Thrice a number subtracted from 10?​

To find the area of the region rr bounded by the graphs of y = 2x and y = 4x - x^2, we need to determine the points of intersection between the two curves. Answer :  4/3 square units.

Setting the equations equal to each other, we have:

2x = 4x - x^2

Simplifying, we get:

x^2 - 2x = 0

Factoring out x, we have:

x(x - 2) = 0

So, x = 0 or x = 2.

Now, we can integrate the difference of the two curves between x = 0 and x = 2 to find the area:

Area = ∫[0, 2] (4x - x^2 - 2x) dx

Simplifying, we have:

Area = ∫[0, 2] (2x - x^2) dx

Integrating, we get:

Area = [x^2 - (x^3)/3] evaluated from 0 to 2

Evaluating at the limits, we have:

Area = (2^2 - (2^3)/3) - (0^2 - (0^3)/3)

Area = (4 - 8/3) - (0 - 0)

Area = (12/3 - 8/3) - 0

Area = 4/3

Therefore, the area of the region rr bounded by the curves y = 2x and y = 4x - x^2 is 4/3 square units.

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The large-sample z statistic is 1.923. Based on this result, we reject the null hypothesis and conclude that there is evidence to suggest that a majority of people prefer the taste of fresh-brewed coffee over instant coffee.

To test the claim that a majority of people prefer fresh-brewed coffee, we need to set up the null and alternative hypotheses:

Null hypothesis: p ≤ 0.5 (i.e., the proportion of people who prefer fresh-brewed coffee is less than or equal to 0.5)

Alternative hypothesis: p > 0.5 (i.e., the proportion of people who prefer fresh-brewed coffee is greater than 0.5)

We will use a one-tailed test with a significance level of α = 0.05.

To calculate the large-sample z statistic, we first need to calculate the sample proportion of people who prefer fresh-brewed coffee

P = (60 - 21) / 60 = 0.65

where 60 is the total number of subjects and 21 is the number who prefer instant coffee.

Next, we need to calculate the standard error of the sample proportion:

SE = sqrt(P(1-P)/n) = sqrt(0.65(1-0.65)/60) = 0.078

where n is the sample size.

Finally, we can calculate the z statistic:

z = (P - p) / SE = (0.65 - 0.5) / 0.078 = 1.923

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The given question is incomplete, the complete question is:

A matched pairs experiment compares the taste of instant with fresh-brewed coffee. Each subject tastes two unmarked cups of coffee, one of each type, in random order and states which he or she prefers. Of the 60 subjects who participate in the study, 21 prefer the instant coffee. Let p be the probability that a randomly chosen subject prefers fresh-brewed coffee to instant coffee. (In practical terms, p is the proportion of the population who prefer fresh-brewed coffee.)

Test the claim that a majority of people prefer the taste of fresh-brewed coffee. Report the large-sample z statistic

Answer:

Candy canes are a classic Christmas treat, traditionally white with red stripes and flavored with peppermint. They have been popular since the 1600s and are thought to have originated in Germany. Today, 90 percent of all candy canes are sold between Thanksgiving and Christmas.

In a bag of Christmas treats, there are 3 red candy canes for every 5 gingerbread men. If there total is 40 treats, then the number of candy canes will be 24. This can be calculated by taking 40 divided by 8 (5+3) which equals 5, and then multiplying this by 3 which equals 15. Therefore, 24 candy canes are included in the bag of 40 Christmas treats.

Step-by-step explanation:

Answer:

m= -20

Step-by-step explanation:

0.45m-9=0.9m

-9+0.45m=0.9m

Solve:

-9+0.45m=0.9m

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add '-0.9m' to each side of the equation.

-9 + 0.45m + -0.9m = 0.9m + -0.9m

Combine like terms: 0.45m + -0.9m = -0.45m

-9 + -0.45m = 0.9m + -0.9m

Combine like terms: 0.9m + -0.9m = 0.0

-9 + -0.45m = 0.0

Add '9' to each side of the equation.

