Question 3

A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.

5, 5, 6, 8, 10, 15, 18, 20, 20, 20, 20, 20, 20

A graph titled Donations to Charity in Dollars. The x-axis is labeled 1 to 5, 6 to 10, 11 to 15, and 16 to 20. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 1 to 5, up to 3 above 6 to 10, up to 1 above 11 to 15, and up to 7 above 16 to 20.

Which measure of variability should the charity use to accurately represent the data? Explain your answer.

The range of 13 is the most accurate to use, since the data is skewed.
The IQR of 13 is the most accurate to use, since the data is skewed.
The range of 20 is the most accurate to use to show that they have plenty of money.
The IQR of 20 is the most accurate to use to show that they need more money.

Question 4

The circle graph describes the distribution of preferred transportation methods from a sample of 400 randomly selected San Francisco residents.

circle graph titled San Francisco Residents' Transportation with five sections labeled walk 40 percent, bicycle 8 percent, streetcar 15 percent, bus 10 percent, and cable car 27 percent

Which of the following conclusions can we draw from the circle graph?

Together, Streetcar and Cable Car are the preferred transportation for 168 residents.
Together, Walk and Streetcar are the preferred transportation for 55 residents.
Bus is the preferred transportation for 45 residents.
Bicycle is the preferred transportation for 50 residents.

Question 5

The line plot displays the number of roses purchased per day at a grocery store.

A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 2. There are two dots above 8. There are three dots above 6, 7, and 9.

Which of the following is the best measure of variability for the data, and what is its value?

The range is the best measure of variability, and it equals 8.
The range is the best measure of variability, and it equals 2.5.
The IQR is the best measure of variability, and it equals 8.
The IQR is the best measure of variability, and it equals 2.5.

Answer:

hence the value of w is 12

Step-by-step explanation:

[tex]area = 2 {w}^{2} - 16w \\ by \: the \: question \: if \: area \: is \: equal \: to \: 8w \\ 8w = 2w {}^{2} - 16w \\ 8w + 16w = 2 {w}^{2} \\ 24w = 2 w {}^{2} \\ w = 12[/tex]

Answer:

t8 term is

[tex] \frac{ 1}{1296} [/tex]

the area of the rhombus is approximately 74.60 square units.

How to solve the question?

To find the area of a rhombus using decomposition, we first need to draw its diagonal lines. Let's label the points where the diagonals intersect as points A and B.

Now we can decompose the rhombus into two congruent triangles, ABC and ABD, where AB is the diagonal and AD and BD are half of the diagonals.

We can find the length of AD and BD using the Pythagorean theorem. Since x=4 units and y=6 units, we have:

AD²= (x/2)² + h²

AD² = (4/2)²+ 5²

AD²= 4² + 5²

AD² = 41

AD = sqrt(41)

Similarly, we can find the length of BD:

BD²= (y/2)² + h²

BD²= (6/2)² + 5²

BD²= 3²+ 5²

BD²= 34

BD = √(34)

Now we can find the area of each triangle:

Area of ABC = (AB * BD) / 2

Area of ABC = (2 * √(41) * √(34)) / 2

Area of ABC = √(1394)

Since the rhombus is made up of two congruent triangles, its total area is twice the area of one triangle:

Area of rhombus = 2 * Area of ABC

Area of rhombus = 2 * √(1394)

Area of rhombus ≈ 74.60 square units

Therefore, the area of the rhombus is approximately 74.60 square units.

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The function that models the total amount of money Julia has after x weeks is f(x) = 27x + 254

An equation is an expression that uses mathematical operations to show how numbers and variables are related to each other.

Let f(x) represent the total amount of money Julia has after x weeks.

Julia has $254 and saves $27 each week, hence:

f(x) = 27x + 254

The function is f(x) = 27x + 254

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Answer:

The process is below and the answer is D.

Step-by-step explanation:

[tex]perimeter \: = 2(l + b) \\ = 2((x + 1)cm + xcm) \\ = 2(x + 1 + x) \\ = 2(2x + 1)[/tex]

[tex](4x + 2)cm[/tex]

I hope it helped you

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In the bottom, To see the number line of |4x-4(x+1)|=4.

The absolute value (or modulus) | x | of a real number x is the non-negative value of x without regard to its sign. For example, the absolute value of 5 is 5, and the absolute value of −5 is also 5. The absolute value of a number may be thought of as its distance from zero along real number line.

