency.

The process you are referring to is called Statistical Process Control (SPC), which involves monitoring and analyzing a process to ensure it is within the acceptable range of variation. This is done by comparing the current amount of outcome variation against the established outcome specifications, allowing for corrective action to be taken if necessary. SPC is widely used in manufacturing, healthcare, and other industries to improve quality and efficiency.

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Process control is based on comparing the current amount of outcome variation against outcome specifications.

Process control is a management approach that involves monitoring and adjusting a process to ensure that it meets its intended outcome specifications.

The goal of process control is to maintain consistent outcomes over time, despite natural variation in the inputs or other factors that may affect the process.

In order to achieve this goal, process control typically involves monitoring the process using statistical methods and comparing the current level of variation in the process outcomes against the desired outcome specifications.

If the variation is within acceptable limits, the process is considered to be under control.

If the variation is outside of acceptable limits, the process may require adjustment or other corrective action to bring it back into control.

Overall, process control is an important tool in quality management, manufacturing, and other fields where consistent outcomes are critical to success.

By monitoring and adjusting processes over time, organizations can ensure that their products and services meet the needs and expectations of their customers, while minimizing waste, errors, and other sources of variation.

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The area of the shaded region with dimensions length=5 units and width=2 units is 10 units².

What is area?

It is the extent to which a flat (2-D) figure, surface, or shape of an object occupies all available space.The area of a flat, two-dimensional figure is the area that is enclosed or covered by the boundary of the figure. Additionally, it is the quantity of unit squares that completely cover a closed figure's surface. Square measurements of area include sq. mm, cm2, and m2. Additionally, it describes the area located inside a closed shape's border or limit.

Area of rectangle = length x width

Given dimensions of outer rectangle:length=9 units & width=6 units

Also given that there is a width of frame is 2 units between outer & inner rectangle on all its boundaries.

To find the area of shaded inner rectangle, we need its dimensions.

Length=length of outer rectangle- 2 times width of frame

           =9 - 2(2)

           =9-4

           =5 units

Widthth=width of outer rectangle- 2 times width of frame

           =6 - 2(2)

           =6-4

           =2 units

Area of shaded portion= area of rectangle

                                      = L x W

                                      = 5 x 2

                                      =10 units²

Area of shaded portion=10 units²

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1.  we can use the first equation to find y = 3x + 1 = 3(9) + 1 = 28 So, the larger integer is 28, (2).  The smaller integer is 9. The larger integer is 10, which is the next consecutive integer.

An integer is a whole number ,neither a fraction or a decimal, in mathematics. Integers can be zero, positive, or negative.

Integer examples include -3, -2, -1, 0, 1, 2, 3, and so forth.

The letter "Z" stands for the set of integers.

In mathematics and allied disciplines such as computer science, physics, and finance, integers are utilized extensively.

A whole number is a non-negative integer in mathematics, which indicates that it is either a positive integer or zero.

Negative and fractional numbers are not included in whole numbers. The full integers 0, 1, 2, 3, 4, and so on are examples.

In many different branches of mathematics as well as in other disciplines, such as arithmetic, algebra, and geometry, whole numbers are used. They are also employed in daily tasks like quantity calculations and object counts.

According to question :-

Let's call the smaller integer x and the larger integer y. We know that:

y = 3x + 1 (the largest of the two integers is one more than three times the smaller)

x + y = 37 (the sum of the two integers is 37)

We can use substitution to solve for y in terms of x:

x + (3x + 1) = 37

4x + 1 = 37

4x = 36

x = 9

Now we can use the first equation to find y:

y = 3x + 1 = 3(9) + 1 = 28

So the larger integer is 28.

Let's call the smaller integer x and the larger integer y. We know that:

y = x + 1 (the integers are consecutive)

x + 2y = 29 (the sum of the smaller and twice the larger is 29)

We can substitute y = x + 1 in the second equation:

x + 2(x + 1) = 29

Simplifying and solving for x:

3x + 2 = 29

3x = 27

x = 9

So the smaller integer is 9. The larger integer is 10, which is the next consecutive integer.

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