Solve for x,
using the secant lines.
4 cm
20 cm
x = [?] cm
X
6 cm
Remember: a b = c.d
Enter

In 1 km races, runner 1 on track 1 with time 2 min and 26.39 s appears to be faster than runner 2 on track 2 with 2 min and 26.53 s. The difference in the length of the tracks, ∆L = L₂ - L₁, is equals to the 0.95, to conclude that runner 1 is faster.

When a body is traveling and it displaces its place from one point to another point, then this displacement of the body for a period of time is known as the velocity of the body. For the calculation of the velocity, both magnitude and direction values should be known. Length of track 1 , L₁ = 1 km = 1000 m

Time of 1ˢᵗ runner, t₂= (2min, 26.39s)

= (2×60 + 26.39) seconds =146.39 s

Time of 2ⁿᵈ runner t₂ = (2min, 26.53s)

= (2×60 + 26.53) s = 146.53 seconds

By using the velocity equation, v = L₁ ×t₁

=> v = 1000 m/146.39 seconds

=> v = 6.8310 m/s

Now by using the same velocity we determine the length of 2ⁿᵈ track,v = L₂/ t₂

6.8310 m/s = L₂/ 146.53

=> L₂ = 146.53 ×6.8310 m/s

=> L₂ = 1000.95 m

So the difference in the length of the tracks, ∆L = L₂ - L₁

= 1000.95 m - 1000 m

= 0.95 m

Hence, required difference is 0.95 m.

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Complete question:

in 1 km races, runner 1 on track 1 (with time 2 min, 26.39 s) appears to be faster than runner 2 on track 2 (2 min, 26.53 s). however, length L₂ of track 2 might be slightly greater than length l of track 1. how large can L₂ - L₁ be for us to conclude that runner 1 is faster?

The value of q according to the given triangle measures is 3 cm.

What is Sine Rule for Traingles?

For any general triangle ABC with 3 angles A, B, and C and 3 sides a, b, and c corresponding to their opposite angle, the formula of sine is always fulfilled :

               [tex]\frac{a}{sin A} = \frac{b}{sin B} =\frac{c}{sin C}[/tex]

Here, we are given that :

s i.e. Side QR = 3.1 cm

Angle Q = 62 degree

Angle R = 114 degree

Firstly we need to find the third angle S using the sum of triangle angles property :

                   [tex]AngleQ + AngleR + AngleS = 180\\[/tex]

                   [tex]Angle S = 180 - 114 - 62[/tex]

                                [tex]= 180 - 176[/tex]

                                [tex]= 4[/tex]

Now, we apply the sine formula for angles Q and S :

                    [tex]\frac{q}{sinQ} = \frac{s}{sinS}[/tex]

                      [tex]q = (sinQ) * s / (sinS)[/tex]

                          [tex]= ( 3.1 * sin(62)) / sin(4)[/tex]

                          [tex]= ( 3.1 * (-0.739)) / (-0.756)[/tex]

                           [tex]= 3.03[/tex]

Hence, the length of side RS i.e. q to its nearest 10th is 3 cm.

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Answer:

Step-by-step explanation:

Okay so you've gotta start with the y-intersect. The line hits the y-axis at 7, so your B is 7 (y=mx+7).

Since the line is going down, it's a negative slope, so your m will be a negative (y=-mx+7)

The line matches up exactly with (1,4), which shows the line moving down 3 for every 1 movement to the right. That makes your equation for the line y=-3x+7 or y=-3/1x+7

Answer: 132 cubic centimeters

Step-by-step explanation:

To find the volume of the block of clay, we need to add the volumes of the two rectangular pieces.

The volume of a rectangular solid can be found by multiplying its length, width, and height. Let's call the first rectangular piece A and the second rectangular piece B. Then the dimensions of A are 6 cm (length), 4 cm (width), and 3 cm (height), and the dimensions of B are 5 cm (length), 4 cm (width), and 3 cm (height).

