If 4 < a < 5 and 2 < b < 4, find all possible values for each expression:

-2a + 3b

The surface area of the pyramid is 113 cm².

A rectangular pyramid is a type of pyramid where the base is a rectangle and the triangular faces meet at a single point called the apex or vertex. It has five faces, including a rectangular base and four triangular faces, and it is a polyhedron with five vertices and eight edges.

The rectangular pyramid has a base of dimensions 7 cm by 5 cm, and the two large triangular faces have a height of 7.6 cm, while the two small triangular faces have a height of 8 cm.

To find the surface area of the pyramid, we need to find the area of each face and then add them up.

Area of the base:

The base of the pyramid is a rectangle with dimensions 7 cm by 5 cm, so its area is:

Area of base = length × width = 7 cm × 5 cm = 35 cm²

Area of the four triangular faces:

Each of the four triangular faces has a base of 5 cm (the width of the rectangle) and a height of either 7.6 cm or 8 cm. Using the formula for the area of a triangle, we can find the area of each face:

Area of each large triangular face = 1/2 × base × height = 1/2 × 5 cm × 7.6 cm = 19 cm²

Area of each small triangular face = 1/2 × base × height = 1/2 × 5 cm × 8 cm = 20 cm²

There are two large triangular faces and two small triangular faces, so the total area of the four triangular faces is:

Total area of four triangular faces = 2 × area of large triangular face + 2 × area of small triangular face

= 2 × 19 cm² + 2 × 20 cm²

= 78 cm²

Total surface area:

Finally, we can find the total surface area of the pyramid by adding the area of the base to the total area of the four triangular faces:

Total surface area = area of base + total area of four triangular faces

= 35 cm² + 78 cm²

= 113 cm²

Therefore, the surface area of the pyramid is 113 cm²

.

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Answer: At equilibrium, the supply and demand are equal, so we can set the two equations equal to each other:

300 + 40x = 9300 - 50x

Simplifying and solving for x:

90x = 9000

x = 100

Now that we know x, we can use either equation to find y:

y = 300 + 40(100) = 4300

So the equilibrium point is when x = 100 and y = 4300.

Step-by-step explanation:

Mohal will be able to paint 9 bookcases for the amount of paint.

An expression for a portion of a whole is a fraction. It is represented by the numerator above the denominator, with a horizontal line separating the two numbers. In mathematics, fractions are used to represent fractions of a whole or values that are not whole numbers. Like whole numbers, they can be multiplied, split, added, and subtracted. Ratios and proportions, which are crucial ideas in many branches of mathematics and science, are also represented by fractions.

Given that, he has 1 1 /8​ gallons of paint.

Thus, number of bookcases are:

1 1/8 ÷ 1/8 = (9/8) ÷ (1/8) = 9

Hence, Mohal will be able to paint 9 bookcases for the amount of paint.

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The volume of air passing through the filter is 800 cubic feet per minute. It is calculated by multiplying the air flow speed (100ft/min) by the area of the filter (8ft²).

The volume of air passing through the HEPA filter can be calculated using the formula for the speed of air flow multiplied by area. The speed of the air flow is given as 100ft/min and the area of the filter is given as 4ft x 2ft, which equals 8 square feet. Therefore, the volume of the air passing through the filter can be calculated as 8ft2 x 100ft/min = 800 cubic feet per minute.

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The statements that provide support for Chloe's claim are A<0 because A is to the left of zero, B>0 because B is to the right of zero. So correct option is A and F.

Comparison algebra is a branch of algebra that deals with inequalities and comparisons between different quantities or expressions. In comparison algebra, the goal is to determine the relationships between different expressions or quantities, such as whether one expression is greater than, less than, or equal to another expression.

Comparison algebra involves the use of comparison symbols, such as "<" (less than), ">" (greater than), and "=" (equal to), to express these relationships. For example, if we have two expressions, A and B, we can use the "<" symbol to express the relationship that A is less than B, as in A < B.

