The greatest possible integer value of the radius of the circle is 7 inches.
The area of a circle is given by the equation[tex]$A = \pi r^2$[/tex]. We know that the area is less than [tex]$60\pi$[/tex] square inches, so the equation can be written as [tex]$60\pi > \pi r^2$[/tex]. We can solve for the radius by dividing both sides by [tex]$\pi$[/tex], which gives us [tex]$60 > r^2$[/tex]. Taking the square root of both sides gives us [tex]$r < \sqrt{60}$[/tex], which is approximately 7.74 inches. Therefore, the greatest possible integer value of the radius of the circle is 7 inches.
To explain this further, we can start with the equation for the area of a circle, which is[tex]$A = \pi r^2$[/tex]. Since the area is less than [tex]$60\pi$[/tex]square inches, this equation can be rewritten as[tex]$60\pi > \pi r^2$[/tex]. We can then divide both sides by [tex]$\pi$[/tex] to get [tex]$60 > r^2$[/tex]. Taking the square root of both sides gives us [tex]$r < \sqrt{60}$[/tex]. This result can then be rounded down to the nearest integer, which is 7. Therefore, the greatest possible integer value of the radius of the circle is 7 inches.
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y = cos x; dx/dt = 4 cm/sec.
The rate of change of y = cos x with respect to time is approximately -1.46 cm/sec.
How to find the value y = cos x; dx/dt = 4 cm/sec.This problem involves finding the rate of change of the dependent variable (y = cos x) with respect to the independent variable (x) at a given rate of change of the independent variable (dx/dt = 4 cm/sec).
Using the chain rule of differentiation, we have:
dy/dt = dy/dx * dx/dt
Taking the derivative of y = cos x with respect to x, we get:
dy/dx = -sin x
Substituting the given value of dx/dt = 4 cm/sec and the value of sin x can be obtained using the identity cos² x + sin² x = 1 and the given value of cos x = cos 0 = 0.95, we get:
dy/dt = dy/dx * dx/dt
= (-sin x) * 4
= (-√(1 - cos² x)) * 4 [Using the identity sin x = √(1 - cos² x)]
= (-√(1 - 0.95²)) * 4
≈ -1.46 cm/sec
Therefore, the rate of change of y = cos x with respect to time is approximately -1.46 cm/sec.
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Attitudes toward school. The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitude toward school, and study habits of students. Scores range from 0 to 200. The mean score for U.S. college students is about 115, and the standard deviation is about 30. A teacher who suspects that older students have better attitudes toward school gives the SSHA to 25 students who are at least 30 years of age. Their mean score isAttitudes toward school. The Survey of Study
Habit= 127.8.
(a) Assuming that ? = 30 for the population of older students, carry out a test of
H0: ?= 115
H0: ?> 115
Report the P-value of your test, and state your conclusion clearly.
(b) Your test in part (a) required two important assumptions in addition to the assumption that the value of ? is known. What are they? Which of these assumptions is most important to the validity of your conclusion in part (a)?
(a) To test the hypotheses H0: µ = 115 and H1: µ > 115, we will conduct a one-sample t-test using the given information.
Step 1: Calculate the t-value.
t = (sample mean - population mean) / (standard deviation / √sample size)
t = (127.8 - 115) / (30 / √25)
t = 12.8 / 6
t = 2.13
Step 2: Determine the degrees of freedom (df).
df = sample size - 1
df = 25 - 1
df = 24
Step 3: Find the P-value.
Using a t-table or calculator, find the P-value corresponding to t = 2.13 and df = 24. The P-value is approximately 0.022.
Step 4: State the conclusion.
Since the P-value is less than the commonly used significance level of 0.05, we reject the null hypothesis (H0: µ = 115) and conclude that the mean score for older students is significantly higher than the mean score for the entire population.
(b) The two important assumptions for the t-test are:
1. The sample is randomly selected from the population.
2. The population is normally distributed.
The most important assumption for the validity of the conclusion in part (a) is the normality of the population. If the population is not normally distributed, the results of the t-test may not be valid, and the conclusion may be inaccurate.
