The range of the data set is, 28
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
The data set is,
74, 64, 90, 74, 92, 68, 71
Now, We know that;
Range of data set is calculating by subtracting the lowest value from highest value.
Hence, The range is,
⇒ Highest value - Lowest value
⇒ 92 - 64
⇒ 28
Thus, The value of range = 28
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The table shows the number of condo sales per month for a new building. Select all
the equations that could represent the number of sales,
Month
1
2
3
4
Sold
12
9
6
3
A. y 12-3(x-1)
B. y+6=-3(x+3)
C. y 12 = 3(x - 1)
Answer:
Option 1 and 5 will be your answer :)
Step-by-step explanation:
Let the equation representing number of sold is,
y - y' = m(x - x')
Where m = number of condo sold per month
(x', y') is a point from the given table,
Slope of line passing through two points and =
Slope of the passing through (1, 8) and (0, 11) will be,
m = = -3
Therefore, equation of the line passing through (3, 2) and slope (-3),
y - 2 = (-3)(x - 3)
y - 2 = -3(x - 3)
Similarly, equation of the line passing through (0, 1) and slope (-3),
y - 11 = -3(x - 0)
Therefore, Option (1) and (5) will be the answer.
There are 10 girls and 30 boys ina class find the ratio of
a. No of girls to no of boys
The ratio of girls to boys in the class is 1:3, meaning that for every one girl there are three boys.
There are 10 girls and 30 boys in the class.
The ratio of girls to boys can be expressed as a fraction: 10/30.
To make the fraction easier to understand, we can simplify it to its lowest form: 1/3.
The ratio of girls to boys in the class is therefore 1:3, meaning that for every one girl there are three boys.
The ratio of girls to boys in a class can be determined by dividing the number of girls by the number of boys. In this case, there are 10 girls and 30 boys, so the ratio is 10/30. This fraction can be simplified to its lowest form, 1/3. This means that for every one girl there are three boys in the class. Knowing the ratio of girls to boys can be helpful in a variety of situations, such as organizing activities or determining the number of supplies needed. This ratio can also be expressed as a percentage, with 10% of the class being girls and 30% being boys. Knowing the ratio of girls to boys can also be a useful tool in understanding the demographics of the class.
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The mean height of the students in Juan's math class is equal to the mean height of the students in his English class. However, while the standard deviation of the heights of students in his math class is 3.2 inches, the standard deviation of the heights of students in his English class is 6.1 inches. Which of the following statements must be true?
A) The mean height of the students in Juan's English class is 2.9 inches greater than the mean height of the students in his math class.
B) The median height of the students in Juan's English class is 2.9 inches greater than the median height of the students in his math class.
C) The median height of the students in Juan's math class is 2.9 inches greater than the median height of the students in his English class.
D) The heights of the students in Juan's math class are less variable than the heights of the students in his English class.
Answer: The statement "The mean height of the students in Juan's math class is equal to the mean height of the students in his English class" means that the center or average of both groups is the same. However, the statement "the standard deviation of the heights of students in his math class is 3.2 inches, the standard deviation of the heights of students in his English class is 6.1 inches" implies that the heights of the students in the English class are more spread out than the heights of the students in the math class.
Therefore, the answer is:
D) The heights of the students in Juan's math class are less variable than the heights of the students in his English class.
Step-by-step explanation:
For a game you roll a dice. If you get a 1-3 you get nothing.
If you get 4 or 5 you break even and if you roll a 6 you win
$20. If the game costs $5 to play what is the expected value
For a game you have a 15% chance to get nothing a 25%
Is that all of the question?
a tabular summary of a set of data showing the fraction of the total number of items in several classes is a group of answer choices cumulative relative frequency distribution. frequency distribution. relative frequency distribution. cumulative frequency distribution.
The cumulative relative frequency distribution is a useful tool for summarizing data and making comparisons between classes. It can also be used to make predictions about future data values.