In comparison algebra, we can also manipulate inequalities and equations in similar ways as we do with regular algebraic expressions. For instance, we can add, subtract, multiply, or divide both sides of an inequality or equation by the same number or expression, while maintaining the inequality's direction.

The statements that provide support for Chloe's claim are:

A. A<0 because A is to the left of zero.

F. B>0 because B is to the right of zero.

Statement A supports Chloe's claim because Point A is to the left of zero on the number line, which means its value is negative. Statement F also supports Chloe's claim because Point B is to the right of zero on the number line, which means its value is positive.

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Answer:

Phn10x12

Step-by-step explanation:

PEANUTS CASHEWS MIXTURE Number of Grams (g) 12 X 12+ X Price per grams Php 10.00 Php 8.00 Php 9.00 Total Price Phn10x12 = Php 120 8x 9 [12+x]​

The solution to the equation 3/5x - 4 - 3√7x + 8 = 0 is x = -10√7/9, which is not one of the options provided.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".

To solve the equation 3/5x - 4 - 3√7x + 8 = 0:

First, simplify the expression by combining like terms:

3/5x - 3√7x + 4 = 0 + 8

3/5x - 3√7x + 4 = 8

Next, move the constant term to the right side:

3/5x - 3√7x = 8 - 4

3/5x - 3√7x = 4

Factor out x from the left side:

x(3/5 - 3√7) = 4

Divide both sides by (3/5 - 3√7):

x = 4 / (3/5 - 3√7)

To simplify the expression, we can multiply the numerator and denominator by the conjugate of the denominator, which is (3/5 + 3√7):

x = 4(3/5 + 3√7) / [(3/5 - 3√7)(3/5 + 3√7)]

x = 12/5 + 12√7/5 / (9/25 - 63/25)

x = 12/5 + 12√7/5 / (-54/25)

x = -10√7/9

Therefore, the solution to the equation 3/5x - 4 - 3√7x + 8 = 0 is x = -10√7/9, which is not one of the options provided.

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The surface area of cylinder M is approximately 131.95 square feet and the surface area of cylinder N is approximately 319.77 square feet.

What is a cylinder?

A cylinder is a three-dimensional geometric shape that consists of two congruent parallel bases in the shape of circles or ellipses, and a curved surface that connects the bases. The height of a cylinder is the perpendicular distance between the bases. A cylinder is a type of prism, and it can be classified as either a right cylinder or an oblique cylinder depending on whether or not its axis is perpendicular to its bases. Right cylinders have circular bases and their axis is perpendicular to the bases, while oblique cylinders have elliptical bases and their axis is not perpendicular to the bases.

Now,

Let the radius of cylinder M be r and its height be h. Then, the radius and height of cylinder N are both 2r, since the radius is equal to the height.

Since the cylinders are similar, their dimensions are proportional, which means:

(height of N) / (height of M) = 5/3

(radius of N) / (radius of M) = (2r) / r = 2

Using the formula for the surface area of a cylinder, we can write:

Surface area of cylinder M: 2πr² + 2πrh

Surface area of cylinder N: 2π(2r)² + 2π(2r)(5/3)h

We are told that the surface area of cylinder N is 256 square feet greater than the surface area of cylinder M. So we can set up the equation:

2π(2r)² + 2π(2r)(5/3)h = 2πr² + 2πrh + 256

Simplifying and solving for h, we get:

4r² + 20rh/3 = r² + rh + 128

3r² - rh - 128 = 0

(3r + 32)(r - 4) = 0

Since the height of the cylinder cannot be negative, we take the positive solution r = 4. Then, the height of cylinder M is (3/5)(4) = 12/5, and the height of cylinder N is 2(4) = 8.

Using the formulas for surface area, we can find the surface areas of both cylinders:

Surface area of cylinder M: 2π(4)² + 2π(4)(12/5) = 131.95 square feet

Surface area of cylinder N: 2π(2(4))² + 2π(2(4))(8) = 319.77 square feet

Therefore, the surface area of cylinder M is approximately 131.95 square feet and the surface area of cylinder N is approximately 319.77 square feet.