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What is the median of the data in the table below?
Answer:24
Step-by-step explanation:
WORTH 23 POINTS - While reading a news article, Bethany noticed that the word "senselessness" had a lot of repeating letters. Bethany wondered about the probabilities of randomly drawing certain letters if each letter in "senselessness" were written on an index card and put into a bag.
Answer:
To determine which letter has the greatest probability of being selected and its corresponding probability, we need to count the number of times each letter appears in the word "senselessness".
The word "senselessness" contains a total of 12 letters, with 4 distinct letters: "e", "s", "n", and "l". We can count the number of times each letter appears as follows:
"e" appears 4 times
"s" appears 4 times
"n" appears 2 times
"l" appears 2 times
Therefore, the letter "e" and "s" have the greatest probability of being selected, as they appear most frequently in the word. The probability of selecting the letter "e" would be 4/12, which simplifies to 1/3 or approximately 0.33. Similarly, the probability of selecting the letter "s" would also be 1/3 or approximately 0.33.
On the other hand, the letter with the least probability of being selected would be either "n" or "l", as they appear the least frequently. The probability of selecting either "n" or "l" would be 2/12, which simplifies to 1/6 or approximately 0.17.
I'm not sure if this answers your question, but i really hope it helps!
Please mark brainliest though, it really helps!
clark was asked to complete a self-administered questionnaire posted at mysurvey. what type of survey did clark complete?
Clark completed a self-administered questionnaire, which is also known as an online survey.
This type of survey is administered online and is completed by the participant (in this case, Clark) without the assistance of a researcher or interviewer. It can be delivered through an online form or through an email or online survey link.
The questionnaire typically includes multiple-choice questions, short-answer questions, and rating scales that the participant can answer with a click or tap. After the participant completes the survey, their answers are collected and analyzed by the researcher. This type of survey is a cost-effective and convenient way to collect data from a large number of people in a short amount of time.
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Two square pyramids are joined at their bases.
Each base is 28 cm long. The distance between the
vertices of the combined pyramids is 21 cm. What
is the volume of the solid formed?
The volume of the solid formed using square pyramids are joined at their bases is 5,487.3 unit ².
Using the formula for the volume of a square pyramid, find the volume and then multiply it by two since there are two square pyramids.
Let V be the volume of the solid formed.
⇒ volume of the solid formed - V = 2 ( [tex]\frac{1}{3} *B*h[/tex] )
Now substitute the values,
⇒V = 2 ( [tex]\frac{1}{3}[/tex] * [tex]28^{2}[/tex] * 10.5 )
⇒V = 2 ( [tex]\frac{1}{3}[/tex] * 784 * 10.5 )
⇒V = 2 ( 261.3 * 10.5 )
⇒V = 2 ( 2,743.65 )
⇒V = 5,487.3 unit ²
Therefore, the volume of the solid formed using square pyramids are joined at their bases is 5,487.3 unit ².
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Prove that the following statement is false. There exists an integer n such that 6n2 + 27 is prime. To prove the statement is false, prove the negation is true. Write the negation of the statement. For every integer n, 6n² + 27 is prime. For every integer n, 6n2 + 27 is not prime. There exists an integer n, such that 6n2 + 27 is not prime. There exists a composite number q = 6n2 + 27, such that n is an integer. There exists an integer n, such that 6n2 + 27 is prime. Now prove the negation. Suppose n is any integer. Express 6n2 + 27 as the following product: 6n2 + 2 Now is an integer because sums and products of integers are integers. Thus, 6n2 + 27 is not prime because it is a
The negation of the statement "There exists an integer n such that 6n2 + 27 is prime" is "For every integer n, 6n2 + 27 is not prime."
To prove the negation, we can use algebraic manipulation to show that 6n2 + 27 is always composite.
Suppose n is any integer. We can factor out 3 from 6n2 + 27 to get 3(2n2 + 9). Since 2n2 + 9 is always odd (2 times any integer is even, and adding 9 makes it odd), we can further factor it as (2n2 + 9) = (2n2 + 6n + 9 - 6n) = [(2n+3)(n+3)] - 6n.
