simplify and find the value of 3(a square +5ab) -5a squared - 12ab , a = 2 & b = 3

a.F=kx is the formula that expresses F as a function of x

b. k=F/x=8/0.3=26.67.

c.72.01 lbs

Hooke's law is a principle of physics that describes the elasticity of springs when stretched or compressed. The amount of stretch or compression of the spring is directly proportional to the force applied, according to the law.What is Hooke's Law and how can you express F as a function of x?Hooke's law is a principle of physics that describes the elasticity of springs when stretched or compressed. The amount of stretch or compression of the spring is directly proportional to the force applied, according to the law. F=kx is the formula that expresses F as a function of x using the constant of proportionality k.What is the value of k in part (a)?It is given that F=kx, and that the weight of 8 pounds stretches a spring from its natural length of 10.4 inches to a length of 10.7 inches. We have to find the value of k.8 pounds, according to Hooke's law, stretches the spring 10.7-10.4=0.3 inches from its natural length.Using F=kx, we can say that the force applied is 8 pounds, or F=8. Therefore, we have k=F/x=8/0.3=26.67.What weight will stretch the spring in part (b) to a length of 13.1 inches?We are given that the spring stretches from its natural length of 10.4 inches to a length of 13.1 inches. To find the force required to produce this extension, we need to subtract the natural length from the final length, as we did before.13.1-10.4=2.7 inches is the distance by which the spring will be stretched.The formula for F is still F=kx, and we know the value of k, which is 26.67. Thus, F=26.67*2.7=72.01 lbs.

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cot⁻¹(-2.1) ≈ -1.068 radians

g⁻¹(f(4π)) = π/2.

When answering questions on the Brainly platform, it is important to be factually accurate, professional, and friendly. Additionally, it is important to be concise and not provide extraneous amounts of detail. Irrelevant parts of the question should be ignored, and any typos should be corrected as necessary. When answering a question, it is helpful to repeat the question in your answer to ensure that the answer is clear and understandable. A step-by-step explanation should be provided in your answer to help the student understand the solution. Finally, when using specific terms in your answer, it is important to define them and use them accurately.

Now, let's answer the given questions:

1. Use a calculator to find the approximate value of the expression.
cot−1(−2.1) cot−1(−2.1)≈
To find the approximate value of cot⁻¹(-2.1), we can use a calculator.
Using a calculator, we get:
cot⁻¹(-2.1) ≈ -1.068
Therefore, cot⁻¹(-2.1) ≈ -1.068 radians (rounded to two decimal places).

2. Let f(x)=sinx, −2π ≤ x ≤ 2π and g(x)=cosx, 0 ≤ x ≤ π. Find the exact value of the composite function.
g⁻¹(f(4π​)) g⁻¹(f(4π​))= (Simplify your answer, including any radicals. Type an exact answer, using π as needed. Use integers or fractions for any numbers in the expression.)
We know that f(x) = sin(x) and g(x) = cos(x).
Therefore,
f(4π) = sin(4π) = 0
Now, we need to find g⁻¹(0).
Since g(x) = cos(x), we know that g⁻¹(x) = cos⁻¹(x).
Therefore, g⁻¹(0) = cos⁻¹(0)
We know that cos(π/2) = 0, so cos⁻¹(0) = π/2 or 90°.
Therefore, g⁻¹(f(4π)) = g⁻¹(0) = cos⁻¹(0) = π/2.
Thus, g⁻¹(f(4π)) = π/2.

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The simplified form of the following expression's is: +3, 0, -6, +3, -4, -11, +31, +1, -60, +100, -49, +1, +30, -70, +28.

Any mathematical statement that includes numbers, variables, and an arithmetic action between them is known as an expression or algebraic expression. In the expression 4m + 5, for instance, the words 4m and 5 are separated from the variable m by the arithmetic symbol +.

(subtracting the two numbers, and keep the sign of the larger number)

(add a positive and negative number with equal magnitudes results in 0)

(add two negative number's results in a negative sum)

(subtracting the two numbers, and keep the sign of the larger number)

(subtract a negative number is the same as adding its positive, so -48 - (-44) becomes -48 + 44 = -4)

(subtract a negative number is the same as adding its positive, so -12 - (-4) becomes -12 + 4 = -8, ten add 3 to get -11)

(subtract a negative number is the same as adding its positive, so +16 - (-15) becomes +16 + 15 = +31)

(subtract a negative number is the same as adding its positive, so -35 - (-36) becomes -35 + 36 = +1)

(multiply a negative number by a positive number results in a negative product)

(multiply two negative numbers results in a positive product)

(multiply a positive number by a negative number results in a negative product)

-4 / -4 = +1

(Dividing a negative number by a negative number results in a positive quotient)

(multiply two negative numbers results in a positive product)

(multiply a negative number by a positive number results in a negative product)

(multiply two negative numbers results in a positive product)

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Answer:

Step-by-ste10p explanation:

The length of the rectangle is 10 inches and the rectangle is 10 inches long and 2 inches wide.