The expression is:

|4x-4(x+1)|=4

First simplify in the absolute value

Distribute

|4x−4x-4|=4

|-4|=4

Taking the absolute value

4 =4

This is always true

X is all real numbers

Pick any value for x and it will be a true statement

Put the value of x=0

|4*0−4(*0+1)|=4

|-4|=4

Let taking a value of x = 5

|4*5−4(5+1)|=4

|20−24|=4

|−4|=4

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1. ∠B is the primage of ∠B'. They are similar triangles.

2. AC ≈AC'

CB ≈ CB'

AB ≈ AB'

When discussing angles, the preimage refers to the original angle before any transformation has occurred.

In geometry, a transformation refers to the process of moving or changing the position, shape, or size of an object. For example, if an angle is rotated or reflected, the resulting image of the angle would be the transformed angle.

The preimage is the angle before the transformation occurred. It is used to determine the relationship between the original angle and the transformed angle, such as whether they are congruent, similar, or related by another geometric property.

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The volume of the box should be 34,560 cubic inches.

v=l*w*h

v=48*22.5*32

(22 1/2 = 22.5)

v=34,560

the probability of rolling two 3's is 1/36.Since we are rolling two number cubes, the sample space contains 6x6 = 36 equally likely outcomes, one for each possible pair of numbers that can be rolled.

what is probability  ?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event is calculated as the number of ways the event can occur, divided by the total number of possible outcomes.

In the given question,

Since we are rolling two number cubes, the sample space contains 6x6 = 36 equally likely outcomes, one for each possible pair of numbers that can be rolled.

To find the probability of rolling two 3's, we need to count the number of outcomes that result in two 3's, and divide by the total number of possible outcomes.

From the diagram, we can see that there is only one outcome that results in two 3's, namely the outcome where the first cube shows a 3 and the second cube shows a 3. Therefore, the number of favorable outcomes is 1.

The probability of rolling two 3's is therefore:

P(rolling two 3's) = favorable outcomes / total outcomes = 1/36

So the probability of rolling two 3's is 1/36.

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The scale factor used to create the image include the following: C. 2.

In Mathematics and Geometry, a scale factor can be calculated or determined through the division of the dimension of the image (new figure) by the dimension of the original figure (pre-image).

Mathematically, the formula for calculating the scale factor of any geometric object or figure is given by:

Scale factor = side length of image/side length of pre-image

By substituting the given side lengths or dimensions into the formula for scale factor, we have the following;

Scale factor = 2/1

Scale factor = 2.

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After  converting 2.340 x 10⁴ to decimal format we will be getting 0.000234. So, the correct answer choice is options (C) which is  0.000234.

In order to convert the given epression i.e. 2.340 x 10⁴ to decimal format, we are required to move the decimal point four places to the left since the exponent is negative.

In order to find the correct decimal format, starting with 2.340, we move the decimal point four places to the left, then the value we will be getting is equal to 0.000234

Therefore, from the above calculation we can draw the inference that the correct answer is option C) i.e 0.000234.

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Answer:

a. $58.57

Step-by-step explanation:

Billy is in a pickle. He has a credit card debt of $3500 with a 16% annual interest rate, and he wants to pay it off in a year. He also wants to ask his boss for a raise, but he doesn't know how much to ask for. Luckily, he has a friend who is good at math and can help him out.

The friend tells Billy that we need to use the formula for the monthly payment of a credit card debt, which is:

P = (r / 12) * B / (1 - (1 + r / 12)^(-n))

where P is the monthly payment, r is the annual interest rate, B is the current balance, and n is the number of months to pay off the debt.

Using this formula, the friend calculates how much Billy is currently paying and how much he would need to pay to clear his debt in 12 months. The friend also finds the difference between these two payments, which is the amount of extra income Billy would need from his raise.

The friend shows Billy the calculations and says:

"Here you go, Billy. You are currently paying $280.42 per month to pay off your debt in 15 months. If you want to pay it off in 12 months, you would need to pay $331.79 per month. That means you would need an additional monthly income of $51.37 from your raise. The closest answer choice to this amount is a. $58.57, so this is the best option."

Billy thanks his friend and says:

"Wow, you are amazing! Thank you so much for helping me out. I'm going to ask my boss for a raise right now. Wish me luck!"

The friend wishes Billy good luck and hopes that he will get his raise and pay off his debt soon.

Using distance formula, the distance between AB is 5 units and the graph of the coordinates from A to F are attached below

To find the length of AB, we have to use distance formula which is given as

AB = √(x₂ - x₁)² + (y₂ - y₁)²

substituting the values into the equation;

AB = √(1 - 6)² + (-7 - (-7))²

AB = 5

The length of line AB is 5 units

To plot the points from A to F, we have to use a graphing calculator, input the points and draw all lines

Kindly find the attached graph of all the coordinates from A to F below

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units Answer:

5

Step-by-step explanation:

Answer: Ashley hit the softball farther.

