The rate is the distance from the other line changing at that moment will be negative 1.5 units per minute.
What is differentiation?The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decrease.
A point moves in the plane of two opposite lines so the result of its good ways from the lines forever is 12 when the fact of the matter is 4 units from one of the lines, its separation from that line is diminishing at the pace of 2 units/min.
Let the coordinate of the pointe be (x, y). Then the function is given as,
[√(x- 0)²] [√(y - 0)²] = 12
[√x²] [√y²] = 12
x y = 12
At x = 4, the value of the variable 'y' is given as,
4y = 12
y = 3
Differentiate the function with respect to time, then we have
xy' + yx' = 0
4 × y' + 3 × 2 = 0
y' = - 6 / 4
y' = - 1.5 units per minute
The rate is the distance from the other line changing at that moment will be negative 1.5 units per minute.
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In 2 minutes, a conveyor belt moves 200 pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt moves the same quantity of cans the same distance in 3 minutes. If both
belts are used, find how long it takes to move the cans to the storage area.
The conveyor belts can move the 200 pounds of recyclable aluminum from the delivery truck to a storage area in minutes
It takes approximately 1.2 minutes to move the cans to the storage area when both conveyor belts are used.
We can begin the problem by using the formula:
work = rate x time
Let's denote the rate of the first belt as R1 and the rate of the second belt as R2. Then, we can write:
R1 = 200 pounds / 2 minutes = 100 pounds per minute
R2 = 200 pounds / 3 minutes ≈ 66.67 pounds per minute
When both belts are used, they work together to move the same 200 pounds of cans. Therefore, we can add their rates to get the total rate:
R = R1 + R2 = 100 + 66.67 = 166.67 pounds per minute
To find the time it takes to move the cans to the storage area, we can rearrange the formula:
time = work / rate
The total work is 200 pounds, so we have:
time = 200 pounds / 166.67 pounds per minute ≈ 1.2 minutes
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The volume of the cylinder is 235.6 cubic feet. Find the height. Round your answer to the nearest whole number.
Answer: 3 feet
Step-by-step explanation:
Here's the complete question:
The volume of the cylinder is 235.6 cubic feet the radius is 5ft. Find the height.
Note that Volume of a cylinder = πr²h
where Volume = 235.6 feet³
Radius = 5 feet
Height = Unknown
Then, we put the values back into the question and this will be:
V = πr²h
235.6 = 3.14 × 5² × h
235.6 = 3.14 × 25 × h
235.6 = 78.5 × h
h = 235.6 / 78.5
h = 3 feet
The height is 3 feet
select all that apply what statements below describe the relative use of dot plots and histograms? select all that apply. multiple select question. dot plots show the relative frequency of data values. histograms are easier to construct. histograms are more useful for large data sets. dot plots are most useful for small data sets.
The statements that apply to the relative use of dot plots and histograms are Dot plots show the relative frequency of data values and Dot plots are most useful for small data sets.
1. Dot plots are a graphical representation of data that show the relative frequency of data values. Each dot in a dot plot represents one data point, and the position of the dot on the axis represents the value of the data point. Histograms, on the other hand, show the frequency distribution of data values in a bar graph format.
2. Dot plots are most useful for small data sets because they allow for the easy visualization of individual data points and their distribution. Histograms, on the other hand, are more useful for large data sets as they provide a summary of the data distribution in a more concise manner. Dot plots can become cluttered and difficult to read when used with large data sets.
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Which of the binomials below is a factor of this trinomial?
x² + 3x - 4
A. X-4
B. x^2+ 4
C. X+4
D. X + 8
Can anyone help please and thanks
Answer:
7.02 ft
Step-by-step explanation:
Tan=opposite/adjacent
Tan(78)=x/33X×Tan(78)=334.70x=33do 33 divided by 4.70then you'll get 7.02 if your calculator is on Radian in modeAnswer:
7.02 ft
hi
your welcome have a good
day
Step-by-step explanation:
Irma is just learning to play the Happy Fairies video game. In the game, players gain and lose points based on how well they take care of the fairies in their fairy gardens. Irma had a total of
–
5 points. Then, her fairy house fell over in the wind and she got
–
3 points.
