There is a 1/12 chance that the three pairwise distances between the locations are smaller than the radius of the circle.
Here,
The first point can be placed anywhere on the circle because it doesn't matter where it is chosen.
A total of 120 degrees and a probability of 1/3 must be provided by the next point, which must be within an arc of 60 degrees on either side. The second point must be 60 degrees or less from the first two.
The third point can be located within an arc with a minimum area of freedom of 60 degrees and a chance of 1/6 if the first two locations are separated by 60 degrees. The third point can be located with a maximum degree of freedom of a 120 degree arc and a 1/3 chance if the first two points are the same.
Up to a maximum of 60 degrees away from the starting point, the likelihood changes linearly.
By averaging the probabilities at either end, we may discover 1/4, the typical likelihood we can position the third point based on a fluctuating second point.
The overall probability is 1 1/3 4 = 1/12.
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A 24-inch board is to be cut into three pieces so that the second piece is twice as
long as the first piece and the third piece is 3 times as long as the first piece. If x
represents the length of the first piece, find the lengths of all three pieces.
Answer:
The answer to your question is: first piece = 4 in, second piece = 8 in, third piece = 12 in
Step-by-step explanation:
Data
total length = 24 inches
first piece = x in
second piece = 2x
third piece = 3x
Equation
x + 2x + 3x = 24
6x = 24
x = 24/6
x = 4 lengths of the first piece
second piece = 2(4) = 8 inches
third piece = 3(4) = 12 inches
hannah claims that -3 is not a rational number because it is not written as a ratio of integers. is she correct? explain why or why not
Answer: -3 is a rational number
Step-by-step explanation:
-3 is a rational number because it can be written as a fraction -3/1 and have the same value of -3. Therefore -3 is a rational number and Hannah is correct.
given a collection of intervals, decide whether there is a subset of non-overlapping intervals of size at least k.
Non-overlapping intervals:
If the intervals(say interval a & interval b) doesn't overlap then the set of pairs form by [a. end, b. start] is the non-overlapping interval.
Interval:
In mathematics, a (real) interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0, 1, and all numbers in between. Other examples of intervals are the set of numbers such that 0 < x < 1, the set of all real numbers {\displaystyle \mathbb {R} }\mathbb {R} , the set of nonnegative real numbers, the set of positive real numbers, the empty set, and any singleton (set of one element).
Overlapping intervals:Let's take the below mentioned overlapping intervals example to explain the idea: If both ranges have at least one common point, then we say that they're overlapping. In other words, we say that two ranges and are overlapping if: On the other hand, non-overlapping ranges don't have any points in common.
Given N set of time intervals, the task is to find the intervals which don’t overlap with the given set of intervals.
Examples:
interval (a) = { {1, 3}, {2, 4}, {3, 5}, {7, 9} }
Output: [5, 7]
The only interval which doesn’t overlaps with the other intervals is [5, 7].
interval (a) = { {1, 3}, {9, 12}, {2, 4}, {6, 8} }
Output: [4, 6] and [8, 9]
There are two intervals which don’t overlap with other intervals are [4, 6], [8, 9].
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explain why two lines through the origin that meet at a right angle can be considered orthogonal subspaces of r2 but two planes through the origin that meet at a right angle can not be considered orthogonal subspaces of r3.
There is a difference between orthogonal and orthogonal subspaces. According to this, two planes cannot be orthogonal in R3.
Considering, in the case of the orthogonal planes, each plane should have a basis of orthogonal vectors, and also, one of the pairs in each of the vector, is shared between the two planes and the other vector that is present, should form a orthogonal pair to each other.
Taking the case of orthogonal subspaces, the main requirement is that each vector of each of the pairs should be orthogonal to each vector of each of the other pair. Also, the dimension of the ambient pair should be not less than 4 (2+2).
When we talk about two planes in R3, planes are orthogonal if and only if, their normal vectors are orthogonal. If this condition is not present, then planes are not orthogonal in R3.
