Convert 20 feet per minute to yards per hour.
400 yards/hour
3600 yards/hour
60 yards/hour
6.3 yards/hour

The probability that Gianna will randomly elect a brown pair or a green pair is 0.75 or 75%.

A practical technique to express the likelihood that an event will occur or not is through probability notation. When working with Venn diagrams, set notation is employed, and we use it to accomplish this.

Capital letters and various Greek characters are frequently used while notating events.

It is also possible to express probability as a percentage and it can only range from 0 to 1. The likelihood that event A will occur is frequently expressed as P (A) P(A) P(A)P, left parenthesis, A, right parenthesis.

The P(A/B) formula is written as P(A/B) = P(AB) / P(B), where the symbol denotes the intersection of events "A" and "B."

A basket containing 5 brown pair, 7 green pair, and 4 blue pair of coloured contacts. total pair of coloured contacts in basket =5+7+4=16

Gianna will randomly select,

P(a brown pair or green pair) =

[tex]\dfrac{\text{number of brown or green pair of colored contacts in basket}}{\text{total pair of colored contacts in basket}}[/tex]

= [tex]$\frac{5 + 7}{16}[/tex]

= [tex]$\frac{12}{16}[/tex]

= 3/4

= 0.75

Thus, the probability that Gianna will randomly elect a brown pair or a green pair is 0.75 or 75%.

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Using Laplace Transformation, the initial value problem y" - 2y' + y = 0 , y(0) = 1 , y'(0) = 2 is y(t) = e^t + te^t.

The differential equation is y" - 2y' + y = 0 and y(0) = 1 , y'(0) = 2

As we know that the Laplace Equation is:

[tex]L(y^n(t)) = s^nf(s) - s^{n-1}y(0) - s^{n-2}y'(0)-\dots-sy^{n-2}(0)-y^{n-1}(0)[/tex]

Now applying the Laplace Transformation in the differential equation

L(y") - 2L(y') + L(y) = 0........(1)

Now finding the value of L(y") using the equation

L(y") = s^2f(s) - s(1) - 2

L(y") = s^2f(s) - s - 2

Now finding the value of L(y') using the equation

L(y') = sf(s) - 1

Now finding the value of L(y) using the equation

L(y) = f(s)

Now putting the values in the equation 1

s^2f(s) - s - 2 - 2(sf(s) - 1) + f(s) = 0

Now solving

s^2f(s) - s - 2 - 2sf(s) + 2 + f(s) = 0

s^2f(s) - s - 2sf(s) + f(s) = 0

Taking common f(s) in term terms of f(s)

(s^2 - 2s + 1)f(s) - s = 0

Add s on both side, we get

(s^2 - 2s + 1)f(s) = s

We can write (s^2 - 2s + 1) as (s - 1)^2

(s - 1)^2f(s) = s

Divide by (s - 1)^2 on both side, we get

f(s) = s/(s - 1)^2

The inverse Laplace of f(s) = s/(s - 1)^2 is

y(t) = e^t + te^t

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Solving provided question, we can say that value of standard deviation will be 3.28634 and Mean (Average) = 5 and Variance (SD) = 10.8

Standard deviation is a statistic that expresses the variability or variance of a group of numbers. While a high standard deviation suggests that the values are more dispersed, a low standard deviation suggests that the values tend to be closer to the established mean. A measure of how dispersed the data are from the mean is the standard deviation (or ). When the standard deviation is low, the data tend to be grouped around the mean, and when it is large, the data are more dispersed. The average variability of the data set is measured as standard deviation. It reveals the average deviation of each score from the mean.

Total Numbers = 6

Mean (Average) = 5

SD = 3.28634

Variance (SD) = 10.8

Population SD = 3

Variance(Population SD) = 9

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All such strings if no repeats are allowed, meaning each of A, B, or C is used once then the total number of combinations is 13.

An array is a collection of elements that are ordered and can be accessed through indices.