-9 + 9 + -0.45m = 0.0 + 9

Combine like terms: -9 + 9 = 0

0 + -0.45m = 0.0 + 9

-0.45m = 0.0 + 9

Combine like terms: 0.0 + 9 = 9

-0.45m = 9

Divide each side by '-0.45'.

m = -20

Simplifying

m = -20

Hope this helps     :)

The angle between sides GM and MT is ∠M.

The 2 sides that include ∠T are MT and GT.

The angle between sides GT and MG is ∠G.

There's not much to say about this, but I can answer questions if you have any.

Answer:

A. 147

Step-by-step explanation:

Using equations we know that approximately 8 liters of water must be added in order to produce a 30% acid solution.

So, we know that:

Liters of water: x

25% of solution: 0.25 × 50

30% of solution: 0.30 (50 + x)

Now, form equations and calculate as follows:

0.25 × 50 = 0.30 (50 + x)

12.5 = 15 + 0.30x

15 + 0.30x = 12.5

15 + 0.30x - 15 = 12.5 -15

0.30x = -2.5

.030x/.30 = -2.5/.30

x = - 8.33

Since we can't add water in negative, hence it will be +.

Rounding off: 8 liters

Therefore, using equations we know that approximately 8 liters of water must be added in order to produce a 30% acid solution.

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The expected on-order inventory is approximately 80 units (rounded to the nearest integer).

1. Determine the average demand during the lead time:

Since the mean demand per period is 60 and the lead time is 2 periods, the average demand during the lead time is

60 × 2 = 120 units.

2. Determine the standard deviation of the demand during the lead time:

As the demand follows a normal distribution with a standard deviation of 10 per period, the standard deviation during

the lead time (2 periods) is calculated as sqrt(2) × 10 ≈ 14.14 units.

3. Calculate the expected on-order inventory:

Subtract the average demand during the lead time from the order-up-to level. In this case, it's 200 (order-up-to level) -

120 (average demand during lead time) = 80 units.

So, the expected on-order inventory is approximately 80 units (rounded to the nearest integer).

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7n - 4 = 5 + 5.7(n+5)

7n - 4 = 5 + 5.7n + 28.5

move 5.7n to the right side, -4 to the right side.

7n - 5.7n = 5 + 28.5 - (-4) = 37.5

1.3 n = 37.5

n = 37.5 / 1.3 = 28.84615...

Answer:

n=29

Step-by-step explanation:

7n-4=5+5.7(n+5)

5.7n+28.5

-5.7n

+5

1.3n-4=33.5

+4

1.3n=37.5

÷1.3

n=28.846...

n=29(1dp)

Answer:

(1,-6)

(-2,-5)

(8,2)

(4,0)

Answer:

m = -1

Step-by-step explanation:

m= -(4+ m) + 2

Distribute

m = -4-m+2

m = -2-m

Add m to each side

m+m = -2-m+m

2m = -2

2m/2 = -2/2

m = -1

Tank 1 initially contains brine with 10 lb of salt, while Tank 2 has pure water. Water flows into Tank 1 and then into Tank 2, both at a rate of 5 gal/min. The initial value problem for the amounts of salt in the tanks, x₁(t) and x₂(t), is solved by integrating the differential equations. The solutions are x₁(t) = ± e^(- (5/150) t + C₁) and x₂(t) = ± (50/3) e^(- (5/150) t + C₁) + C₂. The maximum amount of salt in Tank 2 depends on the initial conditions and integration constants, with the upper bound being x₂_max = (50/3) e^C₁ + C₂.

a. The initial value problem for x₁(t) and x₂(t) can be written as follows:

  dx₁/dt = (5/100)(10) - (5/150)x₁

  dx₂/dt = (5/150)x₁ - (5/50)x₂

  where dx₁/dt represents the rate of change of salt in Tank 1 with respect to time, dx₂/dt represents the rate of change of salt in Tank 2 with respect to time, and x₁(t) and x₂(t) represent the amounts of salt in Tank 1 and Tank 2, respectively, at time t.

