Rewrite in simplest terms: -8(7y-8)-3(7y-7)−8(7y−8)−3(7y−7)

Answer: The volume of the cylinder is approximately 21.2 cubic meters

Step-by-step explanation:

To find the volume of a cylinder, we use the formula:

V = πr^2h

where:

V = volume

r = radius

h = height

In this case, we are given that the cylinder has a height of 3m, but we need to determine the radius.

Since we are not given the radius directly, we can estimate it from the diameter. If the cylinder has a diameter of 3m, then the radius would be half of that, or 1.5m.

So, substituting the values into the formula, we get:

V = π(1.5)^2(3)

V ≈ 21.2 m^3

Rounding to the nearest tenth, the volume of the cylinder is approximately 21.2 cubic meters.

The Values of missing angles are shown below.

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

6. Using Angle sum property

<1 + 72 + 57 = 180

<1 = 51

Now, <2 +72 = 90

<2 = 18

<and, <3+ 57 = 180 (linear pair)

<3 = 123

Now, <4 = 180- 123- 18

<4 = 39

7. <1 = 180- 129 = 51 (linear pair)

<2 = 180- 51 - 95 = 34 (Angle sum property)

<3 = 95 (Vertical opposite angle)

<4= 180- 47 - 95 = 38

<5 = 47  (Vertical opposite angle)

<7= 180-121= 59

<6= 180-59-47= 74

8. Using Angle sum property

13x+ 2 + 5x - 7 + 3x -4 = 180

21x -9 = 180

21x = 189

x= 9

So, angles are 13x+2 = 119, 5x-7 = 38 and 3x-4 = 23

9. Using Exterior Angle property

19x- 18 = 7x+1 + 10x- 9

19x - 18 = 17x  - 8

2x = 10

x= 5

So, angles are 19x-18 = 77, 7x+1 = 36 and 10x-9 = 41

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Answer:

volume of prizm = 1/2 ×6 ×6 ×5 = 90

volume of semi circle = 1/2 x pi x 3^2 x 5 = 70.6858

diff =19.31

Answer:

\(\huge\boxed{\sf x = 3 }\)

Step-by-step explanation:

Given that

f(x) = 4x + 5

Put f(x) = 17

17 = 4x + 5

Subtract 5 to both sides

17 - 5 = 4x

12 = 4x

Divide 4 to both sides

12 / 4 = x

3 = x

OR

x = 3

\(\rule[225]{225}{2}\)

Hope this helped!

The dot plot is in the provided image below;.

To create a dot plot for Ms. Cleary's data, follow these steps:

Label the horizontal axis with numbers from 0 to 10, representing the number of students who were late.

For each value in Ms. Cleary's data set, place a dot above the corresponding number on the horizontal axis.

Repeat this process for each value in the data set.

Ms. Cleary's dot plot should look like this (each dot represents one occurrence of that value in the data set): (look at image)

To create a dot plot for Mr. Tram's data, follow the same process:

Label the horizontal axis with numbers from 0 to 10, representing the number of students who were late.

For each value in Mr. Tram's data set, place a dot above the corresponding number on the horizontal axis.

Repeat this process for each value in the data set.

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A Gallup poll asked 1200 randomly chosen adults what they think the ideal number of children for a family is. Of this sample, 53% stated that they thought 2 children is the ideal number. Construct and interpret a 95% confidence interval for the proportion of all US adults that think 2 children is the ideal number.

Answer:

at 95% Confidence interval level: 0.501776   < p < 0.558224

Step-by-step explanation:

sample size n = 1200

population proportion \(\hat p\)= 53% - 0.53

At 95% confidence interval level;

level of significance ∝ = 1 - 0.95

level of significance ∝ = 0.05

The critical value for \(z_{\alpha/2} = z _{0.05/2}\)

the critical value \(z _{0.025}= 1.96\) from the standard normal z tables

The standard error S.E for the population proportion can be computed as follows:

\(S,E = \sqrt{\dfrac{\hat p \times (1-\hat p)}{n}}\)

