I need help on questions f. and h.

Answer:

x = 10 2/11

Step-by-step explanation:

(x - 52/11) + 20/11 = 80/11

x - 52/11 = 60/11

x = 112/11

x = 10 2/11

The cosine of twice the angle is given as follows:

cos(2θ) = -527/625.

The identity to obtain the cosine of twice the angle is given as follows:

cos(2θ) = cos²(θ) - sin²(θ).

The relation between the sine and the cosine is given as follows:

sin²(θ) + cos²(θ) = 1.

Hence the cosine squared is obtained as follows:

cos²(θ) = (7/25)²

cos²(θ) = 49/625.

The sine squared is given as follows:

sin²(θ) = 1 - cos²(θ)

sin²(θ) = 1 - (49/625)

sin²(θ) = (625/625) - (49/625)

sin²(θ) = 576/625.

Meaning that the cosine of twice the angle is given as follows:

cos(2θ) = cos²(θ) - sin²(θ).

cos(2θ) = 49/625 - 576/625

cos(2θ) = -527/625.

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The calculated value of the function f(3) in the mapping of ordered pairs is -3

From the question, we have the following parameters that can be used in our computation:

The mapping

Where

Mapping implies that we pair x values to y values

On the mapping, we have the following representation

3 ---- -1

This means that the value of  f(3) = -1

This is true because the x values 3 in the domain points to the y value -1 in the range

Hence, the value of  f(3) is -1

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The probability for different conditions that a man between the ages of 25 and 29 was never married is 25% with sample size 40 are,

Mean representing man never married =10.

Standard deviation of the never married man =2.7

probability of the men exactly 13 never married = 0.137.

probability that ten or fewer men never married = 0.056.

probability representing 21 were married = 0.3188

probability of man never married between age 25 and 29 = 25%

Sample size 'n' = 40

Blank 1,

The expected number of men who have never been married is,

Expected value

= n × p

= 40 × 0.25

= 10

The mean number of men who have never been married is 10.

Blank 2,

The standard deviation of the number of men who have never been married can be calculated using the formula,

Standard deviation = √(n × p × (1 - p))

where n is the sample size

and p is the probability of success never been married.

Standard deviation

= √(40 × 0.25 × (1 - 0.25))

= 2.7

The standard deviation of the number of men who have never been married is 2.7.

Blank 3,

The probability of exactly 13 men who have never been married can be calculated using the binomial probability formula,

P(X = a) = ⁿCₐ× pᵃ × (1 - p)ⁿ⁻ᵃ

where n is the sample size,

p is the probability of success never been married,

and k is the number of men who have never been married.

P(X = 13)

= (⁴⁰C₁₃) × 0.25¹³ × (1 - 0.25)⁴⁰⁻¹³

= 0.137

The probability that exactly thirteen men were never married is 0.137.

Blank 4,

The probability of ten or fewer men who have never been married can be calculated using the cumulative binomial probability formula,

P(X ≤ k) = [tex]\sum[/tex]ⁿCₓ × pˣ (1 - p)ⁿ⁻ˣ   for x = 0 to k

where n is the sample size,

p is the probability of success never been married,

and k is the maximum number of men who have never been married.

P(X ≤ 10) = ∑⁴⁰Cₓ × 0.25ˣ × (1 - 0.25)⁴⁰⁻ˣ  for x = 0 to 10

⇒ P(X ≤ 10) = 0.056

The probability that ten or fewer men were never married is 0.056.

Blank 5,

probability of 21 were married

= (⁴⁰C₂₁) × 0.75²¹ × (1 - 0.75)⁴⁰⁻²¹

= 131,282,408,400 × 0.00282475249 ×  0.000000009313

=0.3188

Therefore, the probability for different conditions are,

Mean of the man never married =10.

Standard deviation never married =2.7

probability of exact 13 men never married = 0.137.

probability of ten or fewer men never married = 0.056.

probability of 21 were married = 0.3188

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The volume of the given triangular prism is 144 cm³.

option A.

The volume of a triangular prism can be calculated by multiplying the area of the base triangle by the height of the prism.

The formula for calculating the volume of a triangular prism is:

Volume = Base Area × Height

Given the base of the triangular prism is a triangle with a base of 8 cm and a height of 3 cm, the area of the base triangle can be calculated as:

Base Area = 0.5 × base × height

Base Area = 0.5 × 8 cm × 3 cm

Base Area = 12 cm²

The volume of a triangular prism is calculated as;

Volume = Base Area × Height

Volume = 12 cm² × 12 cm

Volume = 144 cm³

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1. If a value of 120.5° is added to the data, 58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57, D. The mean increases by 3.1°.

