At the initial condition, this weight approached the equilibrium position from a positive direction of 5 units. Also, the weight was descending (down) to the ground, with the spring stretching.
How to describe the initial condition of this experiment?First of all, we would derive an expression for the position with respect to the angle (phase shift) under the appropriate conditions:
Asin(ωt + ø) = c₂sinωt + c₁cosωt.
At t = 0, we have:
y = c₂sin(0) + c₁cos(0).
y = 0 + c₁
y = 0 + 5
y = 5 units.
Therefore, we can logically deduce that at the initial condition, this weight approached the equilibrium position from a positive direction of 5 units. Also, the weight was descending (down) to the ground, with the spring stretching.
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Complete Question:
The angle Φ represents the phase shift, determined by the initial conditions of the experiment or the position of the weight at t = 0. If the weight is at its maximum positive position (weight is above equilibrium) at t = 0, then Φ = 0. If the weight is at its maximum negative position (spring is stretched and weight is below equilibrium) at t = 0, then Φ = π. If the weight is traveling in the negative direction and passing through equilibrium at t = 0, then Φ = π/2. In the response box, describe the initial condition of our experiment; specifically, describe the position of the weight and the direction in which it was traveling.
5x+y=3,5x+y=2 by inspection
Consequently, (3, 5/2) is the answer to the equations 5x+y=3 and 5x+y=2. Either conditional solutions or identities are categories for equations.
what is equation ?Its simplest form is thought to be the number's smallest equivalent fraction. How to determine the simplest form. Look for shared factors in the denominator and numerator. A fractional number can be checked to discover if it is a prime number. A statement having two quadrilateral and an equal sign in the middle is referred to as a mathematical equation. Every variable's degrees are listed in descending order in the general form of any equation. The formula for a linear equation is x + b = 0. The general form of a two-variable linear equation is an x + b y + c = 0. (or something similar). Either conditional solutions or identities are categories for equations. An identity holds true for whatever value of the variables.
given
5x + y = 3
5x + y = 2
x = y-3/ 5
y - 3 +y = 2
2y = 5
y = 5/2
x = 3
Consequently, (3, 5/2) is the answer to the equations 5x+y=3 and 5x+y=2.
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Select the correct answer. Which expression is equivalent to 8x^2^3 sqrt 375x + 2^3 sqrt 3x^7, if x=0?
Note that the expression that is equivalent to 8x² ∛375x + 2∛3x⁷, if x ≠ 0 is: 42x²∛3x (Option B). Even if x = 0, then none of the answers would apply because the expression would automatically = 0.
What is the rationale for the above answer?To prove the above lets us factor and rewrite the radicand in exponential form as follows:
8x² ∛(5³ * 3x) + 2∛(3x⁶ * x)
Rework the expression using
ⁿ√ab = ⁿ√a * ⁿ√b:8x² * ∛5³ * ∛3x + 2∛x⁶ * ∛3x
Simplify the expression 8x² * 5∛3x + 2x² ∛3x
Multiply the monomials to get:
40x² ∛3x+2x²∛3x; Taking the coefficients for the like terms we have:
(40 + 2)x² ∛3x
Calculate the sum to get 42x²∛3x
Thus the simplified version of 8x² ∛375x + 2∛3x⁷, if x ≠ 0 is: 42x²∛3x
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Full Question:
Select the correct answer. Which expression is equivalent to 8x² ∛375x + 2∛3x⁷, if x ≠ 0
A) 42x³
B) 42x²∛3x
C) 10x⁴∛125x
D) 10x²∛125x³
If f(x) = 3x² + 2 and g(x)=x2-9, find (f- g)(x).
OA. 2x² - 7
OB. 2x² +11
OC. 4x²-7
OD. 4x² +11.
