Mathematics College

## Answers

**Answer 1**

**400Answer:**

**Step-by-step explanation: **

## Related Questions

{[(30+40)+(40-30)]x(20+10)}

### Answers

Let's simplify the expression step by step:

First, let's simplify the inner parentheses:

(30 + 40) = 70

(40 - 30) = 10

The expression now becomes:

[(70) + (10)] x (20 + 10)

Next, let's simplify the addition within the parentheses:

(70) + (10) = 80

(20 + 10) = 30

The expression further simplifies to:

80 x 30

Finally, let's multiply:

80 x 30 = 2400

Therefore, the final result of the expression [(30+40)+(40-30)]x(20+10) is 2,400.

I hope this helps! :)

{[(30+40)+(40-30)]x(20+10)}

{[70 + 10]x 30}

{80 x 30}

2400

variable of 10(n+3)=1,000,00

### Answers

**Answer: Distribute the 10 on the left side of the equation:**

**10n + 30 = 1,000,000**

**Subtract 30 from both sides of the equation to isolate the term with n:**

**10n = 1,000,000 - 30**

**10n = 999,970**

**Divide both sides of the equation by 10 to solve for n:**

**n = 999,970 / 10**

**n = 99,997**

**Therefore, the value of the variable n that satisfies the equation 10(n + 3) = 1,000,000 is n = 99,997.**

**Step-by-step explanation:**

HELP PLEASEE PLEASE I NEED TO PASS THIS LESSON

### Answers

The **function **[tex]G(t)= 1024(0.5)^{t-1[/tex] models the number of computer games sold where t is the number of days since the release date and G(t) is the number of computer games sold.

The given table is

Days After Number of

Release Date Games sold

0 1024

1 512

2 256

3 128

Here, the common ratio = 512/1024

= 1/2

The formula to find nth term of the** geometric sequence** is aₙ=arⁿ⁻¹. Where, a = first term of the sequence, r= common ratio and n = number of terms.

Here, [tex]G(t)= 1024(0.5)^{t-1[/tex]

Therefore, the **function **[tex]G(t)= 1024(0.5)^{t-1[/tex] models the number of computer games sold where t is the number of days since the release date and G(t) is the number of computer games sold.

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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

### Answers

The** length **of the **arc** LM is 8.72 cm.

We have,

The** length** of an **arc** is the distance that runs through the curved line of the circle making up the arc.

The** length **of an arc is expressed as;

l = tetha/360 × 2πr

tetha = R

R = 100°

and, radius = 5 units

so, we get,

l = 100/360 × 2 × 3.14 × 5

l = 8.72 cm (1.dp)

therefore the **length **of th**e arc** LM is 8.72 cm

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The centre of a circle is the point with coordinates (-1, 2)

The point A with coordinates (5, 9) lies on the circle.

Find an equation of the tangent to the circle at A.

Give your answer in the form ax + by + c = 0 where a, b and c are integers.

### Answers

The **equation **of the **tangent **to the **circle **at point A is 6x + 7y - 93 = 0

**How do we solve for the equation of the tangent to the circle?**

The **equation **of a **circle** in standard form is (x-h)² + (y-k)² = r²,

(h,k) is the center of the circle

r is the radius.

The **radius **formula ⇒ **√((x₂ - x₁)² + (y₂ - y₁)²).**

Here,

x₁ = -1, y₁ = 2 (center of the circle),

x₂ = 5, y₂ = 9 (point A on the circle).

∴

r = √((5 - (-1))² + (9 - 2)²) = √(36 + 49) = √85.

Now, we have the equation of the circle: (x - (-1))² + (y - 2)² = 85, or (x + 1)² + (y - 2)² = 85.

The slope of the radius from the center of the circle to point A ⇒ (y₂ - y₁) / (x₂ - x₁)

= (9 - 2) / (5 - (-1)) = 7/6.

**tangent line** is the negative reciprocal of the slope of the radius, ∴ -6/7.

The equation of a line in **point-slop**e form is y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line.