The total distance around the outside of the rectangle is termed as Perimeter of a rectangle. It is equal to the sum of the lengths of all four sides of the rectangle.

Let's assume that the width as "w" inches.

As per the problem statement, the length of the rectangle is 5 times its width, which means that the length is 5w inches.

The perimeter of a rectangle is :

P = 2(l + w)

Substituting the values, we get:

24 = 2(5w + w)

Simplifying the above equation, we get:

24 = 12w

Dividing both sides by 12, we get:

w = 2

So, the width of the rectangle is 2 inches.

The length is 5 times of width, that is:-

l = 5w = 5(2) = 10

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A. Using similar triangles, Slope of AB = Slope of AC = 42

B. The y-intercepts = 63; Slope = 42

The slope of a graph refers to the measure of the steepness of a line or a curve on a graph, calculated as the ratio of the vertical change (rise) between two points on the line to the corresponding horizontal change (run). In other words, it represents how much the y-axis changes for a given change in the x-axis.

A. Using similar triangles, we have the following:

Slope of AB = 147 - 105 / 2 -1 = 42/1

= 42

Slope of AC = 147 - 63 / 2 - 0 = 84/2

= 42

B. The line intercepts the y-axis at 63, therefore, the y-intercept is 63.

Slope of the graph is 42.

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Answer:

Assuming an ideal pulley system, the force required to lift a 10 Newton box with one pulley would be 10 Newtons. This is because the force required to lift an object using a pulley system is equal to the weight of the object being lifted. In an ideal pulley system, there is no friction or energy loss, so the force required is equal to the weight of the object. Therefore, if the weight of the box is 10 Newtons, a force of 10 Newtons would be required to lift it with one pulley.

Step-by-step explanation:

They are similar....so they are scaled

to go from   side 16 on the left figure  to the corresponding side 12 on the right figure ,

   multiply by  .75

so    .75 ( y+1) = 21

     .75 y + .75 = 21

              y = 27

Similarly :   .75 ( x-1) = 6

                   .75x - .75 = 6

                        x = 9

Machines A and B worked for 66 minutes and 6 seconds.

An inequality is a mathematical statement that compares two quantities using one of the inequality symbols: "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

Inequalities can be solved just like equations, with the goal of finding the set of values that satisfy the inequality.

Here we have

Machine A can pack 8 boxes per​ minute, and Machine B can pack 11 boxes per minute.

Let Machines A and B work for 'x' minutes

Number of boxes packed by Machine A = 8x

Number of boxes packed by Machine B = 11x

The difference between the number of boxes that Machine B has packed and the number of boxes that Machine A has packed is less than 200.

=> | 11x - 8x| < 200

=> 3x < 200

Divide by 3 into both sides

=> 3x/3 < 200/3

=> x < 66.67

=> x < 66.6

Therefore,

Machines A and B worked for 66 minutes and 6 seconds.

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Answer:

n=5

Step-by-step explanation:

Standard Position of the Angle =(468 n)°

We have to find that value of, n for which terminal side will fall on X axis, that is the angle should be multiple of 180°.

You must be thinking why not multiple of ,360°, because factors of 360 are , 90,180,and 360, in which , multiple of 90 falls on x and y axis ,and multiple of 180 ,falls on X axis only.So, instead of taking factors of 90 or 360, you should take multiple of 180° for which  terminal side fall on the x-axis.

The Unit Digit of , (468 n)°,should be equal to 0, as it is divisible by number 180°.

For, n=5,

→468° × 5=2340°

So, 2340° , is divisible by 180°.

For, n=5, the terminal side ,the angle having Measure (468 n)°,will fall on the X axis.

The sampling distribution could be represented numerically as follows: P [tex]N(0.03, 0.027^2)[/tex]

A sample distribution is a statistical probability that is obtained by taking random samples from a certain population. It depicts the distribution of frequency on how dispersed certain outcomes will be for a particular population and is also referred to as a finite-sample distribution.

Since they enable you to comprehend a particular sample statistic in the context of other potential values, sampling distributions are crucial for inferential statistics. Importantly, they enable you to compute probabilities related to your sample.