\(S,E = \sqrt{\dfrac{0.53 \times (1-0.53)}{1200}}\)

\(S,E = \sqrt{\dfrac{0.53 \times (0.47)}{1200}}\)

\(S,E = \sqrt{\dfrac{0.2491}{1200}}\)

\(S,E = 0.0144\)

Margin of Error E= \(z_{\alpha/2} \times S.E\)

Margin of Error E= 1.96 × 0.0144

Margin of Error E= 0.028224

Given that the confidence interval for the proportion  is  95%

The lower and the upper limit for this study is as follows:

Lower limit: \(\hat p - E\)

Lower limit: 0.53 - 0.028224

Lower limit: 0.501776

Upper limit: \(\hat p + E\)

Upper limit: 0.53 + 0.028224

Upper limit: 0.558224

Therefore at 95% Confidence interval level: 0.501776   < p < 0.558224

Answer:

$4.99

Step-by-step explanation:

hope this helps ;)

Using the quadratic formula to solve quadratic equation, we ge.t L1 = 0.266 m and L2 = 1.23 m.

The compound beam shown in figure 1 is shown below:

Given:

p1 = 840

N p2 = 1150

Nw = 410 N/m.

Point e is located just to the left of 840 N force.

Force equilibrium: ΣFy = 0R1 + R2 = p1 + p2 + wL ----(1)

Moment equilibrium:ΣMy = 0

p1 (L1 + L2) + p2 L2 + wL²/2 = R2 L2 + R1 L1 ----(2)

Here, the length of the first span is L1, the length of the second span is L2, and the total length of the beam is L.

Since point e is located just to the left of 840 N force, it is the location where the first span meets the second span.

Therefore, L1 + e = L2 R1 = ? R2 = ?

Using equation (1),

R1 + R2 = p1 + p2 + wLR1 + R2

= 840 + 1150 + 410 * LR1 + R2

= 1990 + 410 LR2 - R1

= wL R2 - R1

= 410 L - R1

Substituting equation (5) into equation (4),

R1 + 410 L - R1 = 410 LR = 410 L/2R = 205 L.

Therefore, R1 = 205 L - 840 N and

R2 = 1150 + 205 L - 410 L= -255 L + 1150 N.

Now, substituting the values of R1 and R2 into equation (2),

P1 (L1 + L2) + P2 L2 + wL²/2

= (-255 L + 1150 N) L2 + (205 L - 840 N) L1840 (L1 + L2) + 1150 L2 + 410 L²/2

= -255 L³ + 1150 L² + 205 L² - 840 L1 + 840 L1 - 205 L² + 255 L³ 840 L1 + 1395 L² + 895 L - 410 L²/2

= 0L1 + 2.59 L² + 1.06 L - 0.48 = 0.

Using the quadratic formula to solve this quadratic equation, we get L1 = 0.266 m and L2 = 1.23 m.

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Let's assume that the pieces am and N have heights of h_am and h_N respectively, and let k be the number of times the height of piece N fits into the height of piece am (i.e., k is the ratio of the height of piece am to the height of piece N).

We know that the volume of each stack is equal. Let's use the following variables:
- h for the height of each piece of A
- k for the height of each piece of N
- 10 for the number of pieces in stack A
- 8 for the number of pieces in stack N

The equation for the volume of each stack is:
Volume of stack A = h x 10
Volume of stack N = k x 8

Since we know the volumes are equal, we can set the two equations equal to each other:
h x 10 = k x 8

To create an equation relating h and k, we can solve for one variable in terms of the other:
h = (8/10)k
or
k = (10/8)h

Either equation shows how h and k are related to each other. For example, if we know the value of h, we can use the first equation to find k.

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By calculating the equation LHS ≠ RHS, the answer is No solution.

What are the solutions to this system?

There are three types of systems of linear equations in two variables, and three types of solutions:

An independent system has exactly one solution pair (x,y). The point where the two lines intersect is the only solution.

An inconsistent system has no solution.

A dependent system has infinitely many solutions.