b. To find x₁(t) and x₂(t), we solve the initial value problem using the given conditions. Let's integrate the equations with respect to time:

  ∫ dx₁/dt dt = ∫ [(5/100)(10) - (5/150)x₁] dt

  ∫ dx₂/dt dt = ∫ [(5/150)x₁ - (5/50)x₂] dt

  Integrating the first equation, we have:

  x₁(t) = 10 - (5/150)∫ x₁ dt

  Differentiating both sides of the equation, we get:

  dx₁/dt = - (5/150) x₁

  This is a separable differential equation, which can be solved by separating variables and integrating:

  ∫ dx₁/x₁ = - (5/150) ∫ dt

  ln|x₁| = - (5/150) t + C₁

  Exponentiating both sides of the equation, we have:

  |x₁| = e^(- (5/150) t + C₁)

  x₁(t) = ± e^(- (5/150) t + C₁)

  Similarly, integrating the second equation, we get:

  x₂(t) = (5/150)∫ x₁ dt + C₂

  Substituting the expression for x₁(t) into x₂(t), we have:

  x₂(t) = (5/150)∫ (± e^(- (5/150) t + C₁)) dt + C₂

  x₂(t) = ± (5/150) ∫ e^(- (5/150) t + C₁) dt + C₂

  Solving the integral and simplifying, we get:

  x₂(t) = ± (50/3) e^(- (5/150) t + C₁) + C₂

c. To find the maximum amount of salt in Tank 2, we need to determine the maximum value of x₂(t). Since x₂(t) depends on the arbitrary constant C₁, we can't find the exact maximum without additional information about C₁. However, we can find the upper bound for x₂(t) by considering the limiting case.

  As t approaches infinity, the exponential term e^(- (5/150) t + C₁) approaches zero. Therefore, the maximum value of x₂(t) occurs when the exponential term is zero, resulting in:

  x₂_max = ± (50/3) e^C₁ + C₂

  The sign of ± depends on the initial condition and the integration constant C₂. If we assume positive values, then x₂_max = (50/3) e^C₁ + C₂.

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The correct option is (B) 9/13.

The probability that it will not snow on Tuesday is 9/13.

The ratio of the quantity of favorable outputs to the overall number of possibilities of an event is defined as probability.

The number of favorable results for an experiment with 'n' outcomes is denoted by x.

The following formula is used to determine the probability of an event.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n.

Some properties of the probability are mentioned below-

Now, for the stated question;

The probability that it will snow on Tuesday is 4/13.

Use property 1;

Then, the probability that it will not snow on Tuesday is;

= 1 - 4/13

= (13 - 4)/13

= 9/13

Therefore, the probability that it will not snow on Tuesday is 9/13.

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The value of a Chi-Square goodness-of-fit test at a 5% significance level is 13.45

We need to perform a Chi-Square goodness-of-fit test at a 5% significance level.

First we need to calculate the expected count

expected value = ∑(x)/n

= (40 + 33 + 35 + 32 + 60)/5

= 200/5

= 40

Now we need tocalculate the test statistic value

Observed  expected  O - E    (O - E)^t/E       %

40                40             0            0                   0

33                40             -7          1.225          9.11

35                40             -5          0.625         4.65

32                40             -8         1.6                11.90

60                40             20        10                 74.35

Chi square test is 13.45

Therefore, the value of test statistics is 13.45.

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Solution:

Given:

The radius and tangent to a circle at the point of intersection are perpendicular to each other.

Hence, considering the right triangle;

Hence, the length of the missing side can be gotten using the Pythagorean theorem.

Therefore, to the nearest tenth, the length of the missing side is 6.3

An inscribed angle is formed by two chords of a circle that intersect at a vertex located on the circle.

The angle itself is formed by the two sides of the angle, which are the line segments connecting the vertex to the endpoints of the chords. The property that makes inscribed angles interesting is that the measure of an inscribed angle is half the measure of the intercepted arc on the circle.