The volume of A is:

Volume of A = length x width x height = 6 cm x 4 cm x 3 cm = 72 cubic centimeters

The volume of B is:

Volume of B = length x width x height = 5 cm x 4 cm x 3 cm = 60 cubic centimeters

So the total volume of the block of clay is:

Volume of block = Volume of A + Volume of B = 72 cubic centimeters + 60 cubic centimeters = 132 cubic centimeters

Therefore, the volume of the block of clay is 132 cubic centimeters.

Therefore, the area of P is 4 times bigger than the area of Q.

Area is a measure of the amount of two-dimensional space enclosed by a closed figure, such as a square, rectangle, circle, or triangle. It is typically measured in square units, such as square meters (m²) or square centimeters (cm²). The formula for finding the area of a figure depends on the shape of the figure. For example, the area of a rectangle is found by multiplying its length by its width, while the area of a circle is found by multiplying π (pi) by the square of its radius. Knowing the area of a figure can be useful in many situations, such as when calculating the amount of material needed to cover a floor or when determining the capacity of a container. It is also an important concept in geometry, where it is used to compare the sizes of different shapes and to solve problems involving the relationships between them.

Here,

The area of a circle is given by the formula A = πr², where A is the area and r is the radius.

For shape P, the area is:

A_P = (3/4)π(20²) = 300π

For shape Q, the area is:

A_Q = (1/3)π(15²) = 75π

To find how many times bigger the area of P is than the area of Q, we can divide the area of P by the area of Q:

A_P / A_Q = (300π) / (75π) = 4

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There are no real solutions to the equation 0 = x² + 5, and the graph of y = x² + 5 does not intersect the x-axis.

To find the solutions of 0 = x² + 5, we need to find the values of x that make the equation true. One way to do this is by solving the equation algebraically using methods like factoring, completing the square, or using the quadratic formula.

We cannot use the graph of y = x² + 5 directly to find the solutions of 0 = x² + 5, since the graph shows the values of y that correspond to different values of x, not the values of x that satisfy the equation 0 = x² + 5. However, we can use the graph to help us visualize the solution to the equation.

Since 0 = x² + 5 is equivalent to x² = -5, we know that the solutions to the equation must be imaginary numbers, since the square of any real number is always non-negative. Therefore, there are no real solutions to the equation 0 = x² + 5, and the graph of y = x² + 5 does not intersect the x-axis.

In summary, we cannot use the graph of y = x² + 5 directly to find the solutions of 0 = x² + 5, but we can use the graph to see that the equation has no real solutions.

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there are n(n-1)(n-2)/2 simple paths of nonzero length in a tree with n vertices, where two simple paths are regarded as the same if they have the same edges.

In a tree with n vertices, there are (n-1) edges, since a tree is a connected acyclic graph.

To count the number of simple paths of nonzero length in the tree, we can consider each vertex as a starting point for a path and count the number of possible paths from that vertex.

Starting from any vertex, there are at most (n-1) paths that can be formed by moving to any of the neighboring vertices. From each of these neighboring vertices, there are at most (n-2) paths that can be formed by moving to a new neighboring vertex (excluding the vertex that was just visited).

This process can be continued until there are no more vertices to visit. However, to avoid counting the same path twice, we should only consider paths that do not backtrack on themselves.

Therefore, the total number of simple paths of nonzero length in the tree is the sum of all simple paths that start from each vertex:

(number of paths starting from vertex 1) + (number of paths starting from vertex 2) + ... + (number of paths starting from vertex n)

Using the reasoning above, we can see that the number of paths starting from each vertex is at most (n-1) * (n-2), since each path can visit at most (n-2) additional vertices after the starting vertex, and there are at most (n-1) vertices to choose from as the next vertex on the path.

Therefore, the total number of simple paths of nonzero length in the tree is at most n(n-1)(n-2).

However, we have counted each simple path twice (once in each direction), so the actual number of distinct simple paths of nonzero length is half of this maximum value, which is:

n(n-1)(n-2)/2

So, there are n(n-1)(n-2)/2 simple paths of nonzero length in a tree with n vertices, where two simple paths are regarded as the same if they have the same edges.

