To find the volume of a prism, Frank multiplies the area of the base by the height. Frank finds the area

of the base of a rectangular prism is 24 square inches.

How many inch cubes are needed to fill the bottom layer of the prism?

—

The value οf a, b, and c are 3, 5, and 25 respectively.

There are many different ways tο define an equatiοn. The definitiοn οf an equatiοn in algebra is a mathematical declaratiοn that illustrates the equality οf twο mathematical expressiοns.

The given equatiοn is

1/(x + 5) + 2/(x -5) = (ax + b)/ (x² - c)

Sοlve the left-hand side οf the equatiοn:

L.H.S = 1/(x + 5) + 2/(x -5)

= [x-5 + 2(x+5)]/(x + 5)(x -5)

= [x-5 + 2x+ 10]/(x + 5)(x -5)

Cοmbine like terms:

= [3x + 5]/(x + 5)(x -5)

Nοw apply fοrmula (a-b)(a+b) =a² - b²:

= [3x + 5]/(x² - 5²)

= [3x + 5]/(x² - 25)

Put 1/(x + 5) + 2/(x -5) =  [3x + 5]/(x² - 25) in the given equatiοn:

[3x + 5]/(x² - 25) = (ax + b)/ (x² - c)

Nοw cοmpare bοth sides:

a = 3

b = 5

c= 25

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a)Hence the side of the square = 15.5 m

b)Hence the length of the rectangle is 8m and the width is 5m.

c)Hence the rectangle is greater than the square.

a)

The length of each wire =26m

To bend it into a square it has to be bent into four parts = [tex]\frac{26}{4}[/tex] =  5.15m

Hence the side of the square = 15.5 m

b)

A rectangle whose width is 3 m shorter than its length,

let the length of the rectangle = l

And the width of the rectangle h= l-3,

now,

2(l+l-3)=26

4l-6=26

4l=32

l=8m

h=8-3=5

Hence the length of the rectangle is 8m and the width is 5m.

c)

The area of the square=  5.15²=26.52 sq cm

The area of the rectangle = 8*5=40 sq cm

Hence the rectangle is greater than the square.

The complete question is-

A workman has two pieces of wire, each of

length 26 m. One piece is to be bent into a

square. The other piece is to be bent into a

rectangle whose width is 3 m shorter than its

length.

(a) What is the length of a side of the square?

(b) What are the dimensions of the rectangle?

(c) Which shape has the greater area?

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The correct option to model the height is

h = cosine (StartFraction pi Over 6 EndFraction t) + 9.

Here the height of the tip of the hour hand of a wall clock follows a cosine function as the time progresses since the hour hand of a clock completes one full revolution in 12 hours.

We will use the general form of a cosine function to model the height has a function of time t:

Where A is the amplitude, B is the frequency and C is the vertical shift  

Here we have

The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet.

Hence, the applitude A = [9+10]/2 = 0.5.

The period of a cosine function is given by 2π/B,

Since the hour hand completes one full revolution in 12 hours, the period is 12 hours or 2π.

=> B = π/6.

The vertical shift is C = 9.

Thus, the equation that models the height h as a function of time t is:

h = 0.5 cos(π/6 t) + 9.

Therefore,

The correct option to model the height is

h = cosine (StartFraction pi Over 6 EndFraction t) + 9.

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Answer:

A likelihood of 1 is also known as the Discrete probability distribution

This is an Angles and Coordinate Systems problem.
6)  

7)

8)

Positive angle measure is measured counterclockwise and negative angle measure is measured clockwise. These concepts are used in navigation, engineering, and physics.

6)

An angle of 40 degrees measured out in the upper left quadrant will have its initial side along the positive x-axis and its terminal side in the upper left quadrant, making it a counter-clockwise angle.

-(360° - 40°) = -320°

So the angle of 40 degrees is equivalent to a negative angle measure of -320 degrees.

320° + 360° = 680°

So the angle of 40 degrees is equivalent to an angle measure of 680 degrees.