In this case, we are dealing with arrays of character strings, where each string is a sequence of letters. In this problem, there are three possibilities for the characters that can appear in each string: A, B, or C.

(a) Three character strings where repeats are allowed:

Tree:

List: AAA, AAB, ACC, ABA, ABC, ACA

Number of items on list: 6

(b) Three character strings where repeats are not allowed in a row:

List: AB, AC, BAC, BCA, CAB, CBA

Number of items on list: 6

(c) Three character strings with no repeats allowed:

Tree:

ABC

List: ABC

Number of items on list: 1

So, the total number of items on the list is calculated as,

=> 6 + 6 + 1.

=> 13

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Let length of vector is 5 then the vector in the direction of  ⟨−3,−1,5⟩ will be ⟨−15/√35,−5/√35,25/√35⟩.

What is a Vector?

Vectors, in Maths, are objects which have both, magnitude and direction. Magnitude defines the size of the vector. It is represented by a line with an arrow, where the length of the line is the magnitude of the vector and the arrow shows the direction. It is also known as Euclidean vector or Geometric vector or Spatial vector or simply “vector“.

Two vectors are said to equal if their magnitude and direction are the same. It plays an important role in Mathematics, Physics as well as in Engineering. According to vector algebra, a vector can be added to another vector, head to tail. The order of addition of two vectors does not matter, because the result will be the same.

Now,

The idea is based on a concept of scaling and similarity.

Any vector that "has the same direction" as

⟨−3,−1,5⟩

has all the coordinates proportional to this given vector and, therefore, can be described by coordinates

⟨−3f,−1f,5f⟩

where f is a scaling factor.

All we need now is to find a scaling factor that leads to a vector with the length 5

The length of a vector with coordinates

⟨−3f,−1f,5f⟩

equals to√9f^2+f^2+25f^2=√35f

So, if we want the length to be equal to 5, we should choose

f=5/√35

Hence,

          The coordinates of a vector with the same direction as  ⟨−3,−1,5⟩ but with the length 5 will be ⟨−15/√35,−5/√35,25/√35⟩.

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The equation of the third plane is 3x - 8y - z = -1.

An equation is a mathematical statement that shows the equality or balance of two expressions. It is represented by an equal sign (=) and consists of variables, numbers, and mathematical operations. Equations are used to describe relationships between different quantities and can be solved to find unknown values. For example, the equation 2x + 3 = 7 can be solved for x by subtracting 3 from both sides, giving 2x = 4, and then dividing both sides by 2, giving x = 2.

The equation of the first plane is x + y + z = 2.

The equation of the second plane is 8x + y - 2z = 31.

The equation of the third plane is 3x - 8y - z = -38.

The third plane passes through the point (1, 5, 1) and is perpendicular to the plane 2x + y - 2z = 2 and x + 3z = 4. To find the equation of this plane, we can use the cross product of the normal vectors of the two given planes:

(2, 1, -2) × (1, 0, 3) = (3, -8, -1)

So, the equation of the third plane is 3x - 8y - z = -1.

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The irregular total of 1,609.344 metres equals one mile.

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You should re-analyze the data to determine why your results contradicted your hypothesis if the experiment's findings did not support it. You shouldn't change the experiments, observations, or both in order to get results that support your theory.

The Scientific Method is the framework that is most frequently employed while conducting an experiment. Asking a specific question, formulating a hypothesis, conducting experiments to collect data, analyzing the data, and determining if the hypothesis is true in light of the experimental results are all hallmarks of the scientific method.

The results may be published or distributed if the data are consistent with the hypothesis. The experiment's evaluation phase includes the write-up. Regardless of what took place during the experiment, the outcomes must be reported, whether they support or refute the hypothesis.

Next, list any issues that came up throughout the trial, and then include recommendations for changes and next steps in your report. To record what happened during the experiment, a write-up is required. It becomes a part of the background literature for the topic being investigated or put to the test.