The slope of the tangent line (m) is -6/7 and it passes through point A(5,9). Substituting these values in, it becomes

y - 9 = -6/7 (x - 5).

Multiplying every term by 7 to clear out the fraction and to have the equation in the ax + by + c = 0 form, we get:

7y - 63 = -6x + 30,

or

6x + 7y - 93 = 0.

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a pyramid and a cone are both 10 centimeters tall and have the same volume what statement

### Answers

**Answer:**** "The pyramid and the cone have the same volume despite their different shapes."**

**Step-by-step explanation: **If a pyramid and a cone are both 10 centimeters tall and have the same volume, then the statement that can be made is:

**"The pyramid and the cone have the same volume despite their different shapes."**

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Please answer these questions by today

### Answers

41.

Out of the 18 **parts**, we **shade** 5 parts

Out of the 27 **parts**, we **shade** 4 parts

42.

There are 60 **pieces**.

43.

The **fractional** **part** for each person.

44.

10(1/2), 1/21, 2(14/15), and 18.

We have,

41.

a.

1/3 x 5/6

= 5/18

This means,

Out of the 18 parts, we **shade** 5 parts

b.

2/9 x 2/3

= 4/27

This means,

Out of the 27 parts, we **shade** 4 parts

42.

String = 15 feet

Length of each piece = 1/4 feet

Now,

The number of 1/4 feet pieces.

= 15/(1/4)

= 15 x 4

= 60 **pieces**

43.

Original pizza = 1

Half pizza = 1/2

Number of people = 3

Now,

The **fractional** **part** for each person.

= 1/2 ÷ 3

= 1/6

44.

a.

7/6 x 9

= 7/2 x 3

= 21/2

= 10(1/2)

b.

1/7 ÷ 3

= 1/(7 x 3)

= 1/21

c.

4/5 x 3(2/3)

= 4/5 x 11/3

= 44/15

= 2(14/15)

d.

2 ÷ 1/9

= 2 x 9/1

= 18

Thus,

41.

Out of the 18 **parts**, we **shade** 5 parts

Out of the 27 **parts**, we **shade** 4 parts

42.

There are 60 **pieces**.

43.

The **fractional** **part** for each person.

44.

10(1/2), 1/21, 2(14/15), and 18.

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50 Points! Multiple choice geometry question. Photo attached. Thank you!

### Answers

**Answer:**

8 feet

**Step-by-step explanation:**

Let b be the length of the base. Then the height is b+6 ft.

The area of the parallelogram is given by:

Area = b(b + 6) = 160

Solving for b, we get,

[tex]b^2 + 6b - 160 = 0[/tex]

Factoring the expression, we get:

(b - 8)(b + 20) = 0

Therefore, b = 8 or b = -20.

Since the base cannot be negative, b = 8.

Therefore, the length of the base of the parallelogram is 8 feet.

find the quotient of 5/31 divided by 15/23 . reduce your answer to the lowest fraction

### Answers

To find the quotient of 5/31 divided by 15/23, first invert the divisor and multiply. This gives us (5/31) x (23/15). We can simplify this expression by canceling out the common factors of 5 and 15, which gives us (1/31) x (23/1) = 23/31. Therefore, the quotient of 5/31 divided by 15/23, reduced to the lowest fraction, is 23/31.

What is B^2+8b+7??

Can someone explain it step by step please?

### Answers

**Step-by-step explanation:**

B^2+8b+7 is a quadratic expression. It can be factored as (b+7)(b+1).

To factor a quadratic expression, you can use the following steps:

1. Find two numbers that add up to the coefficient of the middle term (8) and multiply to the constant term (7).

2. Write the quadratic expression as a product of two binomials, with the two numbers you found in step 1 as the coefficients of the terms in each binomial.

In this case, the two numbers that add up to 8 and multiply to 7 are 7 and 1. So, we can factor B^2+8b+7 as follows:

(b+7)(b+1)

This means that B^2+8b+7 is equal to the product of (b+7) and (b+1).