σ [tex]=\sqrt{[p(1-p)/n]}[/tex]

where [tex]p[/tex] is the population proportion [tex](0.03)[/tex] , n is the sample size [tex](133)[/tex], and sqrt denotes the square root function.

Substituting in the values, we have:

σ [tex]=\sqrt{ [(0.03)(1-0.03)/133] ≈ 0.027}[/tex]

Since the sample size is large [tex](n = 133)[/tex] and the population proportion is not close to [tex]0[/tex] or [tex]1[/tex], we can use the normal distribution to approximate the sampling distribution of the sample proportion. The mean of the sampling distribution is equal to the population proportion [tex](0.03)[/tex]. Therefore, the distribution of the sample proportion of students drinking more than [tex]3[/tex] cups of coffee each day is approximately normal with a mean of [tex]0.03[/tex] and a standard deviation of [tex]0.027[/tex].

The notation for the sampling distribution can be written as follows:

P [tex]N(0.03, 0.027^2)[/tex]

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The column headings of a check register and the information that go in that location are:

A check register, also known as a cash disbursements journal, is where you record all of your company's check and cash transactions during an accounting period. A check register is used by businesses to calculate the running balance of their checking account.

A check register will usually show the checking account's running balance. It functions similarly to a real-time record of the bank account. The bookkeeper can ensure that the total bank balance and the check register are in sync.

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Carrying an ax in one's teeth is a dangerous and potentially deadly action.

The weight and sharpness of the ax could easily cause injury or even death if it were to slip or the individual were to lose their balance.

Additionally, carrying an ax in this manner would likely result in the person being unable to communicate effectively, as their mouth would be occupied and their ability to speak clearly would be hindered.

If someone were to attempt to carry an ax in their teeth, they would be risking their safety and potentially the safety of those around them.

It is not a recommended or advisable course of action, and anyone who witnessed such behavior should exercise caution and avoid interacting with the individual until the ax has been safely secured.

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The exponential regression equation that fits the given data points is y = [tex]4*3^(x-1).[/tex]

The exponential regression equation that fits these data is y = 4*3^(x-1). To calculate this, we need to first calculate the parameters a and b for the equation y = a*b^x. We can do this by finding the natural logarithm (ln) of both sides of the equation.

ln(y) = ln(a*b^x)

ln(y) = ln(a) + ln(b^x)

ln(y) = ln(a) + x*ln(b)

We can now calculate the parameters a and b by plotting the points (x, ln(y)) and performing a linear regression on the points.

ln(4) = 0.602

ln(8) = 2.079

ln(27) = 3.526

ln(85) = 4.443

ln(250) = 5.52

ln(600) = 6.398

The linear regression equation is ln(y) = 0.175x + 0.602. We can now solve for the parameters a and b by using the linear regression equation.

ln(a) = 0.602

a = e^0.602

a = 4

ln(b) = 0.175

b = e^0.175

b = 3

Therefore, the exponential regression equation that fits these data is y = 4*3^(x-1).

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Answer:

I would say twv

Step-by-step explanation:

Answer:

x > 6

Step-by-step explanation:

3x - 3 < 9

3x < 12

x < 4

Since x < 4 is not true, then the solution is x > 6

The equation of the line is y = (-1/3)x + 2.

This is the equation of the line in slope-intercept form, where the slope is -1/3 and the y-intercept is 2.

What is the equation of the line?

A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.

The place on the x-axis where the line crosses. This is the x-intercept of the linear function.

If the line is horizontal (and not the x-axis), the linear function will have no x-intercept.

Here, the line crosses the x-axis at 6.

The place on the y-axis where the line crosses. This is the y-intercept of the linear function

Here, the line crosses the y-axis at 2.

If a line crosses the x-axis at the point (6,0), it means that the line intersects the x-axis when the y-coordinate is 0 and the x-coordinate is 6. Similarly, if the line crosses the y-axis at the point (0,2), it means that the line intersects the y-axis when the x-coordinate is 0 and the y-coordinate is 2.

We can use these two points to find the equation of the line using the slope-intercept form:

y = mx + b

where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

To find the slope, we can use the two points (6,0) and (0,2):

m = (y2 - y1) / (x2 - x1)

m = (2 - 0) / (0 - 6)

m = -1/3

To find the y-intercept, we can use the point (0,2):

y = mx + b

2 = (-1/3)(0) + b

b = 2

Therefore, the equation of the line is y = (-1/3)x + 2.

This is the equation of the line in slope-intercept form, where the slope is -1/3 and the y-intercept is 2.

