What is the Surface area

\(\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=15\pi \end{cases}\implies 15\pi =2\pi r\implies \cfrac{15\pi }{2\pi }=r\implies \cfrac{15}{2}=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{15}{2} \end{cases}\implies A=\pi \left( \cfrac{15}{2} \right)^2\implies A=\cfrac{225\pi }{4}\implies A=56.25\pi\)

A graph of the exponential function \(f(n)=37000(1.06)^n\) is shown in the image attached below.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

\(f(x)=a(b)^x\)

Where:

Based on the information provided above, your salary can be modeled or represented by the following exponential function;

\(f(n)=37000(1.06)^n\)

Lastly, we would use an online graphing calculator to plot the given exponential function as shown in the graph attached below.

In conclusion, the rate of change of this exponential function is equal to 1.06.

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Answer:

The answer is 1054ft³

Step-by-step explanation:

Volume of rectangular prism =1/3LWH

V=1/3×31/2×51/3×12

V=1054ft³

The value of x is approximately 6.16 cm.We can see that the figure consists of two rectangles and a right triangle. Let's label the dimensions of the rectangles as follows:

Rectangle 1:

length x, width 2x

Rectangle 2:

length 2x, width 3x

Right triangle:

base x, height 3x

The area of Rectangle 1 is given by:Area1 = x * 2x = 2x^2

The area of Rectangle 2 is given by:Area2 = 2x * 3x = 6x^2

The area of the right triangle is given by:Area3 = 1/2 * x * 3x = 3/2 x^2

The total area of the figure is the sum of the areas of the three parts:

Total Area = Area1 + Area2 + Area3 = 2x^2 + 6x^2 + 3/2 x^2 = 399

Simplifying and solving for x, we get:

10.5x^2 = 399

Dividing both sides by 10.5, we have:

x^2 = 38

Taking the square root of both sides, we get:

x = sqrt(38).

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Answer:

(a) \(y'= 2cos(2x - \pi)\)

(b) \(y=2x - \pi + 1\)

(c) \(y=-\frac{x}{2} +\frac{\pi + 4}{4}\)

Step-by-step explanation:

\(y=sin(2x-\pi)+1\)

Find the derivative of this function by using the chain rule and the power rule.

We know that the derivative of sinx = cosx. Find the derivative of this entire function first, \(sin(2x-\pi)+1\), then multiply this by the derivative of the inside function, \(2x-\pi\).

Use the chain rule to find the derivative of sin(2x - π) + 1, which is cos(2x - π), then multiply this by the derivative of (2x - π). The derivative of π is 0, because it is a constant. The derivative of 2x is 2 based on the Power Rule.

Simplify this expression.

This is the derivative of \(y=sin(2x-\pi)+1\); therefore, we can write:

In order to find the equation of the tangent line at \(x=\frac{\pi}{2}\), we will need to find the slope of the tangent line and the x- and y- coordinates (we already know the x- cord).

The steps to finding the equation of the tangent line at a certain are:

We know that y' = 2cos(2x - π). Let's plug x = π/2 into this equation for x to find the slope of the tangent line.

Simplify inside the parentheses.

Now we know that the slope of the tangent line is 2.

Let's plug x = π/2 into the original function, y.

Simplify inside the parentheses.

This tells us that the y-value, when x = π/2, equals 1. Our coordinates that we can use are (π/2, 1).

Now we can use point-slope form to write an equation for the tangent line to y at x = π/2.

Point-slope equation:

We have \((x_1, \ y_1)\), which are the x- and y- coordinates, and \(m\), which is the slope of the tangent line.

Substitute these values into the equation:

Distribute 2 inside the parentheses.

Add 1 to both sides of the equation.

This is the equation of the tangent line of \(y=sin(2x-\pi)+1\) at \(x=\frac{\pi}{2}\).

In order to find the equation of the normal line at x = π/2, we can use the information that the tangent line is perpendicular to the normal line.

This information is helpful because this means that their slopes are opposite reciprocals.

Let's use the point-slope equation again, but instead of m = 2, m will be the opposite reciprocal of 2 ⇒ -1/2. We will still use the same coordinate points.

Distribute -1/2 inside the parentheses.

Add 1 to both sides of the equation.

You can leave it written as this, or write it as:

This is the equation of the normal line of \(y=sin(2x-\pi)+1\) at \(x=\frac{\pi}{2}\).

Answer:

The expected number of hunters who hit the duck they aim at is 3.6

Step-by-step explanation:

Given;

number of hunters, n = 6

the probability of killing a duck, p = 0.6

The expected number of hunters who hit the duck they aim at?