7)

To convert the angle measure of 50 degrees in the lower right quadrant to a positive angle measure, we add 360 degrees to it since one full revolution around the coordinate system is equal to 360 degrees.

To convert the angle measure to a negative angle measure, we subtract it from 360 degrees, since a negative angle is measured in the clockwise direction.

To find an angle measure that is greater than 360 degrees, we simply add 360 degrees to the positive angle measure.

8)

The angle 60 degrees measured in the lower right quadrant in a counter-clockwise direction is equivalent to the angle 360 degrees - 60 degrees = 300 degrees measured in the upper right quadrant in a counter-clockwise direction.

To convert the angle measure of 300 degrees to a positive angle measure, we add 360 degrees to it since one full revolution around the coordinate system is equal to 360 degrees.

To convert the angle measure to a negative angle measure, we simply add a negative sign to the positive angle measure.

To find an angle measure that is greater than 360 degrees, we simply add 360 degrees to the positive angle measure.

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Answer:122

Step-by-step explanation:

sum of the interior angles of a rectangle is equal to 360 degrees. sum of neighbor angles is equal to 180 degrees. the if one of the neighbor angle is 90 then, other is 180-90=90.

a+76+72+90=360

a+238=360

a=122

Mei worked 8 hours and Kara worked 7 hours when Mei can build a computer in 0.8 hours , and Kara can build a computer in 1 hour.

Let's use the following variables to represent the unknowns in the problem:

Let M be the number of computers Mei built

Let K be the number of computers Kara built

We can set up a system of equations based on the given information:

M + K = 17 (the total number of computers built is 17)

0.8M + K = 15 (the total time worked is 15 hours)

We can solve for one of the variables in terms of the other by using the first equation:

M = 17 - K

Now we can substitute this expression for M into the second equation:

0.8(17 - K) + K = 15

13.6 - 0.8K + K = 15

0.2K = 1.4

K = 7

So Kara built 7 computers. We can use the first equation to find how many computers Mei built:

M + 7 = 17

M = 10

Therefore, Mei built 10 computers.

Now we can find how long each girl worked by multiplying the number of computers by their respective build times:

Mei: 10 computers x 0.8 hours per computer = 8 hours

Kara: 7 computers x 1 hour per computer = 7 hours

Therefore, Mei worked 8 hours and Kara worked 7 hours.

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The complete question is :

Mei and Kara build computers from parts and sell them to make a profit. Mei can build a computer in 0.8 hours , and Kara can build a computer in 1 hour. together they worked 15 hours and built 17 hours and built 17 computers. how many hours did each girl work ?

Values of y that corresponds with the value of x as per quadratic functions are as follows:

6

0

-2

0

6

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree. A quadratic function must have at least one second-degree term. It performs algebraic operations.

The parent quadratic function connects the locations whose coordinates have the type f(x) = x2 and is of the kind (number, number2).

Just need to evaluate the function for each value of X.

for x=1 y=2(1-3)²-2= 6

for x=2 y=2(2-3)²-2= 0

for x=3 y=2(3-3)²-2= - 2

for x=4 y=2(4-3)²-2= 0

for x=5 y=2(5-3)²-2= 6

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Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

The sequence of transformations that maps HIJK to ABCD is sequence B: reflection over line HÌ, then a translation 6 units to the right and 3 units down.

What is quadrilateral ?

A quadrilateral is a polygon with four sides and four vertices. The term "quadrilateral" comes from the Latin words "quadri" meaning "four" and "latus" meaning "side". Quadrilaterals can have different shapes and properties, including rectangles, squares, parallelograms, trapezoids, and kites.

Since quadrilaterals HIJK and ABCD are congruent, we can map one onto the other using a sequence of transformations. We need to determine which of the given sequences of transformations maps HIJK to ABCD.

Sequence A involves a 270° rotation about point J, followed by a translation 9 units to the right and 8 units down.

Sequence B involves a reflection over the line HÌ, followed by a translation 6 units to the right and 3 units down.