Here is a step-by-step explanation of how to factor B^2+8b+7:

1. The coefficient of the middle term is 8.

2. The constant term is 7.

3. The two numbers that add up to 8 and multiply to 7 are 7 and 1.

4. Therefore, B^2+8b+7 can be factored as (b+7)(b+1).

B^2+8b+7 is a quadratic expression.

To solve it, you can use the quadratic formula, which is:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 1, b = 8, and c = 7.

So, substituting the values, we get:

x = (-8 ± √(8^2 - 4(1)(7))) / 2(1)

x = (-8 ± √(64 - 28)) / 2

x = (-8 ± √36) / 2

x = (-8 ± 6) / 2

x = -1 or -7

Therefore, B^2+8b+7 is equal to -1 or -7.

Multiply the following binomials (2x - 3y)(8x - y)

### Answers

**Answer:**

16x + [tex]3y^{2}[/tex] - 26xy

**Step-by-step explanation:**PEMDAS

(2x - 3y)(8x - y)

= 16x - 2xy - 24xy + [tex]3y^{2}[/tex]

= 16x + [tex]3y^{2}[/tex] - 26xy

Solve (D ^ 2 - 6D + 9) * y = 0

### Answers

The solution to the given **differential equation** is y(x) = (C1 + C2x) * e^(3x), where C1 and C2 are arbitrary constants.

To solve the given differential equation, we need to find the function y(x) that **satisfies **the equation:

(D^2 - 6D + 9)y(x) = 0,

where D represents the differentiation operator.

Let's break down the solution process step by step:

Characteristic Equation

First, we'll find the **characteristic **equation associated with the given differential equation. For a second-order linear homogeneous differential equation of the form aD^2y + bDy + cy = 0, the characteristic equation is obtained by replacing D with λ:

λ^2 - 6λ + 9 = 0.

Solving the Characteristic Equation

Now, we solve the characteristic equation to find the **values **of λ. Factoring the equation, we get:

(λ - 3)^2 = 0.

From this, we see that λ = 3 (with a multiplicity of 2).

General Solution

The general **solution **of the differential equation is given by:

y(x) = C1e^(λ1x) + C2xe^(λ2*x),

where C1 and C2 are **arbitrary **constants, and λ1, λ2 are the distinct roots of the characteristic equation.

In our case, since we have repeated roots, the general solution simplifies to:

y(x) = C1e^(3x) + C2xe^(3*x).

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Change 0.12 to a ratio.

### Answers

Answer:

3:25

Step-by-step explanation:

The photo shows how it's solved.

**Answer: 3:25**

**Step-by-step explanation:**

Step 1) Convert the decimal number to a fraction by making 0.12 the numerator and 1 the denominator

0.12 = 0.12/1

Step 2) Multiply the numerator and denominator by 100 to eliminate the decimal point.

0.12 x 100

------------ = 12/100

1 x 100

Step 3) Simplify the fraction in the previous step by dividing the numerator and the denominator by the greatest common factor (GCF) of 12 and 100. (The GCF of 12 and 100 is 4.)

12 ÷ 4

--------- = 3/25

100 ÷ 4

Step 4) Convert the fraction in the previous step to a ratio by replacing the divider line with a colon like this:

3

25 = 3:25

50 Points! Multiple choice algebra question. Photo attached. Thank you!

### Answers

**Answer:**

**B. 108 ft³**

**Step-by-step explanation:**

solution given:

**We have Volume of solid = Area of base * length**

over here

base : 9ft

height : 6 ft

length : 4ft

Now

Area of base : Area of traingle:½*base*height=½*9*6=27 ft²

Now

Volume : Area of base*length

Volume: 27ft²*4ft

Therefore **Volume of the solid=108 ft³**

Express log 161 in the form of loga + logb.