A cumulative relative frequency distribution is a table that shows the cumulative relative frequency of a set of data. A cumulative relative frequency is the sum of all relative frequencies up to a certain point in the data set. For example, if the first three entries in a data set are 20, 30, and 10, the cumulative relative frequency of the first entry would be 0.2, the cumulative relative frequency of the second entry would be 0.5, and the cumulative relative frequency of the third entry would be 1.0.
In a cumulative relative frequency distribution, the data is organized into classes, and each class has a relative frequency associated with it. The relative frequency is the fraction of the total number of items in the class compared to the total number of items in the data set. The cumulative relative frequency is the sum of the relative frequencies of all the classes up to that point.
For example, if there are five classes in a data set, the cumulative relative frequency of the first class would be the relative frequency of the first class. The cumulative relative frequency of the second class would be the sum of the relative frequencies of the first and second classes, and so on.
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hospital records show that 12% of all patients are admitted for heart disease, 16% are admitted for cancer (oncology) treatment, and 4% receive both coronary and oncology care. what is the probability that a randomly selected patient is admitted for coronary care, oncology or both? (note that heart disease is a coronary care issue.)
The probability of randomly selected patient selected for coronary, oncology or both is equal to P( H∪C ) = 0.24.
Let patient admitted with heart disease represented by P(H)
P(H) = 12%
= 0.12
And patient admitted for cancer disease represented by P(C)
P(H) = 16%
= 0.16
Percent of patient received both coronary and oncology = 4%
P( H∩C ) = 0.04
Probability of randomly selected patient admitted for coronary, oncology or both is :
P( H∪C ) = P(H) + P(C) - P(H∩C )
⇒P( H∪C ) = 0.12 + 0.16 - 0.04
⇒ P( H∪C ) = 0.24
Therefore, the probability of randomly selected patient getting treatment for coronary, oncology or both is given by P( H∪C ) = 0.24.
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pls im not understanding anything and its a test
Melitha would like to purchase a music system worth of R12 000.And she is offered an interest rate of 7.5 p.a on a hire purchase agreement.The terms or the agreement on the loan are that 10% deposit is paid initially and the loan will be paid back monthly over a period of 3 years.
a.Calculate the cash deposit Melitha paid.
b.Calculate how much Melitha will have to pay over 3 years.
c.Calculate the monthly installment which Melitha will have to make.
d.What is the total amount that Melitha paid for the music system?
a) The cash deposit (down payment) that Melitha paid is R1,200.
b) The total amount (sum of periodic payments) that Melitha paid over 3 years is R12,094.20.
c) The monthly installment Melitha made is R335.95.
d) The total amount that Melitha paid for the music system is R13,294.20, including the total installments and initial deposit.
What is the down payment?The down payment is the initial cash deposit made for the purchase of an item on credit.
The down payment provides financial evidence of the transaction and testifies about the borrower's ability to undertake the credit arrangement.
a) Cash deposit = R1,200 (R12,000 x 10%)
N (# of periods) = 36 months
I/Y (Interest per year) = 7.5%
PV (Present Value) = R10,800 (R12,000 - R1,200)
FV (Future Value) = R0
Results:
Monthly Payment (PMT) = R335.95
Sum of all periodic payments = R12,094.20
Total Interest = R1,294.20
Total amount paid for the music system = R13,294.20 (R1,200 + R12,094.20)
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How would you check values for x and y after solving linear equations in x and y?
Answers:
1. substitute the x and y values into the original equations
2. divide the x and y values into the original equations
3. cross-multiply the x and y values by the original equations
4. subtract the x and y values from the original equations
How many solutions does the system have?
O One solution at (0,-4)
O One solution at (-3,0)
O No solution
O Infinitely many solutions
The system of equations has infinite solutions.
How to solve thisGiven:
y = -6x +2
-12x - 2y= -4
To solve for Equation 2,
The value of y is already given in equation 1,
Thus,
substituting the value of y in equation 2,
-12x -2(-6x +2) = -4
-12x - 12x = -4 +4
0=0
The solution of the two equations is 0. Also, we can see that both equations are in ratio.