In binomial distribution, the expected value is equal to the product of the number of trials and the probability of success.

The expected number of hunters who hit the duck they aim at is calculated as follows;

E = np

E = 0.6 x 6

E = 3.6

Therefore, the expected number of hunters who hit the duck they aim at is 3.6

The expression of the length of the arc is  4πb⁵

The circle has a radius of 9b³. An arc subtend an angle at the centre of 80b² degrees. Therefore, the expression for the length of the arc can be solved as follows:

length of arc = ∅ / 360 × 2πr

where

Therefore,

length of arc = 80b² / 360 × 2 × π × 9b³

length of arc = 144b⁵π / 36

Therefore,

length of arc = 4πb⁵

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The steps to conduct the steps of hypothesis testing on these data are:

The hypothesis will be:

Since we are comparing (GPAs) of three groups (students who check e-mail day by day, students  who check mail at least 2x a week, and students who check mail less than 2x a week), one can be able to make use of one-way analysis of variance (ANOVA) as the fitting test measurement.

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Answer:

The original price is 180$

Answer:

Step-by-step explanation:

If there is a 10 percent discount, that means that this is 90 percent of the total.

So, let us find 10 percent is made up of how many dollars.

$162/9=$18 (do note that the slash sign means divide! When you write down the equation on a paper, please write the actual divide sign. Sorry for the inconvenience)

Since the original price is 100 percent, and we have 10 percent, that means we can just multiply the 10 percent by 10, to get 100 percent, as 10 times 10 is hundred.

$18x10=$180

Hope this helped! If you need another method, along with a different explanation, or separate, do comment below, so I can know. Any part you do not understand, please don't be afraid to tell me. If you think I can improve my answer, or change any parts to perhaps make it clearer, i'm open to suggestions!

Part A (Printer): $12.63

Part B (Computer): $180.83

A:

"take advantage of the cash discount" Since Janet is taking the cash discount we need to use the terms.

2/10 => Means if paid in 10 days apply a 2% discount

($880 - $100) = $780  (This is because of the trade discount stated also)

$780 * 0.98 = $764.40  

(Note: 0.98 is the term "2/10" it is the 2% discount, represented as (1-0.02) )

$764.40 * 0.07 * (20/360) = $2.9726666 (Note: Here 20/360, 20 represents the rest of the days left in the term agreement)

No Discounts: ($780 - 764.40) = $15.60

Discounts: $2.9726666

How much would Janet save?

$15.60 - $2.9726666 = $12.62733 = $12.63

===============================================

Question has a part B:

"On the computer, what is the difference in the final payment between choices 1 and 2?"

Note: Computer Price w/ Trade Discount => $4,000 - ($4,000*0.25) = $3000

(1) "$155 per month for 17 months" => $155 × 17 = $2,635

Last payment $3,000 – $2,635 = $365

(2)-------------- Note: 18 Months = 1.5 Years

$3,000 × 0.07× 1.5 = $315

$3,000 + $315 = ($3,315) / 18 Months = $184.1666

Difference in the final payment?

$365 - $184.1666 = $180.8334 = $180.83

A. Janet would save $12.63

B. Computer: $180.83

Since Janet is taking the cash discount we need to use the terms.

"take advantage of the cash discount"

2/10 => Means if paid in 10 days apply a 2% discount

($880 - $100) = $780  (This is because of the trade discount stated also)

$780 * 0.98 = $764.40  

[0.98 is the term "2/10" it is the 2% discount, represented as (1-0.02)]

$764.40 * 0.07 * (20/360) = $2.9726666 (Note: Here 20/360, 20 represents the rest of the days left in the term agreement)

No Discounts: ($780 - 764.40) = $15.60

Discounts: $2.9726666

Janet would save = $15.60 - $2.9726666 = $12.62733 = $12.63

Computer Price w/ Trade Discount => $4,000 - ($4,000*0.25) = $3000

(1) "$155 per month for 17 months" => $155 × 17 = $2,635

    Last payment $3,000 – $2,635 = $365

(2) 18 Months = 1.5 Years

    $3,000 × 0.07× 1.5 = $315

    $3,000 + $315 = ($3,315) / 18 Months = $184.1666

Difference in the final payment= $365 - $184.1666 = $180.8334 = $180.83

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The width of the field is 230 feet and the length is 310 feet.

Let's denote the width of the field as "x" feet.

The length of the field is 80 feet longer than the width, so it can be represented as "x + 80" feet.