### Answers

**log 161** can be expressed as **log 7 + log 23** in the form of loga + logb.

To express log 161 in the form of loga + logb, first we need to find suitable values for a and b such that their **logarithmic** **product is equal to log 161.**

Let's find the factors of 161 :

161 = 7 * 23

Now, we can express log 161 as product of two logarithms :

log 161 = log (7 + 23)

Using the logarithmic property **log(a*b) = log a + log b :**

log 161 = log 7 + log 23

Therefore, log 161 can be expressed as log 7 + log 23.

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Ochenta y nueve en número romano ??

### Answers

**Answer:**

LXXXIX

**Step-by-step explanation:**

ochenta y nueve es 89.

89 en numero romano es LXXXIX.

The slop of the graphed line is 2/3

### Answers

The formulas that represent the** linear function **in this problem are given as follows:

y - 2 = 2/3(x - 1).y - 4 = 2/3(x - 4).f(x) = 2x/3 + 4/3.

How to define a linear function?

The **slope-intercept **equation for a linear function is presented as follows:

y = mx + b

The line has a **slope of 2/3, **hence:

y = 2x/3 + b.

When x = 1, y = 2, hence the** intercept b **is obtained as follows:

2/3 + b = 2

b = 6/3 - 2/3

b = 4/3.

Hence the **slope-intercept** equation of the line is given as follows:

f(x) = 2x/3 + 4/3.

The line goes through points (1,2) and (4,4), hence the **point-slope equations** to the line are given as follows:

y - 2 = 2/3(x - 1).y - 4 = 2/3(x - 4).

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In the figure below, k || 1 and m II n. Find the values of x and y.

xo

(Sy-98)

#

77°

X =

y=

### Answers

x+77=180

x=180-77=103°

x+5y-98=180

=> 103+5y-98=180

=> 5y=180-5

=> y=175/5=35°

Find the volume of a cone of radius 3.5cm and vertical height 12 cm.

### Answers

**Answer:**

Volume ≈ 153.93804 cm^3

Rounded to the nearest whole number, the volume of the cone is approximately 154 cm^3.

**Step-by-step explanation:**

2.

5 m

50 m

18 m

25 m

### Answers

As per the given data, the **area** of the rectangular **field** is approximately 204 square meters.

To find the area of the **rectangular** **field**, we need to multiply its length by its width.

Given that the **length** is 18 2/5 m and the **width** is 11 2/23 m, we need to convert these mixed fractions into improper fractions for easier calculation.

Length: 18 2/5 m = (5 * 18 + 2)/5 = 92/5 m

Width: 11 2/23 m = (23 * 11 + 2)/23 = 255/23 m

Now, we can calculate the **area** of the rectangular field:

Area = Length * Width

= (92/5) m * (255/23) m

= (92 * 255)/(5 * 23) m^2

= 23460/115 m^2

= 204 m^2 (rounded to the nearest whole number)

Therefore, the **area** of the rectangular field is approximately 204 square meters.

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Your question seems incomplete, the probable complete question is:

A rectangular field is 18 2/5 m long and 11 2/23 m wide. Find its area.

If you reflect AFGH across the y-axis, What will be the coordinates of the vertices of the image AFGH?

### Answers

The **coordinates** of the vertices of the **image** F'G'H' after **reflecting** FGH across the y-axis are:

F' = (2, -1)

G' = (-2, 2)

H' = (-4, -3)

We have,

When **reflecting** a point across the y-axis, the x-coordinate of the point is negated while the y-coordinate remains the same.

Applying this **transformation** to each vertex, we get:

F' = (-(-2), -1) = (2, -1)

G' = (-(2), 2) = (-2, 2)

H' = (-(4), -3) = (-4, -3)

Therefore,

The **coordinates** of the vertices of the **image** F'G'H' after **reflecting** FGH across the y-axis are:

F' = (2, -1)

G' = (-2, 2)

H' = (-4, -3)

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Two cars leave towns 850 kilometers apart at the same time and travel toward each other. One car's rate is 16 kilometers per hour less than the other's. If they meet in 5 hours, what is the rate of the slower car? Do not do any rounding.