To determine which sequence maps HIJK to ABCD, we can apply each sequence to the vertices of HIJK and see if the resulting image matches the vertices of ABCD.

Starting with sequence A, we apply the rotation and translation to the vertices of HIJK:

Vertex H(-2, 1) is rotated 270° about J(-2, 2) to get H'(0, 0). Then we translate 9 units to the right and 8 units down to get H''(9, -8).

Vertex I(-3, -1) is rotated 270° about J(-2, 2) to get I'(1, -3). Then we translate 9 units to the right and 8 units down to get I''(10, -11).

Vertex J(-2, 2) is fixed by the rotation and then translated 9 units to the right and 8 units down to get J''(7, -6).

Vertex K(0, 0) is rotated 270° about J(-2, 2) to get K'(-2, -2). Then we translate 9 units to the right and 8 units down to get K''(7, -10).

The resulting image of HIJK under sequence A has vertices H''(9, -8), I''(10, -11), J''(7, -6), and K''(7, -10). We can see that these vertices do not match the vertices of ABCD, so sequence A does not map HIJK to ABCD.

Next, we apply sequence B to the vertices of HIJK:

Vertex H(-2, 1) is reflected over line HÌ to get H'(-4, 3). Then we translate 6 units to the right and 3 units down to get H''(2, 0).

Vertex I(-3, -1) is reflected over line HÌ to get I'(-1, 1). Then we translate 6 units to the right and 3 units down to get I''(5, -2).

Vertex J(-2, 2) is reflected over line HÌ to get J'(-4, 4). Then we translate 6 units to the right and 3 units down to get J''(2, 1).

Vertex K(0, 0) is reflected over line HÌ to get K'(-2, 2). Then we translate 6 units to the right and 3 units down to get K''(4, -1).

The resulting image of HIJK under sequence B has vertices H''(2, 0), I''(5, -2), J''(2, 1), and K''(4, -1). We can see that these vertices match the vertices of ABCD, so sequence B maps HIJK to ABCD.

Therefore, the sequence of transformations that maps HIJK to ABCD is sequence B: reflection over line HÌ, then a translation 6 units to the right and 3 units down.

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To rotate triangle ABC 90 degrees clockwise about a point P, we can follow these steps:

Draw a line segment from each vertex of the triangle to the point P.

Measure the distance from each vertex to the point P and make note of the lengths.

Rotate each line segment 90 degrees clockwise by swapping the x and y coordinates and changing the sign of the new y-coordinate. For example, if a vertex has coordinates (x, y), the new coordinates after rotation will be (y, -x).

Use the new endpoints of the line segments to draw the new triangle, A'B'C'.

For example, suppose the coordinates of triangle ABC are A(1,2), B(3,4), and C(5,2), and the point of rotation is P(3,3). Then the distances from each vertex to the point P are:

AP = sqrt((3-1)² + (3-2)²) = sqrt(5)

BP = sqrt((3-3)² + (3-4)²) = 1

CP = sqrt((3-5)² + (3-2)²) = sqrt(5)

After rotating each vertex 90 degrees clockwise about P, we get:

A'(4,1)

B'(2,3)

C'(4,5)

Using these new coordinates, we can draw the new triangle A'B'C', which is the result of rotating triangle ABC 90 degrees clockwise about P.

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction of the bar. ABC rotates 90 degrees clockwise about point p to from A’B’C

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Wilbur's flight took about 43.7 seconds.

Let x be the rate of Orville in feet per second and 2x be the rate of Wilbur in feet per second. Let t be the time it took for Orville to complete the flight and t - 6 be the time it took for Wilbur to complete the flight.

We know that the distance traveled by both brothers is the same, which we can express with the equation:

distance = rate × time

For Orville:

distance = x * t

For Wilbur:

distance = 2x * (t - 6)

Since the distance is the same for both brothers, we can set the two equations equal to each other:

x * t = 2x * (t - 6)

Expanding and simplifying the right-hand side:

xt = 2xt - 12x

12x = xt

x = t/12

So, Orville's rate is x = t/12 feet per second.