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B)

To solve the equation 2x^2 + 5x - 3 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Where a = 2, b = 5, and c = -3.

Plugging in the values, we get:

x = (-5 ± √(5^2 - 4 * 2 * -3)) / 2 * 2

x = (-5 ± √(25 + 24)) / 4

x = (-5 ± √49) / 4

x = (-5 ± 7) / 4

So, the two solutions are:

x = ( -5 + 7 ) / 4 = (2) / 4 = 1/2

x = ( -5 - 7 ) / 4 = (-12) / 4 = -3

So, the two solutions to the equation 2x^2 + 5x - 3 = 0 are x = 1/2 and x = -3.

Answer:

The answer is B) x = 1/2, -3.

Step-by-step explanation:

The equation 2x^2 + 5x - 3 = 0 can be solved using the quadratic formula, which states that the solutions to a quadratic equation of the form ax^2 + bx + c = 0 are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

where a, b, and c are the coefficients of the equation and ± represents both the positive and negative square root.

In this case, a = 2, b = 5, and c = -3. Plugging these values into the formula gives us:

x = (-5 ± √(5^2 - 4 * 2 * -3)) / (2 * 2)

x = (-5 ± √(25 + 24)) / 4

x = (-5 ± √(49)) / 4

x = (-5 ± 7) / 4

So the two solutions are:

x = (-5 + 7) / 4 = 2 / 4 = 1/2

x = (-5 - 7) / 4 = -12 / 4 = -3

Therefore, the solutions to the equation 2x^2 + 5x - 3 = 0 are x = 1/2 and x = -3, which corresponds to option B) x = 1/2, -3.

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In the function f(x) = 3x = 2, when input is 3 output is 11, and when input is

10 output is 32.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Suppose we have a function f(x) = 3x = 2.

Here, 'x' is the input, and f(x) is the output.

Now, When the input is 3,

f(3) = 3×3 + 2.

f(3) = 9 + 2.

f(3) = 11.

Again when the input is 10,

f(10) = 3×10 + 2.

f(10) = 30 + 2.

f(10) = 32.

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Because the general solution involves an arbitrary constant of integration that can only be discovered by providing an extra beginning condition, the solution to this equation with the starting condition y(0) = 0 is not unique.

An algebraic equation, also known as a polynomial equation, is a mathematical equation of the form P=0, where P is a polynomial with coefficients in some field, most commonly the field of rational numbers. An algebraic equation is a mathematical statement that sets two expressions equal to each other. An algebraic equation is typically made up of a variable, coefficients, and constants.

Here,

The equation y' = xy is a separable differential equation, which means it can be solved for y in terms of x by separating and integrating the variables. The solution to this equation with the starting condition y(0) = 0 is not unique since the general solution contains an arbitrary constant of integration that can only be found by giving an additional initial condition.

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USD 651.83 is equal to 600 Euros (USD). The euro, denoted by the sign €, is the currency and monetary unit of the European Union.

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This statement implies that Mike and Chance were picking apples together and that Chance picked three times as many apples as Mike.

Let's say Mike picked "x" apples. Then, according to the statement, Chance picked 3 times as many apples as Mike, which would be 3x apples.

Let x be the number of apples picked by Mike.

Then, the number of apples picked by Chance would be 3 times that, or 3x apples.

So, the equation can be written as:

x + 3x = total number of apples picked by both Mike and Chance.

Combining like terms, we get:

So the total number of apples picked by Mike and Chance together would be x + 3x = 4x apples.

Therefore, for every apple Mike picked, Chance picked three, and their combined total was four times the number of apples that Mike picked.

Total number of apples picked by both Mike and Chance = 4x.

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Incomplete Question

How many apples did Mike and Chance pick together if for every apple Mike picked, Chance picked three?

(0.25 s) = -1.8 m/s ,the numerical value of the vertical velocity of the car at time t = 0.25s, which was found to be -1.8m/s.