Further, the image also shows that the line of the two equations are coinciding.
Hence, the system of equations has infinite solutions.
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How many solutions does this linear system have?
y = -6x +2
-12x - 2y= -4
one solution: (0, 0) one solution: (1, –4) no solution infinite number of solutions.
-Identity the measures of the reference angle for 521°.
-Identify the measure of the largest negative angle co-terminal with 521°
The reference angle would be 155 degrees.
What is reference angle?An angle's reference angle is the measure of the smallest, positive, acute angle formed by the terminal side of the angle and the horizontal axis.
The positive reference angles have terminal sides that lie in the first quadrant and can be used as models for angles in other quadrants.
The reference angle is acute angle, it must be < 90°.
The terminal side lies in Quadrant II.
The positive measure is:
=180-25
=155°.
And the negative measure is:
= 155-360
= -205°.
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The altitude of an airplane is represented by the equation shown below, where Y represents the altitude, in feet, of the airplane and x represents the number of minutes the airplane has been descending:
Y = 1025x + 24,600
Part A: Create a table for the values when x = 0, 5, 8, 10, 30.
Include worked-out equations used to identify the values within the table.
Part B: Identify the altitude after 5 minutes and after 30 minutes. Use 1-2 sentences to explain the altitude at these two times and describe what is happening to the airplane at these time intervals.
The way the altitude changes is 24,600 (0 minutes), 19,475 (5 minutes), 16,400 (8 minutes), 14,350(10 minutes), and 6,150 (30 minutes).
How does the altitude change over time?To calculate the change in the altitude, let's use the formula given:
0 minutes:
Y = - 1025 x 0+ 24,600
Y = 24,600
5 minutes:
Y = - 1025 x 5+ 24,600
Y = -5125 + 24, 600
Y = 19,475
8 minutes:
Y = - 1025 x 8+ 24,600
Y = -8200 + 24, 600
Y = 16,400
10 minutes:
Y = - 1025 x 10+ 24,600
Y = -10250 + 24, 600
Y = 14,350
30 minutes:
Y = - 1025 x 30+ 24,600
Y = -30,750 + 24, 600
Y = 6,150
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If you double the down payment what happens to the total cost and payment of the vehicle? What two ways can you lower your monthly payment?
Doubling the down payment reduces the total cost of the vehicle, and increasing the down payment or extending the loan term are two ways to lower the monthly payment.
Let's assume that you're planning to buy a car worth $20,000. The down payment is the initial amount you pay towards the purchase of the car, and it is usually expressed as a percentage of the total cost of the car. Let's assume that the down payment is 10% of the total cost, which means you have to pay $2,000 initially.
If you double the down payment from 10% to 20%, you will have to pay $4,000 initially. This means that the amount you borrow from the bank to buy the car will be reduced. As a result, the total cost of the vehicle will decrease because the interest on the loan will also decrease.
Now, let's move on to ways to lower your monthly payment.
Increase the down payment: As we discussed earlier, making a higher down payment reduces the loan amount, which, in turn, reduces the monthly payment. So, if you can increase the down payment, you can lower the monthly payment.
Increase the loan term: The loan term is the length of time you have to repay the loan. If you extend the loan term, the monthly payment will be lower. However, keep in mind that a longer loan term means you'll end up paying more interest over the life of the loan, which will increase the total cost of the vehicle.
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Hi can someone please help this is due tonight.
a. It is not specified in the given information what the total number of seniors at Lewis High is, so it is not possible to directly compare the number of seniors who apply for college to the number of seniors at Lewis High.