This relationship holds true for any inscribed angle in a circle, making it a useful concept in geometry for solving problems involving angles, arcs, and circles.

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The probability of rolling a total of 7 in two rolls of a standard die if you get an even number on the first roll is \(\frac{1}{9}\).

There are two main steps involved in solving this problem.

The first step is to figure out the probability of rolling an even number on the first roll of a standard die, which is \(\frac{1}{2}\) since there are three even numbers (2, 4, and 6) and three odd numbers (1, 3, and 5) on a standard die.

The second step is to figure out the probability of rolling a total of 7 in two rolls of the die given that an even number was rolled on the first roll.

This probability can be calculated using conditional probability.

Conditional probability is the probability of an event occurring given that another event has occurred.

In this case, the event we are interested in is rolling a total of 7 in two rolls of a standard die, and the other event is rolling an even number on the first roll of the die.

We can use the following formula to calculate the conditional probability of rolling a total of 7 given that an even number was rolled on the first roll:

\(P(total of 7 | even on first roll) = \frac{P(total of 7 and even on first roll)}{P(even on first roll)}\)

To calculate the numerator of this equation, we need to figure out the probability of rolling a total of 7 and an even number on the first roll of the die.

There are two ways this can happen: either a 2 is rolled on the first roll and a 5 is rolled on the second roll, or a 4 is rolled on the first roll and a 3 is rolled on the second roll.

The probability of each of these events is

\(\frac{1}{6}\times\frac{1}{6}=\frac{1}{36}\)

since there is only one way to roll a 2 or a 4 and one way to roll a 5 or a 3 on a standard die.

Therefore, the numerator of the equation is

\(\frac{1}{36} + \frac{1}{36} =\frac{2}{36} =\frac{1}{18}.\)

To calculate the denominator of the equation, we simply need to use the probability of rolling an even number on the first roll that we calculated earlier, which is \(\frac{1}{2}.\)

Therefore, the conditional probability of rolling a total of 7 given that an even number was rolled on the first roll of a standard die is:

\(P(total of 7 | even on first roll) = \frac{(\frac{1}{18}) }{\frac{1}{2}} =\frac{1}{9}\).

In other words, the probability of rolling a total of 7 in two rolls of a standard die if you get an even number on the first roll is \(\frac{1}{9} .\)

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Answer:

\(\frac{1}{4}\)

Step-by-step explanation:

Just take the larger exponent and subtract the smaller exponent and it becomes --> \(\frac{1}{2^{2}}\)

\(\frac{1}{2^{2}}\) = \(\frac{1}{4}\)

Answer:

  D.  10 square units

Step-by-step explanation:

The area of a triangle is given by the formula ...

  A = 1/2bh

__

This triangle has a base of 4 units and a height of 5 units. (These dimensions can be counted from the graph, or found by subtracting coordinate values.) Its area is ...

  A = 1/2(4 units)(5 units) = 10 square units

_____

Additional comment

The first two coordinates lie on the line x=0. The length of that segment is the difference of the y-values: 4 -(-1) = 5.

The first and last coordinates lie on the line y=-1. The length of that segment is the difference of the x-values: 4 -0 = 4.

In order to meet the sample assumption associated with parametric statistics, the number of subjects needed depends on the specific statistical test being used. Generally, the rule of thumb is to have a minimum of 30 subjects in each group being compared.

However, this number may increase or decrease depending on factors such as the effect size, variability in the data, and the statistical power desired.

It is important to have enough subjects so that the data is normally distributed, and there is enough content loaded to meet the assumptions of the statistical test.

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The artifact was made about 3102.5 years ago.

An artifact from an ancient tomb contains 70% of the carbon-14 that is present in living trees, how long ago was the artifact made?

Carbon dating is used to estimate the age of organic materials, and it is used to determine the age of an artifact in this situation. The method used to estimate the age of an artifact based on its carbon-14 content is known as carbon dating. Carbon-14 has a half-life of 5,730 years. As a result, the amount of carbon-14 present in an object can be used to determine how long it has been since the object was last in contact with the atmosphere, and therefore how long it has been since it was alive.