Answer:
B. 2x² + 11
Step-by-step explanation:
(f - g)(x) means:
f(x) - g(x)
We've been given what each of these is equal to, so substitute that in:
3x² + 2 - (x² - 9)
Simplify. Don't forget to distribute that minus in the middle to both terms in x² - 9
3x² + 2 - x² + 9
Next, combine like terms.
2x² + 11
Help ASAP Please right now 1&2
1. The statement that is false is: If two figures have the same shape, then they are congruent.
2. The dashed line appears to be a line of symmetry.
Properties of congruent shapes.When two or more shapes have their length of sides and measure of internal angles to be equal, then it can be inferred that they are congruent. But shapes can be similar, but not congruent.
A line of symmetry is a straight line drawn in such a way that it divides a given shape into two equal parts. So that a shape may have more than one line of symmetry.
From the given questions, we can deduce that;
1. If two figures are similar, they may not be congruent. So that the statement that is false among the given option is A. If two figures have the same shape, then they are congruent.
2. Considering the dashed line drawn through the shape, it appears that it is a line of symmetry.
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Find the margin of error
11.13 < μ < 15.03
The margin of error of the intervals 11.13 < μ < 15.03 is 1.95
How to solve for the margin of errorIn order to get the margin of error, we would first have to find the samole mean.
The sample mean x = the upper limit + lower limit / 2
the upper limit = 15.03
The lower limit = 11.13
Then we would have: 15.03 + 11.13 / 2
= 26.16 / 2
= 13.08
Then the margin of error would be
upper limit - sample mean
= 15.03 - 13.08
= 1.95
The margin of error is given as 1.95
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How much horsepower is a 160hp engine using at 65% efficiency
Answer:
The power is 15 watts.
Step-by-step explanation:
It is equivalent to:
0.02012 mechanical horsepowers
0.02039 metric horsepowers
0.02011 electrical horsepowers
0.001529 boiler horsepowers
The difference of x and one third is greater than or equal to one third of x
value of x is greater than or equal to half.
What is inequality?A mathematical expression shows the unequal comparison between two or more terms.
Inequalities can be greater than, less than, greater than or equal and less than or equal.
What is the expression of the above inequality?The difference of x and one third is greater than or equal to one third of x.
The statement can be written as x -1/3 ≥ x1/3
x -1/3 ≥ x/3
x - x/3 - 1/3 ≥ x/3- x/3 [ subtract x/3 from both parts]
2x/3 - 1/3 ≥ 0
now add 1/3 on both parts
we get, 2x/3 -1/3 + 1/3 ≥1/3
2x/3 ≥ 1/3
2x ≥ 1
x ≥1/2
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, Which recursive sequence would produce the sequence
2,-6, 34
Recursive sequence would produce the sequence 2,-6, 34 is a1 = 2 and an = 2an-1 - 4
How can the recursive sequence be found?To identify a recursive sequence in which terms are defined using one or more preceding terms that are presented.Step 1, Find the nth term (an) of an arithmetic progression and the common discrepancy, d.Step 2, Use the formula an+1 = a + d to plug in the values and find the (n+1)th term, which will then reveal the following terms.A recursive formula is written in two parts: the first term is stated, and the formula connecting the succeeding terms is also stated. 10 through 35 in the following numerical order. Come up with a recursive formula. An arithmetic sequence is shown in this example (the same number, 5, is added to each term to get to the next term).Recursive sequence would produce the sequence 2,-6, 34 is a1 = 2 and an = 2an-1 - 4.To learn more about Recursive sequence refer to:
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a quadrilateral with one right angle must be rectangle ?
Answer:
[tex]\Huge \boxed{\boxed{\textbf{False}}}[/tex]
Step-by-step explanation:
A quadrilateral must have four right angles in order to be a rectangle, not simply one. A quadrilateral with a single right angle, however, can take on a wide range of shapes, like a right angled triangle or an irregular quadrilateral. A shape having multiple sides and one right angle, for example, could be an irregular quadrilateral.