Substituting this expression back into 3(2n2 + 9), we get 3[(2n+3)(n+3) - 6n]. Since (2n+3)(n+3) - 6n is an integer, 3[(2n+3)(n+3) - 6n] is composite for every integer n. Therefore, 6n2 + 27 is not prime for any integer n.
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The table represents an exponential function. What is the multiplicative rate of change of the function?
The multiplicative rate οf change οf the given expοnential functiοn is 1/5.(1st οptiοn).
What is expοnential functiοn?An expοnential functiοn is a Mathematical functiοn which is οf the fοrm
f (x) = aˣ, where “x” is variable here and a real number and “a” is a cοnstant which is called the base οf the functiοn where a shοuld be greater than zerο.
The expοnential functiοn is given here in tabular fοrm.
Here frοm the table οf expοnential functiοn we get when x= 2 then
y= 2/5
again when x= 3 then y= 2/25
sο (2/5)×(1/5) = 2/25
again fοr x= 4 , y= 2/125
(2/25)×(1/5) = 2/125
sο every time the expοnential functiοn is multiplied by 1/5 and we get the next result.
Hence, The multiplicative rate οf change οf the given expοnential functiοn is 1/5.
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In a certain math game, each problem is either easy or hard, and problems of the same difficulty level are worth the same number of points. Sandra
played this game twice.
. In the first game, she correctly answered 10 easy problems and 8 hard problems for a total of 94 points.
. In the second game, she correctly answered 5 easy problems and 16 hard problems for a total of 143 points.
The system below can be used to determine z, the number of points per easy problem, and y, the number of points per hard problem.
10z + 8y = 1
(5z + 16y=143
Which is the quickest method of finding the number of points per easy problem?
O Subtract 2 times the bottom equation from the top equation.
Subtract 2 times the top equation from the bottom equation.
Add 2 times the bottom equation to the top equation.
O Add 2 times the top equation to the bottom equation.
Answer: 18.75%
Step-by-step explanation:
To find the percent increase, we need to calculate the difference between the new speed and the old speed, divide that by the old speed, and then multiply by 100 to get the percentage increase.
The difference between the new speed and the old speed is:
38 - 32 = 6
To find the percentage increase, we divide the difference by the old speed and multiply by 100:
(6 / 32) x 100 = 18.75%
Therefore, Matt's typing speed increased by 18.75%.
a beer and wine store series 10 licensee is allowed to serve beer and wine samples on the premises if it holds sampling privileges. true or false? false true`
False. A Beer and Wine Store Series 10 Licensee is not allowed to serve beer and wine samples on the premises, even if they hold sampling privileges.
This is because beer and wine samples are not allowed to be sold under this type of license, according to the Texas Alcoholic Beverage Code. Under the TABC, beer and wine samples may only be sold in certain locations, such as restaurants and stores that have a TABC permit for the purpose of selling alcoholic beverages for on-premises consumption.
Beer and wine sampling privileges are reserved for other types of establishments, such as bars and taverns, that have a TABC permit for the purpose of selling alcoholic beverages for on-premises consumption. As such, a Beer and Wine Store Series 10 Licensee is not allowed to serve beer and wine samples on the premises, even if they hold sampling privileges.
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a measure is reliable if it a) results in similar scores for the same person. b) contains a large amount of true score. c) contains little measurement error. d) all of these
The measure is reliable if it contains little measurement error. So the correct option is c) contains little measurement error.
What is a measure?A measure is a tool that is used to evaluate a person's traits, values, and performance in a given task or activity. A measure is used to obtain a score that can be used to evaluate a person's characteristics, abilities, or tendencies.
It is critical that the measure is reliable and valid to be able to use it to evaluate people. Reliability is one of the qualities of a good measure. Reliable measure A measure is reliable if it yields consistent scores across different samples of individuals or across different occasions for the same individual.