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The expression that has the greatest value when n is equal to 4 is option B, n + 30, with a value of 34.

To determine which mathematical expression has the greatest value when n is equal to 4, we can simply substitute 4 for n in each expression and compare the results.

A. 5n = 5(4) = 20

B. n + 30 = 4 + 30 = 34

C. 50 - n = 50 - 4 = 46

D. 80 ÷ n = 80 ÷ 4 = 20

The complete question is: Which expression has the greatest value when n is equal to 4? A. 5n B. n + 30 C. 50 – n D. 80 ÷ n

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The student's is incorrect because the greatest common factor of 12 and 8 is 2z, so the correct expression is 2x (6x+4).

Expression is the communication of emotion or ideas through words, art, music, or other forms of communication. It is the way in which a person or artist conveys their thoughts and feelings in a creative and meaningful way. Expression can be seen in the form of art, writing, music, dance, and other creative outlets. Expression is a powerful tool that can be used to communicate a message or to evoke a feeling in the audience. Expression can be used to inspire, educate, motivate, and even to heal. Expression is a way to connect people and cultures, and a way to share stories and experiences. It is a way to express oneself in a meaningful and powerful way.

This is because 12z+8 can be written as 2z(6x+4), where the greatest common factor of 12 and 8 (2z) is factored out.

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Complete Question:
The expression 12z+8 is equivalent to the expression a (bx + c), where b and c are constants and have no common factors. A student wrote the answer as 2 (6x+4).

Which statement best explains whether the student's answer is correct or incorrect?

OA. The student's answer is incorrect because the greatest common factor of 12 and 8 is 2z, so the correct expression is 2x (6x+4).

OB. The student's answer is incorrect because the greatest common factor of 12 and 8 is 4z, so the correct expression is 4z (3x+2).

C. The student's answer is incorrect because the greatest common factor of 12 and 8 is 4, so the correct expression is 4 (3x+2).

OD. The student's answer is incorrect because the greatest common factor of 12 and 8 is 8, so the correct expression is 8 (4x+1).

Answer:

-2.5

Step-by-step explanation:

follow BIMDAS.

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Answer:

hope this will help you...

a) the exponential equation equivalent to log8 1/64 = 2 is 1/64 = [tex]8^{(-2)}[/tex]

b)  the logarithmic equation equivalent to 3^0 = 1 is log3 1 = 0.

What is exponential equation?

An exponential equation is one in which the exponent contains a variable.

(a) We can rewrite the logarithmic equation as an exponential equation by using the definition of logarithms. The logarithmic equation

log8 1/64 = 2

means that 8 raised to the power of 2 is equal to 1/64:

[tex]8^2 = 1/64[/tex]

Thus, we can write the exponential equation as:

[tex]1/64 = 8^{(-2)}[/tex]

Therefore, the exponential equation equivalent to log8 1/64 = 2 is 1/64 = [tex]8^{(-2)}.[/tex]

(b) We can rewrite the exponential equation as a logarithmic equation by using the definition of logarithms. The exponential equation

[tex]3^0 = 1[/tex]

means that the logarithm of 1 to the base 3 is equal to 0:

log3 1 = 0

Therefore, the logarithmic equation equivalent to 3^0 = 1 is log3 1 = 0.

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Answer:

B.

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

the description is very confusing and lacks any hint about the behavior of the curve before the change.

but ok, let's assume that the curve (line ?) is in general going up. in other words, if the traveled miles go up, so does the profit.

I also don't know how they could drive the miles without paying the driver, but again, let's assume they did.

now they pay the driver. $0.25 per mile.

this has to come out of their profit.

so, the Y (profit) values all go down by 0.25.

therefore, the y-intercept is going down too.

that eliminates C. and D.

for this to be true they have to have some overhead costs that apply even if there are 0 miles traveled (which is the meaning of the y-intercept : the y-value when x = 0).

so, the line must be in a form

y = ax + b

with "b" <> 0.

and since we assumed the line to go up (positive slope), a "sinking" line means that the x-intercept (the break-even point, where the line goes from below the x-axis and therefore negative (y) profit up into positive profit) will move to the right (become greater).

because now that they have additional costs (paying the driver), it takes longer (more driven miles) to make a positive profit.

and that eliminates A, leaving B. as the right answer.