2. If a shoe size of 6 is added to the ordered data, 5, 5.5, 6, 6.5, 6.5, 7, 7.5, 8, 8, 8.5, B. The IQR remains a 2.

3. If a value of 101° is added to the data, 58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57, B. The mean increases by 1.6°.

4. If a shoe size of 9 is added to the ordered data, 5, 5.5, 6, 6.5, 6.5, 7, 7.5, 8, 8, 8.5, the median that was 6.75, now D. The median increases to 7.

5. If a value of 60° is added to the data, 58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57, C. The median decreases to 77°.

6. If a value of 80.2° is added to the data, 58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57, C. The range stays at 48°.

7. If a value of 58° is added to the data, (57, 58, 61, 66, 71, 77, 80.8, 82, 91, 95, 100, 102, 105), the measure that chances the most is the D. IQR with the new value as 32°.

To compute the interquartile range, determine the median of the data's lower and upper half and subtract quartile 1 from quartile 3.

1. Average high temperatures for a city:

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

Total = 965°

Average = 80.4° (965° ÷ 12)

New average with 120.5° added:

New total = 1,085.5° (965° + 120.5°)

Average = 83.5° (1,085.5° ÷ 13)

The difference in mean = 3.1° (83.5° - 80.4°)

2. Shoe Sizes:

5  5.5  6  6.5   6.5   7  7.5  8  8  8.5

Median = 6.75 (6.5 + 7)/2

Interquartile = 8 - 6 = 2

Add shoe size 6 to the data:

5  5.5  6    6   6.5   6.5   7  7.5  8  8  8.5

Median = 6.5

IQR = 8 - 6 = 2

3. Average Temperature:

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

Total = 965°

Mean = 80.4° (965° ÷ 12)

If a value of 101° is added to the data, the new mean becomes:

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57, 101

Total = 1,066

Mean = 82° (1,066 ÷ 13)

The difference in the mean = 1.6° (82° - 80.4°)

4. Raw Data:

 5.5   6   7     8.5   6.5

 6.5   8   7.5  8      5

Arranged:

5  5.5  6  6.5   6.5   7  7.5  8  8  8.5

Median of data = 6.75 (6.5 + 7) ÷ 2

When 9 is added to the data:

5  5.5  6  6.5  6.5  7  7.5  8  8  8.5  9

Median = 7

5. 58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

Ordered Data:

57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105

Median = 79.5 (77 + 82)/2

Add 60°, the new ordered data:

57, 58, 60, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105

Median = 77

6. Range:

Highest value = 105

Lowest value = 57

Difference = 48

Range = 48 (105 - 57)

Add 80.2°, the range stays at 48° (105 - 57)

7. Average high temperatures:

Raw Data:

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

Ordered Data:

57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105

Total = 965

Mean = 80.4 (965 ÷ 12)

Median = 79.5 (77 + 82)/2

IQR = 39 (100 - 61)

Range = 48 (105 - 57)

A new temperature of 58° is added,

57, 58, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105

Total = 1,023

Mean = 78.7 (1,023 ÷ 13)

Median = 77

IQR = 32 (93 - 61)

Range = 48 (105 - 57)

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Answer:

y=x+8

Step-by-step explanation:

The answer is y=x+8

Answer:

Step-by-step explanation:

Center is at (0, 0)  for circle  you need to find the slope from center to point so that you can find perpendicular slope.  

slope = (4-0)/(4-0) =1

the perpendicular slope needs to be flipped and opposite sign

m(tan)= -1   point for tan = (4,4)   put in point-slope form

y-4= -1(x-4)

y-4 =-1x+4

y = -x +8

The benefit-cost ratio of the program intervention is 12:7. This means that for every $7 spent on the program, $12 worth of benefits are realized.

What is ratio?

A ratio is a way of comparing two or more quantities that are measured in the same units. It is a mathematical expression that shows the relationship between two numbers or quantities.

The benefit-cost ratio (BCR) is a ratio of the total benefits of a program intervention to its total costs. In this case, the BCR can be calculated as:

BCR = Total benefits / Total costs

From the given information, the total cost of the program intervention is $1.75 million, and the savings resulting from the program are $3 million. Therefore, the total benefits are $3 million, and the BCR can be calculated as:

BCR = $3 million / $1.75 million

Simplifying this fraction, we can divide both the numerator and denominator by 0.25 million (or 250,000):

BCR = $12 / $7

Therefore, the benefit-cost ratio of the program intervention is 12:7. This means that for every $7 spent on the program, $12 worth of benefits are realized.