How to explain the informationb. The same issue applies to this question as well. It is not specified what the total number of seniors at Lewis High is, so it is not possible to directly compare the number of seniors who apply for college with those who don't.
c. If two out of every three seniors at Lewis High apply for college, then one out of every three seniors does not. Therefore, the fraction of graduating seniors at Lewis High who do not apply to college is 1/3.
d. If three out of every five seniors at Lewis High who apply for college are female students, then two out of every five are male students. Therefore, the fraction of seniors who are males who apply for college is 2/5. Again, without knowing the total number of graduating seniors at Lewis High, it is not possible to directly compare the number of males who apply for college with the number of graduating seniors.
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Two of every 3 seniors at Lewis High apply for college. Three of every 5 seniors at Lewis High who apply for college are female students.yout
a. How does the number of seniors who apply for college compare to the number of seniors at Lewis High?
b. How does the number of seniors who apply for college compare to those who don't?
c. What fraction of the graduating seniors at Lewis High do not apply to college?
d. What fraction of the seniors are males who apply for college? How does the number of males who apply for college compare with the number of graduating seniors?
HELP!!
A plane left Kennedy Airport on Tuesday morning for a 730-mile, 6-hour trip. For the first part of the trip, the average speed was 115 mph. For the remainder of the trip, the average speed was 125 mph. How long did the plane fly at each speed?
A. First part of trip: __ h
B. Second part of trip: __ h
The first part of the trip took approximately 6.39 hours and the second part of the trip took approximately 5.84 hours.
Solving for Time and Average Speed in a Two-Part Plane TripIn this problem, we are given the distance, total time, and average speeds for two parts of a plane trip.
Using the formula for average speed
Distance = average speed x time,
We can set up two equations and solve for the times spent flying at each speed.
We define t₁ as the time spent flying at 115 mph and t₂ as the time spent flying at 125 mph.
From the equation
730 miles = 115 mph x t₁,
we solve for t₁ and get
t₁ = 6.391304347826087 hours.
Similarly, from the equation
730 miles = 125 mph x t₂,
we solve for t₂ and get
t₂ = 5.84 hours.
Therefore, the plane flew at an average speed of 115 mph for approximately 6.39 hours and at an average speed of 125 mph for approximately 5.84 hours.
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Your friend hides a dollar bill under one of three plastic cups. Under the other
two cups is a paper clip. You get to keep whatever is under the cup you
choose, but you don't know which contains the dollar bill. After you choose,
your friend lifts one of the other cups to reveal a paper clip and then gives you
the option of changing your choice.
Should you switch to the other cup?
A. No. The probability of winning the dollar is regardless of the cup
your choose.
B. Yes. If you switch cups, the probability of winning the dollar
increases from to 1/1.
OC. Yes. If you switch cups, the probability of winning the dollar is 3.
D. No. If you switch cups, the probability of winning the dollar is.
Answer: B
Step-by-step explanation:
if you multiply the left side of an equation by 4, what must you multiply the right side of the equation by? 3
If you multiply the left side of an equation by 4, what must you multiply the right side of the equation by 4
Here you you multiply the left side of an equation by 4.
According to the solving for unknow rule you must perform same function to both side of the equation. If you multiply the left side of an equation by any integer then you must multiply the same integer on right hand side of the equation
To maintain equality, you must multiply the right side of the equation by 4 as well.
This is because the left side of the equation represents the same quantity as the right side, so any operation that is performed on one side must also be performed on the other side to preserve the equality.
Therefore, you must multiply the right side of the equation by 4
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Transcribed image text: T8.7 A marketing assistant for a technology firm plans to randomly select 1000 customers to estimate the pro- portion who are satisfied with the firm's performance. Based on the results of the survey, the assistant will construct a 95% confidence interval for the propor- tion of all customers who are satisfied. The market- ing manager, however, says that the firm can afford to survey only 250 customers. How will this decrease in sample size affect the margin of error? (a) The margin of error will be about 4 times larger. (b) The margin of error will be about 2 times larger. (c) The margin of error will be about the same size. (d) The margin of error will be about half as large. (e) The margin of error will be about one-fourth as large. T8.8 Thirty-five people from a random sample of 125 work- ers from Company A admitted to using sick leave when they weren't really ill. Seventeen employees
The answer is (b) The margin of error will be about 2 times larger.