How many total points does Irma have now?
points
If Irma is just learning to play the Happy Fairies video game and her fairy house fell over in the wind and she got –3 points. The number of total points that Irma have now is -8 points.
How to find the total point?Using this formula to determine the total points
Total points = Irma total point + Point gotten after her fairy house fell over
Where:
Irma total point = -5
Point gotten after her fairy house fell over = -3
Let plug in the formula
Total points = -5 + (-3)
Total points = -8
Therefore we can conclude that her total points is -8.
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A well, whose diameter is 3 m, has been dug 21 m deep and the earth dug out is used to form an embankment 4 m wide around it. Find the height of the embankment.
Answer:
31.875 m
Step-by-step explanation:
We can begin solving the problem by using the formula for the volume of a cylinder and the volume of a cone.
The volume of the well is given by the formula for the volume of a cylinder:
V = πr^2h
where r is the radius of the well (half the diameter, which is 3/2 = 1.5 m) and h is the depth of the well (21 m).
V = π(1.5)^2(21) = 42.5π m^3
The embankment is formed by the earth that was dug out of the well, and it has the shape of a cone. The volume of the cone is given by the formula:
V = 1/3 πr^2h
where r is the radius of the base of the cone (4 m) and h is the height of the embankment.
V = 1/3π(4)^2h = 4/3πh m^3
Now we know that the volume of the embankment is equal to the volume of the well:
V = 42.5π m^3 = 4/3πh m^3
Then we can solve for h by dividing both sides by 4/3π:
h = 42.5π m^3 * 3/4π = 31.875 m
So the height of the embankment is 31.875 m.
If Q(t)= C/4t - 1 an equation for Q-¹(t) is
If Q(t)= C/4t - 1 an equation for Q-¹(t) is y = C + t/4t.
Define equation.A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.
Given,
Q(t) = C/4t -1
Put a "y" in place of the "Q(t)":
y = C/4t -1
Change the t and y since each (t, y) has a corresponding (y, t) companion.
t = C/4y -1
Distribute t by multiplying into the bracket to find y.
t × 4y -1 = C
t × 4y - t = C
Add both sides of the equation together now.
t × 4y = C +t
4t divided by both sides
y = C + t/4t
If Q(t)= C/4t - 1 an equation for Q-¹(t) is y = C + t/4t.
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A candy store sells caramels and milk chocolate by the pound. The table below shows the total cost, in dollars, for a pound of each type of candy the store sells.
Type of Candy Price per pound (dollars)
Caramels $9.28
Milk Chocolate $12.80
How much more is the cost for 1 3/4 pounds of milk chocolate than the cost for 1 3/4 pounds of caramel?
The cost for \(1\frac{3}{4}\) pounds of milk chocolate is $ 6.16 more than the cost for \(1\frac{3}{4}\) pounds of caramels.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The cost of each pounds of Caramels = $ 9.28,
So, the cost of \(1\frac{3}{4}\) pounds of caramels = \(1\frac{3}{4}\)×9.28
=7/4×9.28=$16.24
The cost of each pounds of milk chocolate = $ 12.80
So, the cost of \(1\frac{3}{4}\) pounds of milk chocolate = \(1\frac{3}{4}\) ×12.8
=$22.24
∵ 22.4 > 16.24,
the cost of \(1\frac{3}{4}\) pounds of milk chocolate > The cost of \(1\frac{3}{4}\)pounds of caramels
22.4-16.24=6.16
Hence, the cost for \(1\frac{3}{4}\) pounds of milk chocolate is $ 6.16 more than the cost for \(1\frac{3}{4}\) pounds of caramels.
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Find the volume of a right circular cone that has a height of 17.7 cm and a base with a diameter of 15.8 cm. Round your answer to the nearest tenth of a cubic centimeter.