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The department of management science at Tech has sampled 250 of its majors and complied the following frequency distribution of grade point averages (on a 4.0 scale) for the previous semester:GPA Frequency0-0.5 1.5-1 41-1.5 201.5-2 352-2.5 672.5-3 583-3.5 473.5-4 181)Please calculate the probability of a student obtaining GPA at each range listed in the table above. You should calculate 8 probabilities, one for each GPA range. Please show your detailed calculation.2)What is the probability that a student’s GPA is higher than 1.5 (not include GPA = 1.5)?3)What is the probability that a student’s GPA between 2.5 (not include 2.5) and 3.5 (include 3.5)?
1) The probability table is calculated by the formula. 2) the probability that a student scores higher than 1.5 is 0.9, and 3) the probability a student scores between 2.5-3.5 is 0.47.
1)
We know that the probability of any event
= no. of observation for the event/total n. of observation
Here, the total no. of observations is 250
Hence we get the following probability table
GPA Frequency
0-0.5 1/250
0.5-1 4/250
1-1.5 20/250
1.5-2 35/250
2-2.5 67/250
2.5-3 58/250
3-3.5 47/250
3.5-4 18/250
2)
The probability that a student's GPA is higher than 1.5 is
P(1.5-2) + P(2-2.5) + P(2.5-3) + P(3-3.5) + P(3.5-4)
= (35 + 67 + 58 + 47 + 18)/250
= 225/250
= 0.9
3)
The probability that a student's GPA is between 2.5 and 3.5
= P(2.5-3) + P(3-3.5)
= (58 + 47)/250
= 105/250
= 0.42
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Complete Question
The department of management science at Tech has sampled 250 of its majors and compiled the following frequency distribution of grade point averages (on a 4.0 scale) for the previous semester:
Please calculate the probability of a student obtaining a GPA at each range listed in the table above. You should calculate 8 probabilities, one for each GPA range. Please show your detailed calculation.2)What is the probability that a student’s GPA is higher than 1.5 (not include GPA = 1.5)?3)What is the probability that a student’s GPA is between 2.5 (not include 2.5) and 3.5 (include 3.5)?
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pls help! picture is below. pls help by pst sunday december 4 , 2022 12:00 p.m.
Answer: August 12th
Step-by-step explanation: 4 and 6 have common multiples of 2, so you need to multiply 6 by 2 and 4 by 3. Both get you 12, so the earliest they have tennis practice is the 12th of August (12 days after July 31st).
Answer:
August 12
Step-by-step explanation:
To solve this question, we need to find the Least Common Multiple (LCM) of 4 and 6.
Since we know that Nick and Mark both had practice on July 31st, we can simply add {LCM of 4 and 6} days to that date to get when they will next both have practice.
To find the LCM of 4 and 6, find the prime factorization of both:
[tex]4 = 2 \times 2[/tex] [tex]6 = 2 \times 3[/tex]
Now, take the largest quantity of each distinct prime number and multiply them together:
The largest number of 2's is 2. The largest number of 3's is 1. So, we multiply
[tex](2 \times 2) \times (1 \times 3)[/tex]
[tex]= 4 \times 3[/tex]
[tex]= 12[/tex]
Therefore, the LCM of 4 and 6 is 12.
This means that Nick and Mark will have practice on the same day in 12 days.
The last step to solve this problem is to add 12 days to July 31.
[tex]\textrm{July } 31 + 12 \textrm{ days} = \textrm{August } 12[/tex]
Nick and Mark will next have practice on the same day on August 12.
How much is 76 divided by 6?
Answer:
If you divide 76 by 6, you would get 12.6666667.
76 divided by 6 is equal to 12 and 2/3, or simply 12.67 when expressed as a decimal.
To divide 76 by 6, we perform the division operation to find the quotient.
