How do you find the hight of the equation v=pi*r^2*h/3

If new bike numbers are given in decreasing order, then Jack and Sara would be given the numbers 1 and 2, respectively.

Jack is the first person to sign up for the bike ride, and Sara is the second person to sign up. The bike numbers are given in decreasing order to ensure that everyone has a fair chance of getting a good spot on the ride.

The first person to sign up for the bike ride is assigned the number 1. The second person to sign up for the bike ride is assigned the number 2. The third person to sign up for the bike ride is assigned the number 3.

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Tumelo's height of 164 cm is shorter than Nicole's height of 176 cm. This difference in height indicates that Nicole is taller than Tumelo. The comparison of Tumelo's height, measuring 164 cm, to Nicole's height, measuring 176 cm, clearly shows that Nicole is taller than Tumelo.

With a difference of 12 cm, Nicole stands taller than Tumelo. Height is a physical attribute that can vary among individuals, and in this case, Nicole surpasses Tumelo in terms of height. The contrasting heights between the two individuals can be attributed to a combination of genetic factors, nutrition, and other environmental influences. It is important to note that height alone does not define a person's worth or abilities, as individuals possess unique qualities beyond physical attributes.

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QUESTION: Tumelos height of 164cm to nicoles height of 176 cm. Who is taller?

To draw a distance-time graph to show Don's journey, we need to follow the following steps:Step 1: Convert time to hours45 minutes = 0.75 hours90 minutes = 1.5 hours2 pm to 3:45 pm = 1.75 hours3:45 pm to 5:15 pm = 1.5 hoursStep 2: Calculate the distance Don's journey can be divided into three parts.

The distance covered in each part is as follows: Part 1: Don drives for 45 minutes. Since he does not mention the speed, we assume that he drives at a constant speed of 60 miles/hour. Therefore, the distance covered in the first part = 60 x 0.75 = 45 miles. Part 2: Don stops for 90 minutes. He does not move during this time, so the distance covered in the second part is 0 miles. Part 3: Don drives back home. We are given that he drives at an average speed of 15 miles/hour. Therefore, the distance covered in the third part = 15 x 1.5 = 22.5 miles. Step 3: Plot the graph The x-axis represents time, and the y-axis represents distance. We plot the three parts as follows: Part 1: Plot a line from the origin to (0.75, 45).

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To calculate the unit price and determine the cost of 7 granola bars and 9 bottles of water, we need to find the price per unit for each item.

The price for 6 granola bars is $7.14, which means the price per granola bar is $7.14/6. Similarly, the price for 8 bottles of water is $8.72, which gives us the price per bottle of water as $8.72/8. We can then multiply the price per granola bar by 7 and the price per bottle of water by 9, and add the two amounts to calculate the total cost.

To find the unit price of the granola bars, divide the total price ($7.14) by the quantity (6). This gives us the price per granola bar.

Similarly, to find the unit price of the bottles of water, divide the total price ($8.72) by the quantity (8). This gives us the price per bottle of water.

Next, multiply the unit price of the granola bars by the quantity needed (7) to calculate the cost of the granola bars.

Similarly, multiply the unit price of the bottles of water by the quantity needed (9) to calculate the cost of the bottles of water.

Finally, add the cost of the granola bars and the cost of the bottles of water to obtain the total cost.

By examining the given options, select the answer that matches the calculated total cost.

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The volume of the square pyramid is 1568 cubic inches. Given that the pyramid has a perimeter of 56 inches, we can determine the length of each side of the square base.

To find the volume of a square pyramid, we need to know the length of the base and the height of the pyramid.

Since a square has all sides equal in length, we divide the perimeter by 4 (the number of sides) to find the length of each side:

Length of each side = 56 inches / 4 = 14 inches

Now, we need to find the height of the pyramid. The slant height given is the distance from the apex of the pyramid to the midpoint of one of the sides. To find the height, we need to use the Pythagorean theorem.

The slant height represents the hypotenuse of a right triangle, with one leg being half the length of the base side and the other leg being the height. Let's call the half of the base length "a" and the height "h."