### Answers

**Answer:9.5**

**Step-by-step explanation:**

Graph the equation shown below by transforming the given graph of the parent

function.

### Answers

**Answer:**

**Step-by-step explanation:**

it is only moving 3 to the right, so shift the green dot to (3,0)

I used desmos . com for the graph

Phil spends no more than 12 hours per week knitting. It takes him 2 hours to knit a hat and

3 hours to knit a scarf. He uses 150 yards of yarn for each hat and 400 yards of yarn for each

scarf. Which combinations of complete hats and scarves can Phil knit if he has 900 yards of yarn?

Select all of the correct answers.

A. 1 hat, 1 scarf

B. 3 hats, 2 scarves

C. 6 hats, 0 scarves

D. 4 hats, 1 scarf

E. 0 hats, 4 scarves

F. 2 hats, 1 scarf

### Answers

The correct options regarding the **inequality** are:

A. 1 hat, 1 scarf

D. 4 hats, 1 scarf

F. 2 hats, 1 scarf

How to explain the inequality

Based on the time **constraint**, Phil can spend a maximum of 12 hours knitting, so we can set up the following inequality:

2h + 3s ≤ 12,

Phil can knit at most 6 hats per week, because 6 hats * 2 hours/hat = 12 hours.

Phil can knit at most 4 scarves per week, because 4 **scarves** * 3 hours/scarf = 12 hours.

Phil can use at most 900 **yards** of yarn, because he has 900 yards of yarn.

Phil can knit 1 hat and 1 scarf, because 1 hat * 150 yards/hat + 1 scarf * 400 yards/scarf = 550 yards < 900 yards.

Phil can **knit** 4 hats and 1 scarf, because 4 hats * 150 yards/hat + 1 scarf * 400 yards/scarf = 900 yards.

Phil can knit 2 hats and 1 scarf, because 2 hats * 150 yards/hat + 1 scarf * 400 yards/scarf = 700 yards < 900 yards.

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Multiplying polynomials 4n2(n2 + 5n - 8)

### Answers

**Answer:**

4n^4 + 20n^3 - 32n^2

**Step-by-step explanation:**

We have to distribute 4n2 to each term.

4n2 x n2. We can multiply the two n2 together resulting in 4n^4.

Now we do 4n2 x 5n. Here we multiply 4 x 5 which equals 20. Then, we multiply the n2 and n. Which results in n^3. Now we put them together; 20n^3.

Finally, we multiply 4n2 by -8. Since 8 doesn't have any variables, we just multiply the 4 and -8. Which equals to -32, now we just combine -32 and the variable; -32n2.

Now we combine these terms together. Our final answer is, 4n^4 + 20n^3 -32n^2.

^ represents an exponent.

100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

### Answers

Angle C of the triangle **measures **68°.

**Side** AC = 22.90

**Side** BC = 14.26

**Given** triangle,

∠A = 37°

∠B = 75°

AB = 22

**Now**,

Sum of all the** interior **angles of triangle is 180.

**So**,

∠A + ∠B +∠C = 180°

37° + 75° + ∠C = 180°

∠C = 68°

Now,

**According** to sine rule,

**Ratio** of side length to the sine of the opposite angle is equal.

Thus,

a/SinA = b/SinB = c/SinC

**Let**,

BC = a

AC = b

AB = c

So,

a/Sin37 = b/Sin75 = c/Sin68

a/0.601 = b/0.965 = 22/0.927

**Solving**,

BC = a = 14.26

AC = b = 22.90

Thus with the properties of** triangle** side length and angles can be calculated.

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Find the x-intercept and the y-intercept of the line below. Click on "None" if applicable.

6543/2

-24

1-3-

### Answers

**Answer:**

x intercept at( -2)

y intercept at (4)

The x-intercept and the y-intercept are **-2 and 4 **respectively.

The **X-intercept** is the point where the line of an equation intersects the X-axis. While **y-intercept** is the point where the line of an equation intersects the Y-axis. Here, the X-axis is the horizontal axis, and the Y-axis is the vertical axis.