Part D:

In order to find the expression for the vertical velocity of the car, we need to use both the chain and product rules of differentiation. The chain rule states that if f(x) is a function of g(x), then the derivative of the function is equal to the derivative of g(x) multiplied by the derivative of f(x). The product rule states that if two functions, f(x) and g(x), are multiplied together, then the derivative of the product is equal to the derivative of f(x) multiplied by g(x) plus the derivative of g(x) multiplied by f(x).

Using the chain rule, we can find the derivative of the position-time equation:

y'(t) = yo'e-21 -yde (a cos(wt) + w sin(wt))

Using the product rule, we can find the derivative of the position-time equation:

v(t) = owyo'e-21 -yde (a cos(wt) + w sin(wt)) cos(wt) sin(wt) + yoe- (cos(wt) + aw cos(wt))

Simplifying the expression, we find:

v(t) = ayo'e-20t -w cos(wt) sin(wt)

Part E:

In order to evaluate the numerical value of the vertical velocity of the car at time t = 0.25s, we need to plug the given values for yo, a, and w into the expression for the vertical velocity.

Substituting the given values into the expression, we find:

v(0.25s) = 0.75e-20(-6.3)cos(6.3*0.25)sin(6.3*0.25)

Simplifying the expression, we find:

v(0.25s) = -1.8 m/s

In this example, we used the chain and product rules of differentiation to find the expression for the vertical velocity-time relationship for the car from its position-time relationship. We then used this expression to evaluate the numerical value of the vertical velocity of the car at time t = 0.25s, which was found to be -1.8m/s.

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Form of a Line in Point-Slope, By using the substitution approach, you may solve for b by first plugging the slope and the (x, y) point values into the equation y is mx + b. The formula for the point-slope form is (x 1, y 1) is y y 1 is m (x x 1), where m is the slope and (x, y 1) is the provided point.

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Therefore , the solution of the given problem of rational numbers  comes out to be A) 0.75 can be written as 75/100.

Rational numbers are those that may be written as a ratios (or fraction) of 2n. A fraction with a nonzero denominator is said to be rational. A few instances of rational numbers are 1/2, 1/5, and 3/4. As a real function, "0" can also be stated in a number of different ways, such as 0/1, 0/2, etc 0/3. But 1/0, 2/0, 3/0, and so forth. The number seven makes sense. A rational number is produced when three integers are split. To get the rational number 7, divide whole 7 ps by the total number 1. Since 7 can be obtained by dividing two integers, it is referred to as a real function.

Here,

Given :

=> Any number that can be expressed as a straightforward fraction is considered rational. This is the shape of a fraction: => a/b

where the denominator is "b" and the numerator is "a". Since both are integers, b 0.

=>Simple fractions cannot be used to represent irrational values.

So,

A) 75/100 is equivalent to 0.75 rational.

B) √√3 is irrational.

C) √√√9 is irrational.

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Table: x         2  5  9

   f ( x )   5  8  11

Domain: {2, 5, 9}, Range: {5, 8, 11}.

The domain of a function is the set of all the input values, while the range is the set of all output values. In this example, the function f(x) is represented in a table with three values. For the domain, the input values are 2, 5 and 9. This means that the domain of f(x) is {2, 5, 9}. The range of f(x) is the set of all output values. The output values for this problem are 5, 8, and 11. This means that the range of f(x) is {5, 8, 11}. Therefore, the domain and range of f(x) can be written as {2, 5, 9} and {5, 8, 11} respectively.

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Integral (2x + 15)dx =from 0 to 10

Area = (10 + 0)/2 * (2*10 + 15 - 2*0 + 15)

Area = (10 + 0)/2 * (35)

Area = 175

The integral, in this case, is the area under the line y = 2x + 15 between x = 0 and x = 10. The diagram for this looks like a trapezoid with the base of 10, the left side y = 15, the right side y = 25, and the height of 10. To calculate the area, we use the formula for the area of a trapezoid, which is (b1 + b2)/2 * h, where b1 and b2 are the lengths of the two bases and h is the height. For this problem, b1 is 0 and b2 is 10, and h is 10, so the area of the trapezoid is (10 + 0)/2 * (2*10 + 15 - 2*0 + 15). This simplifies to (10 + 0)/2 * (35), which is 175.