Answer:
\(1156.8cm^3\)
Step-by-step explanation:
The volume of a cone is given as:
\(V =\frac{1}{3} \pi r^2h\)
where r = radius
h = height of cone
The height of the cone is 17.7 cm and its base radius is 7.9 cm (diameter is 15.8 cm).
Its volume is:
\(V = \frac{1}{3} * \pi = 7.9^2 * 17.7\\ \\V = 1156.8cm^3\)
Answer:
1157.3cm^3
Step-by-step explanation:
voume of a cone =V=πr^2h^3
Diameter = 15.8cm
Height = 17.7cm
Radius = diameter/2
= 15.8/2 = 7.9cm
Pi = 22/7
V = 22/7 ×7.9×7.9×17.7/3
= 22/7×62.41×5.9
V = 1157.25cm^3
Hence the volume of the cone is 1157.3cm^3
to the nearest 10th
What is the surface area of the right cylinder below?A. 509 sq. unitsB. 72 sq. unitsC. 113 sq. unitsD. 622 sq. units
The surface area of a cylinder is found using the following formula:
\(SA=2\pi r^2+2\pi rh\)Replace for the given values of radius and height:
\(\begin{gathered} SA=2\pi(9)^2+2\pi(9)(2) \\ SA=2\pi(81)+2\pi(18) \\ SA=622 \end{gathered}\)It means that the surface area of the cylinder is 622.
The correct answer is D. 622 sq units.
calculate the coefficient of variation for a sample of cereal boxes with a mean weight of 340 grams and a standard deviation of 5.2 grams.? 0.15% A
1.53% B
15.29% C
0.65% D
The coefficient of variation (CV) is a measure of relative variability and is calculated by dividing the standard deviation by the mean, and then multiplying by 100 to express it as a percentage.
In this case, the mean weight is 340 grams, and the standard deviation is 5.2 grams.
CV = (Standard Deviation / Mean) * 100
CV = (5.2 / 340) * 100
CV ≈ 1.53%
Therefore, the correct answer is option B: 1.53%.
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severe difficulty in making mathematical calculations as a result of a brain disorder
Dyscalculia is a learning disorder that affects a person’s ability to do the math.
A learning problem called dyscalculia diminishes a person's capacity for math. Similar to how dyslexia impairs reading-related brain regions, dyscalculia interferes with the knowledge and skills connected to math and numbers. Although dyscalculia often first manifests in childhood, it can even affect adults who are unaware of it.
The signs of this condition typically emerge in childhood, particularly as kids start to master the fundamentals of math. However, many adults who suffer from dyscalculia are unaware of it. When forced to do the math, people with dyscalculia frequently experience mental health problems like anxiety, depression, and other distressing emotions.
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Find the measure of indicated unknown angle
Answer:
60
Step-by-step explanation:
90÷2=45
45+75+m=180(sum of triangle)
120+m =180
m=180-120
m=60
Let the students decide which study location best fits their learning style. This design will enable researchers to determine what type of learner works best in which environment. The researcher should try to match the 2 groups to be as alike as possible on all characteristics that might be relevant to study success so the each group would have the same distribution of GPA's, ACT's, socioeconomic background's etc. The researchers should decide study locations in the best interest of each student.
Required:
Use an objective chance procedure (like flipping a fair coin) to decide study locations.
In order to decide the best study locations, the researchers must determine which study location is the most suitable for each student. This ensures that students are able to learn effectively and have the best chance of succeeding.
A randomized study location experiment will help researchers find out which study locations are best suited to each type of learner.
To decide study locations, the researcher should use an objective chance procedure, such as flipping a fair coin. The objective chance procedure will guarantee that each student has an equal chance of being assigned to a specific study location.
The researcher should ensure that both groups are matched as closely as possible in terms of characteristics that may be relevant to study success, such as ACT scores, GPAs, and socioeconomic backgrounds.