If a measure is reliable, it will yield similar scores for the same person every time it is administered. It is essential that a measure is reliable because if it is not, it will be difficult to determine if the score reflects the person's true characteristics or is a result of measurement error. Measurement error is a measure's inaccuracies, inconsistencies, or instability in its results.
Measurement error is a potential source of unreliable measurements. It is necessary to minimize measurement error to achieve reliable measurement. Measurement error can be reduced by ensuring that the measure is standardized, that the scoring is done consistently, and that the measure is free from external factors that may influence the results.
Hence, a measure is reliable if it contains little measurement error. So the correct option is c) contains little measurement error.
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9 3/4, 10 1/2, 9 1/4, 10 1/4, 11, 10 1/4, 9 1/2 make a line plot that displays the lengths of the books on the bottom shelf
The line-plot of the the given data 9 3/4, 10 1/2, 9 1/4, 10 1/4, 11, 10 1/4, 9 1/2 that displays the lengths of the books on the booom shelf is attached.
What is line plot?
A line plot is a type of graph that represents the kind of data representation. It is line plot or a line chart shows the data in a visual form or visual representation. The graph is plotted with help of straight lines and points or dots. The x-axis is represented by straight lines or the it is labelled about the data. The y-axis is represented by the dots or frequency of the data. It is generally used to represent the small data set. This graph uses symbols to show or represent the frequency of the observations.
The data represented here is 9 3/4, 10 1/2, 9 1/4, 10 1/4, 11, 10 1/4, 9 1/2
we can make the frequency table using the above values, after which it can be plotted on the line-plot graph.
1-9 1/4--1 dot
2-9 1/2--1 dot
3-9 1/2--1 dot
4-10 1/4-2 dots
5-10 1/2--1 dot
6-11--1 dot
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Attached is a line-plot of the given data showing the lengths of the books on the book shelf: 9 3/4, 10 1/2, 9 1/4, 10 1/4, 11, 10 1/4, and 9 1/2.
What is line plot?An example of a graph that shows this sort of data representation is a line plot. The data is presented visually in the form of a line plot or a line chart. With the aid of straight lines, points, or dots, the graph is drawn. Straight lines or labels that describe the data are used to depict the x-axis. The dots or frequency of the data are used to depict the y-axis. It often serves as a representation for a tiny group of data. The frequency of the observations is shown or represented by symbols on this graph.
9 3/4, 10 1/2, 9 1/4, 10 1/4, 11, 10 1/4, and 9 1/2 are the numbers shown.
Using the aforementioned variables, we can create the frequency table, which can then be plotted on the line-plot graph.
1-9 1/4--1 dot
2-9 1/2--1 dot
3-9 1/2--1 dot
4-10 1/4-2 dots
5-10 1/2--1 dot
6-11--1 dot
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Find the area of a circle that has a radius of 7/2 centimeters. Use 22/7 as an approximation for π.
Answer: The answer is 38.5 cm^2
Step-by-step explanation:
Given:
Radius(r) = 7/2
Pie (π) = 22/7
We know that:
The area of Circle is = πr^2 = π * r * r
So, ans is = (22/7) * 7/2 * 7/2 = 38.5 cm^2
Answer:
A≈ 38.5cm^2
Step-by-step explanation:
Given:
The approximation of pi is 22/7 or 3.141592
The radius is 7/2 or 3.5
Work:
A=πr(2)=π·3.5(2)≈38.48451
now let's round it to 38.5cm^2
Help me Pleaaee it’s urgent
in a trendline based on five observations, if the average of y is 100 and the slope of the line is 22 then the intercept is:
c = -880
The intercept for a trendline based on five observations with an average of y = 100 and slope of the line = 22 is -880. This can be calculated using the formula for the equation of a straight line: y = mx + c, where m is the slope and c is the intercept. We know that the slope (m) is 22 and the average of y (the y-intercept) is 100. Plugging in the given values, we get:
100 = 22x + c
c = -880
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The work shows the first steps of writing a partial fraction decomposition.