Note that to obtain the ratio of 12:7, we first simplify the fraction by dividing both the numerator and denominator by the highest common factor, which is 250,000 in this case. This gives us a new fraction of 12/7, which can be expressed as the ratio of 12 to 7.

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Using implicit differentiation the second derivative is d²y/dx² = [-2x³y² × dy/dx  + 2y³x²]/y⁶

Since we have the function x⁴ + y⁴ = 16, we desire to find the second derivative by implicit differentiation. We proceed as follows.

Since  

x⁴ + y⁴ = 16

Taking the first derivative of the function, we have that

d(x⁴ + y⁴)/dx = d16/dx

dx⁴/dx + dy⁴/dx = d16/dx

4x³ + 4y³ × dy/dx = 0

4y³ × dy/dx = -4x³

dy/dx =  -4x³/4y³

dy/dx = -x³/y³

We now differentiate again to take the second derivative of the function. So, we have that

dy/dx = -x³/y³

Using the quotient rule, we have dy/dx = (udv/dx - vdu/dx)/v² where u = -x³ and v = y³.

So, substituting this into the equation, we have that

d(dy/dx)/dx = (-x³dy³/dx - y³d-x³/dx)/(y³)²

= [-x³dy³/dy × dy/dx  - y³d(-x³/dx)]/(y³)²

= [-x³2y² × dy/dx  + y³2x²]/(y³)²

d²y/dx² = [-2x³y² × dy/dx  + 2y³x²]/y⁶

The second derivative is d²y/dx² = [-2x³y² × dy/dx  + 2y³x²]/y⁶

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Answer:

10.30089

Step-by-step explanation:

This is true because to find the radius of a circle is pie x r^2 so if the circle is 4 across then the radius is 2 and 2^2 is 4 so pie x 4pie and there is three circles so the total area of all of the circles is 12pie and the area of the rectangle is 48 because it is 4 wide and 12 tall because its height is 3 times its width and 48- 12pie is 10.30089

Answer: 0.525

Hope this helps. Have a nice day!

The algebraic description of this transformation is (x, y) = 2/3(x, y)

From the question, we have the following parameters that can be used in our computation:

The scale factor is calculated as

Scale factor  = P'/P

Substitute the known values in the above equation, so, we have the following representation

Scale factor  = (-6, 8)'/(-9, 12)

Evaluate

Scale factor  = 2/3

So, the scale factor  is 2/3

This means that the algebraic description is (x, y) = 2/3(x, y)

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Answer:

18573.85

Step-by-step explanation:

Area of rectangle = 42 * 9 * 35 = 13230 cm
Area of half-circle cylinder = 42 * (9^2 * pi) / 2 = 5343.8491 cm

13230 + 5343.8491 = 18573.8491

rounded = 18573.85

A sequence is a list of numbers that follow a specific pattern. Each number in the sequence is called a term. Sequences can be finite (meaning they have a specific number of terms) or infinite (meaning they continue without end).

Arithmetic sequences are a type of sequence where each term is found by adding a constant value to the previous term. This constant value is called the common difference, denoted as d. The formula for the nth term (or any term) of an arithmetic sequence is:

an = a1 + (n-1)d

In other words, we can find any term of an arithmetic sequence by adding the common difference to the previous term.

(i) The next term in the sequence is 27.

(ii) To get this answer, we can see that each term is 6 greater than the previous term

b) To find the tenth term we can write the formula for the nth term of the sequence using the common difference d = 6 and the first term a1 = 3:

an = a1 + (n - 1)d

Substituting n = 10, a1 = 3, and d = 6, we get:

a10 = 3 + (10 - 1)6

a10 = 3 + 54

a10 = 57

Therefore, the 10th term of the sequence is 57

Answer:

Step-by-step explanation:

yes it is

Answer:  

Step-by-step explanation:

This is a 30-60-90 triangle so the shorter leg is your x

the longer leg is [tex]x\sqrt{3}[/tex]

and the hypotenuse is 2x

They gave you the longer leg because it is across from the 60, no the 30 angle.

so 16=[tex]x\sqrt{3}[/tex]

    x=[tex]\frac{16}{\sqrt{3} }[/tex]    you cannot have a root on the bottom so multiply by [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex]

    [tex]x=\frac{16\sqrt{3} }{3}[/tex]   this is the short leg

the long leg multiply by 2   so long leg = [tex]\frac{32\sqrt{3} }{3}[/tex]

The volume and the surface area of the cylindrical bottle is 200.96 cm³ and 226.08 cm² respectively.