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Answer:

The equation that describes the number of mini trains Kolton would need in each row would be:

n = 12 + 5(r - 1)

where n is the number of mini trains in a given row, and r is the number of the row.

To find the number of mini trains in row 15, we simply substitute r = 15 into the equation and solve for n:

n = 12 + 5(15 - 1)

n = 12 + 5(14)

n = 12 + 70

n = 82

Therefore, Kolton would need 82 mini trains in the 15th row.

8760 hours in a​ year, one television was on for 438 hours. 5% is the percentage of 8760 hours television was on.

The percentage is the a ratio in which the value of the whole (denominator) is always 100. For example, if Ram scored 40% marks in his math test, it means that he scored 40 marks out of 100. It is written as 40/100 in the fraction form and 40:100 in terms of ratio. Here "%" signifies the symbol of percentage and is read as "percent" or "percentage".

Total number of hours in a year=8760hrs

Television was on for=438hrs

percentage=438/8760 x 100 = 5

Therefore, 438hr is 5 percent of 8760hr.

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Answer:

To find the vertex of the quadratic function y = -2x² - 4x - 5, we can use the formula:

x = -b/2a

where a = -2 and b = -4 are the coefficients of the quadratic term and the linear term, respectively.

x = -(-4)/(2*(-2)) = -(-4)/(-4) = 1

To find the y-coordinate of the vertex, we substitute x = 1 in the function:

y = -2(1)² - 4(1) - 5 = -2 - 4 - 5 = -11

Therefore, the vertex of the quadratic function is (1, -11).

Answer:

(-1, -3)

Step-by-step explanation:

If wendy can build a fort in 12 hours, al can build the same fort in 8 hours, the time taken by Wendy and Al working together to build the fort is 24/5 hours

To solve this problem, we need to use the concept of work and time. Let's assume that the fort is the unit of work that needs to be completed, and the time required to complete this unit of work is the time taken by Wendy and Al working together.

Let's denote the time taken by Wendy to build the fort as TW and the time taken by Al to build the fort as TA. From the problem, we know that TW = 12 hours and TA = 8 hours.

Let's also denote the time taken by Wendy and Al working together to build the fort as T. We can use the formula:

Work = Rate x Time

where the rate is the amount of work done per unit time.

Let's assume that Wendy's rate of work is RW, and Al's rate of work is RA. Then the rate of work of both of them working together is the sum of their individual rates of work:

RW + RA = 1/T

We can also express their individual rates of work as the inverse of the time taken by them to complete the work:

RW = 1/TW

RA = 1/TA

Substituting these values in the above equation, we get:

1/TW + 1/TA = 1/T

Substituting the given values of TW and TA, we get:

1/12 + 1/8 = 1/T

Simplifying this equation, we get:

5/24 = 1/T

T = 24/5 hours

In other words, it would take them 4 and 4/5 hours to complete the work if they worked together.

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The measure of the angle x of the polygon is 100 degrees if the polygon has 5 sides. The interior angle measures are 117°, 104°, 113°, 106°.

A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight line segments are joined and to end to form a closed shape. The vertices also known as corners, are the points where two lines segments meet and form an angle.

We know that the sum of the interior angles in a polygon is given by:-

180(n-2) here, n is 5.

therefore, 180(5-2) = 540° .

117°+104°+106°+x= 540°.

440°+x= 540°

x= 540°-440°

x= 100° .

Thus, the measure of the angle x is 100° .

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Answer: 106.81 in

Step-by-step explanation:

c = 2πr

r = 17 in

2π(17) = 106.8141502

I'm not sure how you want it rounded, but it is commonly rounded by the hundredths decimal.

Answer:

The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle and π (pi) is a mathematical constant approximately equal to 3.14159.

If the radius of the circle is 17 inches, then we can substitute this value into the formula:

C = 2πr

C = 2π(17)

C = 34π

So the circumference of the circle is 34π inches, which is approximately 106.81 inches when rounded to two decimal places.

163.79 students were surveyed.