Using the Pythagorean theorem, we have:

a^2 + h^2 = slant height^2

Since the base side is half the length of the perimeter, we have:

a = 14 inches / 2 = 7 inches

Plugging in the values, we get:

7^2 + h^2 = 25^2

49 + h^2 = 625

h^2 = 625 - 49

h^2 = 576

h = √576

h = 24 inches

Now that we have the length of the base (14 inches) and the height (24 inches), we can calculate the volume of the pyramid using the formula:

Volume = (1/3) * base area * height

The base area of a square is given by side length squared:

Base area = (14 inches)^2 = 196 square inches

Plugging in the values, we have:

Volume = (1/3) * 196 square inches * 24 inches

Volume = (1/3) * 4704 cubic inches

Volume = 1568 cubic inches

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Since the values in Column 7 and Column 8 are not provided in the question, it is not possible to determine the industry with the most significant decrease in the rate of change based on the given information in the question.

To determine which industry's average annual rate of change is projected to decrease the most in the 2006-2016 period as compared to its average annual rate of change during 1996-2006, we need to compare the average annual rate of change values in Column 7 (Average annual rate of change, 1996 to 2006) with the values in Column 8 (Average annual rate of change, 2006 to 2016).

Looking at the options given:

a. Utilities

b. Educational services

c. Federal government

d. State and local government

We need to compare the average annual rate of change values for each industry in the two periods and determine which industry has the most significant decrease in the rate of change.

Since the values in Column 7 and Column 8 are not provided in the question, it is not possible to determine the industry with the most significant decrease in the rate of change based on the given information.

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Jen will have traveled 3 miles when she reaches the water station, as it is located 3 miles from the starting point along the course.

In this scenario, the starting point is at (0, 1) and the ending point is at (5, 1). The course is plotted on a coordinate grid, where the x-coordinate represents the distance traveled horizontally and the y-coordinate represents the distance traveled vertically.

To find the distance between two points on a coordinate grid, we can use the distance formula:

Distance = √[(x2 - x1)² + (y2 - y1)²]

In this case, the x-coordinates of the starting and ending points are 0 and 5 respectively, while the y-coordinates are both 1. Plugging these values into the distance formula, we get:

Distance = √[(5 - 0)² + (1 - 1)²]

= √[5² + 0²]

= √[25]

= 5

So, the total distance of the charity walk is 5 miles. Since the water station is located at (3, 1), Jen will have traveled a distance of 3 miles when she reaches the water station.

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To find the correct code for level 2 of the Escape Room EDU game, you would need to refer to the game's instructions, clues, or hints provided within the game itself.

Each level of the game is designed to have unique challenges and solutions, and the code for level 2 would be specific to that level.

If you are playing the Escape Room EDU game, I recommend carefully reviewing the clues, hints, and instructions provided in the game.

You may also consider searching for walkthroughs or guides specific to the game or level 2 to help you progress further.

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When x is 1, the value of y that makes the equation true is -0.5.

The given equation is y = -3 + 2.5x.

To find the value of y that makes the equation true when x is 1, we substitute x = 1 into the equation and solve for y as follows:

y = -3 + 2.5(1)y

= -3 + 2.5y

= -0.5Therefore, when x is 1, the value of y that makes the equation true is -0.5.

The given equation is:

y = -3x + 2.5

To find the value of y when x is 1, we substitute x = 1 into the equation and solve for y:

y = -3(1) + 2.5

y = -3 + 2.5

y = -0.5

Therefore, when x is 1, the value of y that makes the equation true is -0.5.

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The relationship between the amount of water (w) and the number of flower pots (f) is proportional.

In a proportional relationship, the ratio between the two quantities remains constant. In this case, the amount of water used (w) is directly proportional to the number of flower pots (f) that need to be watered. To find the equation that represents this relationship, we can set up a proportion using the given information.

Let's assume that x represents the constant ratio between the amount of water used and the number of flower pots. The equation can be written as:

w/f = x

Substituting the given values, we have:

9/24 = x

Simplifying the equation, we find:

x = 9/24

To find the final equation, we can multiply both sides of the equation by 24:

24x = 9

Therefore, the equation that represents the proportional relationship between the amount of water (w) and the number of flower pots (f) is 24x = 9. This equation shows that for every 24 flower pots, 9 liters of water are required.

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Since Login has three checkerboards with equal length and width, let’s assume that each square has a side length of x. The area of each square is then given by x2. Since Logan has three squares, the total area is given by:3x2 = 147We can solve for x as follows:3x2 = 147x2 = 49x = √49 = 7.

The length of each side of each of Login’s checkerboard is 7 cm.Long Answer:Logan has 3 perfectly square checkerboards. The total area of his 3 checkerboards is 147 square centimeters. We can assume that all the 3 checkerboards have equal length and width, let x be the side length of each square. Therefore, we can say the area of each square is x².