Substituting this into one of the equations for distance, we can solve for t:

distance = x * t

852 = (t/12) * t

852 = t² / 12

t² = 12 * 852

t² = 10224

t ≈ 101.1 seconds (rounded to the nearest tenth)

So, Orville's flight took about 101.1 seconds.

Now we can use the equation for Wilbur's distance to find his rate:

distance = 2x * (t - 6)

852 = 2(2x) * (101.1 - 6)

852 = 4x * 95.1

x ≈ 5.64 feet per second (rounded to the nearest hundredth)

So, Orville's rate is about 5.64 feet per second, and Wilbur's rate is twice that or about 11.28 feet per second.

To find Wilbur's time, we can use the equation for distance again:

distance = 2x * (t - 6)

852 = 2(11.28) * (t - 6)

852 = 22.56t - 135.36

22.56t = 987.36

t ≈ 43.7 seconds (rounded to the nearest tenth)

So, Wilbur's flight took about 43.7 seconds.

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I think you are correct, I am not sure why. Maybe you ask your teacher and she or he made a mistake with this question.

Answer:

Slope m = 1/3

Step-by-step explanation:

Slope of the line can be found by taking two points on the line, (x1, y1) and (x2, y2)

Find the difference in y coordinates, y2 - y1  (called rise)

Find the difference in corresponding x coordinates x2 - x1 (called run)

Rise/Run gives the slope

Two distinguishable points on the line graph are (0, 2) and (3, 3)

rise = 3 - 2 = 1

run = 3 - 0 = 3

Slope = 1/3

Answer:25 sticks

Step-by-step explanation:

each time you will add 4 sticks

Answer: 37

Step-by-step explanation:

Add 4

Force on the object is 7.04 pounds in the x-direction

Force on the object is -2.52 pounds in the y-direction

The total force on an object being pushed with 5 pounds of course in the θ=45˚ direction and also with 7 pounds of force in the θ =-60˚ direction can be found by resolving each force into its x- and y-components, and then adding them to obtain the net force acting on the object.An object being pushed with 5 pounds of course in the θ=45˚ direction and also with 7 pounds of force in the θ =-60˚ direction is shown below:An object being pushed with 5 pounds of force in the θ=45˚ direction and also with 7 pounds of force in the θ=-60˚ direction.To resolve the forces, we use the following identities:Fx = Fcosθ, andFy = Fsinθ.The x- and y-components of the 5-pound force in the θ=45˚ direction are:Fx = Fcosθ = 5 cos 45˚ = 3.54 pounds,andFy = Fsinθ = 5 sin 45˚ = 3.54 pounds.The x- and y-components of the 7-pound force in the θ=-60˚ direction are:Fx = Fcosθ = 7 cos (-60˚) = 3.5 pounds,andFy = Fsinθ = 7 sin (-60˚) = -6.06 pounds.The total force acting on the object is the sum of the x- and y-components of the forces acting on it, or:Fx = 3.54 pounds + 3.5 pounds = 7.04 pounds,Fy = 3.54 pounds - 6.06 pounds = -2.52 pounds.Therefore, the total force on the object is 7.04 pounds in the x-direction and -2.52 pounds in the y-direction.

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Answer:

arc DB = 45°

Step-by-step explanation:

the measure of an arc is the same as the central angle that intercepts it.

∠ DCB = 180° - 135° = 45°

∠ DCB is the central angle intercepted by arc DB , then

arc DB = 45°

Answer:

The picture shows that the side lengths and the angle are the same because of the lines

Step-by-step explanation:

The answer is given and VS=WT but add the line symbol above that

Answer:

1/3

Step-by-step explanation:

There are only two ways to roll a die and get a number bigger than 2 (not1 or not 2) and smaller than 5 (not 5 and not 6) You can roll a 3 (bigger than 2, smaller than 5) OR you can roll a 4 (also bigger than 2 a, smaller than 5)

There are only 6 different results when you roll a die (1-6).