This guarantees that any variations in academic performance between the two groups are most likely due to differences in the study location and not to other external factors.
Therefore in order to decide the best study locations, the researchers must determine which study location is the most suitable for each student. This ensures that students are able to learn effectively and have the best chance of succeeding.
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give two examples of each of linear equations
Answer:
(2x + 5)/(x + 4) = 1
and
6x - 19 = 3x - 10
Step-by-step explanation
Linear euqations are the equation for the straight line. When graphed both equations will be straight lines.
Hope this helps you!
If y varies directly as x, and y= 12 when x = 4, what is y when x = 8?
Answer:
24 !!
Step-by-step explanation:
Simple, x got doubled, and since y varies directly as x, 12 doubled = 24. I hope this helps!!!
The given forecast errors of 5, 0, -4 and 3, what is the mean absolute deviation:
A). 4
B). 3
C). 2.5
D). 2
E). 1
The mean absolute deviation of the given forecast errors of 5, 0, -4 and 3 is 3. The correct option is B.
The mean absolute deviation of the given forecast errors is 3 and can be found by following these steps:
1. Find the mean of the data set by adding all the values and dividing by the number of values. In this case, the mean is (5 + 0 + -4 + 3) / 4 = 1.
2. Find the absolute deviation of each value by subtracting the mean from each value and taking the absolute value. The absolute deviations are |5 - 1| = 4, |0 - 1| = 1, |-4 - 1| = 5, and |3 - 1| = 2.
3. Find the mean of the absolute deviations by adding them and dividing by the number of values. The mean absolute deviation is (4 + 1 + 5 + 2) / 4 = 3.
Therefore, the correct answer is B). 3. The mean absolute deviation of the given forecast errors is 3.
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Round 576.558 to the nearest tenths place
Answer:
576.6
(look at the number by the 10th place and round)
The value of 576.558 after rounding to the nearest tenth-place value is
576.6.
Option A is the correct answer.
What is place value?The place value of a number is given as:
Example:
1234.567
1 = thousand place value
2 = hundred place value
3 = tens place value
4 = ones place value
5 = tenths place value
6 = hundredths place value
7 = thousandths place value
We have,
576.558
The number in the tenth place is 5 bolded underscore.
576.558
Now,
The next value is 5 which is greater or equal to 5 so we will change the tenth place value 5 into 6.
If the next value was 4 or less we will keep the tenth place value 5 as 5.
Now,
The value of 576.558 after rounding to the nearest tenth-place value is
576.6.
Thus,
The value of 576.558 after rounding to the nearest tenth-place value is
576.6.
Option A is the correct answer.
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When examining the statistical validity of a frequency claim, one should look for the?
When examining the statistical validity of a frequency claim, one should look for the margin of error estimate.
What is statistical validity?
Statistical validity is defined as a procedure or an extent of drawing conclusions to which research works or studies can be considered precise and accurate which are derived from the already existing or reliable statistical tests.
It can also be the statistics which are derived from the research works or studies.
What is frequency in statistics?
Frequency in statistics can be defined as the number of times an observation or a record or a value occurred in the duration of the research work. The frequencies of different records are represented in a tabular form.
For a given set of data the frequency can either be 0 or more than that.
Frequency of a given record or an observation cannot be negative as the least number of times the instance of an object can appear is zero.
What is margin of error estimate?
The margin of error estimate is a percentage figure which can be some percentage more or less than the actual or ideal value.
The margin of error is the range of values greater or lesser than the sample outcome statistic in the accuracy or confidence region or the interval.
Hence, when examining the statistical validity of a frequency claim, one should look for the margin of error estimate.
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Ricardo makes a tessellation using the trapezoid shown. This
trapezoid has two right angles. What is the measure of each
angle with vertex A?
Tell how you can represent and connect ideas about
angle measure.
I can use objects and drawings to model the problem.
.
. I can write an equation to solve the problem.
.
I can use drawings, objects, or tools to support my results.