When dividing, we start with the largest multiple of 6 that is less than or equal to 76, which is 72. We divide 72 by 6, which equals 12.
Next, we subtract the product of 6 and 12 from 76 to find the remainder:
76 - (6 x 12) = 76 - 72 = 4
Since there is still a remainder of 4, we can express the result as a mixed number: 12 and 4/6.
To simplify the mixed number, we can reduce the fraction. The greatest common divisor of 4 and 6 is 2, so we can divide both the numerator and denominator by 2:
4/2 ÷ 6/2 = 2/3
Therefore, 76 divided by 6 is equal to 12 and 2/3, or simply 12.67 when expressed as a decimal.
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Multiples of 3 and factors of 45??
Answer:
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30
Factors of 45: 1, 3, 5, 9, 15, and 45
Step-by-step explanation:
1. Write a rule for g(x)=3f(x) + 1 when f(x) = x³ - 2x + 3.
2. Describe the graph if g as a transformation of the graph of f.
The equation of transformation in g(x ) is 3x³ - 6x + 8
what is transformation?
A point, line, or geometric object can be changed in four different ways that are all collectively referred to as transformations. The pre-image is the shape of the object as it was originally, and the transformed shape of the object is termed the image.
solution:
1. f(x) = x³ - 2x + 3.
Then g(x) = 3f(x) + 1
substitute f(x) in g(x)
g( x ) = 3 (x³ - 2x + 3) + 1
= 3x³ - 6x + 9 + 1
g( x ) = 3x³ - 6x + 8
2. The graph of the function f(x) = x³ - 2x + 3 is obtained by just moving the graph of g( x ) = 3x³ - 6x + 8 by 2 units up.
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now use the binomial probability formular, calculate the probability of observint 4 heads in 10 coin flips. (1pt) is the estimated probability from exercise 1 close to the true proability? (1pt)
By using Binomial distribution of probability, it can be calculated that
Probability of getting 4 heads in 10 coin flips = [tex]\frac{105}{512}[/tex]
What is Binomial distribution of probability?
Binomial distribution of probability is a discrete probability distribution where the probability mass function is given by
P(X = x) = [tex]{n \choose x}p^xq^{n - x}[/tex]
Where p is the probability of success and q is the probability of failure.
Here, Binomial distribution of probability is used
n = 10
Probability of getting a head = [tex]\frac{1}{2}[/tex]
Probability of getting a tail = [tex]\frac{1}{2}[/tex]
Probability of getting 4 heads in 10 coin flips = [tex]{10 \choose 4}(\frac{1}{2})^4(\frac{1}{2})^{10 - 4}[/tex]
= [tex]\frac{210}{1024}[/tex]
= [tex]\frac{105}{512}[/tex]
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4.) numbers is a game in which you bet $1 on any 3-digit number from 000 to 999. if your number comes up, you get $500. find the expected payback.
As the probabilities of random variables are negative so we can expect to lose roughly 50 cents on each $1.00 ticket we purchase.
How did the math game function?
The rules of the "numbers" game are simple: a player selects a three-digit number between 000 and 999. Anyone who picks the winning number receives a payout equal to 600 times their original wager. The winning number is decided by a publicly disclosed source. The majority of bets were for $1 or less, and frequently.
What does a probability arrangement mean?
A permutation is an arrangement (or ordering) of a collection of items. (We can also arrange only some of the objects in the set.) The arrangement of the objects in a permutation depends on their order.
The random variable-0.499/1000
The random variable "winning" are $1 and $600.
and their probabilities are 999/1000 and 1/1000, respectively.
The expected "winnings" are calculated as follows:
=(999/1000)(-1)+(1/1000)(500)
=-0.499/1000
=-0.499 cents
so we can expect to lose roughly 50 cents on each $1.00 ticket we purchase.
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which hypotheses can be used to perform the test in the following scenario? the mean startup time of two competing computers is to be compared to see if they are equal or not. eighteen startup times are randomly sampled from each computer. both populations have normal distributions with known standard deviation.