To write a probability you put the total number of ways on the bottom. Put 2 on top because there's two ways to roll the desired result.

P = 2/6 and simplify

P = 1/3

If I walk 3.5 miles in 2 hours, then I can walk 14 miles in 8 hours.

If I walk 3.5 miles in 2 hours, then I can use a simple proportion to calculate how far I can walk in 8 hours. I know that in 2 hours I can walk 3.5 miles, and I want to calculate how far I can walk in 8 hours. To do this, I can set up a proportion. The fraction representing the time I spent walking and the distance I walked must be equal on both sides of the equation. On the left side of the equation, I set up 2/3.5, and on the right side I set up 8/x, where x is the unknown distance I can walk in 8 hours. I can then solve for x by cross-multiplying and dividing. After solving, I find that I can walk 14 miles in 8 hours.

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The two primary components of an angle are the limbs and the vertex. The angle sum property of a triangle is 20+21+29=180 70x=180 x=180/70.

An angle is the result of the intersection of two lines.

An "angle" is the length of the "opening" between these two beams.

Angles are commonly measured in degrees and radians, a measurement of circularity or rotation.

In geometry, an angle can be created by joining the extremities of two rays. These rays are intended to represent the angle's sides or limbs.

The two primary components of an angle are the limbs and the vertex. The joint vertex is the common terminal of the two beams.

According to the given question,

angle sum property of triangle-

20+21+29=180

70x=180

x=180/70.

Hence, With the angle sum property of triangle, x=180/70.

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By the given parameters, Gethyn needs to drink 2 more cups of water today.

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

Amount = 8 cups

Today = 48 ounces

There are 8 fluid ounces in one cup.

So, to convert 48 fluid ounces to cups, we divide by 8:

48 fluid ounces / 8 fluid ounces per cup = 6 cups

Therefore, Gethyn has already drnk 6 cups of water today.

To reach his goal of 8 cups, he still needs to drink:

8 cups - 6 cups = 2 cups

So Gethyn needs to drink 2 more cups of water today.

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The value of x for all the figures are given below respectively.

The branch of mathematics that studies the relationships between the sides and angles of triangles is known as Trigonometry.

1. In given figure base = 5 and hypotenuse = 10 .

to find x i.e height we will use trigonometry-

tan 60° = x/5

√3 = x/5

5√3=x

Therefore, the value of x is 5√3.

2. In given figure base = 1 and height = √3  and angle given is 60°.

to find x i.e hypotenuse we will use trigonometry-

sin 60° = √3/x

√3/2 = √3/x

x = √3×2/ √3

x = 2

Therefore ,value of x is 2.

3. In given figure base = 3 and hypotenuse = 6 .

to find x i.e height we will use trigonometry-

tan 60° = x/3

√3 = x/3

3√3 = x

Therefore,value of x is 3√3.

4. In given figure base = 1 and height = 1  and angle given is 45°.

to find x i.e hypotenuse we will use trigonometry-

sin 45° = 1/x

1/√2 = 1/x

x = √2

Therefore ,value of x is √2.

5.  In given figure height = 4√2  and angle given is 45°.

to find x i.e hypotenuse we will use trigonometry-

sin 45° = 4√2/x

1/√2 = 4√2/x

x = 4√2 × √2

x = 8

Therefore,value of x is 6.

6. In given figure hypotenuse = 10 and angle given is 45°.

to find x i.e base we will use trigonometry-

cos 45° = x/10

1/√2 = x/10

10/√2 = x

Therefore,value of x is 10/√2.

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The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle and π (pi) is a constant approximately equal to 3.14.

To find the circumference of the circle, we need to know the radius. If we are not given the radius directly, we may be given another measurement that we can use to calculate it. For example, we may be given the diameter, which is the distance across the circle passing through its center. The radius is half the diameter.