Answer:

Vertex: (-2, -1)

Axis of Symmetry: x = -2

Y-intercept: (0, 3)

Min/Max: Min

Domain: All Real

Range: y ≥ -1

Step-by-step explanation:

Given the graph:

Answer:

So, the answers to the question is:

Vertex: (-2, -1)

Axis of Symmetry: x = -2

Y-intercept: (0, 3)

Min/Max: Min

Domain: All Real

Range: y ≥ -1

The missing step in the proof is: D. ADCA

In the statements, we are given that AD || BC and ZDAC = ZBCA (alternate interior angles theorem), so we can conclude that triangle ADCA is similar to triangle BCA (by AA similarity criterion).

Therefore, we have the following proportional sides:

DC/AC = AC/BC

Given that DC = BA (given statement), we can substitute BA for DC in the proportion:

BA/AC = AC/BC

Now, we can cross-multiply to get:

BA * BC = AC²

Using the given statement that AC = AC (reflexive property of congruence), we can substitute AC for AC in the equation:

BA * BC = AC * AC

Use the definition of congruent sides to replace BA with DC:

DC * BC = AC * AC

And finally, use the substitution property of equality to replace BC with 6 units (given statement):

DC * 6 = AC * AC

From this equation, we can see that DC = 6 units, which completes the proof. Therefore, the missing step is statement D. ADCA.

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Answer:

The Correct answer is Carter

Answer:

40 units

Step-by-step explanation:

a = 8

b = 15

To find c, we can use the formula: [tex]a^{2} +b^{2} =c^{2}[/tex]

[tex]8^{2} +15^{2} =x^{2}[/tex]

64 + 225 = c^2

289 = c^2

c = 17

a + b + c = perimeter

8 + 15 + 17 = 40

Answer:

  40 units

Step-by-step explanation:

You want the perimeter of the triangle shown in the graph.

You can count the grid squares to find the horizontal and vertical dimensions of the triangle. You find they are 8 units and 15 units, respectively.

The length of the slant side is the hypotenuse of a right triangle with sides 8 and 15. If you don't recognize this {8, 15, 17} Pythagorean triple, you can find the hypotenuse using the Pythagorean theorem:

  c² = a² +b²

  c² = 8² +15² = 64 +225 = 289

  c = √289 = 17

The long side of the triangle is 17 units.

The perimeter of the triangle is the sum of the lengths of its sides:

  P = 8 + 15 + 17 = 40

The perimeter is 40 units.

__

Additional comment

A "Pythagorean triple" is a set of three integer side lengths that form a right triangle. The triple is "primitive" if the numbers have no common factor. There are a few Pythagorean triples that regularly show up in algebra, trig, and geometry problems. Some of them are ...

  {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}

You will also see multiples of these, for example, 2·{3, 4, 5} = {6, 8, 10}.

The smallest is {3, 4, 5}, and it is the only set that is an arithmetic sequence (has constant differences between lengths). In every case, the sum of the numbers is even. (A right triangle cannot have integer side lengths and an odd perimeter value.)

Answer:

40%

Step-by-step explanation:

We Know

You have a bag with 4 red marbles, 3 green marbles, 2 blue marbles, and 1 purple marble.

4 + 3 + 2 + 1 = 10 marbles total

What is the probability of drawing a red marble out of the bag?

We Take

(4 ÷ 10) x 100 = 40%

So, 40% of drawing a red marble out of the bag.

The absolute value equation that has -8 and -2 as the solution set is |x + 5| = 3

What is an absolute value equation?