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________________________________________________________
There are 2 boats for
every 5 cars. If altogether
there are 56 boats and
cars, how many cars are
there?
Answer:
Below
Step-by-step explanation:
5 out of ( 5 + 2) vehicles are cars 5 / 7 are cars
5/7 * 56 = 40 cars
Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (x,y) be the unknown endpoint. Apply the midpoint formula, and solve the two equations for x and y.)
midpoint: (-21,8) endpoint: (-13,6)
the other endpoint is------------------------.
Using formula of midpoint of a line, the endpoint have coordinates of (-29, 10)
What is Midpoint of a LineThe midpoint of a line is a point that divides the line into two equal parts. The coordinates of the midpoint can be found by taking the average of the x-coordinates of the endpoints and the average of the y-coordinates of the endpoints.
The formula of midpoint of a line is given as
M(x, y) = (x₂ + x₁) / 2, (y₂ + y₁) / 2
-21, 8 = (x₂ + x₁) / 2, (y₂ + y₁) / 2
For x - coordinate;
-21 = (x₂ + x₁) / 2
-21 = -13 + x₁ / 2
-21 * 2 = -13 + x₁
-42 = -13 + x₁
x₁ = -42 + 13
x₁ = -29
For y - coordinate
8 = (y₂ + y₁) / 2
8 = (6 + y₁) / 2
16 = 6 + y₁
y₁ = 16 - 6
y₁ = 10
The endpoint is (-29, 10)
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You are knitting a blanket at a rate of 4 inches per day.After 4 days, you have knitted 16 inches. a. Write an equation that represents the number of inches y you have knitted after x days. B. How many inches will you have knitted after 7 days? C. Will you have knitted 100 inches after 30 days?
a. The equation that represents the number of inches y you have knitted after x days will be y = 4x.
b. The inches you have knitted after 7 days will be 28 inches.
c. After 30 days, you'll have knitted 100 inches.
How to illustrate the equation?From the information, you're You are knitting a blanket at a rate of 4 inches per day and after 4 days, you have knitted 16 inches.
The equation that represents the number of inches y you have knitted after x days will be:
y = 4 × x
y = 4x
The inches you have knitted after 7 days will be:
= 7 × 4
= 28 inches.
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Lynn O. Liam earns $22.25 per hour. She worked 50 hours last week. She makes
time and a half overtime pay for each hour over 40. What is Lynn's gross pay?
Your answer
Answer:
$1223.75
Step-by-step explanation:
40 times $22.25 = $890
$22.25 times 1.5 to get overtime pay = $33.375
$33.375 times 10 hours overtime = $333.75
$890 + $333.75 = $1223.75
Select all the equations where z=5z=5z, equals, 5 is a solution.
All the equations in which z = 5 are a solution are given as follows:
A. 8 = z + 3.
D. 12z = 60.
E. 12 + z = 17.
How to solve the equations?The first equation is defined as
8 = z + 3.
Isolating the variable z, applying the subtraction operation, which is the inverse of the addition, the solution is given as follows:
z = 8 - 3
z = 5.
The second equation is given as follows:
z - 1 = 6.
Applying the addition operation, which is the inverse of the subtraction, the solution is given as follows:
z = 7.
The third equation is given as follows:
20 = 40z
Applying the quotient operation, which is the inverse of the multiplication, the solution is given as follows:
z = 20/40
z = 0.5.
The fourth equation is given as follows:
12z = 60.
Applying the quotient operation, which is the inverse of the multiplication, the solution is given as follows:
z = 60/12
z = 5.
The fifth equation is defined as
12 + z = 17.
Isolating the variable z, applying the subtraction operation, which is the inverse of the addition, the solution is given as follows:
z = 17 - 12
z = 5.
Missing InformationThe equations are given by the image presented at the end of the answer.
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Solve the equation -4x+3y=12 for y.
What is the difference between 2D coordinate system and 3D coordinate system?