Hypothesis:
H0: The mean startup time for both computers is equal.
H1: The mean startup time for both computers is not equal.
A hypothesis is a potential explanation for a phenomenon.A hypothesis must be testable in order to be considered scientific according to the scientific method. Scientists typically base their scientific hypotheses on prior observations that cannot be adequately explained by the body of knowledge. Despite the fact that the terms "hypothesis" and "theory" are frequently used interchangeably, they are not the same thing. A working hypothesis is a theory that has been tentatively accepted and is put forth for further study after starting with an educated guess or idea.
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what is the probability that someone who tests positive has the genetic disease? (enter the value of the probability in decimal format and round the final answer to three decimal places.)
The probability that someone who tests positive has the genetic disease is 0.142
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
Let E be the people test positive
Let F be the people who has disease
P(F)= 1/10000 = 0.0001
P(E/F)= 99.5% = 0.995
P(E/F bar ) = 0.06 % = 0.0006
Baye's theorem:
P(F/E) = [ P(E/F) * P(F) ] / [ P(E/F) * P(F) + P(E/F bar ) * P( F bar ) ]
conditional probability :
P(B/A) = P ( A [tex]\cap[/tex] B ) / P(A)
Complement rule is given by:
P (F bar ) = 1 - P(F) = 1 - 0.0001 = 0.9999
The probability that someone who tests positive has the genetic disease :
P(F/E) = [ P(E/F) * P(F) ] / [ P(E/F) * P(F) + P(E/F bar ) * P( F bar ) ]
= ( 0.995 * 0.0001 ) / ( 0.995 * 0.0001 + 0.0006 *0.9999)
= 0.142
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Nicholas bought 5 pens for $3. At this rate, how much will he spend on 10 pens?
$10
$6
$5
$3
The correct answer is $6
How did we figure out this?To solve this question, we need to multiply the numbers given.
Given:
[tex]10,5,3,2[/tex]
Therefore, the equation goes like this:
[tex]5*2\\3*2[/tex]
5 x 2 = 103 x 2 = 6Therefore, the correct answer is $6
14.95x4.1
HELPPPPPP
me please i need helppp
Answer:
down below
Step-by-step explanation:
Assuming you meant multiplying:
61.295
Hope this helps! :)
y-2/3x =-6 what does y equal.
Answer:
Solve for Y
by simplifying both sides of the equation, then isolating the variable.
Hope this helped
Step-by-step explanation:
The answer would be: y=-18x+2
Weight
Weight
9. John mixed cashews and almonds.
Weight
John bought 4 pounds of almonds for a total cost of $22
The cost per pound for cashews is 60% more than the cost per
pound for almonds.
John bought enough cashews that, when he mixed them with the
almonds, the mixture had a value of $6.50 per pound
Approximately what percent of the mixture by weight was cashews?
Answer:
30%
Step-by-step explanation:
4 pounds of almonds is $22 --> 1 pound of almonds is $5.50
Cashew price per pound = 160/100 * $5.50. = $8.80
22 + 8.80x = 6.50(4+x)
22 + 8.80x = 26 + 6.50x
2.30x = 4
x = 1.739130435 approx 1.74 lbs of cashews
percent of the mixture, by weight, for cashews =
1.739130435 / (4 + 1.739130435) = 0.303030303 approx 30%
the manager of a store buys marine radios in lots of 48. suppose that, on the average, 2 out of each group of 48 are defective. the manager randomly selects 4 radios out of the group to test. assume independence. (round your answers to 4 decimal places.) (a) what is the probability that he will find 2 defective radios?
The probability that he will find 2 defective radios is 0.0350.
Given that,
The store's management purchases maritime radios in quantities of 48. Let's say that, on average, 4 people out of every 48 make up a faulty group. Out of the group, the manager chooses four radios at random for testing.