Use equations to solve the problem. Then use another
method to support your answer.
Eight same-size angles are arranged around point A. The sum
of their measures is 360°, and 360° +8= 45°. So, each angle
measures 45°.
I can also use a protractor to measure one of the acute angles.
Represent Problems
in Multiple Ways
Represent and Connect
Use the tessellation shown above. What is the measure of each obtuse
angle with vertex B?
1. What is the sum of the measures of the angles arranged around point B?
2. What is the sum of the measures of just the two obtuse angles arranged
around point B? Explain.
3. What is the measure of each obtuse angle? What method did you use
to find the answer?
This cοnfirms that each οbtuse angle measures 135°, since their sum is equal tο the remaining part οf the 360° angle.
The sum οf the measures οf the angles arranged arοund pοint B is 360°. the twο acute angles and the twο οbtuse angles must add up tο 360°, and we knοw the measure οf the acute angles, sο we can subtract their sum frοm 360° tο find the sum οf the twο οbtuse angles. Prοtractοr cοnfirms that each οbtuse angle measures 135°, since their sum is equal tο the remaining part οf the 360° angle.
1. The sum οf the measures οf the angles arranged arοund pοint B is 360°.
2. There are fοur angles arranged arοund pοint B, and twο οf them are acute angles with a measure οf 45° each (since the trapezοid has twο right angles). Therefοre, the sum οf the measures οf just the twο οbtuse angles arranged arοund pοint B is:
360° - 2(45°) = 270°
This is because the twο acute angles and the twο οbtuse angles must add up tο 360°, and we knοw the measure οf the acute angles, sο we can subtract their sum frοm 360° tο find the sum οf the twο οbtuse angles.
3. Tο find the measure οf each οbtuse angle, we can divide the sum οf their measures (270°) by the number οf angles (2):
270° ÷ 2 = 135°
Therefοre, each οbtuse angle with vertex B measures 135°.
We cοuld alsο use a prοtractοr tο measure οne οf the οbtuse angles directly and cοnfirm that it measures 135°, οr we cοuld use the fact that the sum οf the measures οf all fοur angles arοund pοint B must be 360° tο check οur answer:
= 2(45°) + 2(135°)
= 90° + 270°
= 360°
Therefοre, This cοnfirms that each οbtuse angle measures 135°, since their sum is equal tο the remaining part οf the 360° angle.
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What is the value of x in the triangle?
Answer: \(D. 6\sqrt{x} 2\) is the answer
Step-by-step explanation:
Your friend says that the table represents an exponential function because y is multiplied by a constant factor. Is your friend correct? Explain.
A.Yes. Because y is multiplied by a constant factor, the function is exponential.
B.Yes. Because y increases by greater amounts as x increases, the function is exponential.
C.No; Because y is multiplied by a constant factor, the function is not exponential.
D. No; Because x increases by different amounts, the function is not exponential.
x: 0,1,3,6
y: 2,10,50,250
Answer:
C.No; Because y is multiplied by a constant factor, the function is not exponential.
Step-by-step explanation:
For a set of number to be exponential, there is need for it to show a logical increase of a given time frame when the set of number is multiplied by a constant factor. In the table given, though the Y function is multiplied by a constant factor, the increase of the function is irregular so therefore cannot be said to be exponential.
HELP
Can someone help me with number 26 plss
Answer:
(-2,-9)
(-1,8)
(0,-5)
(1,0)
(2,7)
Step-by-step explanation:
Need help answering this question
Speed is the ratio of distance and time.
It shows how fast an object is moving at a given time.
The rate of change of the distance below the sea level with respect to time is 11 feet per second.
What is speed?Speed is the ratio of distance and time.
It shows how fast an object is moving at a given time.
We have,
The table has a linear relationship.
We can choose two data from the table.
At time = 15,
Distance below the sea level = 545 feet.
At time = 27,
Distance between the sea level = 677
Now,
The rate of change of the distance below the sea level with respect to time.