An absolute value equation can be written as |expression| = value

To have -8 and -2 as the solution set, we need an absolute value equation that produces these two values when the expression inside the absolute value is either positive or negative.

We can write,

|x + 5| = 3

To solve for x, we have two cases,

Case 1: x + 5 is positive

If x + 5 is positive, then the equation becomes x + 5 = 3

Solving for x,

x = -2

This matches one of the solutions we want.

Case 2: x + 5 is negative

If x + 5 is negative, then the equation becomes -(x + 5) = 3

Solving for x,

x = -8

This also matches the other solution we want.

Therefore, the absolute value equation that has -8 and -2 as the solution set is |x + 5| = 3.

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Step-by-step explanation:

to find the interest she needs to pay back every month, we need to use this formula:

I = PRT/12

in this case the principle is $300,000, the rate is 7% p.a. and the amount of time is 1 year, if we substitute in our values we:

I = (300,000)(7)(1)/12 = $17,500 in interest every month

to find her yearly income from rent, we have to multiply the monthly rent by 12

1500 × 12 = $18,000

to calculate her loss percentage in a year, we have to subtract 18,000 from 3000 which is 15,000

she said that she hopes the property's value will increase to cover the loss she made.

to cover the loss of $15000 per year, the property needs to increase in value by at least $15000. the percentage increases value can be written as

Percentage increase = (difference in increase/Original price) × 100

so

percentage increase = (15000/300000) × 100 = 5%

so the property needs to increase in value by at least 5% per year to cover the loss.

The woman needs to pay $1750 monthly as interest. Her yearly income from the rent is $18,000. After considering all other costs, she is at a loss of $6000 per year, so the property needs to increase in value by 2% per year to cover this loss.

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Answer: The formula for compound interest is:

A = P(1 + R/100)^t

where A is the amount after t years, P is the principal amount, R is the rate of interest per annum, and t is the time period in years.

Here, P = Rs. 3,500, R = 8%, and t = 2 years.

So, the amount after 2 years will be:

A = 3,500(1 + 8/100)^2

= 3,500(1.08)^2

= 3,892.32

Therefore, the compound interest for 2 years will be:

CI = A - P

= 3,892.32 - 3,500

= 392.32

Hence, the compound interest on Rs. 3,500 for 2 years at the rate of 8% per annum is Rs. 392.32.

Step-by-step explanation:

By answering the presented question, we may conclude that As a result, the linear function denoted by the table is y = 2x - 2.

A line's slope shows how steep it is. A mathematical equation for the gradient is referred to as "gradient overflow" (the change in y divided by the change in x). The slope is defined as the ratio of vertical change (rise) to horizontal change between two points (run). The slope-intercept form of an equation is used to represent the equation of a straight line, which is written as y = mx + b. The y-intercept is located where the line's slope is m, b is b, and (0, b). The slope and y-intercept of the equation y = 3x - 7 are two examples (0, 7). The line's slope is m. b is b at the y-intercept, and (0, b).

To obtain the slope and y-intercept of a linear function in slope-intercept form, we must first establish the slope and y-intercept.

With two locations on the line, we can first determine the slope. Let us start with the first and last points in the table:

slope = (y change) / (change in x)

slope = (16 - (-8)) / (9 - (-3))

slope = 24 / 12

slope = 2

We can now use the slope and one of the points to get the y-intercept. Let's take the point (1, 0) as an example:

y = mx + b 0 + b b = 2(1) + b b = -2

Hence the linear function's slope-intercept equation is:

y = 2x - 2

As a result, the linear function denoted by the table is y = 2x - 2.

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Answer: The area of the door can be calculated as:

Area of door = width x height

= 0.9 m x 2.1 m

= 1.89 square meters

The area of one window can be calculated as:

Area of window = width x height

= 1.5 m x 1.2 m

= 1.8 square meters

Since there are four windows, the total area of the four windows is:

Total area of four windows = 4 x Area of window

= 4 x 1.8 square meters

= 7.2 square meters

Therefore, the total area of the door and the four windows is:

Total area = Area of door + Total area of four windows

= 1.89 square meters + 7.2 square meters

= 9.09 square meters

Hence, the total area of the door and the four windows is 9.09 square meters.