Since the given graph shows the line intersecting the X-axis i.e. the horizontal axis at -2, the x-intercept of the line would be -2. Whereas, since the line intersects the Y-axis at 4, the y-intercept is 4. The points that show these intercepts are **(-2,0)** for the x-intercept and **(0,4)** for the y-intercept.

∴ The intercepts are -2,4 respectively.

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4

(1 pa

10. The table shows the results from home games for a specific team during the season leading up

to the World Series. The team's home field has a roof that can be closed for weather. If it is

closed, the fans could make more noise for the home team and possibly give them an

advantage. Find the test statistic needed to test independence for the contingency table.

Closed roof

Open roof

034.215

00.093

00.798

03.841

Win

36

15

Loss

17

11

### Answers

The **test** **statistic** χ² is approximately 1.47.

We have,

To **test** **independence** for the contingency table, we need to calculate the **test** **statistic**.

The most commonly used test statistic for testing independence in a 2x2 contingency table is the chi-square test statistic.

The **chi**-**square** test statistic (χ²) is calculated using the formula:

χ² = Σ [(Observed - Expected)² / Expected]

Where:

Σ represents the sum over all cells of the contingency table.

Observed is the observed frequency in each cell.

Expected is the expected frequency in each cell if the variables were independent.

First, we calculate the expected frequencies for each cell. To do this, we use the formula:

**Expected** **frequency** = (row total x column total) / grand total

Grand total = sum of all frequencies = 36 + 17 + 15 + 11 = 79

Expected frequency for the cell "Closed roof - Win" = (53 * 51) / 79 = 34.49

Expected frequency for the cell "Closed roof - Loss" = (53 * 28) / 79 = 18.51

Expected frequency for the cell "Open roof - Win" = (26 * 51) / 79 = 16.51

Expected frequency for the cell "Open roof - Loss" = (26 * 28) / 79 = 9.49

Now, we can calculate the test statistic using the formula:

χ² = [(36 - 34.49)² / 34.49] + [(17 - 18.51)² / 18.51] + [(15 - 16.51)² / 16.51] + [(11 - 9.49)² / 9.49]

Calculating each term and summing them up:

χ² ≈ 0.058 + 0.482 + 0.58 + 0.35 ≈ 1.47

Therefore,

The **test** **statistic** χ² is approximately 1.47.

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100 Points! Geometry question. Photo attached. Use the Pythagorean Theorem to find x. Please show as much work as possible. Thank you!

### Answers

The **value** of x is,

⇒ x = 21.65

We have to given that,

A **right triangle** is shown in image.

Since, The **Pythagoras theorem **states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

Hence, We get;

⇒ 25² = 12.5² + x²

⇒ 625 = 156.25 + x²

⇒ x² = 625 - 156.25

⇒ x² = 468.75

⇒ x = 21.65

Thus, The value of x is,

⇒ x = 21.65

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A truck travels from warehouse A at (–4,8) to warehouse B at (–4,–1). If each unit represents 20 miles per hour, how long will it take the truck to travel this distance?

### Answers

It will take the truck 9 **hours **to travel from warehouse A to warehouse B.

To determine the time it takes for the truck to **travel **from warehouse A at (-4, 8) to warehouse B at (-4, -1), we need to calculate the distance between these two points and then convert it to time using the given unit of 20 miles per hour.

First, let's find the vertical **distance **between the two points. The y-coordinate of warehouse A is 8, and the y-coordinate of warehouse B is -1. So the vertical distance is 8 - (-1) = 9 units.

Next, we **convert** the vertical distance to miles. Since each unit represents 20 miles per hour, we multiply the vertical distance by 20: 9 units × 20 miles/unit = 180 miles.

Now, we can calculate the time it takes to travel this distance. We divide the distance by the **speed **of the truck, which is 20 miles per hour: 180 miles / 20 miles per hour = 9 hours.

Therefore, it will take the truck 9 hours to travel from **warehouse **A to warehouse B.

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