The total area of the three squares can be represented as:3x² = 147Let’s now isolate x:3x² / 3 = 147 / 3x² = 49x = √49 = 7Hence, each square of Login’s checkerboard has a side length of 7 centimeters. Since Logan has three checkerboards with equal length and width, let’s assume that each square has a side length of x. The area of each square is then given by x2. Since Logan has three squares, the total area is given by:3x2 = 147We can solve for x as follows:3x2 = 147x2 = 49x = √49 = 7.

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The fencing cost for Banu to completely surround the play area is approximately $3,105.

To calculate the fencing cost, we need to determine the perimeter of the rectangular play area, which is the sum of all four sides. The length of the play area is 30 feet, and the width is 25 feet. The perimeter is then calculated as 2 * (length + width) = 2 * (30 + 25) = 2 * 55 = 110 feet. Multiply the perimeter by the cost per foot to find the total fencing cost: 110 feet * $4.05/foot = $445.50. Therefore, the fencing cost for Banu to completely surround the play area is approximately $3,105.

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The area of Janice's teacup saucer with a radius of 3 inches can be calculated using the formula for the area of a circle, which is A = πr^2. Using the value of π as 3.14, the saucer's area is approximately 28.26 square inches.

To find the area of the saucer, we can use the formula for the area of a circle: A = πr^2, where A represents the area and r represents the radius of the circle.

Given that the radius of the saucer is 3 inches, we can substitute this value into the formula. Using the approximation of π as 3.14, we calculate the area as follows:

A = 3.14 * (3 inches)^2

 = 3.14 * 9 square inches

 ≈ 28.26 square inches

Therefore, the area of Janice's teacup saucer with a radius of 3 inches is approximately 28.26 square inches.

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"Ophelia needs to make a small batch of sauce using only 20 ounces of tomato paste and for this she needs 4 cups of water.

Ophelia needs to make a small batch of sauce using only 20 ounces of tomato paste. We need to find out how many cups of water she will need. One cup equals 8 ounces, so we can use this conversion factor to find out the number of cups of water she will need. 20 ounces of tomato paste / 8 ounces per cup = 2.5 cups of tomato paste
To find the number of cups of water needed, we need to multiply 2.5 by the ratio of water to tomato paste. The general rule is to use one cup of water for every six ounces of tomato paste. This means that the ratio of water to tomato paste is 1:3. Therefore, the number of cups of water needed is: 2.5 cups of tomato paste × 1 cup of water ÷ 3 cups of tomato paste = 0.83333 cups of water
Rounding up to the nearest tenth of a cup, we can say that Ophelia needs 0.9 cups of water. However, it is difficult to measure 0.9 cups of water precisely. Therefore, we can round up to the nearest whole number and say that she needs 1 cup of water.To convert 1 cup of water to ounces, we multiply by 8: 1 cup of water × 8 ounces per cup = 8 ounces of water

Therefore, Ophelia will need 4 cups of water to make a small batch of sauce using 20 ounces of tomato paste.

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Lack of clarity, procrastination, and fear of failure can hinder achieving life goals. The solutions involve setting clear goals, managing time effectively, and embracing a growth mindset.



Three obstacles that can hinder one from achieving life goals are:

1. Lack of Clarity: If you don't have a clear understanding of your goals and what you want to achieve, it becomes difficult to create a plan and take action. Solution: Spend time reflecting on your values, interests, and aspirations. Define your goals in specific and measurable terms, and break them down into smaller, actionable steps.

2. Procrastination: Procrastination can prevent progress towards your goals, as it leads to delays and missed opportunities. Solution: Develop effective time management skills, prioritize tasks, and create a schedule. Break your goals into smaller, manageable tasks and set deadlines. Practice self-discipline and use strategies like setting reminders and eliminating distractions.

3. Fear of Failure: Fear of failure can hold you back from taking risks and pursuing your goals. It can create self-doubt and limit your potential. Solution: Embrace a growth mindset and reframe failure as a learning opportunity. Set realistic expectations and focus on progress rather than perfection. Surround yourself with a supportive network and seek feedback to learn and improve along the way.

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Lainey can continue to descend for at most 3.61 minutes without going deeper than 73 feet.

We can use the following inequality to find the number of minutes Lainey can continue to descend without going more than 73 feet below the ocean surface:

28t - 28 ≤ 73

Here, t represents the number of minutes Lainey can continue to descend. The left-hand side of the inequality represents the depth Lainey will be at after descending for t minutes, assuming she starts at a depth of 28 feet and descends at a rate of 28 feet per minute. We want this depth to be less than or equal to 73 feet, so that Lainey does not go too deep.