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The amount that is needed to be deposited is $15,609.61

According to the Question

The formula for the future value of an investment may be used to determine the amount that must be deposited today in order to have $20,000 in 4 years:

FV = PV * (1 + r)^n

Where:

FV = future value = $20,000

PV = present value = x

r = annual interest rate = 5%

n = number of years = 4

To solve for PV, rewrite the formula as follows:

PV = FV / (1 + r)^n

Putting the values:

x = $20,000 / (1 + 0.05)^4

⇒ x = $15,609.61

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The amount that is needed to be deposited is $15,609.61

According to the Question

The formula for the future value of an investment may be used to determine the amount that must be deposited today in order to have $20,000 in 4 years:

FV = PV * (1 + r)^n

Where:

FV = future value = $20,000

PV = present value = x

r = annual interest rate = 5%

n = number of years = 4

To solve for PV, rewrite the formula as follows:

PV = FV / (1 + r)^n

Putting the values:

x = $20,000 / (1 + 0.05)^4

⇒ x = $15,609.61

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The spices cost 6.15 in dollars. Porter is visiting India and bought species cost 6.15 dollars.

Here, these values are given, which is important for our solution,

So, after putting the values,

Porter bought species cost 452.95 rupees after visiting to India.

Current exchange rate = 1 dollar = 73.6500 rupees.

Here , 73.6500 rupees = 1 dollar

So, 1 rupee = 1/ 73. 6500 dollar

Then , 452. 95 rupees = 452. 95/ 73.6500 dollar.

After diving the rupees value by dollar values,

We get these values,

So, here,  452.95 rupees became 6.15 dollars.

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Answer: $6.15

Step-by-step explanation:

The statements given are mostly true, except for the statements that V_4 is parallel to V_3 and that V_3 is greater than V_1.

The magnitude of a vector can be different in different coordinate systems. True

It is possible to add a scalar to a vector. True

A 2D vector can have a magnitude equal to zero even when one of its components it nonzero. True

The direction of a vector can be different in different coordinate systems. True

A 2D vector can have a component equal to zero even when its magnitude is nonzero. True

The components of a vector can be different in different coordinate systems. True

It is possible to multiply a vector by a scalar. True

If V_3 = V_1 + V_2, then V_4 = 3V_1 + 3V_2 is parallel to V_3. False

If V_3 = V_1 + V_2, then V_3 - V_2 is parallel to V_1. True

If V_3 = V_1 + V_2, then V_3 = V_1 + V_2. True

If V_3 = V_1 + V_2, then V_3 > V_1. False

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Volume of a sphere would be 6912.

What is Volume of this sphere ?

The volume of a sphere is calculated as V = 4/3πr^3, where V = volume and r is radius.

The fact that a sphere can be measured for its volume and surface area is due to the fact that it is a three-dimensional shape as opposed to a circle, which is a two-dimensional shape.

According to given question,

    [tex]Volume\ of \ sphere=\frac{4}{3} \pi r^{3} \\\\Volume\ of \ sphere=\frac{4}{3} \pi 12^{3} \\\\Volume\ of \ sphere=\frac{4}{3} (3){1728}\\\\Volume\ of \ sphere=6912[/tex]

Hence, Volume of a sphere would be 6912.

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The amount of money left after 8 quarters is $3,547,878

The theory used in this question is exponential decay, which describes how the value of a quantity decreases over time.

In this case, the value of the original investment decreases by 7% each quarter.