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Population parameters are the real values of the variance, mean, and standard deviation of a population. These parameters are often unknown but can be estimated from a sample of the population.

When conducting a survey, it is important to select participants in a way that avoids bias and represents the population as accurately as possible. Simple random selection, in which individuals are selected randomly and every individual has an equal chance of being selected, is one way to achieve this.

Deviation score is the difference between an individual score and the mean of the population or sample. In this case, the deviation score for X = 45 in a population with a mean of 50 is -5.

In systematic sampling, every Kth member of the population is selected, making it a more efficient way of sampling compared to random sampling, but it requires that the population is well-ordered and homogeneous.

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Answer: (x-y)

Step-by-step explanation:

To find the range you must subtract the largest number from the smallest.  

the domain is D = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, and the range is R = {0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100}.

Why is it?

The graph shows all the possible test scores when there are only 10 equally weighed problems, and no partial credit is given. The domain represents all possible values of the independent variable, which in this case is the number of correct answers. The range represents all possible values of the dependent variable, which in this case is the score.

Looking at the graph, we can see that the domain consists of all non-negative integers from 0 to 10, inclusive. So the domain can be written as:

D = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

On the other hand, the range consists of all possible scores, which range from 0 to 100. So the range can be written as:

R = {0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100}

Therefore, the domain is D = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, and the range is R = {0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100}.

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The total percentage increase in the investor's stock account is 3.7%.

a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

The initial total value of the investor's stock account was $2000 + $4240 = $6240.

The new value of the stock in Company A is 1% more than last year's value, which means it is worth 1/100 * $2000 = $20 more than last year. Therefore, its new value is $2000 + $20 = $2020.

The new value of the stock in Company B is 5% more than last year's value, which means it is worth 5/100 * $4240 = $212 more than last year. Therefore, its new value is $4240 + $212 = $4452.

The new total value of the investor's stock account is $2020 + $4452 = $6472.

To calculate the percentage increase, we need to find the difference between the new and old values and express it as a percentage of the old value:

Percentage increase = ((New value - Old value) / Old value) x 100%

= (($6472 - $6240) / $6240) x 100%

= 3.7% (rounded to one decimal place)

Therefore, the total percentage increase in the investor's stock account is 3.7%.

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Based on the deliveries of each day, the total number of deliveries made by the drivers is 521.

In order to determine the total deliveries, add the number of deliveries for each day together.

The addition is determining the total value or summing two or more numbers. The addition is one of the four basic operations in mathematics. The other basic operations are subtraction, multiplication and division. The sign that represents addition is +.

Here is the complete question: To schedule enough drivers for an upcoming week. a local pizza shop manager recorded the number of deliveries each day from the previous week 38,54,44,61,97,103,124. What is the total number of deliveries?

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The object will be 6.1 m from the ground after 2 seconds.

The falling object model is used to calculate the height of an object after it has been dropped for a certain period of time. The equation used is h=h0−1/2gt2, where h0 is the initial height, g is the acceleration due to gravity and t is the time elapsed.

For example, if an object is dropped from a height of 15 m and falls for 2 seconds, we can calculate the height it will be at after 2 seconds.

The equation is then h=15−1/2(9.8)22

h=15−4.9•4

h=6.1 m

Therefore, the object will be 6.1 m from the ground after 2 seconds.

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As per the unitary method, the amount saved by Aaron after one year is  $780

We can use the following formula to find out how much Aaron saves per month:

Amount saved per month = Total amount saved / Number of months

We can use this formula to find out how much Aaron saves per month for each period:

For the first period (3 months):

Amount saved per month = 195 / 3

= 65

For the second period (4 months):

Amount saved per month = 260 / 4

= 65

For the third period (6 months):

Amount saved per month = 390 / 6

= 65

For the fourth period (7 months):

Amount saved per month = 455 / 7

= 65

We can see that Aaron saves $65 per month, regardless of the time period. Therefore, we can use this value to find out how much he will save in one year (12 months):

Amount saved in 1 year = Amount saved per month x Number of months

= 65 x 12

= 780

Therefore, we can predict that Aaron will save $780 after one year.

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The top of the ladder is sliding down the wall at the rate of 1.5 ft/s.

Given: A ladder is 25 ft long and is leaning against the wall of a house.

The base of the ladder is sliding away from the house at the rate of 2 ft/sec.

Asked: How fast is the top of the ladder sliding down the wall when its base is 15 feet from the wall?

Let the distance of the top of the ladder from the wall be x ft.