To find the total amount of fencing material needed, we sum up the lengths of all four sides of the rectangular field:

2(length) + 2(width) = perimeter

Substituting the given values:

2(x + 80) + 2(x) = 1080

2x + 160 + 2x = 1080

4x + 160 = 1080

4x = 920

x = 920/4

x = 230

Therefore, the width of the field is 230 feet.

Now we can find the length by adding 80 feet to the width:

Length = Width + 80 = 230 + 80 = 310 feet.

So, the width of the field is 230 feet and the length is 310 feet.

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Answer:

So, Katelyn deposited $2500 in a CD, and the interest rate is 4.25% compounded daily. That means her money will grow every day at a rate of 4.25%/365 (since there are 365 days in a year).

To find out how many years it will take Katelyn to earn $250 in interest, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the amount of money in the account after t years

P is the principal amount (the initial deposit)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the time in years

In this case, we know:

P = $2500 (the initial deposit)

r= 0.0425 (4.25% as a decimal)

n = 365 (compounded daily)

t is what we're trying to find

We also know that Katelyn wants to earn $250 in interest, so her total balance after t years should be $2500 + $250 = $2750.

Plugging all of this into the formula, we get:

$2750 = $2500(1 + 0.0425/365)^(365t)

Simplifying a bit, we get:

1.01 = (1 + 0.0425/365)^(365t)

Taking the natural log of both sides, we get:

ln(1.01) = ln(1 + 0.0425/365)^(365t)

Using the property of logarithms that ln(a^b) = b*ln(a), we can simplify further:

ln(1.01) = 365t * ln(1 + 0.0425/365)

Finally, we can solve for t:

t = ln(1.01) / (365 * ln(1 + 0.0425/365))

Plugging this into a calculator, we get:

t ≈ 4.69 years

So it will take Katelyn about 4.69 years to earn $250 in interest on her CD.

I hope that helps!

9514 1404 393

Answer:

  A, C, D, E, F

Step-by-step explanation:

The figure has 4 sides: 2 pairs of parallel sides, all of equal length. The angles are right angles.

The figure is a ...

Answer:

A, and F.

Step-by-step explanation: I hope this helps.

Four sides are called a quadrilateral.

Three sides are called a triangle.

Five sides are called a pentagon.

Six sides are called hexagons.

A rectangle is a quadrilateral with four right angles.

A square is a quadrilateral with four right angles.

A rhombus is a quadrilateral with four equal sides.

A parallelogram is a quadrilateral with two pairs of parallel sides.

A trapezoid is a quadrilateral with one pair of parallel sides.

Acute angles are less than 90°

Right angles are exactly 90°

Obtuse angles are more than 90°

Acute triangle has three acute angles.

Right triangle has one right angle.

An obtuse triangle has one obtuse angle.

Isosceles triangle has the minimum of two sides that are equal length.

Equilateral triangle has three sides that are at an equal length.

Scalene triangles have three sides of different lengths,

Acute triangles with three equal sides are called an equiangular triangle.

Answer:

420 is the answer of yhis lenthiest question u nedd to aubract them by 1000 and 580

Step-by-step explanation:

Just eubtract them

The average rate of change of the function f(x) = √(x+4) over the interval 2 ≤ x ≤ 6 is approximately 0.29 to the nearest hundredth.

To find the average rate of change of the function f(x) = √(x+4) over the interval 2 ≤ x ≤ 6, we need to calculate the change in the function divided by the change in the input variable over that interval.

The change in the function between x = 2 and x = 6 is:

f(6) - f(2) = √(6+4) - √(2+4) = √10 - √6

The change in the input variable between x = 2 and x = 6 is:

6 - 2 = 4

So, the average rate of change of the function over the interval 2 ≤ x ≤ 6 is:

(√10 - √6) / 4

To approximate the answer to the nearest hundredth, we can use a calculator or perform long division to get:

(√10 - √6) / 4 ≈ 0.29

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The requried, local minimum and maxium for the given function is √2 and -√2.

We need to find the local maximum and local minimum of the function \(f(x) = 2x + 4x^{(-1)}.\)

First, we find the derivative of f(x):

\(f'(x) = 2 - 4x^{(-2)} = 2 - 4/x^2\)

Setting f'(x) = 0 to find the critical points:

\(2 - 4/x^2 = 0\)

Solving for x, we get:

x = ±√2

To determine whether these critical points are local maxima or minima, we need to examine the sign of the second derivative:

\(f''(x) = 8x^{(-3)}\)

When x = √2, f''(√2) = 8/(√2)³ = 8√2 > 0, so x = √2 is a local minimum.