Given that a cylindrical bottle has radius 2 of cm and height of 16 cm.

Surface area = 2 π × radius × (radius + height)

= 2 × 3.14 × 2 × (16+2)

= 12.56 × 18

= 226.08

∴ The surface area of the bottle is 226.08 cm².

Volume = π × radius² × height

= 3.14 × 2² × 16

= 200.96 cm³

∴ The volume of the bottle is 200.96 cm³.

Hence, the volume and the surface area of the cylindrical bottle is 200.96 cm³ and 226.08 cm² respectively.

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The relative frequency table can be completed as follows:

January - June (Men) = 60%

January - June (Women) = 40%

July - December (Men) = 40%

July -December (Women) = 60%

The estimation showed a high degree of nearness to the original values.

To complete the frequency table, we will begin by making the estimate as the question instructs. Finally, we will compare the values of the new estimated table with the original table.

The January - June record for men shows a frequency rate of 60% if we do the estimation. With the original figures, the value is 57.1% and this figure is very close to 60%. So, estimates give us a good insight into the correct values of numbers.

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The end of the stencil is located at, (x_2,y_2)=(9,3) is the required answer.

The given line is divided in the ratio 1:3 and the coordinate of the point P at which the line is divided is (3,0).

The best approach is to use the section formula which relates to the internal division of a line.

Given a line from (x_1,y_1) \: to\: (x_2,y_2) which is divided in the ratio m:n, the coordinates of the point P of division is derived using the formula:

[tex]P(x,y)=\left(\dfrac{mx_2+nx_1}{m+n} ,\dfrac{my_2+ny_1}{m+n}\right)[/tex]

In our given case,

P(x,y)=(3,0)

m:n=1:3

(x_1,y_1) =(1,-1)

Our goal is to determine the end of the stencil (x_2,y_2)

Thus:

[tex](3,0)=left(\dfrac{1x_2+3(1)}{3+1} ,\dfrac{1y_2+3(-1)}{3+1}\right)\\Matching \: coordinates\\dfrac{1x_2+3(1)}{3+1}=3\\x_2+3=3*4\\x_2=12-3=9\dfrac{1y_2+3(-1)}{3+1}=0\y_2-3=0*4\y_2=3+0=3[/tex]

Therefore, the end of the stencil is located at, (x_2,y_2)=(9,3) is the required answer.

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The area of the shaded part is 704mm²

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.

The area of the shaded part = area of the whole shape - area of the unshaded part

Area of the whole shape = l×w

= 54 × 16

= 864mm²

Area(1) of the unshaded part = 1/2bh

= 1/2 ×16×8

= 64mm²

Area( 2) of the unshaded part = 1/2bh

= 1/2 ×8 × 8

= 32mm²

Area(3) of the unshaded part = l×w

= 8×8 = 64mm²

therefore the total area of the unshaded part =

64+32+64 = 160mm²

therefore the area of the shaded part = 864-160 =

704mm²

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There are 17,297,280 ways to choose 7 letters, without replacement, from 12 distinct letters when the order matters.

What is permutation?

A permutation of 2 lines is a reordering of two distinct elements. In other words, given two elements, a permutation of 2 lines is a way of arranging them in a different order. For example, if the two elements are A and B, the possible permutations of 2 lines are AB and BA.

If the order of the choices matters, we need to use the concept of permutations. The number of ways to choose 7 letters from 12 distinct letters without replacement and with order mattering is given by:

12P7 = 12! / (12-7)!

= 12! / 5!

= 12 x 11 x 10 x 9 x 8 x 7 x 6

= 17,297,280

Therefore, there are 17,297,280 ways to choose 7 letters, without replacement, from 12 distinct letters when the order matters.

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Triangles ABC and MNO are congruent with each other using Side Side Side Rule of Congruency.

There are four rules of congruency of two triangles.

The rules are:

RHS: where in two right angled triangles, right angle, hypotenuse and another length of side are equal, so they are said to be congruent.

SSS: where in any two triangles if each three sides of a triangle are equal to corresponding sides of another triangle then that triangles are called congruent.