Let C0 be the amount of carbon-14 present in living trees and C1 be the amount of carbon-14 present in the wooden artifact. After 5,730 years, C1 will have decayed to 1/2 of C0. After 2(5,730) = 11,460 years, C1 will have decayed to 1/4 of C0. After 3(5,730) = 17,190 years, C1 will have decayed to 1/8 of C0. After 4(5,730) = 22,920 years, C1 will have decayed to 1/16 of C0. After 5(5,730) = 28,650 years, C1 will have decayed to 1/32 of C0.

We'll have to solve the following equation to find the age of the artifact.

C1 = (70/100) * C0

Substitute the value of C0 into the equation and solve for t,

t = ln(0.7) / ln(1/2) = 3102.5 years

The artifact was made about 3102.5 years ago.

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The value that would complete the table to make the relationship between the two quantity proportional is 4.

When two quantities are proportional, their relationship is constant for all values and as one quantity rises, the other rises as well.

A proportional relationship exists between two quantities if they can be written in the general form y = kx, where k is the proportionality constant. In other words, the ratio between these amounts never changes. In other words, no matter which pair of the two numbers you divide, you always obtain the same number k.

The value that would complete the table to make the relationship between the two quantity proportional is 4.

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To measure the quality characteristics of an organization, one statistical technique that can be employed is Statistical Process Control (SPC).

SPC is a method used to monitor and control processes to ensure they are operating within predetermined limits. It involves the use of control charts to analyze process data and identify any variations that may occur.

SPC provides a visual representation of process performance over time, allowing organizations to identify and address any issues that may affect quality. Control charts, such as the X-bar and R charts or the X-bar and S charts, are commonly used in SPC to monitor the mean and variability of a process.

For example, let's say a manufacturing company wants to measure the quality characteristics of its production line. The company can collect data on key quality indicators, such as product dimensions or defects, at regular intervals. Using SPC, the company can create control charts to track these measurements over time. If the data points fall within the control limits, it indicates that the process is stable and in control. However, if there are any data points outside the control limits or any patterns or trends observed, it may indicate a problem that requires investigation and corrective action.

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Answer:

t=V‒x/a

Step-by-step explanation:

V=x+at (add ‒x in both side)

V‒x=x+at‒x

V‒x=at

V‒x/a=at/a

V‒x/a=t

so the formula is t=V‒x/a

Yes, there are diminishing returns to labor in the given production function.

There are diminishing returns to labor in the given production function. As more units of labor (L) are added while holding capital (K) constant, the increase in output (y) becomes smaller and smaller. This is indicative of diminishing marginal product of labor.

When the wage rate (w) is 1 and the capital (K) is fixed at 64, the profit-maximizing choice of labor (L) can be found by equating the marginal product of labor (MPL) to the wage rate. In this case, MPL = 12L^2K.

Setting MPL = w, we have 12L^2K = 1. Substituting K = 64, we get 12L^2 * 64 = 1. Solving for L, we find L ≈ 0.0917.

The profit-maximizing output level (y) can be calculated by substituting the values of L and K into the production function. Thus, y = 4L^3K = 4(0.0917)^3 * 64 ≈ 0.026.

The maximized profit can be determined by subtracting the total cost (TC) from the total revenue (TR). Since the fixed cost is given as 64, TC = 64 + wL = 64 + 1(0.0917) ≈ 64.092. TR is the product of the output level and the price, which is 0.026 * 3 = 0.078.

Profit = TR - TC ≈ 0.078 - 64.092 ≈ -63.014.

Diminishing returns to labor imply that as more labour is employed while holding other factors constant, the incremental increase in output becomes smaller. In the given production function, this phenomenon is observed. In the short run, with a fixed capital level of 64, we determine the profit-maximizing choice of labour (L) when the wage rate (w) is 1. By equating the marginal product of labour (MPL) to the wage rate, we find L ≈ 0.0917. Substituting this value into the production function, we calculate the profit-maximizing output level as y ≈ 0.026. The maximized profit is determined by subtracting the total cost (TC) from the total revenue (TR), resulting in a profit of approximately -63.014. This analysis helps understand the relationship between input choices, output levels, and profit optimization in the short run.