Slope:
= (677 - 545) / (27 - 15)
= 132 / 12
= 11 feet per second
Thus,
The rate of change of the distance below the sea level with respect to time is 11 feet per second.
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The rate of change of distance for the submarine is given by 11 feet/sec.
How to find the slope for two given points?In order to find the slope between two points (x₁, y₁) and (x₂, y₂), take the ratio of the difference of the respective coordinates as (y₂ - y₁)/(x₂ - x₁).
Given that,
The table for distance travelled versus time taken for a submarine.
In order to find the slope, take two values of distance and time from the given table as 380 feet at t = 0 and 545 feet at t = 15.
Now, the slope can be found as,
slope = (545 - 380)/(15 - 0)
= 165/15
= 11
Hence, the rate of change of distance below sea level with respect to time is given as 11 feet/sec.
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What is the product?
(-3s + 2t)(4s - t)
0 -1252-212
-1252 +212
-1252 +8 st - 2+2
O -1252 +11st - 2:2
Answer:
The product of the expression is -12s² + 11st - 2t²
Step-by-step explanation:
(-3s + 2t)(4s - t)
Use the foil method to multiply the terms. So, we distribute -3s to (4s - t) and we will also distribute 2t to (4s - t) as well.
-12s² + 3st + 8st - 2t²
Now combine like terms.
-12s² + 11st - 2t²
What is the probability that a z-score from a standard normal distribution would be less than 0.4 standard deviation above the mean
The means that approximately 65.54% of the observations in a standard normal distribution would have a z-score less than 0.4 standard deviation above the mean. The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.
The probability that a z-score from a standard normal distribution would be less than 0.4 standard deviation above the mean can be calculated using a standard normal distribution table or calculator. This probability can be found by calculating the area under the standard normal distribution curve to the left of the z-score of interest.Using a standard normal distribution table or calculator, the probability of a z-score from a standard normal distribution being less than 0.4 standard deviation above the mean is approximately 0.6554 or 65.54%.
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Can someone explain to me where the triangle came from??
The volume of the cylinder is 188.4m³.
How to calculate the volume?It should be noted that from the diagram given, there is a cylinder. It should be noted that the volume of a cylinder is given as:
= πr²h
where,
r = radius = 4m/2 = 2m
h = height = 15m
Therefore, the volume of the cylinder will be:
=πr²h
= 3.14 × 2² × 15
= 188.4m³
Therefore, the volume of the cylinder is 188.4m³.
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Sam is writing a report on cell phone usage. he collects data from a random sample of eight graders in his school, and finds that 18 out of 20 eight graders have cell phones. if there are 310 eight graders in his school,estimate the number of eighth graders who have cell phones.
A school has 100 students in grade 12. 30 of them are part of a basketball team, 25 are part of a baseball team and 40 are part of a soccer team. 10 are part of both baseball and basketball, 15 are part of both basketball and soccer, 18 are part of soccer and baseball and 5 are part of all them. How many grade 12 students are not part of any team?
a) 12 students
b)10 students
c) 5 students
d) 43 students
the number of grade 12 students who are not part of any team is 43.
Let's denote the number of grade 12 students not part of any team as X. Using the principle of inclusion-exclusion, we can calculate X by considering the individual team sizes and the number of students who are part of multiple teams.
According to the given information, we have:
Number of students in the basketball team = 30
Number of students in the baseball team = 25
Number of students in the soccer team = 40
Number of students in basketball and baseball = 10
Number of students in basketball and soccer = 15
Number of students in baseball and soccer = 18
Number of students in all three teams = 5
To find the total number of students who are part of at least one team, we sum the individual team sizes and subtract the students who are part of multiple teams:
Total students in at least one team = (30 + 25 + 40) - (10 + 15 + 18) + 5 = 57
Finally, we subtract the total number of students in at least one team from the total number of grade 12 students:
X = 100 - 57 = 43
Therefore, the number of grade 12 students who are not part of any team is 43.
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