The margin of error in a confidence interval is affected by the sample size, so decreasing the sample size will generally increase the margin of error. Specifically, the margin of error is inversely proportional to the square root of the sample size.
That is, if we reduce the sample size by a factor of k, then the margin of error will increase by a factor of sqrt(k).
In this case, the original sample size was 1000, and the proposed sample size is 250, which is 1/4 of the original size. Therefore, the margin of error for the smaller sample will be:
sqrt(1000/250) times the original margin of error.
Simplifying this expression, we get:
sqrt(4) times the original margin of error.
So the margin of error for the smaller sample will be about 2 times the original margin of error.
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Help im having trouble
Answer:
3 square units
Step-by-step explanation:
You want the area of the triangle defined by the points (-1, -4), (0, -2), and (2, -4).
TriangleThe plot of the grid points and the triangle is attached. By counting grid squares, you can see that the base of the triangle is 3 units, and its heigh perpendicular to the base is 2 units.
AreaThe area formula for a triangle is ...
A = 1/2bh
For base b=3 and height h=2, the area is ...
A = 1/2(3)(2) = 3 . . . . . square units
The area of the triangle is 3 square units.
Simplify √, where a20.
Which expression is equivalent to √√a²?
O
O
O
DONE
a².aº
aª.a
a³ a
a a
The expression √a²√a² when simplified is (d) a * a
How to simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
√a²√a²
Express as product expression
So, we have the following representation
√a²√a² = √a² *√a²
Evaluate the exponents
This gives
√a²√a² = a * a
Hence, the expression is (d) a * a
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Complete question
Simplify √a²√a²
Which expression is equivalent to √a²√a²
a².aº
aª.a
a³ a
a a
Someone help me please
Answer:
Area = 4
Step-by-step explanation:
Russell surveyed 16 students at his school and found that 4 of them planned to take orchestra as their next elective. If Russell surveys 12 more students, how many of them are probably planning on taking orchestra as an elective, based on past data?
Answer:
3 students are probably planning on taking orchestra as their next elective.
Step-by-step explanation:
Russell's results of the 16 surveyed students tells us that (4/16), or 25%, of the students planned on taking orchestra as their next elective. If we assume this sampling is valid for other students (i.e., the sampled students were chosen at random and are believed to be representative of the rest of the students), we may use the same percentage for the next 12 students:
(12 students)*(25%) = 3 students are probably planning on taking orchestra as an elective.
A group of hikers walked from Hawk Mt. Shelter to Blood Mt. Shelter along the Appalachian Trail, a total distance of 20.5 mi. It took 2 days for the walk. On the second day, the hikers walked 4.1 mi less than they did on the first day. How far did they walk each day?
They walked 12.3 miles on first day and 8.2 miles on second day. The solution has been obtained by using linear equation.
What is a linear equation?
The linear equation with this degree of one is the largest. This shows that linear equations with exponents greater than one have no variables. Such an equation gives rise to a straight line on the graph.
We are given that a group of hikers walked from Hawk Mt. Shelter to Blood Mt. Shelter along the Appalachian Trail, a total distance of 20.5 mi which took them 2 days.
Let the distance traveled on first day be 'x'.
Since, on the second day, the hikers walked 4.1 mi less than they did on the first day so,
Distance traveled on second day = (x - 4.1)
From this, we get a linear equation as
⇒x + (x - 4.1) = 20.5
⇒2x - 4.1 = 20.5
⇒2x = 24.6
⇒x = 12.3
So, (x - 4.1) = 12.3 - 4.1 = 8.2 miles
Hence, they walked 12.3 miles on first day and 8.2 miles on second day.
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Scatter plot 8 grades, help please!!!