Assuming we have been given the diameter of the circle, we can calculate the circumference as follows:

Write down the formula for the circumference of a circle: C = 2πr

Identify the diameter of the circle. Let's say it is 10 cm.

Calculate the radius by dividing the diameter by 2: r = 10/2 = 5 cm.

Plug in the value of the radius into the formula: C = 2π(5) = 10π.

Use the approximation of π as 3.14: C = 10(3.14) = 31.4 cm.

Therefore, the circumference of the circle is approximately 31.4 cm, to the nearest tenth of a centimeter.

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Complete question:

A circle of radius 3 cm is drawn .Given that the measurement is in centimeters, find the circumference of the circle to the nearest tenth. (Use 3.14 for π)

A) 9.4 cm

B) 18.8 cm

C) 37.7 cm

D) 56.6 cm

The experiment that is most likely to produce a uniform discrete distribution is the number of patrons arriving every 3 minutes at a sandwich shop.

Test scores on a college entrance exam, such as the ACT or SAT, is an example of continuous distribution.

A uniform distribution is a kind of probability distribution in which all of the potential outcomes have an equal likelihood of occurring. A uniform distribution with a limited set of potential outcomes is referred to as a discrete uniform distribution. In a discrete uniform distribution, there is a finite number of potential outcomes that are all equally probable.

It is important to note that the sum of the probabilities of all possible outcomes in a uniform distribution is always equal to 1 since the outcomes are equally likely to happen. The following experiments are less likely to generate a uniform discrete distribution:

Test scores on a college entrance exam, such as the ACT or SAT: Because test scores are continuous data, a uniform distribution is unlikely to occur.

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(a) To find the mean squared error (MSE) of X bar, we need to first find its expected value and variance.

The expected value of X bar is:

E(X bar) = E((X1 + X2 + ... + Xn) / n) = (n * E(X)) / n = E(X) = θ

The variance of X bar is:

Var(X bar) = Var((X1 + X2 + ... + Xn) / n) = (1/n^2) * Var(X1 + X2 + ... + Xn) = (1/n^2) * n * Var(X) = θ/n

Therefore, the MSE of X bar is:

MSE(X bar) = Var(X bar) + [E(X bar) - θ]²= θ/n + [θ - θ]² = θ/n

(b) To find the limit of MSE when n tends to infinity, we can take the limit of the MSE formula as n approaches infinity:

lim(n → ∞) MSE(X bar) = lim(n → ∞) θ/n = 0

Therefore, as the sample size becomes larger, the MSE of X bar approaches zero. This means that X bar becomes a better and better estimator of the true parameter θ as the sample size increases.

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In conclusion, Amy used a snowball sampling method to collect data for her survey. This method is useful when the population is hard to locate or identify, and when other sampling methods are not possible

Amy used a snowball sampling method. Snowball sampling is a non-probability sampling method where the participants recruit other members of the population.

It is useful when the population is difficult to locate or identify, as it relies on word of mouth or referrals from already recruited participants. In this case, Alfred was able to introduce other international students who might be interested in participating in Amy's survey. This allowed Amy to collect enough data to conduct her analysis. Snowball sampling is useful when the sample size is not known, when time is limited, or when a random selection is not possible.

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To solve this inequality, the left side can be divided by $2.50 and the value of x can be determined. The solution to this inequality is that Becky can afford to buy a maximum of 8 fish.$2.50x ≤ $20

$2.50x ≤ $20

The given situation is that Becky wants to buy some fish for her aquarium and she has $20 to spend and the cost of the fish is $2.50 each. To determine how many fish, x, Becky can afford to buy, an inequality can be written. Since the cost of each fish is $2.50, the total cost for buying x number of fish is $2.50x. To find out how many fish Becky can afford to buy, the inequality $2.50x ≤ $20 can be written. To solve this inequality, the left side can be divided by $2.50 and the value of x can be determined. The solution to this inequality is that Becky can afford to buy a maximum of 8 fish.

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