When x = -√2, f''(-√2) = 8/(-√2)³ = -8√2 < 0, so x = -√2 is a local maximum.

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The values of the spaces at the right hand side are: 4, 1, 64 and 0 respectively.

The index of a number is a figure reflecting price or quantity compared with a base value. The base value always has an index number of 100. The index number is then expressed as 100 times the ratio to the base value. Note that index numbers have no units.

The index of a number is the power to which a number is raised.

\(\left[\begin{array}{ccc}4&4&\\0&1\\\end{array}\right]\) = \(\left[\begin{array}{ccc}4^{n} & - \\0&1&\\\end{array}\right]\)

Equating each value at the left hand side with the value at the right hand side we have

4\(^{1} = 4^{n}\)

Dividing the powers because they are uniform we have

n = 1

Also, 4*4*4*4 = 64

This implies that \(4^{4} = 64\)

In the same way, 0 = 0¹

= 0

Lastly, 1 = 1¹

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Answer: just to press anyone it does not mark you for it lol

Step-by-step explanation:

The value of side c to the nearest tenth is 4.2.

The law of cosines signifies the relation between the lengths of sides of a triangle with respect to the cosine of its angle.

It is expressed as:

c² = a² + b² - ( 2ab × cosC )

From the diagram:

a = 7

b = 8

Angle C = 32 degrees

Plug these values into the above formula and solve for c.

c² = a² + b² - ( 2ab × cosC )

c = √( a² + b² - ( 2ab × cosC ) )

c = √( 7² + 8² - ( 2 × 7 × 8 × cos32 ) )

c = √( 49 + 64 - ( 112 × cos32 ) )

c = √( 113 - 94.98 )

c = √18.02

c = 4.2

Therefore, the value of c is 4.2.

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Given are three vectors in set B.

To show that B is dependent

The determinant

Hence vectors are dependent

b) The given equation

Let us try parametrically

These 3 vectors are collinear and hence equation would be

c) Basis for B would be only 2 dimensional

i.e. any two vectors out of 3 form basis

The basis would be (1,0,1) and (0,1,2)

Answer:

Yes, since the total pay of $120 is more than the $100 cost of the MP3 player.

Step-by-step explanation:

hourly pay: $5/hour

number of hours: 24 hours

total pay = hourly pay × number of hours

total pay = $5/hour × 24 hours

total pay = $120

MP3 player costs $100.

Total pay is $120.

Answer: Yes, since the total pay of $120 is more than the $100 cost of the MP3 player.

The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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Answer:

350

Step-by-step explanation:

Let,

 x = bench

 x + 35 = garden table

EQUATION:

   (x) + (x + 35) = 735

   2x = 735 - 35

   2x = 700

   x = 350

SUBSTITUTE:

  bench costs 350 and garden table costs 385

Hello!

Based on the info we have we can form 2 equations :

(Keep in mind x is the cost of the garden table and y is that of the bench)

Now substitute x in the first equation.

⇒ y + 35 + y = 735

⇒ 2y = 700

⇒ y = 350

∴ The cost of the bench is \(\fbox {350}\)

1. Number of athletes did not own any of the three items = 259 - 228

= 31.

2. Number of athletes own a convertible and a TV but not a store = 44 - 9

= 35.

3. Number of athletes own a convertible or a TV = 110 + 91 - 44

= 157.

4. Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.

5. Number of athletes owned at least one type of item = 259 - 31

= 228

6. Number of athletes own a TV or a store, but not a convertible = 13 + 34 +71

= 118.

The number of athletes did not own any of the three items need to subtract the number of athletes who own at least one item from the total number of athletes surveyed.

Total number of athletes surveyed = 259

Number of athletes own at least one item = 110 + 91 + 120 - 15 - 43 - 44 + 9 = 228

Number of athletes who did not own any of the three items = 259 - 228 = 31.

The number of athletes who owned a convertible and a TV but not a store need to subtract the number of athletes who own all three items from the number of athletes who own a convertible and a TV.

Number of athletes who own a convertible and a TV = 44

Number of athletes who own all three items = 9

Number of athletes who own a convertible and a TV but not a store = 44 - 9 = 35

The number of athletes who owned a convertible, or a TV need to add the number of athletes who own a convertible to the number of athletes who own a TV and then subtract the number of athletes own both a convertible and a TV.

Number of athletes who own a convertible or a TV = 110 + 91 - 44

= 157.