The survey asked randomly selected students whether they preferred vanilla ice cream or chocolate ice cream. 58% of the students said they preferred vanilla ice cream, with a 5% margin of error. To calculate the total number of students surveyed, we can use the following formula:

Number of Students Surveyed = (100 - Margin of Error) ÷ (Percentage that Prefer Vanilla/100)

In this case, we get:

Number of Students Surveyed = (100 - 5) ÷ (58/100)

Number of Students Surveyed = 95 ÷ 0.58

Number of Students Surveyed = 163.79

Therefore, 163.79 students were surveyed.

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The correct option- The perpendicular bisector of AB has the slope -1/3.

The difference between the change in y-values and the change in x-values is known as the slope of a line. This figure represents the slope of a line.

Formula for slope m = (y2 - y1)/(x2 - x1)

Line segment AB coordinates :

A (1,5) and B (9,17).

Slope m1 = (17 - 5)/(9 - 5)

m1 = 12/4

m1 = 3

The line perpendicular to AB.

Let the slope of m2.

The relation between the slopes of perpendicular lines:

m1 x m2 = -1

3 x m2 = -1

m2 = -1/3.

Thus, the slope of the line perpendicular to the given line AB is found as:  -1/3.

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Complete question:

AB in the coordinate plane has endpoints with coordinates A (1,5) and B (9,17). Which of the following is true?

The perpendicular bisector of  AB has slope 3/2.

The perpendicular bisector of AB has slope -2/3.

The perpendicular bisector of AB  has slope -2/3.

The perpendicular bisector of AB has slope -1/3.

The mathematician William Jones is credited with first using the Greek letter π

The mathematician William Jones is credited with first using the Greek letter π to represent the ratio of a circle's circumference to its diameter in a 1706 publication. He wrote, "there is no other more proper than Pi," and thus the symbol caught on among mathematicians. However, it's important to note that the concept of pi and its calculation had been around for thousands of years prior to Jones' use of the symbol.

Ancient Egyptian, Babylonian, and Indian mathematicians all had methods for approximating pi, and Archimedes famously used a geometric method to calculate it to a high degree of accuracy in the third century BCE.

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For square a of perimeter 24 cm and square b has an area equal to one-fourth the area of the square a, the perimeter of square b is 12 cm.

Given that a square has a perimeter of 24 cm. And another square b has an area equal to one-fourth of the area of square a. To find the perimeter of square b, we need to find the length of the side of square b using the area of square

Area of the square a = side² of the square a
The perimeter of the square a = 4 × side of the square a

Given that, Perimeter of square a = 24 cm⇒ 4 × side of square a = 24 cm⇒ side of square a = 24 / 4 cm⇒ side of square a = 6 cm.

Area of square b = 1/4 × Area of square a = 1/4 × side² of square a= 1/4 × 6² cm²= 9 cm²

Side of square b = √9 cm = 3 cm
Perimeter of square b = 4 × 3 cm = 12 cm

Therefore, the perimeter of square b is 12 cm.

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a) 32nd unit will take approximately 20.4 hours to produce b) T2 = 59.4 and graph of curve can be plotted similarly for T4, T8, T16

a) Using the learning curve formula, we can estimate how long it will take to make the 32nd unit:

[tex]Tn = T1 * n^k[/tex]

where n: total number of units created, Tn: time it takes to produce the nth unit, T1 is the time it takes to make the first unit, and k is the rate of learning.

T1 is assumed to be 72 hours, and k is specified to be [tex]log(0.85)/log(2)-0.278[/tex].

With the use of these numbers, we may determine T32 as follows:

[tex]T32 = T1 * 32^k \sT32 = 72 * 32^(-0.278) (-0.278)[/tex]

20.4 hours in T32

Hence, it will take about 20.4 hours to generate the 32nd unit.

b) The time it takes to create each unit for a variety of values of n can be determined using the same technique as previously in order to illustrate the learning curve. Therefore, using n as the x-axis and Tn as the y-axis, we may plot these numbers on a graph.