Answer:
Step-by-step explanation:
go up to the 85 on the grade track that over until you meet the dot.
that dot says it would be 3 hours
What are the names of these polygons?
a)
b)
c)
D)
Answer:
b) octogon
c) irregular pentagon
d) irregular hexagon
Step-by-step explanation:
through: (0,-5) and (-2,-3)
The equation of the linear function is y = x - 5
How to determin the equation of the linear functionFrom the question, we have the following parameters that can be used in our computation:
The ordered pairs (0,-5) and (-2,-3)
A linear equation is represented as
y = mx + c
Where
c = y when x = 0
This means that
y = mx - 5
Using the other point (-2, -3), we have
-2m - 5 = -3
Evaluate the like terms
-2m = 2
Divide by 2
m = 1
Substitute the known values in the above equation, so, we have the following representation
y = x - 5
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Complete question
Find the equation of the linear function represented by the line that goes through: (0,-5) and (-2,-3) in slope-intercept form.
y = ___?___
How would you
write the name of a segment differently than the name of a line? What
symbols would you use?
The primary difference between writing the name of a segment and the name of a line is the use of symbols.
What is symbol?A symbol is an object, image, or action that stands for or represents something else. Symbols can be used to convey a wide variety of ideas and concepts, from the literal, such as a heart to represent love, to the abstract, such as a peace sign to represent a call for world peace. Symbols are often used to communicate complex ideas quickly and easily.
To denote a segment, a line is usually written with two arrows pointing in opposite directions, such as ↔. To denote a line, the line is usually written with a single arrow pointing in one direction, such as →.
For example, if you were writing the name of a segment called "AB", then you would use the symbol ↔ AB. If you were writing the name of a line called "AB", then you would use the symbol → AB.
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The area of the floor is (x2-169) sq units. Find the width of the floor if the length is (x - 13) units.
The width of the floor if the length is (x - 13) units is (x+13) units.
What is Area of Rectangle?The area of Rectangle is length times of width.
Given that area of the floor is (x²-169) sq units.
We have to find the width of the floor when length is (x - 13) units.
Area=Length×Width
x²-169=(x-13)width
We know that (a²-b²)=(a+b)(a-b)
(x-13)(x+13)=x-13width
Divide both sides by (x-13)
x+13=width
Hence, the width of the floor if the length is (x - 13) units is (x+13) units.
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Which of the following is equal to √16 x 4
A. √16 x √4
B. 32
C. √16/4
D. 64
Answer:
None
Step-by-step explanation:
Let's clarify that a radical symbol beside a number means what number squared (or to the power of 2) can give me the number in the symbol.
In this case it would be 4 because
[tex]4*4=16[/tex]
A method I use is to find the square root is dividing the number in the radical symbol 2 times
First by the original number, and then by the product of the last equation. It will not always work, but it works in some cases like this one.
[tex]\frac{16}{2} = 8\\ \\\frac{8}{2}=4\\ \\\sqrt{16}=4[/tex]
Second step, multiply 4 by 4, which equals 16.
Since the square root of 16 is 4, you can substitute 4 in the rest of the equations instead of the radical expression.
None of the following equations equal 16, which means none of the following equations if equal to [tex]\sqrt{16} *4[/tex]
Perform the operation and simplify the resulting fraction: 7/3a - 8/5 + 4/15a
After solving the given expression 7/3a - 8/5 + 4/15a, the resultant answer is fractions is 39/15a - 8/5.
What are fractions?A fraction in mathematics is a number that is stated as a percentage, such as 1/2 or 2/3.
The number on top denotes the component of the unit under consideration, while the number at the bottom indicates the total number of parts that make up one unit.
An element of a whole is a fraction.
The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction.
A fraction appears in the numerator or denominator of a complex fraction.
So, we have the operations:
7/3a - 8/5 + 4/15a
Now, solve as follows:
7/3a - 8/5 + 4/15a
7/3a + 4/15a - 8/5
7*5 + 4 /15a - 8/5
39/15a - 8/5
Therefore, after solving the given expression 7/3a - 8/5 + 4/15a, the resultant answer is fractions is 39/15a - 8/5.
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