For this, you can substitute one of the y's with the other equation

-2x + 2 = -2x - 2

Add 2x to both sides

2 = 0x - 2

Add 2 to both sides

4 = 0

Since 2 does not equal 0 the answer is No solution

Hence, by calculating the equation LHS ≠ RHS, the answer is No solution.

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Answer:

y = 24

Step-by-step explanation:

We can dilate the other sides to figure out what the scale factor is. Once we know the scale factor we can find y.

Divide 12 by 4.

12 / 4 = 3

The scale factor is 3.

Now we must multiply 8 by 3.

8 * 3 = 24.

y = 24.

The difference in elevation between the two points is

An elevation can be defined as the height or depth of a point using the sea level as the reference point. Thus when an object is above the sea level, its elevation or altitude can be determined. But if the object is below the sea level, its depth can be determined.

The sea level is taken to be zero, while elevation is positive. but depth is taken as negative.

Therefore, the difference in elevation between the volcano and oceanic trench can be determined by taking the sea level as 0.

elevation between the two points = elevation - depth

                               = 13741 - (-21151)

                               = 13741 + 21151

                               = 34892

elevation between the two points = 34892 feet.

The difference in elevation between the two points is 34892 feet.

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Answer:

1:3

Step-by-step explanation:

To find the probability of selecting a certain type of item from a collection, simply divide the number of items of that type by the total number of items.

There are 3 + 2 + 1  = 6 marbles in total. There are 2 yellow marbles, so the probability of choosing a yellow marble on the first draw is 2/6. This can be further simplified to 1:3.

Answer:

i would say 2:4

Step-by-step explanation:

think about them as basketball teams

The yellow team has two players

the mix team has 4 players

so the game is 2 players on 4 players

We must first establish the slope of line FG and then locate the negative reciprocal of that slope in order to find the equation of a line that is perpendicular to line FG and passes through the point (2, 0).

The following formula can be used to determine line FG's slope:

slope is equal to y2 - y1 / x2 - x1.

The slope of line FG at points (4, 9) and (1, 3) is:

slope = (3 - 9) / (1 - 4) = -6 / -3 = 2

We choose the negative reciprocal of the slope, which is -1/2, since we want a line that is perpendicular to FG.

The slope (-1/2) and the line's intersection location (2, 0) are now known. The point-slope form of a linear equation can be used to create

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The combined present worth of the costs associated with the proposed bridge design is $9,583,333.

This value is obtained by calculating the present worth of both the construction cost and the annual operating cost over an infinite life of the bridge, considering a MARR (Minimum Attractive Rate of Return) of 12%.

To determine the present worth, we use the formula:

PW = A / (1 + i)^n

Where PW is the present worth, A is the annual cost, i is the interest rate, and n is the number of years.

For the construction cost, we have a one-time expense of $9,000,000. Since it is a single payment, the present worth is equal to the construction cost itself.

For the annual operating cost, we need to calculate the present worth over an infinite life. Using the formula above, we divide the annual cost of $700,000 by the MARR of 12% to obtain $5,833,333.33. Thus, the combined present worth is the sum of the construction cost and the present worth of the annual operating cost, resulting in $9,000,000 + $5,833,333.33 = $9,583,333.

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Step-by-step explanation:

To have an equal number of buns and sausages, Arthur needs to find the least common multiple (LCM) of 6 and 10.

The LCM of 6 and 10 is 30.

Therefore, he should buy at least 30 packs of buns and 30 packs of sausages to get an equal number of buns and sausages.

That way, he would have 30/6 = 5 packs of buns and 30/10 = 3 packs of sausages.

Answer:

17

Step-by-step explanation:

the answer would have been 16.75 but you cant divide a class, so you round up.