The main difference between the 2D and 3D coordinate systems is that the 3D coordinate system adds a third axis (Z) to the two axes of the 2D coordinate system.
What is coordinates system?A coordinate system is a two-dimensional or three-dimensional system which is used to identify the location of a point or object in the space. It is represented by a set of axes, which are perpendicular and equally spaced from each other to form a grid-like structure. The coordinates of a point or object are determined by the intersection of the two or three axes. Common coordinate systems used in mathematics and science include the Cartesian, polar, and spherical coordinate systems.
A 2D coordinate system is a system in which two axes (X and Y) are used to define a point in a two-dimensional space. This system is used to describe the position of a point in relation to the origin, which is located at the intersection of the two axes. The two axes form a coordinate plane, which provides a visual representation of the system.
A 3D coordinate system is a system in which three axes (X, Y, and Z) are used to define a point in a three-dimensional space. This system is used to describe the position of a point in relation to the origin, which is located at the intersection of the three axes. The three axes form a coordinate space, which provides a visual representation of the system.
This third axis allows points in the 3D coordinate system to be represented in the third dimension. Additionally, the 3D coordinate system provides a more detailed representation of points, as it can represent points in all three dimensions.
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What is the oldest prime number?
The concept of the oldest prime numbers is an ancient one and has been known since ancient times. The ancient Greeks were the first to systematically study prime numbers
The largest and oldest data collection in mathematics is prime numbers. What is it about them that has intrigued mathematicians for millennia?
They were very much aware of the existence of prime numbers and the fundamental theorem of arithmetic, the statement that every positive integer greater than 1 can be represented uniquely as the product of primes. So, it is hard to determine the oldest prime number known, but it's been studied throughout human history.
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vi. The value of a machine depreciates 20% annually. If its present value is Rs. 20,000, its value
after 2 years will be
step-by-step
Answer:
12,800
Step-by-step explanation:
20% of 20000 is 4000
20000-4000=16000
20% of 16000 is 3200
16000-3200=12,800
What are the types of graphs for Class 7?
Frequency distribution graphs, exponential graphs, logarithmic graphs, trigonometric graphs, and statistical graphs are among the six types of graphs (such as bar, pie, and line graphs).
A straightforward two-dimensional graph is created when a vertical and horizontal line join at the origin. The y axis is vertical whereas the x axis is horizontal. In simple line graphs, the x and y axes are split into regularly spaced sections and assigned integer values.
There are eight main categories of graphs: linear, power, quadratic, polynomial, and they are all used to organise how information is presented.
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An inflatable ball can be modeled as a hollow sphere. Miguel
measures the outer diameter of the ball to be 50 cm. If the
material that makes up the ball has a thickness of 1.25 cm, find
the total volume of material that makes up the ball. Round your
answer to the nearest hundredth if necessary. (Note: diagram is
not drawn to scale.)
we can find the total volume of material that makes up the ball by subtracting the volume of the hollow space from the volume of the sphere:
V = 20,834 cm^3 - 19,848.44 cm^3
= 985.56 cm^3
what is volume?Volume is a measure of the amount of space occupied by an object or a substance. It is typically measured in units such as cubic meters (m^3), cubic centimeters (cm^3), or cubic feet (ft^3).
What is diameter?Diameter is a measure of the distance across the widest part of a circular object, such as a circle or a sphere. It is equal to twice the radius of the object and is typically measured in units such as millimeters (mm), centimeters (cm), or inches (in). It is a linear measurement.
To find the total volume of material that makes up the ball, we need to find the volume of the sphere and then subtract the volume of the hollow space in the center.
We can begin by calculating the volume of the sphere using the formula for the volume of a sphere:
V = (4/3) * pi * r^3
Where V is the volume, pi is approximately 3.14, and r is the radius of the sphere.
The outer diameter of the ball is 50 cm, so the radius of the sphere is (50/2) = 25 cm.