3x+9/(x+1)(x-5)=A/x+1+B/x-5
3 x + 9 = A (x minus 5) + B (x + 1)
3 x + 9 = A x minus 5 A + B x + B
What is the partial fraction decomposition in terms of x?
it's C
The partial fraction decomposition of 3x+9/(x+1)(x-5) in terms of x is C = A/(x+1) + B/(x-5).
To find the values of A and B, we solve the system of equations formed by equating coefficients of x and the constant term in equation 3x + 9 = A(x-5) + B(x+1). Solving for A and B, we get A=-3/4 and B=3/4. Substituting these values back into the partial fraction decomposition, we get C = -3/4/(x+1) + 3/4/(x-5).
Therefore, the partial fraction decomposition of 3x+9/(x+1)(x-5) in terms of x is C = -3/4/(x+1) + 3/4/(x-5).
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Answer:
Answer is C
Step-by-step explanation:
Precalc Edge 2023
In P, answer the following:
A. Name a radius
B. Name a diameter
C. Name a cord
D. Name a central angle
E. Name a tangent to the circle
Answer:
radius=PC
diameter=AB
chord=AC
central angle=angleAPC
tangent=AD
given = g(x)=-6x+8,find g(2)
Answer:
Step-by-step explanation:
g(2) = -6(2) + 8 = -12 + 8 = -4
Graph the system below and write its solution
Answer:
the answer is one solution and to graph you'll need to make the second equation like this y=-2x+7
For what values of a are the following expressions true?
(PLease help ASAP)
|a +5| = −5−a
|a +5 |=a +5
The equation |a + 5| = −5 − a is not true for any value of a, while the equation |a + 5| = a + 5 is true for values of a greater than or equal to -5.
The absolute value of a number is defined as the distance of the number from zero on a number line. Thus, |a + 5| is equal to the distance of (a + 5) from zero on a number line. Since distance is always non-negative, |a + 5| is always non-negative.
On the other hand, the expression −5 − a is always negative, since the sum of a negative number (-5) and any number (a) is always negative.
Therefore, for the equation |a + 5| = −5 − a to be true, the absolute value of (a + 5) would have to be negative, which is impossible since absolute value is always non-negative.
For the equation |a + 5| = a + 5 to be true, a must be greater than or equal to -5, because when a is greater than or equal to -5, (a + 5) is already non-negative, so the absolute value of (a + 5) is equal to (a + 5).
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Ms Kowal invests £6000 in a simple interest account.
After 5 years her investment has earned £450 interest.
What rate of interest does the account pay?
Answer:
We can use the simple interest formula I = Prt to find the rate of interest that the account pays. Here, P is the principal amount (£6000), t is the time period (5 years), and I is the interest earned (£450). Substituting these values in the formula gives us: 450 = 6000 * r * 5. Solving for r, we get r = 0.015 or 1.5%. Therefore, the account pays a simple interest rate of 1.5%
Tanya painted a mural that was 8 feet tall. The area of the mural was 224 square feet. What is the length of Tanya’s mural?
The length of Tanya's mural is 28 feet.
What is the length of Tanya’s mural?A rectangle is a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.
Area of a rectangle is expressed as;
Area = length × width
We know that the area of Tanya's mural is 224 square feet, and the height of the mural is 8 feet.
So we can use these values to find the length of the mural:
Area = length × width
224 = length × 8
To solve for the length, we can divide both sides of the equation by 8:
length = 224 ÷ 8
length = 28 feet
Therefore, the dimension of the length is 28 feet.
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In a laboratory test of pus, the number of bacteria detected in the infected wound of a person on Wednesday is 2.4 x 10. If the antibiotic decreases the number of bacteria by 60% per day and it is started consuming since Wednesday, find the number of bacteria that will find in the laboratory test of coming Friday?
Step-by-step explanation:
We can approach this problem using exponential decay, where the number of bacteria decreases by 60% per day. Let N be the initial number of bacteria on Wednesday, then the number of bacteria on Friday can be calculated as:
N_Friday = N_Wednesday x (0.4)^2
where (0.4)^2 is the factor by which the number of bacteria decreases from Wednesday to Friday.