Answer:

1. a) SR = 23

b) QV = 25

c) QT = 20

d) PQ = 40

e) VS = 4·√6

2. a) LH = 16

b) EL = 2·√185

c) JG = 30

d) EK = 22

e) KG = 30

3. a) XT = 37

b) TZ = 34

c) ZW = 17

d) XZ = 21

e) SY = 69

Step-by-step explanation:

The circumcenter ΔPQR is the center of the circle that circumscribes ΔPQR

The length of the radius of the circle ≡ VR = VP = QV = 25

a) Given that VR ≅ VP - Radius of circumcircle

VS ≅ VS Reflective property

∠VPS ≅ ∠VRS - Base angles of an isosceles triangle

Right triangle VPS ≅ Right triangle VRS -Hypotenuse and one Leg HL congruency

Therefore, SR ≅ PS -Corresponding parts of congruent triangles are congruent CPCTC

SR + PS = PR = 46

SR + PS = SR + SR = 2·SR = 46

∴ SR = 46/2 = 23

b) QV = VR = 25 = Radius of circumcircle of ΔPQR -Given V = center and Q = vertices of the triangle circumscribed by the circle referred to in the question

c) QT = √(QV² - TV²) = √(25² - 15²) = √400 = 20

d) TV ≅ TV - Reflexive property of congruency

ΔTQV ≅ ΔTVP - Hypotenuse and one Leg (HL) congruency

QT ≅ TP -Corresponding parts of congruent triangles are congruent CPCTC

PQ = QT + TP Given

∴ PQ = QT + QT since QT = TP

PQ = 2·QT = 2 × 20 = 40

e) VS = √(VR² - SR²) = √(25² - 23²) = √96 = 4·√6

2.  The incenter is the center of the incircle of ΔEFG

  a) LH = LK = JL = 16 -Radius of incircle of ΔEFG

b) EL = Hypotenuse of right triangle LHE = √(LH² + EH²) = √(16² + 22²) = √740 = 2·√185

c) JG = Leg length of right triangle JGL = √(LG² - JL²) = √(34² - 16²) = √900 = 30

d) EK = Leg length of right triangle LKE = √(EL² - LK²) = √(740 - 256) = 22

e) KG = Leg length of right triangle LKG = √(LG² - LK²) = √(34²- 16²) = √900 = 30

3. Point Z id the centroid of ΔRST

a) XT = XS - point X on ST bisected by median line RX

ST = XT + XS = XT + XT = 2.XT = 74

XT = 74/2 = 37

b) TZ = 2/3×TW  - Length from a vertex to the centroid on a median line is equal to two third the length of the median line

TZ = 2/3×51 = 34

c) TZ + ZW = TW

∴ ZW = TW - TZ = 51 - 34 = 17

d) RZ = 42 = 2/3×RX - Length from a vertex to the centroid on a median line is equal to two third the length of the median line

∴ RX = 3/2×42 = 63

RZ + XZ = RX - Given

XZ = RX - RZ = 63 - 42 = 21

e) SZ = 2/3×SY - Length from a vertex to the centroid on a median line is equal to two third the length of the median line

SZ + ZY = SY

∴ ZY = SY - SZ = SY - 2/3×SY = 1/3×SY = 23

Which gives;

SY = 3 × 23 = 69.

Let's begin by identifying key information given to us:

A is a 3 x 2 matrix

B is a 2 x 3 matrix

AB is the product of 3 x 2 matrix & 2 x 3 matrix. We obtain a 3 x 3 matrix

Therefore, the size of the product of A & B (that is AB) is a 3 x 3 matrix whenever these products exist

Answer:

(-4, 5),  (-3, 9),  (2, 9)

Step-by-step explanation:

Mathematics: Explain/define.

When you translate a figure, you are moving only changing the location of the figure.

(X-COORDINATE): LEFT - SUBTRACT / RIGHT - ADD

(Y-COORDINATE): DOWN - SUBTRACT / UP - ADD

                               ↓            

For example, in this problem, the figure must be translated 7 units left and 3 units up.

This means to subtract the x-coordinates from 7 and add the y-coordinates to 3. (x - 7, y + 3)

Mathematics: Solve.

Original coordinates:

(3, 2) → (-4, 5).

(4, 6) → (-3, 9).

(9, 6) → (2, 9).

Mathematics: Conclude.

Therefore the new coordinates are: (-4, 5),  (-3, 9),  and (2, 9).