Step-by-step explanation: Ashley hit the softball farther, since her distance of 65 meters is greater than Nicole's distance of 6,700 centimeters.To compare these distances, we need to convert Nicole's distance from centimeters to meters, since Ashley's distance is given in meters.To do this, we can divide Nicole's distance by 100, since there are 100 centimeters in a meter:6700 cm / 100 cm/m = 67 mTherefore, Ashley hit the softball 65 meters, which is less than the 67 meters that Nicole hit it. This means that Ashley hit the softball farther.

Therefore , the solution of the given problem of unitary method comes out to be the athletes completed a total of 12 laps.

Finish the project using the tried-and-true basic methodology, the actual variables, and any pertinent knowledge you gain from the broad and specific questions. In response, customers might be given another opportunity to sample expression the products. We'll miss out on important breakthroughs in programming comprehension if these changes don't take place.

Here,

In accordance with the information provided, for each sprint around the track, the runners jogged three times. So, three times as many laps are jogged around the track.

Furthermore, it is known that the runners jogged six more laps than they ran. Therefore, we can construct the following equation:

Jogging laps equals sprinting laps plus six.

=> 3x = x + 6

=> 3x - x = 6

=> 2x = 6

=> x = 6/2

=> x = 3

Total laps equal 3x + x = 4x times the amount of jogged and sprinting laps.

By changing the value of x, we obtain:

Laps completed = 4 (3) = 12

As a result, the athletes completed a total of 12 laps.

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The  probability that this particular fuel pump system  when put into the required condition would not remain functional  for the full 50 hours is 0.0199.

Therefore, the probability of a fuel pump failing in a mission can be evaluated using the formula designed for probability of failure in a system with two pumps in series connection

P(failure) = P(pump 1 fails) + P(pump 2 fails) - P(both pumps fail)

Here  
P(pump 1 fails) = P(pump 2 fails) = 0.01
P(both pumps fail) = (0.01)² = 0.0001.

Now,

P(failure) = 0.01 + 0.01 - 0.0001 = 0.0199

The  probability that this particular fuel pump system  when put into the required condition would not remain functional  for the full 50 hours is 0.0199.

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Part A

According to the equation, the values of a is a = 2009 + f(a) and b is b = 800 + f(b).

Part B

Approximately it takes 8 years from 2009 for the population of wild tigers in Nepal to reach 800.

To find these values, we need to set the equation for the population of wild tigers equal to 800 and solve for x. The equation becomes 800 = 121(2)ˣ.

Taking the logarithm of both sides, we get

=> log(800) = log(121) + x log(2).

Solving for x, we get

=> x = (log(800) - log(121))/log(2).

Moving on to the second part of the problem, we are asked to determine approximately how many years from 2009 it will take for the population of wild tigers in Nepal to reach 800. Using the equation we derived in Part A, we can plug in values of a and use trial and error to find the answer. However, this can be time-consuming.

Instead, we can use a calculator to get an approximate answer. Plugging in the values for log(800) and log(121) into the equation we derived in Part A, we get x = 7.75.

Therefore, it will take approximately 8 years from 2009 for the population of wild tigers in Nepal to reach 800.

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The domain is all real numbers, range is all positive real numbers. As x decreases, h(x) will decrease. As x increases, h(x) will increase.

The domain of the exponential function h(x) = 125x is all real numbers, as x can take on any value.

The range of the function is all positive real numbers, as the base (125) raised to any power (x) will always be positive.

As x decreases, h(x) will decrease. This is because when the base of an exponential function is greater than 1, as is the case here with 125, the function increases as the exponent increases, and decreases as the exponent decreases. So, as x becomes more negative, h(x) becomes smaller.

As x increases, h(x) will increase. This is because, as mentioned above, when the base of an exponential function is greater than 1, the function increases as the exponent increases. So, as x becomes more positive, h(x) becomes larger.

Overall, the function h(x) = 125x is an increasing function with a domain of all real numbers and a range of all positive real numbers.

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An equation in slope-intercept form for the perpendicular bisector of the line segment with endpoints (-1, -8) and K (5, 4) is y = 2x - 6.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (4 + 8)/(5 + 1)

Slope (m) = 12/6

Slope (m) = 2.

At data point (-1, -8) and a slope of 2, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-8) = 2(x - (-1))

y + 8 = 2x + 2

y = 2x - 6.

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The revenue from muffins was $8,000. To find the revenue from doughnuts: 4.5x = 4.5 * 8,000 = $36,000 Therefore, the cupcake delight shop sold $8,000 worth of muffins and $36,000 worth of doughnuts.