P = 4/48 = 0.083
n=4
P(X=x) = nCₓ Pˣ (1-P)ⁿ⁻ˣ
a) The probability that he will find 2 defective radios P(X=2)
P(X=x) = nCₓ Pˣ (1-P)ⁿ⁻ˣ
P(X=2) = 4C₂ (0.083)² (1-0.083)²
P(X=2) = 0.0350
Therefore, P(X=2) is 0.0350
Therefore, the probability that he will find 2 defective radios is 0.0350.
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0.14 and the probability that the flight will be delayed is 0.06. The probability that it
will not rain and the flight will leave on time is 0.82. What is the probability that it is
raining and the flight is delayed? Round your answer to the nearest thousandth.
Pass please! next question
One measure of an angle in a triangle is 96°. The other two angle measures are represented by 2 and + 12. Determine the other two degree measures for the missing angles.
The measure of missing angles is 48° and 36°.
Define angle sum property.The angle sum property of a triangle states that the sum of the three internal angles of a triangle equals 180 degrees. Three line segments combine to form a triangle, a closed shape having interior and exterior angles. When the values of the other two angles are known, one may utilize the angle sum property to determine the measure of an unknown interior angle.
Given Measure of one angle= 96, one angle= 2x, other angle= x + 12.
Using the angle sum property, we get
96 + 2x + x + 12 = 180
108 + 3x = 180
3x = 180 - 108
3x = 72
x = 72/3
x = 24
So, one angle = 2(24
= 48
The other angle is
x + 12 = 24 +12
= 36
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The complete question is:
One measure of an angle in a triangle is 96°. The other two angle measures are represented by 2x and x + 12. Determine the other two degree measures for the missing angles."
please help me asap plssss
Answer: 9
Step-by-step explanation: The number of sides that a regular polygon has can be determined by the measure of one of its exterior angles. A regular polygon is a polygon with sides of equal length and angles of equal measure.
The measure of one exterior angle of a regular polygon is equal to 360° divided by the number of sides of the polygon. Therefore, if one exterior angle of a regular polygon measures 40°, we can use the following equation to find the number of sides of the polygon:
exterior angle measure = 360° / number of sides
40° = 360° / number of sides
number of sides = 360° / 40°
number of sides = 9
Therefore, a regular polygon with one exterior angle measuring 40° has 9 sides.
what is the solution to the following equation
x2 + 3x + 7 = 0
Answer:
its C.
Step-by-step explanation:
The length of a rectangle is 2 meters longer than the width. If the area is 22 square meters, find the rectangle's
dimensions. Round to the nearest tenth of a meter.
Answer:
5.8x3.8
Step-by-step explanation:
x times (x+2) = 22
At higher altitudes, water boils at lower temperatures. This relationship between altitude and boiling point is linear. At an altitude of 1000 feet, water boils at 210 °F. At an altitude of 3000 feet, water boils at 206 °F. Use an equation in point-slope form to find the boiling point of water at an altitude of 6000 feet.
Answer: Water at sea level boils at a temperature of 212 degrees Fahrenheit. For every increase in altitude of 1000 feet, the boiling point drops by 1.8 degrees. Write a linear function that gives the boiling point of water as a function of the altitude. What is the boiling point of water at 15,000 feet?
Draw a chart with the column heading as follows
Step-by-step explanation:
If Z (4, 3) is translated to Z (2, 7), what is the translation?
Answer: Left 2, Up 4
Step-by-step explanation:
We see the x decrease by 2 from 4 to 2 so the translation is left 2, and the y increases by 4 from 3 to 7, so it is up 4!
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Which pairs of triangles are similar? check all that apply. △abc ~ △def △def ~ △ghi △ghi ~ △abc △ghi ~ △jkl △jkl ~ △abc
The pairs of triangles that are similar are △jkl ~ △abc and their corresponding angles are congruent.