Step-by-step explanation:

The histogram should be modified as follows:

A histogram is a type of graphical representation that displays the distribution of a dataset. It is a bar graph-like chart where the data is divided into intervals, called "bins", which are represented by adjacent rectangular bars of varying heights.

Then the height of the histogram gives the number of observations into each data interval.

Hence the histogram should be modified as follows:

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Answer: Let's say that the width of the rectangle is x meters. Then, according to the problem, the length of the rectangle is 6 meters longer than the width, which means that the length is (x + 6) meters.

The formula for the area of a rectangle is:

Area = Length x Width

We are given that the total area of the rectangle is 16m². Substituting the expressions for length and width, we get:

(x + 6) x = 16

Expanding the product and rearranging, we get a quadratic equation:

x² + 6x - 16 = 0

We can solve this equation by factoring or by using the quadratic formula. Factoring, we get:

(x + 8) (x - 2) = 0

This equation is satisfied when either x + 8 = 0 or x - 2 = 0. Therefore, the possible values for the width are x = -8 or x = 2. However, since the width of a rectangle cannot be negative, we reject the solution x = -8.

Therefore, the width of the rectangle is x = 2 meters. The length is 6 meters longer than the width, so the length is (2 + 6) = 8 meters.

Therefore, the dimensions of the rectangle are 2 meters by 8 meters.

Step-by-step explanation:

Step-by-step explanation:

data given

men 330 ,days30

men? ,days11

from

men(m) are inversely proportional todays (d)

m=k/d

330×30=k

k=9900

now,

m=9900/11m

m=900

data given

friends 20, time 2hours

friends 30, time?

from

friends (f) are inversely proportional to time (t)

f=k/t

k=20×2

k=40

now,

t=40/30

t=1.3(1:18)

100 people = 360° of circle

For n people, the degree for the circle is (n×360)÷100

30 people = (30×360)÷100 = 108°

15 people = 54°

12 people = 43.2° ≅ 43°

14 people = 50.4° ≅ 50°

29 people = 104.4° ≅ 104°

Answer: 0.0295

Step-by-step explanation: To solve for r in the equation $425.83=400(1+r)^5$, we can rearrange the equation to isolate the variable.

Dividing both sides by 400 gives $(1+r)^5=1.064575$, and taking the fifth root of both sides gives:

$1+r=\sqrt[5]{1.064575}$.

Subtracting 1 from both sides gives $r\approx 0.0295$.

Therefore, your answer would be 0.0295.

The total net amount the supermarket owes the wholesaler for the order is $231.31.

A discount is a reduction in the price of a product or service. It is often offered by businesses to encourage customers to buy more or to make a purchase they might not otherwise make. A discount can be expressed as a percentage or a specific dollar amount, and it is usually subtracted from the original price of the item or service.

To find the total net amount the supermarket owes the wholesaler for the order, we need to first calculate the cost of each case of soup and baked beans after the 39% trade discount is applied, and then multiply those costs by the number of cases ordered.

The trade discount rate is 39%, which means the supermarket will receive a discount of 39% off the list price of each case of soup and baked beans. To calculate the cost of each case after the discount is applied, we can use the following formula:

Discounted cost = List price - (Discount rate x List price)

For the soup, the discounted cost per case is:

$18.90 - (0.39 x $18.90) = $11.51

For the baked beans, the discounted cost per case is:

$33.50 - (0.39 x $33.50) = $20.42

Now we can calculate the total net amount owed by the supermarket to the wholesaler:

Total net amount = (Number of cases of soup x Cost per case) + (Number of cases of baked beans x Cost per case)

Total net amount = (13 x $11.51) + (4 x $20.42)

Total net amount = $149.63 + $81.68

Total net amount = $231.31

Therefore, the total net amount the supermarket owes the wholesaler for the order is $231.31.

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