The steps for this process are as follows

Convert the percentage to a decimal. 7% = 0.07

Substitute the values into the equation: y = 5,000,000(1 - 0.07)t

Simplify the equation by multiplying the numbers in the parentheses: y = 5,000,000(0.93)t

Substitute the number of quarters into the equation: y = 5,000,000(0.93)8

Calculate the amount of money left after 8 quarters: y = 5,000,000(0.93)8 = 3,547,878

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The Normal model is a good approximation for the sampling distribution.

a) According to the Central Limit Theorem, the theoretical mean and standard deviation for a sample size of 20 should be 0.05 and 0.02, respectively. For a sample size of 100, the theoretical mean and standard deviation should be 0.05 and 0.01, respectively.

b) The observed mean and standard deviation for a sample size of 20 was 0.052 and 0.021, respectively. For a sample size of 100, the observed mean and standard deviation was 0.051 and 0.012, respectively. These values are fairly close to the theoretical values.

c) Looking at the histograms in Exercise 1, I would be comfortable using the Normal model as an approximation for the sampling distribution at a sample size of 100.

d) The Success/Failure Condition states that the sample size should be large enough for the sampling distribution of the sample proportions to be approximately normal. Since I chose a sample size of 100, which satisfied the condition, I can be confident that the Normal model is a good approximation for the sampling distribution.

The sample size of 100 is large enough for the sampling distribution of the sample proportions to be approximately normal, and the observed mean and standard deviation is close to the theoretical values. Therefore, the Normal model is a good approximation for the sampling distribution.

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Answer: a/c

Step-by-step explanation: cancel out the common factor b. to find the excluded values would be b = 0, c = 0

The values of r for which the differential equation y''' - 5y'' - 6y' = 0 are -6, -1 and 0

Given y = e^(rx)

Now, y' = re^(rx) = ry

        y'' = r²e^(rx) = r²y

        y''' = r³e^(rx) = r³y

We are asked to find the values of r for  y''' - 5y'' - 6y' = 0

Put y', y'', y''' in the differential equation:

                                      r³y - 5(r²y) - 6(ry) = 0

                                      y(r³ - 5r² - 6r) = 0

Solving r³ - 5r² - 6r = 0

            r(r² - 5r - 6) = 0

            r(r - 6)(r + 1) = 0

                             r = -6 or -1 or 0

Hence, the values of r are -6, -1 and 0

The question is incomplete. The complete question is

"Determine the values of r for which the differential equation y''' - 5y'' - 6y' = 0 has a solution of the form y = e^(rx)."

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The answer is 42.25

I hope this is the answer you're looking for.

Answer:

42.25

Step-by-step explanation:

We can use the long division method to solve this.

[tex]\textrm{ } \ \ \ \ 42.25 \\9 \, \overline{\smash{)} \, 380.25}\\\text{ }\: \underline{ \text{- } 36}\\\text{ } \ \ \ \ 20\\\text{ } \ \ \underline{ \text{- } 18}\\\text{ } \ \ \ \ \, \ 2\, 2\\\text{ } \ \ \ \ \underline{ \text{- } 18}\\\text{ } \ \ \ \ \ \ \ \, 45\\\text{ } \ \ \ \ \ \, \underline{ \text{- } 45}\\\text{ } \ \ \ \ \ \ \ \ \ 0[/tex]

Answer:

81

Step-by-step explanation:

tens: 8

ones: 8 - 7 = 1

The assessment value of the house will be $97,200.

The fair market value of a house refers to its calculated selling price under current market conditions. Assessed value is used by government tax assessors to determine how much property taxes a new homeowner may anticipate to pay.

Both fair market value and tax-assessed value contribute to determining a home's worth.

FMV is a fictitious value derived by estimating how much a buyer and seller would likely agree on under "normal" conditions. In contrast, market value is the price at which a property will actually sell.

As per the data given in the questions,

We have,

The market value of the home = $135,000

For finding the market value of the house, we simply multiply the market value by the assessment rate:

So, the market value will be: $135,000 * 0.72 = $97,200.

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