Substituting these values into the formula, we get:
V = (4/3) * 3.14 * (25 cm)^3
= (4/3) * 3.14 * 15,625 cm^3
= 20,834 cm^3
Next, we need to find the volume of the hollow space in the center of the ball, which is the same as the volume of a smaller sphere with a radius of (25 cm - 1.25 cm) = 23.75 cm.
So the volume of the hollow space is :
V = (4/3) * pi * (23.75 cm)^3
= (4/3) * 3.14 * (23.75 cm)^3
= 19,848.44 cm^3
Finally, we can find the total volume of material that makes up the ball by subtracting the volume of the hollow space from the volume of the sphere:
V = 20,834 cm^3 - 19,848.44 cm^3
= 985.56 cm^3
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SOMEONE HELP PLSSSS
Which equation does the graph below represent?
(image below)
Answer:below
Step-by-step explanation:
y=1/3x
read the picture plssssss
The possible algebraic equations, obtained based on the algebraic expressions in the question are;
1. [tex]\frac{x}{8} = y[/tex]
2. 15 - n = m
3. 25 + x = y
What is an algebraic expression?An algebraic expression is a collection of numbers and variables that are combined together, but without indicating the value indicated by the collection.
What is an algebraic equation?
An algebraic equation is a mathematical statement that expresses the equivalence of two expressions.
The algebraic expressions can be presented as follows;
1. Some number divided by 8
Let x represent the number divided by 8, and let y represent the result when x is divided by 8. The variables x and y can be defined based on the details in the question
The equation with x as the number and y as the result can be presented as follows;
[tex]\frac{x}{8} =y[/tex]2. n less than 15
The expression n less than 15 is; 15 - n
Let m represent the value of the expression; 15 - n, an algebraic equation based on the details is therefore;
15 - n = m3. 25 more than a number
Let x represent the number, we get
25 more than a number = 25 + x
The y represent the result or value of the expression 25 + x, we get the following algebraic equation;
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Find the slope of a line perpendicular to the line whose equation is x - 2y = 14.
Fully simplify your answer.
The slope of a line perpendicular to the line whose equation is x - 2y = 14 is -2
What is the equation of straight line ?
The equation of straight line is
y = mx + b
where m is slope of the straight line .
Given ,
The equation is x - 2y = 14 .
So, the equation in slope-intercept form would be 2y = x -14,
which then becomes y = 0.5x - 7
giving a slope of -0.5.
The slope of the perpendicular line is a negative reciprocal,
so 0.5 is the same as (1/2), so the positive reciprocal of that is -2,
meaning the slope of the perpendicular line will be -2.
Hence, The slope of a line perpendicular to the line whose equation is x - 2y = 14 is -2
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This week, the price of apples at the farmers market increased 20%. If the price this week is $1.68, what was the price before the increase?
Answer: $1.4
Step-by-step explanation:
let the price before the increase be x
1.2*x = 1.68
x=1.68/1.2 = 1.4
Price before increase = $1.4
1
Write the place value of the underlined digit in each number. The place values are
spelled correctly for you here:
hundreds
tens
ones
tenths
hundredths
Therefore , the solution of probability problem In the absence of digit usage restrictions, 1000000 postcodes are possible, as are 900000 when the first integer cannot be 9.
Why do you use the word probability?The ratio of all possible outcomes to all outcomes in a large group of equally as likely alternatives that result in a specific event determines how likely it is for that event to occur. A branch of mathematics that studies probability a situation or occurrence that is likely to occur the characteristic or state of just being likely of range 0 to 1.
Here ,
1) If there aren't any digit restrictions, there are 1000000 zip codes, or 10*10*10*10*10.
2) 9*10*10*10*10=900000 is the maximum number of postal codes that could exist if the initial number is not 7.
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What is the number of solutions for the system x 2y 0 and 3x 4y 20 0?
The number of solutions for the system of equations x - 2y = 0 and 3x + 4y = 20 is one.