The number of athletes owned exactly one type of item need to add up the number of athletes who own a convertible only the number of athletes own a TV only and the number of athletes who own a store only.

Number of athletes own a convertible only = 110 - 15 - 9 = 86

Number of athletes own a TV only = 91 - 44 - 9 = 38

Number of athletes own a store only = 120 - 15 - 43 - 9 = 53

Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.

The number of athletes who owned at least one type of item can use the result from part (1).

Number of athletes who owned at least one type of item = 259 - 31

= 228

The number of athletes who owned a TV or a store but not a convertible need to subtract the number of athletes who own all three items, and the number of athletes own a convertible and a TV from the number of athletes own a TV or a store.

Number of athletes own a TV or a store = 91 + 120 - 43 - 9 = 159

Number of athletes own a TV or a store not a convertible = 13 + 34 +71

= 118.

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Answer:

The surface area of a square pyramid is the sum of the areas of all its 4 triangular side faces with the base area of the square pyramid. If a, h, and l are the base length, the height of the pyramid, and slant height respectively, then the surface area of the square pyramid = a2+ 2al (or) a2+2a √a24+h2 a 2 4 + h 2 .

Step-by-step explanation:

Answer:

hey dude, sorry if this is wrong but i think its 6cm

Step-by-step explanation:

Answer:

Profit Percent​= 20%.

Step-by-step explanation:

Let's find how much the shopkeeper was charging for each book. For that, we divide the total amout of money earned by selling 4 books:

Rs 360/4 books= Rs 90/1 book., the books had a price of Rs 90/each.

Now, if he sells the remaining books (3 books) at the same price (Rs 90), he would be earning a total of Rs 90* 7= Rs 630.

To find his profit percent you can either divide the difference between total earnings and total costs by the total costs, or divide the difference of earnings of 1 book and the cost of 1 book by the cost of each book. Let's do it with the total amounts:

\(\frac{|Rs630-Rs525|}{Rs525}*100 =20.\)

In this case, the 20% is a profit percent, because the earnings were a larger amount than the costs.

The correct answer is Confidence interval lower bound: 32.52 cm,Confidence interval upper bound: 37.48 cm

To calculate the confidence interval for the true mean height of the loaves, we can use the t-distribution. Given that the sample size is small (n = 10) and the population standard deviation is unknown, the t-distribution is appropriate for constructing the confidence interval.

The formula for a confidence interval for the population mean (μ) is:

Confidence Interval = sample mean ± (t-critical value) * (sample standard deviation / sqrt(sample size))

For the first situation:

n = 15

Confidence level is 95% (which corresponds to an alpha level of 0.05)

x = 35 (sample mean)

s = 2.7 (sample standard deviation)

Using RStudio or a t-table, we can find the t-critical value. The degrees of freedom for this scenario is (n - 1) = (15 - 1) = 14.

The t-critical value at a 95% confidence level with 14 degrees of freedom is approximately 2.145.

Plugging the values into the formula:

Confidence Interval = 35 ± (2.145) * (2.7 / sqrt(15))

Calculating the confidence interval:

Lower Bound = 35 - (2.145) * (2.7 / sqrt(15)) ≈ 32.52 (rounded to 2 decimal places)

Upper Bound = 35 + (2.145) * (2.7 / sqrt(15)) ≈ 37.48 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 32.52 cm, and the upper bound is approximately 37.48 cm.

For the second situation:

n = 37

Confidence level is 99% (which corresponds to an alpha level of 0.01)

x = 82 (sample mean)

s = 5.9 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (37 - 1) = 36.

The t-critical value at a 99% confidence level with 36 degrees of freedom is approximately 2.711.

Plugging the values into the formula:

Confidence Interval = 82 ± (2.711) * (5.9 / sqrt(37))

Calculating the confidence interval:

Lower Bound = 82 - (2.711) * (5.9 / sqrt(37)) ≈ 78.20 (rounded to 2 decimal places)

Upper Bound = 82 + (2.711) * (5.9 / sqrt(37)) ≈ 85.80 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 78.20 cm, and the upper bound is approximately 85.80 cm.

For the third situation:

n = 1009

Confidence level is 90% (which corresponds to an alpha level of 0.10)

x = 0.9 (sample mean)

s = 0.04 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (1009 - 1) = 1008.

The t-critical value at a 90% confidence level with 1008 degrees of freedom is approximately 1.645.

Plugging the values into the formula:

Confidence Interval = 0.9 ± (1.645) * (0.04 / sqrt(1009))

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