As an illustration, we can compute T2 as follows:

[tex]T2 = T1 * 2^k \sT2 = 72 * 2^(-0.278) (-0.278)[/tex]

59.4 hours in T2.

Similar calculations can be made for T4, T8, T16, and so forth. Then, we may graph these numbers to get a learning curve.

The resulting learning curve will demonstrate how, as production volume grows, each unit's production time gets smaller until it approaches an asymptote. The learning rate will determine how steep the curve is. A steeper curve indicates a faster rate of improvement, and a higher learning rate will produce it. In contrast, a flatter curve indicates a slower rate of improvement than a higher learning rate.

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Answer: whole number

Step-by-step explanation:such as 9/1=9 6/1=6

Answer:

n-2x180

Step-by-step explanation:

to be abke to find it wouldnt you use n-2x180

The newborn department allows more patients per nurse than the surgical department.

Number is a mathematical object used to count, measure, and label. In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers. Numbers can be represented in a variety of ways, including words, symbols, or images. Additionally, numbers are used in many different areas, including science, engineering, finance, economics, and computing.

The newborn department allows more patients per nurse than the surgical department. This is because the newborn department follows a lower nurse-to-patient ratio. The graph for the newborn department shows that for every two nurses, there are three patients, while the table for the surgical department shows that for every one nurse, there are two patients. This means that the newborn department has a ratio of 1:1.5 nurses to patients, while the surgical department has a ratio of 1:2 nurses to patients. This means that the newborn department allows more patients per nurse than the surgical department.

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The newborn department allows more patients per nurse than the surgical department.

Number is a mathematical object used to count, measure, and label. In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers. Numbers can be represented in a variety of ways, including words, symbols, or images. Additionally, numbers are used in many different areas, including science, engineering, finance, economics, and computing.

The newborn department allows more patients per nurse than the surgical department. This is because the newborn department follows a lower nurse-to-patient ratio. The graph for the newborn department shows that for every two nurses, there are three patients, while the table for the surgical department shows that for every one nurse, there are two patients. This means that the newborn department has a ratio of 1:1.5 nurses to patients, while the surgical department has a ratio of 1:2 nurses to patients. This means that the newborn department allows more patients per nurse than the surgical department.

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complete questions as follows-

The graph of the function f given by f(Θ) = 2 sin(Θ) is attached below the sum,

Use the form

a sin(bx−c)+d to find the variables used to find the amplitude, period, phase shift, and vertical shift.

a=2

b=1

c=0

d=0

Find the amplitude |a|.

Amplitude: 2

Find the period of 2 sin(x).

Its 2π.

List the properties of the trigonometric function.

Amplitude: 2

Period: 2π

Phase Shift: None

Vertical Shift: None

x      y

0     0

[tex]\frac{\pi }{2}[/tex]     2

[tex]\pi[/tex]     0

[tex]\frac{3\pi }{2}[/tex]    -2

[tex]2\pi[/tex]    0

Then we can plot the according to the given function f(Θ) = 2 sin(Θ).

Hence the graph is attached below.

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Answer:

4.68 dollars.

Step-by-step explanation:

We are looking for how much money Sam spent on grapes. We know that each pound is 90 cents. We also know that Sam bought 5.2 pounds of grapes. We need to find how much he spent.

Our equation would be like this:

0.9 * 5.2 = x

To find X, we multiply 0.9 and 5.2.

4.68 = x

We now know that Sam spent 4.68 dollars on grapes.

Ray's car will use 4.68 kiloliters of gasoline and travel 39.54 kilometers

Every week, Ray fills his car with 45 liters of gasoline. To calculate the total amount of gasoline used by Ray's car over two years, we must first convert liters to kiloliters. One kiloliter is equal to 1,000 liters, so 45 liters is equal to 0.045 kiloliters. Therefore, in two years, Ray's car will use 0.045 kiloliters x 104 weeks (2 years x 52 weeks per year) = 4.68 kiloliters of gasoline.