We are given that the number of bacteria on Wednesday is 2.4 x 10, so we can substitute this into the equation:
N_Friday = 2.4 x 10 x (0.4)^2
Simplifying this expression, we get:
N_Friday = 0.96
Therefore, the number of bacteria that will be detected in the laboratory test on Friday is 0.96. Note that the units are not specified in the question, so we assume that the number is given in some arbitrary units.
find the probability that when he enters the restaurant today it will be at least 5 minutes until he is served.
The probability that it will take at least 5 minutes until the student is served when he enters the restaurant today is 50%.
This is because there is an equal chance that it could take less than 5 minutes or more than 5 minutes until the student is served.
In probability terms, the student's wait time is a random variable with two possible outcomes - wait time less than 5 minutes, or wait time greater than or equal to 5 minutes. Since there is an equal chance of either outcome occurring, the probability of the wait time being greater than or equal to 5 minutes is 50%.
This is also known as the Law of Large Numbers.
To further illustrate this concept, imagine that the student flips a fair coin. The two possible outcomes of the coin toss are heads or tails. Since each outcome has an equal chance of occurring, the probability of either heads or tails is 50%.
In this case, the probability of the student's wait time being at least 5 minutes is the same as the probability of the coin toss being heads or tails, hence making the probability 50% or 0.5.
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A county recreation department cleared a mile long walking trail. If the trail will be marked every mile with a small sign, how many signs are needed?
Answer:
Step-by-step explanation:
If the trail is a mile long and is marked every mile with a sign, then there will be one sign at the end of the trail. In addition, there will be signs marking each mile along the trail, including the starting point. Since there are 1 mile markers between the starting point and the end of the trail, there will be a total of:
1 (at the end) + 1 (at the starting point) + 1 (for each mile marker) = 1 + 1 + 1 = 3
Therefore, three signs are needed to mark a mile-long walking trail.
If a₁ = 9, and an an-1 - 1 then find the value of a4.
A. 5
B. 6
C. 9
D. 4
Answer:
it’s b
Step-by-step explanation:
I just did it
ELEPHANTS In the wild, an African elephant typically consumes 2.5 × 10² pounds of food a day. If there are approximately 4.15 × 10⁵ African elephants in the wild, how many pounds of food are consumed by African elephants in one day?
Answer:
Approximately 1.05 × 10⁹ pounds of food are consumed by African elephants in one day.
Step-by-step explanation:
Answer:
Step-by-step explanation:
its 7 or 6\
3) the line that passes through
(8,5) and (1,5)
Slope:
55 divided by 11 * 7 x (2 + 14)
560
1) PEMDAS so 2+14=16
2)55/11=5
3)5x7=35
4)35(16)=560
a trapezoid has a base length of 4 meters and 2.5 meters. if the height of the trapezoid is 4 meters, what is the area of the trapezoid?
The area of the trapezoid is 13 meters.
The area of a trapezoid is calculated by taking the sum of the two bases and multiplying that by the height, then dividing that by two. In this case, the sum of the two bases is 4 meters + 2.5 meters = 6.5 meters. Multiplying this by the height of 4 meters gives us a result of 26 meters. Finally, we divide that by two to get the final area of 13 meters.
To calculate the area of a trapezoid, you first need to calculate the sum of its two bases. The two bases are the bottom and the top lengths of the trapezoid, which in this case are 4 meters and 2.5 meters respectively. Once you have the sum of the two bases, you can then multiply that sum by the height of the trapezoid, which in this case is 4 meters. This will give you the total area of the trapezoid. Lastly, you divide this total area by two to get the final area.
In summary, to calculate the area of a trapezoid with a base length of 4 meters and 2.5 meters, and a height of 4 meters, you need to first calculate the sum of its two bases, which in this case is 6.5 meters. Multiply this by the height of 4 meters to get the total area of 26 meters. Finally, divide this by two to get the final area of the trapezoid, which is 13 meters.
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