The minimum value is 0.5 and the maximum value is 3.5.

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The correct answer is B) Impossible to determine.

Based on the given information "W 8 Y 2 Z," it is not possible to determine whether the two triangles are similar or not. In order to determine the similarity of triangles, we need additional information such as the measurements of their angles and sides.

The options provided are:

A) Yes; SSS; A VWX - AYZX

B) Impossible to determine.

C) Yes: SAS; AVWX - AYZX

D) The triangles are not similar.

However, none of these options can be determined solely based on the given information. The option A suggests that the triangles are similar based on the Side-Side-Side (SSS) similarity criterion and the similarity statement "A VWX - AYZX." However, we don't have any information about the lengths of the sides of the triangles, so we cannot conclude whether the SSS criterion is met.

Therefore, the correct answer is B) Impossible to determine.

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Suppose there are two triangles with no measurements, angles and sides. Then, W 8 Y 2 Z Are the two triangles similar? If so, state the reason and the similarity statement. A) Yes; SSS; A VWX - AYZX B) Impossible to determine. C) Yes: SAS; AVWX - AYZX D) The triangles are not similar.

Answer:

D. 95800

Step-by-step explanation:

958x10^2

958 x 100

95800 Alternative Form: 9.58 x 10^4

Answer:D

Step-by-step explanation: All you need to do is move the non existent decimal in 958 2 spaces to the right. So it would go from 958. to 95,800.

To match decimal values with their corresponding hexadecimal values, we need to convert the decimal numbers into their hexadecimal equivalents using division and remainders.

To match each decimal value on the left with the corresponding hexadecimal value, we need to convert the decimal numbers into their hexadecimal equivalents.

Here are a few examples:

1. Decimal 10 = Hexadecimal A

To convert 10 to hexadecimal, we divide it by 16. The remainder is A, which represents 10 in hexadecimal.

2. Decimal 25 = Hexadecimal 19

To convert 25 to hexadecimal, we divide it by 16. The remainder is 9, which represents 9 in hexadecimal. The quotient is 1, which represents 1 in hexadecimal. Therefore, 25 in decimal is 19 in hexadecimal.

3. Decimal 128 = Hexadecimal 80

To convert 128 to hexadecimal, we divide it by 16. The remainder is 0, which represents 0 in hexadecimal. The quotient is 8, which represents 8 in hexadecimal. Therefore, 128 in decimal is 80 in hexadecimal.

Remember, the hexadecimal system uses base 16, so the digits range from 0 to 9, and then from A to F. When the decimal value is larger than 9, we use letters to represent the values from 10 to 15.In conclusion, to match decimal values with their corresponding hexadecimal values, we need to convert the decimal numbers into their hexadecimal equivalents using division and remainders.

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The nth derivative of f(x) = e^(-yx) - 1 is (-1)^(n+1)y^ne^(-yx).

(a) Let's find the first few derivatives of f(x) = e^(-x^n):

f(x) = e^(-x^n)

f'(x) = -nx^(n-1)e^(-x^n)

f''(x) = (-n(n-1)x^(2n-2) + nx^n)e^(-x^n)

f'''(x) = (n(n-1)(2n-2)x^(3n-3) - 2n(n-1)*x^(2n-1))e^(-x^n)

From these first few derivatives, we can observe the pattern that the nth derivative is given by:

f^(n)(x) = e^(-x^n)P_n(x)

where P_n(x) is a polynomial of degree n-1 in x, given by the recurrence relation:

P_1(x) = -n

P_k(x) = -n(k-1)P_(k-1)(x) + nx^n(k-1)!

Therefore, the nth derivative of f(x) = e^(-x^n) is e^(-x^n)*P_n(x).

(b) Let's find the first few derivatives of f(x) = e^(-yx) - 1:

f(x) = e^(-yx) - 1

f'(x) = -ye^(-yx)

f''(x) = y^2e^(-yx)

f'''(x) = -y^3*e^(-yx)

From these first few derivatives, we can observe the pattern that the nth derivative is given by:

f^(n)(x) = (-1)^(n+1)y^ne^(-yx)

Therefore, the nth derivative of f(x) = e^(-yx) - 1 is (-1)^(n+1)y^ne^(-yx).