Let's use the given terms and set up a system of equations to solve this problem:

Let x be the revenue from muffins, and y be the revenue from doughnuts. We know the following:

1. y = 4.5x (Cupcake Delight Shop made 4 1/2 times as much revenue on doughnuts as muffins)
2. x + y = 44,000 (Total sales were $44,000)

Now we'll solve the system of equations step-by-step:

Step 1: Replace y with 4.5x in the second equation (using equation 1):
x + 4.5x = 44,000

Step 2: Combine the x terms:
5.5x = 44,000

Step 3: Divide both sides by 5.5 to solve for x:
x = 8,000

Step 4: Plug x back into equation 1 to find y:
y = 4.5 * 8,000
y = 36,000

So, Cupcake Delight Shop sold $8,000 worth of muffins and $36,000 worth of doughnuts.

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The dollar amount of muffins sold is $8,000, and the dollar amount of doughnuts sold is $36,000.

To solve this problem, let's assign variables to the revenue for doughnuts and muffins:
Let D = revenue from doughnuts
Let M = revenue from muffins
We are given that the shop made 4 1/2 times as much revenue on doughnuts as muffins:
D = 4.5M
We are also given that the total sales were $44,000:
D + M = 44,000
Now, we can solve for the dollar amount of each item sold:
Replace D with 4.5M in the second equation:
4.5M + M = 44,000
Combine like terms:
5.5M = 44,000
Divide by 5.5 to isolate M:
M = 44,000 / 5.5
M = 8,000
Plug the value of M back into the first equation to find the value of D:
D = 4.5M
D = 4.5 × 8,000
D = 36,000.

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Answer: The Arithmetic Mean is the average of the numbers: a calculated "central" value of a set of numbers.

Step-by-step explanation: You can find the mean, or average, of a data set in two simple steps: Find the sum of the values by adding them all up. Divide the sum by the number of values in the data set.

The graph of the solution set can be seen in the image at the end.

Here we have the inequality:

-(6 + 1/2)y + 9 > -17

First, we need to isolate the variable y, then we will get:

9 + 17 > (6 + 1/2)y

26 > 6.5y

26/6.5 > y

4 > y

The graph of this will be an open circle at y = 4, and an arrow that goes to the left, the graph can be seen in the image at the end.

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Therefore , the solution of the given problem of ratio comes out to be this indicates that there are 4 black pens in the package for every red pen.

A group comprising values both variable "a" and "" that seem to be equal is found using the straightforward formula "a / b," whenever "b" might be a greater number than zero. A ratio is created by combining two ratios. The ratio , fraction could have been 1:1 if there were just one guy and three women. There are 1/4 men and 3/4 women in the group.

Here,

By dividing the numerator and denominator by their greatest common divisor (GCD), the ratio 3/12 can be made simpler.

Due to the fact that both 3 and 12 can be divided by 3, their GCD equals 3.

The result of dividing the numerator and denominator by 3 is:

=> 3 ÷3 = 1.

=> 12 ÷ 3 = 4

Thus, 1/4 is the simple ratio that corresponds to 3/12.

Let's now use a simplified equivalent ratio to represent the ratio of red to black pens in the package:

Black pens 3: 12 Red pens:

=> 3 ÷ 3 = 1

=> 12 ÷ 3 = 4

Consequently, the rounded equivalent ratio of red to black pens is 1 to 4.

This indicates that there are 4 black pens in the package for every red pen.

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Answer:

  C. Vertical angles

Step-by-step explanation:

Given angles 5 and 8 where line c crosses line a, you want to know what type they are.

Where two lines cross, four angles are formed. They all share the vertex point where the lines intersect. If they share a side (and no interior space), they are adjacent angles that form a linear pair. As such, they are supplementary.

In the given figure the supplementary angle pairs where line c crosses line a are ...

  (5, 6), (6, 8), (7, 8), (5, 7)

If the angles do not share a side, but are formed from opposite rays, they are "vertical angles" and are congruent.

The vertical angle pairs there are ...

  (5, 8), (6, 7)

Angles 5 and 8 are vertical angles, choice C.

__

Additional comment

Angle pairs (1, 8) and (2, 7) are "alternate exterior angles." Angle pairs (3, 6) and (4, 5) are "alternate interior angles."

Assuming lines b and c are parallel, considering also angles where line b crosses line a, there are additional supplementary pairs of angles:

  (1, 2), (2, 4), (3, 4), (1, 3), (1, 6), (1, 7), (2, 5), (2, 8), (3, 5), (3, 8), (4, 6), (4, 7)

When parallel lines are crossed by a transversal, all of the acute angles are congruent, all of the obtuse angles are congruent, and the acute angles are supplementary to the obtuse angles. The angles are referred to by different names (and different theorems), depending on where they are in relation to the transversal and the parallel lines.