To calculate how many kilometers the car will travel with 4.68 kiloliters of gasoline, we need to know the car's fuel efficiency rating. Assuming the car has an average fuel efficiency rating of 8.5 kilometers per liter, we can calculate that the car will travel 8.5 kilometers x 4.68 kiloliters = 39.54 kilometers with 4.68 kiloliters of gasoline.

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The Average cost, after calculations, comes up to 210/x + 2.

To find the following functions such as Revenue, Cost, Profit and Average cost, we have given the equations as below:

Number of DVD's sold each day: n(x) = x

Selling price for each DVD: p(x) = 8.5 - 0.02x  Daily fixed costs: f(x) = 210  Daily variable costs: v(x) = 2x

To Find the following functions:

a. Revenue = R(x) = the product of the number of DVD's sold each day and the selling price of each DVD.

b. Cost = C(x) = the sum of the fixed costs and the variable costs.

c. Profit = P(x) = the difference between revenue and cost

d. Average cost = C (x) C¯(x) = the quotient of cost and the number of DVD's sold each day.

Number of DVD's sold each day: n(x) = x

Selling price for each DVD: p(x) = 8.5 - 0.02x  Daily fixed costs: f(x) = 210  Daily variable costs: v(x) = 2x

a. Revenue = R(x) = the product of the number of DVD's sold each day and the selling price of each DVD.R(x) = n(x) × p(x) = x × (8.5 - 0.02x) = 8.5x - 0.02x2

b. Cost = C(x) = the sum of the fixed costs and the variable costs.C(x) = f(x) + v(x) = 210 + 2x = 2x + 210

c. Profit = P(x) = the difference between revenue and cost.P(x) = R(x) - C(x) = 8.5x - 0.02x2 - (2x + 210) = -0.02x2 + 6.5x

d. Average cost = C(x)C¯(x) = the quotient of cost and the number of DVD's sold each day. C¯(x) = C(x) / x = (210 + 2x)/x = 210/x + 2

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The volume of the solid with base bounded by the semi-circle and the x-axis whose cross sections perpendicular to the x-axis are squares is equal to 8π/3.

To find the volume of the solid with base bounded by the semi-circle and the x-axis whose cross sections perpendicular to the x-axis are squares is shown below.

The diagram shows that the cross-sectional area of the solid is a square of side x whose area is x². Since the base of the solid is bounded by the semi-circle and the x-axis, the radius of the semi-circle is equal to the side of the square as shown in the diagram.

The diameter of the semi-circle is equal to the width of the rectangle whose height is x, that is:2r = x

Substituting the value of r in terms of x in the formula for the area of a semi-circle, we have: A = πr²/2 = π(x/2)²/2 = πx²/8

Therefore, the volume of the solid is given by: V = ∫₀^4 πx²/8 dx

The limits of integration are from 0 to 4 since the semi-circle has a diameter of 4 units, which is equal to the width of the square whose area is the cross-sectional area of the solid.

Integrating, we have: V = [πx³/24]₀⁴V = (π/24) x (4³ - 0³) = (π/6) x 16 = 8π/3.

Therefore, The volume of the solid is 8π/3.

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The answer is option a: a survey in which people are asked to indicate how much they trust a number of different politicians using a scale of 1-5, with 1 being the least amount of trust. This is an example of quantitative research.

Quantitative research requires participants to quantify their feelings and opinions using numerical values. It involves measuring variables and collecting numerical data, which can then be analyzed statistically. In this case, the survey data can be analyzed to measure the amount of trust people have in politicians.

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The cost of one avacado is equal to 0.5$ and it is found by the use of division method.

One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. an a person who knows what I mean by just calling it what they do when they just want to go to the store. Just call it what they call it, whatever ites. Really, whatever it is, these are the same people. It is a mathematical operation used for equal distribution and equal grouping.
One of the fundamental mathematical operations is division, which involves breaking a larger number into smaller groups with the same number of items.
We are given the cost of 8 avacados= $4.

The cost of 1 avacado= 1/8 * 4 = 1/2 = 0.5.

Hence, the cost of one avacado is equal to $0.5.

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