The fact that, When two triangles are comparable, their corresponding sides have a proportional ratio and their corresponding angles have a congruent relationship.
In this issue
△jkl ~ △abc
Because the proportion between its corresponding sides
Verify
CA/LJ=BC/KL
replace the specified values
14/7=20/10
2=2 >>>>> is correct
so
The proportion between the corresponding sides is linear.
therefore △jkl ~ △abc are similar.
Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.
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Answer: b & e
Step-by-step explanation: cuz
In the figure below, points D, E, and F are the midpoints of the sides of ABC
Answer:
DF=28 AC=64 CF=32
Step-by-step explanation:
The horsepower (hp) that a shaft can safely transmit varies jointly with its speed (in revolutions per minute - rpm) and the cube of the diameter. if the shaft of a certain material 3 inches in diameter can transmit 45hp at 100 rpm, what must the diameter be in order to transmit 60hp at 150rpm?
The the diameter of the shaft is to be in order to transmit 60 hp at 150 rpm 1.88 inch.
Explain the term horsepower?Power is measured in hp, which is the standard abbreviation for horsepower. The rate of job completion can be used to describe power in this context. Most frequently, the term "horsepower" is used to describe an engine or motor's output.We must first obtain the formula for calculating horsepower.
The phrase to use is as follows:
hp = k × v × d³ ......eq(1)
Where:
hp is horsepowerv is speed (in rpm)d is diameterk is constant of horsepower.Since k is a constant, it will always have the same value when the shaft is transferring 60 horsepower at 150 rpm.
Therefore, using the first set of information, we can determine the value of k and subsequently the diameter.
When we solve for k in (1), we get:
k = hp / (v × d³)
Put the values;
k = 45 / (100 × 3³)
k = 0.02
Put the value of k and solve for diameter.
d = ∛hp / (k × v)
d = ∛60 / (150 × 0.06)
d = 1.88 inch
Thus, the the diameter of the shaft is to be in order to transmit 60 hp at 150 rpm 1.88 inch.
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need help as quickly as possible
The measure of the unknown angles in the kite are as follows;
x = 66 degreesy = 158 degreesHow to find the measure of a kite?A kite has two pairs of adjacent equal sides.
In other words, a kite is a quadrilateral that has 2 pairs of equal-length sides and these sides are adjacent to each other.
One pair of opposite angles is equal. Diagonals are perpendicular to each other.
A kite has four interior angles and the sum of these interior angles is 360°
Therefore, the measures of the
x = 66 degrees.
Let's find y.
y = 360 - 70 - 66 - 66
y = 158 degrees.
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the probability distribution function for the discrete random variable where x is equal to the number of red lights drivers typically run in a year is as follows. x 0 1 2 3 p(x) 0.72 0.11 0.02 (a) fill in the missing probability. x 0 1 2 3 p(x) 0.72 0.11 0.02 0.15 correct: your answer is correct. (b) what is the mean of this discrete random variable?
(a) The value of p(x) is 0.15 when x = 3.
(b) The mean of the discrete random variable is 0.1
What is meaning of discrete random variable?
A discrete random variable has a countable number of different possible values, such as 0,1,2,3,4, etc. Usually, but not always, discrete random variables are counts. A random variable is discrete if it can only take a finite number of different values.
Given table is
X 0 1 2 3
P(x) 0.72 0.11 0.02
The sum of the probability of an event is 1.
Therefore
P(0) + P(1) + P(2) + P(3) = 1
Putting the value of P(0), P(1), P(2)
0.72 + 0.11 + 0.02 + P(3) = 1
0.85 + P(3) = 1
P(3) = 1- 0.85
P(3) = 0 .15
The mean of the discreate random variable is Σ xp(x) / Σ x
=[(0 × P(0)) + (1 × P(1)) + (2 × P(2)) + (3 × P(3))]/(0 + 1 + 2 + 3)
= (0 + 0.11 + 0.04 + 0.45) / 6
= 0 .1
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