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The purpose of stories "Here at the given any rate is said the bachelor, and then collecting his belongings preparatory to leaving the carriage, then he kept them quiet for ten minutes, which was more than you were able to do."

Here we need to excerpt from the storyteller best supports the theme that the purpose of stories.

While we look the bachelor says at the end they said that he kept them quiet for ten minutes, which was more than you were able to do and then he is implying that no matter what she thought of his story and how much "better" she thought she could've done it, and then his was able to capture the attention of these kids and that is the matter of the issue because, therefore for a story and then entertaining is more important than proper form

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Answer:

Y=7/5x+8

Is the answer to question don't ask me how I know I cheated

The equation y = 7x/5 + b represents a line which is parallel to the line 7x-5y=-30.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

We have an equation,

7x-5y=-30

Simplifying,

y = 7x/5 + 30/5

y = 7x/5 + 6.

The general formula of line parallel to a given line is,

y = 7x/5 + b, where b is the y-intercept of the line.

Therefore, y = 7x/5 + b is the required line.

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Pregunta completa :

Wolfrich vivió en Portugal y Brasil para aprender portugués durante un período de 14 meses. Aprendió un promedio de 130 palabras nuevas por mes cuando vivió en Portugal y un promedio de 150 palabras nuevas cuando vivió en Brasil. En total aprendió 1920 palabras nuevas. ¿Cuánto tiempo vivió Wolfrich en Portugal y cuánto tiempo vivió en Brasil?

Responder:

Portugal = 9 meses

Brasil = 5 meses

Explicación paso a paso:

Dado que:

Total de meses pasados ​​tanto en Brasil como en Portugal) 14 meses

Dejar ;

tiempo pasado en Brasil = b

Tiempo pasado en Portugal = p

Promedio de palabras aprendidas por mes en Brasil = 150

Promedio de palabras aprendidas por mes en Portugal = 139

Total de palabras aprendidas = 1920

Matemáticamente;

150b + 130p = 1920 - - - (1)

b + p = 14 - - (2)

b = 14 - p

De 1)

150 (14 - p) + 130p = 1920

2100 - 150p + 130p = 1920

2100 - 20p = 1920

2100 - 1920 = 20p

180 = 20p

p = 9

b = 14 - p

b = 14 - 9

b = 5

Por lo tanto;

Portugal = 9 meses

Brasil = 5 meses

Answer:

x = 22°

w = 30°

y = 30°

z = 52°

Step-by-step explanation:

From ΔACD,

AD is the diameter and ∠ACD is the angle subtended by the diameter.

Therefore, m∠ACD = 90°

By triangle sum theorem,

m∠DAC + m∠ACD + m∠CDA = 180°

w° + 90° + 60° = 180°

w = 180 - 150

w = 30°

AB║ED and AD is a transversal line.

Therefore, m∠BAD = m∠ADE

(w + 22)° = z°

30 + 22 = z

z = 52°

Since, ∠CEB and ∠BAC are the inscribed angles subtended by the same arc BC,

Therefore, m∠CEB = m∠BAC

x = 22°

Similarly, ∠CED and ∠DAC are the inscribed angles subtended by the same arc CD,

m∠CED = m∠DAC = 30°

y = 30°

A dependent variable is the variable that being check in a scientific experiment.

The dependent variable is "dependent" on the other independent variable. As the experimenter alter the independent variable, the change in the dependent variable is observed and recorded. When you take data in an experiment, the dependent variable is the one being advised.

A scientist is testing the effect of light and dark on the efforts of moths by turning a light on and off. The independent variable is the amount of light and the moth's reply is the dependent variable.

A change in the independent variable (total amount of light) straight source a change in the dependent variable (moth behavior).

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