Then we have,

x² + y² = 25² (by Pythagoras theorem)

Differentiating both sides with respect to time t,

we get, 2x(dx/dt) + 2y(dy/dt) = 0 ...(1)

Given dx/dt = 2, and x = 15 ft.

⇒ 2(15)(dx/dt) + 2y(dy/dt) = 0

⇒ 30 × 2 + 2y(dy/dt) = 0 (substituting the given values)

⇒ 2y(dy/dt) = - 60⇒ dy/dt = - 30/ y

The negative sign indicates that y is decreasing (getting smaller) with time.

The values of y are negative because it lies below the level of the ground.

Substituting the value of x = 15 in the equation x² + y² = 25², we get

15² + y² = 25²

⇒ y² = 25² - 15² = 400

⇒ y = - 20

Substituting the values of dy/dt and y in the above equation, we get,

dy/dt = - 30/ (- 20)

dy/dt = 1.5 ft/s

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Answer:x = 10

Step-by-step explanation:

13+7=20

2 x 10 = 20

x=10

Answer:

x = 10

Step-by-step explanation:

[tex]2x-7=13[/tex]

First, add 7 to both sides.

[tex]2x-7 + 7=13 + 7[/tex]

This cancels the -7 on the left side because [tex]-7 + 7 = 0[/tex].

[tex]2x=20[/tex]

Then, we can divide both sides by 2 to isolate one multiple of x.

[tex]2x=20\\\overline{\ 2\ } \ \ \ \ \overline{\, 2 \: }[/tex]

[tex]\boxed{x = 10}[/tex]

Using trigonometric functions, the width of the volleyball court is approximately 31.13 meters.

What are trigonometric functions?

Trigonometric functions are mathematical functions that relate the angles and sides of a right triangle.

The basic trigonometric functions are:

Sine (sin): the ratio of the length of the side opposite an angle to the length of the hypotenuse of the triangle.

Cosine (cos): the ratio of the length of the side adjacent to an angle to the length of the hypotenuse of the triangle.

Tangent (tan): the ratio of the length of the side opposite an angle to the length of the side adjacent to the angle.

We can use basic trigonometry to solve this problem.

Let's assume that the width of the volleyball court is "x" meters.

From the corner of the court to the opposite player, we have a right triangle with the following sides:

the adjacent side: x meters (since it is parallel to the court's sideline)

the opposite side: 18 meters (since it is perpendicular to the sideline)

the hypotenuse: we don't know it yet, but we can find it using the given angle.

We can use the tangent function to find the hypotenuse:

tan(30) = opposite / adjacent

tan(30) = 18 / x

Multiplying both sides by x:

x * tan(30) = 18

x = 18 / tan(30)

x = 18 / 0.5774

x ≈ 31.13 meters

Therefore, the width of the volleyball court is approximately 31.13 meters.

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The height of the balcony from which the ball was kicked is 40 feet.

A ball was kicked into the air from the balcony of an apartment building.

The height of the ball, in feet, can be represented by the equation y= -16t^2+24t +40

where t is the time in seconds since the ball was kicked and y is the height of the ball.

The equation to represent the height of the ball is given as:

y = -16t² + 24t + 40Where y represents the height of the ball in feet and t represents the time in seconds since the ball was kicked.

To find the height of the balcony from which the ball was kicked, we need to find the initial height of the ball.

That is when the ball is at the balcony of the apartment building.

This happens when t = 0.

Substituting t = 0 in the equation, we get:

y = -16(0)² + 24(0) + 40y = 40

Therefore, the height of the balcony from which the ball was kicked is 40 feet.

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The answer to this question is that it depends. The distance of Ken’s house from the park cannot be determined without knowing the distance of the school and the pet shop from the park, and other factors such as terrain, local roads, and traffic can also affect the distance between Ken’s house and the park.

Distance is the amount of space between two points. It is a physical quantity that can be measured in various units such as meters, kilometers, miles and light-years. Distance can be calculated using the formula d = s × t, where d is the distance, s is the speed, and t is the time.

Ken lives at a point between the school and the pet shop, so it is impossible to answer this question without knowing how far away the school and the pet shop are from the park. If the park is close to the school or the pet shop, then Ken’s house would be close to the park, but if the park is further away from the school or the pet shop, then Ken’s house would be further away from the park. Therefore, the distance of Ken’s house from the park cannot be determined unless the distances of the school and the pet shop from the park are known.

In addition, other factors such as terrain, local roads, and traffic can also affect the distance between Ken’s house and the park. For example, if there is a hilly terrain between Ken’s house and the park, then the distance between them may be greater than if the terrain were flat.

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