SAS: In two triangles, two sides and angle between them are equal for one triangle to another, so the triangles are said to congruent,

AAS: In two triangles, two angles and one side are equal for one triangle to another, so the triangles are said to congruent,

Here in the picture given that, in triangle ABC and triangle MNO,

AC = MO

AB = NO

BC = MN

So the triangles ABC and MNO are congruent with each other using Side Side Side Rule of Congruency.

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The total surface area of the figure is 315π square feet, or approximately 988.8 square feet if we use a value of 3.14 for π.

Given information:

The cylinder is sitting on the base of the cone.

The diameter of the base is 14 feet.

The slant height of the cone is 9 feet and the height of the cylinder is 11 feet.

To find the total surface area of the figure, we need to find the surface area of the cone and the surface area of the cylinder and add them together.

The surface area of the cone:

The radius of the cone is half of the diameter, which is 7 feet.

The lateral surface area of the cone can be found using the formula:

L = πrs, where r is the radius and s is the slant height.

L = π(7)(9) = 63π square feet

The base of the cone is a circle with a radius of 7 feet, so its area is:

A = πr² = π(7²) = 49π square feet

The surface area of a cylinder:

The radius of the cylinder is also 7 feet since it shares the same base as the cone.

The lateral surface area of the cylinder is:

L = 2πrh, where r is the radius and h is the height.

L = 2π(7)(11) = 154π square feet

The base of the cylinder is another circle with a radius of 7 feet, so its area is:

A = πr² = π(7²) = 49π square feet

Total surface area:

Adding the lateral surface area and the base area of the cone and cylinder, we get:

63π + 49π + 154π + 49π = 315π square feet

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The value of x, y and z in the triangle is 6.0, 8.8 and 12.4 respectively.

A triangle is a plane shape with three sides.

To calculate the value of x in the triangle above, we use the formula below

Formula:

Where:

Substitute these values into equation 1 and solve for x

Similarly, to calculate the value of y, we use the formula below

Where:

Substitute these values into equation 2 and solve for y

Also to find the value of z we use the formula below

Where:

Substitute into equation 3 and solve for z

Hence, the values of z is 12.4.

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The value of [tex]cos(2\theta) = -527/625.[/tex]

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

We know that:

[tex]cos(2\theta) = 2cos^2(\theta) - 1[/tex]

First, we need to find cos^2(a). We can do this by squaring both sides of the given equation:

[tex]cos^2(\theta) = (7/25)^2 = 49/625[/tex]

Now, we can substitute this value into the equation for cos(2a):

[tex]cos(2\theta) = 2(49/625) - 1Simplifying:cos(2\theta) = 98/625 - 625/625cos(2\theta) = -527/625[/tex]

Therefore, The value of [tex]cos(2\theta) = -527/625.[/tex]

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Answer:

Step-by-step explanation:

28

V=b*w*h

b=2

w=2

h=7

V=2*2*7=28

Answer:

B.28

Step-by-step explanation:

Volumn=Base*Height

=2*2*7

=28

Answer:

A. To form an even number, the last digit must be either 8 or 5, since they are the only even digits in the set. Since a digit can be used at most once, there are two choices for the last digit.

For the first digit, there are four choices (1, 3, 5, or 7), since we cannot use 0 or the last digit.

For the second digit, there are four choices remaining (since one digit has been used), and for the third digit, there are three choices left.

Therefore, the total number of four-digit even numbers that can be formed is: 2 x 4 x 4 x 3 = 96.

B. To form a number less than 3000, the first digit must be 1, 3, or 5. There are three choices for the first digit.

For the second digit, there are four choices remaining (since one digit has been used), and for the third digit, there are three choices left.

For the fourth digit, there are two choices remaining (since we cannot use the first digit).

Therefore, the total number of four-digit numbers less than 3000 that can be formed is: 3 x 4 x 3 x 2 = 72.

The point (3, b) lies on the circle with radius 6 and center (-1, -1), the possible values of b are 3.47 or -5.47.

In Mathematics and Geometry, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²

Where:

Substituting the given points into the equation of a circle formula, we have the following;

(x - h)² + (y - k)² = r²

(x - (-1))² + (y - (-1))² = 6²

(x + 1)² + (y + 1)² = 36.

Since the point (3, b) lies on the circle, we have;

(3 + 1)² + (b + 1)² = 36.

16 + b² + 2b + 1 = 36

b² + 2b - 19 = 0

By solving the quadratic function, the possible values of b is given by;

x = 3.47 or x = -5.47.

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