For the given pair of equations x − 2y = 0 and 3x + 4y = 20;
a₁/a₂ = 1/3
b₁/b₂ = -2/4 = -1/2
c₁/c₂ = 0/-20 = 0
As the given pair of linear equation satisfies a₁/a₂ ≠ b₁/b₂,
The graph of these equations will be a pair of lines intersecting at a unique point, which is the solution of the given pair of equations.
Let's verify this by calculating the solution of the given system
x = 2y eqn(1)
3x + 4y = 20 eqn(2)
Now, put the value of x in eqn(2), we get
3 × 2y + 4y = 20
10y = 20
y = 2
Now, put the value of y in eqn(1), and we get
x = 2 × 2 = 4
Thus, the solution is x = 4, y = 2.
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Guadalupe can text 91 words in 14 minutes. At this rate, how many minutes would it take her to text 143 words?
Fill out the table of equivalent ratios until you have found the value of x.
Answer:
It would take her 22 minutes to text 143 words.
Step-by-step explanation:
First, you take 91 and divide that by 14.
You then get 6.5
Then you divide. 143/6.5
You then get 22.
Guadalupe can text 143 words in 22 minutes.
What is ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given, Guadalupe can text 91 words in 14 minutes.
Since,
Guadalupe can text 91 words in = 14 minutes.
Thus, Guadalupe can text 1 word in = 14/91 minutes.
So, Guadalupe can text 143 words in = 14*143/91 minutes.
Guadalupe can text 143 words in = 22 minutes.
Therefore, in 22 minutes, Guadalupe can text 143 words.
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1/216 as a power of 6
1/216 as a power of 6 is 6^-3. The solution has been obtained by using the concept of exponents.
What is an exponent?
A number's exponent demonstrates how many times we are multiplying a given number by itself. For instance, 2^4, indicates that we are multiplying 2 itself by four times. 2*2*2*2 is its expanded form. The power of a number is another name for an exponent. A whole number, fraction, negative number, or decimal are all acceptable.
We are given 1/216 which is to be written as a power of 6.
We know that 216 is the cube of 6.
This means that 216 can be written as 6^3.
Also, 1/n is written as n^-1
So, 1/216 can be written as 6^-3.
Hence, 1/216 as a power of 6 is 6^-3.
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Which of the following illustrates the truth value of the given conditional statement? If 5 = 3 + 2, then 3 + 2 = 5. F T → T F F → F T T → T T F → F
The option that illustrates the truth value of the given conditional statement is; T T → T
How to interpret Truth conditional statements?A conditional statement is considered to be true when the antecedent and consequent statements are both true or if the antecedent is false. When the antecedent is false, it means that the truth value of the consequent does not matter; the conditional will always be true.
We are given the conditional statements at;
If 5 = 3 + 2, then 3 + 2 = 5
Now, a conditional statement, signified by t f which means true and false, is an if-then statement with t being a hypothesis and f being an inference. The statement that illustrates the truth value is T T → T because 5 = 3 + 2 which is true and 3 + 2 = 5 which is also true.
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because x is an unbiased estimator for μ
A unbiased estimator is a statistic that accurately reflects the population mean, μ. A statistic is unbiased when the mean of its sampling distribution is equal to μ.
Mathematically, this can be expressed as:
E(x) = μ
Where E(x) is the expected value of x and μ is the population mean.
This means that if we take a sample from a population and calculate the mean from that sample, the expected value of that mean should be equal to the population mean. This can be seen in the following example:
Let's say we have a population with a mean of 30. We take a sample of size 5 from this population and calculate the sample mean, x. The expected value of x should be equal to 30. We can calculate this using the formula:
E(x) = ∑xi/n
Where xi are the values in the sample and n is the sample size.
For our example, E(x) = (30 + 30 + 30 + 30 + 30) / 5 = 30
This shows that x is an unbiased estimator of μ.
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