The problem here is mostly concerned with vocabulary. The "how to do this" is "learn the vocabulary."

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The width of the rectangular box is 12 inches.

Remember that the volume of a box of length L, width W, and height H is:

V = H*W*L

Here the volume is 3,840 cubic inches. The length of the box is 20 inches and the height of the box is 16 inches. Replacing that in the formula we will get:

3840 = 20*16*W

Solving that for W we will get:

3840/(20*16) = W

12 = W

The width is 12 inches.

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Step-by-step explanation:

The value of the expression can be calculated using the order of operations, also known as PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

The expression is:

2 + [(15 + 3) × 2]

According to PEMDAS, we should first evaluate the expression within the parentheses:

15 + 3 = 18

So, the expression becomes:

2 + [18 × 2]

Next, we perform the multiplication:

18 × 2 = 36

Now, we substitute the result back into the original expression:

2 + 36

Finally, we perform the addition:

2 + 36 = 38

So, the value of the given expression is 38.

The weight of the plane if it is carrying gallons of fuel is 2336 pounds, under the condition of when carrying 10 gallons, and 45 gallons he airplane weighs 2056  and 2252 pounds.
We can utilize the two given points to create two linear equations

y = mx + b
2056 = 10m + b
2252 = 45m + b

We can find m and b by subtracting the first equation from the second equation:

(45m + b) - (10m + b) = 2252 - 2056
35m = 196
m = 5.6

For finding b by substituting m into one of the original equations:

2056 = 10(5.6) + b
b = 2000

The equation is

y = 5.6x + 2000

To evaluate  how much the airplane weighs when carrying 60 gallons of fuel,  now lets substitute x into the equation

y = 5.6(60) + 2000
y = 336 + 2000
y = 2336

The weight of the plane if it is carrying gallons of fuel is 2336 pounds, under the condition of when carrying 10 gallons, and 45 gallons he airplane weighs 2056  and 2252 pounds.

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The complete question is
Suppose that the weight (in pounds) of an airplane is a linear... Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 10 gallons of fuel, the airplane weighs 2056 pounds. When carrying 45 gallons of fuel, it weighs 2252 pounds. How much does the airplane weigh if it is carrying 60 gallons of fuel?

Answer: the height of the hockey puck is approximately 0.835 inches.

Step-by-step explanation: The formula for determining the volume of a cylinder is as follows:

The formula for the volume (V) of a cylinder can be expressed mathematically as V = πr2h, where r represents the radius of the cylinder's base and h represents the height of the cylinder. This formula is derived from the concept that the volume of a cylinder can be calculated by multiplying the area of its base (which is represented by the term πr2) by its height (h).

The present study utilizes the conventional nomenclature in which V denotes the volume, r represents the radius, and h stands for the height.

As the diameter of the hockey puck is measured to be 3 inches, it follows that the radius is equivalently calculated as 1.5 inches, or precisely half of the diameter.

It is established that the hockey puck has a volume of 7.1 cubic inches; accordingly, by substituting these known values into the relevant formula and performing the appropriate calculations, the measurement of h may be ascertained.

The expression 7.1 = π(1.5)^2h can be reformulated in a more academic manner. It can be said that the equation represents the mathematical relationship between the volume of a cylinder and its dimensions, wherein the value of 7.1 denotes the volume of the cylinder, whereas π, 1.5, and h refer to the mathematical constants of pi, radius, and height, respectively. Thus, the formula can be expressed as V = πr^2h, where V represents the volume of the cylinder, r denotes the radius, and h denotes the height.

The process of reducing something to its simplest form. Rewritten: The act of simplification involves distilling a concept or idea to its most basic, essential components. This process aims to facilitate a clear and concise understanding of the subject matter, allowing for greater comprehension and ease of communication.

The numerical expression 7.1 = 2.25πh can be written in a more formal and academic manner. Specifically, the equation can be rephrased as an algebraic relationship between the variables involved. More concisely, the equation describes the result of a multiplication between the constant factor 2.25π and the variable h, which according to the equation equals 7.1. As such, it can be represented by the following expression: 2.25πh = 7.1

Dividing each side by 2.25π is a logical mathematical operation utilized to simplify an equation or expression.

The aforementioned equation may be expressed in an academic tone as follows: The value of h is equivalent to the quotient obtained from dividing 7.1 by 2.25 times the mathematical constant π.

The employment of a calculator to compute the aforementioned expression:

The observed value of h is approximately equal to 0.835 inches.