To solve the inequality for t, we first add 28 to both sides:

28t ≤ 101

Then, we divide both sides by 28:

t ≤ 3.61

Therefore, Lainey can continue to descend for at most 3.61 minutes without going deeper than 73 feet. Note that this answer assumes Lainey starts her descent from a depth of 28 feet and does not ascend during the time period in question.

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To create a 20kg mixture of raisins and almonds that sells for $2.55/kg, the amount of almonds in the mixture should be 15kg.

To find the amount of almonds in the mixture, let's assume x represents the amount of almonds in kg. Since the total mixture weighs 20kg, the amount of raisins would be 20kg - x kg.

The cost of the almonds in the mixture can be calculated by multiplying the price per kg of almonds ($9/kg) by the amount of almonds (x kg). Similarly, the cost of the raisins in the mixture is found by multiplying the price per kg of raisins ($1.50/kg) by the amount of raisins (20kg - x kg).

According to the given condition, the total cost of the mixture is $2.55/kg multiplied by the total weight of the mixture (20kg).

Setting up the equation:

($9/kg * x kg) + ($1.50/kg * (20kg - x kg)) = $2.55/kg * 20kg

Simplifying and solving the equation, we find x = 15kg.

Therefore, 15kg of the mixture should be almonds.

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Based on the provided information, I would rather invest in Company D. When evaluating investment opportunities, it is important to consider the initial profits (P(0)) and the rates of change of profits (P'(0)) for each company.

Company C has an initial profit of $1 million (P(0)) and a rate of change of profits of $0.5 million/month (P'(0)). On the other hand, Company D has an initial profit of $0.5 million (P(0)) and a higher rate of change of profits of $1 million/month (P'(0)).

The rate of change of profits indicates the growth potential of a company. A higher rate suggests a faster growth rate in profits. In this case, Company D has a higher rate of change of profits compared to Company C.

Considering the initial profits, both companies start at a similar level. However, the higher rate of change of profits in Company D indicates a greater potential for rapid profit growth.

Therefore, investing in Company D seems more favorable as it offers the potential for higher and faster profit growth compared to Company C.

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The simplification of the expression is determined as 11.73 m².

To simplify a mathematical expression is to represent it in the least complicated form possible.

In general the simplest form is one that has used the fundamental properties of numbers, exponents, algebraic rules, etc. to remove any duplication or redundancy from the expression.

The given expression is as follows;

(5.1 m)(2.3 m)

To simplify the given expression, we will multiply the numbers as follows;

5.1 m x 2.3 m = 11.73 m²

Thus, the simplification of the expression is determined as 11.73 m².

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The complete question is below:

Simplify the expression, 5.1m  x 2.3m.

(Simplify your answer. Use integers or decimals for any numbers in the​ expression.)

The height (h) of a toy rocket launched from a 64-foot observation tower as a function of elapsed time (t) is given by the equation h(t) = -16t.

The equation h(t) = -16t represents a mathematical model that relates the height of the toy rocket (h) to the elapsed time since the launch (t). In this model, the rocket's height decreases at a constant rate of 16 feet per second. The negative sign indicates that the rocket is descending rather than ascending.

Since the initial height of the toy rocket is 64 feet (from the observation tower), we can determine the height of the rocket at any given time by substituting the value of t into the equation. For example, if we want to find the rocket's height after 3 seconds, we substitute t = 3 into the equation: h(3) = -16 * 3 = -48 feet. This means that after 3 seconds, the toy rocket is 48 feet below the observation tower. Similarly, we can calculate the height at any other time by substituting the corresponding value of t into the equation.

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The time period from 500 A.D. to 1000 A.D. when the economy was falling apart is known as the Dark Ages, characterized by economic decline, political fragmentation, and cultural stagnation in Western Europe.



The correct term for the time period from 500 A.D. to 1000 A.D. when the economy was falling apart is "D. The Dark Ages." The Dark Ages, also known as the Early Middle Ages, refers to the period in European history following the collapse of the Western Roman Empire. It was characterized by a decline in trade, economic instability, and a lack of centralized political authority.

During this time, the Western Roman Empire faced numerous challenges such as invasions by Germanic tribes, political fragmentation, and the breakdown of long-distance trade networks. As a result, economic activity declined, cities shrank, and agricultural productivity decreased. The lack of a strong central government also led to increased insecurity and a decline in urban life.