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The value of K is approximately 0.00000086938. The solution can be found in the  following manner.

To find the value of K, we need to integrate the joint probability density function over the entire domain and set it equal to 1, since the total probability of all possible outcomes must be 1.

So, we have:

∫∫f(x, y) dx dy = 1

∫20³⁰ ∫20³⁰ K(x² + y²) dx dy = 1

We can simplify this expression by using polar coordinates, where:

x = r cos(θ)

y = r sin(θ)

and the Jacobian is:

dx dy = r dr dθ

So, the integral becomes:

∫0²π ∫20³⁰ K(r²)(r dr dθ)

K ∫0²π ∫20³⁰ r³ dr dθ

K ∫0²π [1/4 r⁴]20³⁰ dθ

K ∫0²π (1/4)(30⁴ - 20⁴) dθ

K = 1 / [π(30⁴ - 20⁴)/4]

K = 1 / [π(810000 - 160000)]

K = 1 / 1151401.09

So, the value of K is approximately 0.00000086938.

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Therefore , the solution of the given problem of expressions comes out to be 0.872x is the equation that, in terms of x, expresses the total sum Damian paid at the register.

Shifting numbers, variable which could be expanding, decreasing, or blocking, should be used instead of random estimations. They were only able to assist one another by swapping tools, information, or fixes for problems. The statement of reality equation may include the justifications, elements, or quantitative remarks for techniques like greater dispute, fabrication, and blending.

Here,

Damian paid the following sum at the register, which is stated as follows:

=> Total price = regular price + tax.

The original price less 20% of the original price is the discounted price, which is written as follows:

=> Price after discount = x - 0.2x = 0.8x

The tax is represented as: The tax is 9% of the discounted price.

=> Tax = 0.09(0.8x) = 0.072x

Damian spent a total of x dollars at the register, hence the following phrase describes that total amount in terms of x:

Total price equals regular price plus tax.

=> Total = 0.8x+0.072x

=> Amount total = 0.872x

So, 0.872x is the equation that, in terms of x, expresses the total sum Damian paid at the register.

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The advantages of the 'Monthly Reporting Form' are given below:a) Reduced administrative hassle compared to single shot: Monthly reporting forms reduce the workload of administrative work that may have been required if it was a single-shot.

For instance, when it comes to accounting and finance, monthly reporting can help to reduce the administrative burden that comes with running a business. This is because monthly reporting makes it easier to keep track of financial data, ensuring that records are updated on a more frequent basis.

There is a lower rate associated with monthly reporting forms as they can offer a reduction in cost compared to single-shot options. This is because they can save time and money in the long run, reducing the amount of work and administration required to keep track of things.

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The position function is obtained by integrating the acceleration function twice and applying initial conditions: s(t) = -5/16 sin(4t) + 9/4t + 6.

To find the position function, we need to integrate the acceleration function twice with respect to time (t) and apply the initial conditions.

Given:

Acceleration function: a(t) = 5 sin(4t)

Initial velocity: v(0) = 1

Initial position: s(0) = 6

First, integrate the acceleration function to find the velocity function:

v(t) = ∫(a(t)) dt = ∫(5 sin(4t)) dt = -5/4 cos(4t) + C1

Next, apply the initial velocity condition to solve for the constant C1:

v(0) = -5/4 cos(0) + C1 = 1

C1 = 1 + 5/4 = 9/4

Now, integrate the velocity function to find the position function:

s(t) = ∫(v(t)) dt = ∫(-5/4 cos(4t) + 9/4) dt = -5/16 sin(4t) + 9/4t + C2

Finally, apply the initial position condition to solve for the constant C2:

s(0) = -5/16 sin(0) + 9/4(0) + C2 = 6

C2 = 6

Therefore, the position function is:

s(t) = -5/16 sin(4t) + 9/4t + 6 (Expression using t as the variable).

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