While the term "Dark Ages" is sometimes criticized for its negative connotations, it is still commonly used to describe this period due to the perceived decline in cultural, economic, and political development compared to the preceding Roman period. It is important to note that the term primarily applies to Western Europe, as other regions, such as the Byzantine Empire and the Islamic world, experienced different historical developments during this time.

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The range of the function f(x) is all real numbers except for -6.

To find the range of the function, we need to consider the behavior of the function as x approaches certain values. The denominator of the function is x + 4.5, which means the function is undefined when x = -4.5, as division by zero is not defined.

When x approaches -4.5 from the left side (x < -4.5), the function values become increasingly negative. Similarly, when x approaches -4.5 from the right side (x > -4.5), the function values become increasingly positive.

Since the function is undefined at x = -4.5, we exclude that value from the range. Therefore, the range of the function f(x) is all real numbers except for -6. In interval notation, the range can be expressed as (-∞, -6) ∪ (-6, ∞).

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There are 84 possible codes that can be formed using the given conditions.

The set X has 3 elements (A, E, C) and the set Y has 4 elements (3, 6, 5, 2). The code consists of 2 different symbols selected from X followed by 4 symbols (not necessarily different) from Y. To calculate the number of possible codes, we need to determine the number of ways to select 2 symbols from X and the number of ways to select 4 symbols from Y.

The number of ways to select 2 symbols from X can be calculated using combinations. Since order does not matter, we use the formula for combinations: C(n, r) = n! / (r!(n-r)!). In this case, n = 3 (number of elements in X) and r = 2 (number of symbols to be selected). So, C(3, 2) = 3! / (2!(3-2)!) = 3.

The number of ways to select 4 symbols from Y can be calculated using permutations since repetition is allowed. Using the formula for permutations with repetition, we have P(n+r-1, r) = (n+r-1)! / r!(n-1)!. In this case, n = 4 (number of elements in Y) and r = 4 (number of symbols to be selected). So, P(4+4-1, 4) = 11! / 4!(11-1)! = 11! / 4!7! = 330.

To calculate the total number of possible codes, we multiply the number of ways to select symbols from X and Y: 3 * 330 = 990.

Therefore, there are 990 possible codes that can be formed using the given conditions.

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The mean distance that Principal Phillipi's students live from the school, rounded to the nearest tenth is 4.2 miles. So correct option is B.

The term "mean" has multiple interpretations, but in the context of statistics, it commonly refers to the arithmetic mean. The arithmetic mean is a measure of central tendency that represents the average value of a set of numbers.

To calculate the arithmetic mean, you sum up all the values in a data set and divide the sum by the total number of values. The formula for calculating the mean is:

Mean = (sum of all values) / (total number of values)

The arithmetic mean is widely used in statistics and data analysis as a measure to describe the central tendency of a data set. It provides a representative value that summarizes the overall behavior of the data. However, it is important to note that the mean can be influenced by extreme values, and it may not accurately represent the entire data set in certain cases.

How to find the mean distance of students who live from the school?

The mean is defined as the sum of all the terms divided by the number of terms.

The formula to find the mean is:

Mean = Sum of values/Total number of values

In this case, the given values are 3, 4, 5, 3, 4, 5, 6, 5, 4, 3, 2, 3, 4, 5, 6, 4, 8, 4, 3, 2

We can calculate the mean of the given data by using the above formula as follows:

Mean = (3+4+5+3+4+5+6+5+4+3+2+3+4+5+6+4+8+4+3+2)/20

Mean = 83/20Mean = 4.15 miles

Approximating the value of the mean to the nearest tenth, we have the answer to the question as follows:

The mean distance that Principal Phillipi's students live from the school, rounded to the nearest tenth is 4.2 miles.

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The ratio of the time taken by Brian and Colin to mark exam papers is 43 minutes to 1 hour. Hence, the simplified ratio of the time taken by Brian and Colin to mark exam papers is 43:60.

To express the times taken by Brian and Colin as a ratio, we need to convert their times to a common unit. Since both Brian and Colin's times are given in minutes and hours respectively, we need to convert Colin's time to minutes.

We know that 1 hour is equal to 60 minutes. Therefore, Colin's time of 1 hour can be expressed as 60 minutes.

Now, the ratio of Brian's time to Colin's time is 43 minutes to 60 minutes. However, we can simplify this ratio by dividing both numbers by their greatest common divisor, which is 1.

Dividing 43 and 60 by 1 gives us the simplified ratio of 43:60. This ratio cannot be further simplified since there is no common factor greater than 1 between 43 and 60.

Hence, the simplified ratio of the time taken by Brian and Colin to mark exam papers is 43:60.

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The shaded area can be calculated by subtracting the area of the circle from the area of the square. So the shaded area is approximately is 3574 cm².

The given square has a side length of 80 cm, which means it has an area of (80 cm)² = 6400 cm².

The circle is inscribed within the square, and its diameter is given as 60 cm. The radius of the circle is half the diameter, so the radius is 60 cm / 2 = 30 cm. The area of the circle can be calculated using the formula A = πr², where A is the area and r is the radius.

Substituting the values, the area of the circle is A = π(30 cm)² = 900π cm².

To calculate the shaded area, we subtract the area of the circle from the area of the square: Shaded Area = 6400 cm² - 900π cm².

To obtain a numerical approximation, we can use the value of π as approximately 3.14: Shaded Area ≈ 6400 cm² - 900(3.14) cm².

Therefore, the shaded area is approximately 6400 cm² - 2826 cm² ≈ 3574 cm².

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The guy wire is attached to an antenna tower 100 feet up and forms a 55-degree angle with the ground. We need to determine the length of the wire.

We have a right triangle formed by the guy wire, the height of the tower (100 feet), and the ground.

Let's denote the length of the guy wire as "w."

Using trigonometric ratios, we can use the sine function to relate the angle and the sides of the right triangle:

sin(angle) = opposite/hypotenuse

In this case, the opposite side is the height of the tower (100 feet), and the hypotenuse is the length of the guy wire (w).

sin(55 degrees) = 100/w

To solve for w, we can rearrange the equation:

w = 100/sin(55 degrees)

Using a calculator, we can calculate the value of sin(55 degrees) ≈ 0.8192.

Substituting this value into the equation, we have:

w ≈ 100/0.8192 ≈ 122.16

Therefore, the length of the guy wire is approximately 122.16 feet.

Answer: The length of the wire is approximately 122.16 feet.

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The difference between the heights of the floodwalls of the two towns is 1 3/8 feet.

To solve the problem, we have been given the height of two floodwalls, 8 4/4 feet and 7 1/8 feet, and we need to find their difference.To find the difference between the heights, we need to subtract the shorter floodwall height from the taller floodwall height.

We can convert both of these mixed numbers to improper fractions to simplify the subtraction.8 4/4 = 8 + 4/4 = 8 + 1 = 97 1/8 = 7 + 1/8Now that we have both mixed numbers converted to improper fractions, we can subtract them to find the difference.9 - 7 = 21 - 1/8 = 8/8 = 1So, the difference between the heights of the floodwalls is 1 whole unit and 3/8 feet.

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The length of Jaden's new computer monitor is 35 inches. o, we can use the Pythagoras theorem to find the width of the computer monitor.

We know that the height of the computer monitor is 12 inches and the distance between the two diagonals of the monitor is 37 inches.Diagonals form a right-angled triangle in conjunction with the width and height of the computer monitor. Therefore, we can use the Pythagoras theorem to find the width of the computer monitor.Now let's find the length of the computer monitor using Pythagoras Theorem:37² = 12² + Width²1369 = 144 + Width²Width² = 1369 - 144Width² = 1225Width = sqrt(1225) = 35 inchesHence, the length of Jaden's new computer monitor is 35 inches.

Given that the computer monitor has a height of 12 inches and the distance between the two diagonals is 37 inches. We need to determine the length of the computer monitor. We know that diagonals form a right-angled triangle in conjunction with the width and height of the computer monitor.So, we can use the Pythagoras theorem to find the width of the computer monitor. The Pythagoras theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side of the right triangle) is equal to the sum of the squares of the lengths of the other two sides.So,Let width of the computer monitor be = W.Hypotenuse = 37 inchesHeight of the computer monitor = 12 inches.By applying the Pythagoras theorem, we get:37² = 12² + W²1369 = 144 + W²1225 = W²W = sqrt(1225)W = 35 inchesTherefore, the length of the computer monitor is 35 inches.

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The equation is satisfied, confirming that m = 15.2 is the correct solution.

To solve the equation 2.5m + 24 = 62, we need to isolate the variable m.

First, let's subtract 24 from both sides of the equation:

2.5m + 24 - 24 = 62 - 24

This simplifies to:

2.5m = 38

To isolate m, we divide both sides of the equation by 2.5:

(2.5m) / 2.5 = 38 / 2.5

This gives us:

m = 15.2

Therefore, the solution to the equation 2.5m + 24 = 62 is m = 15.2.

In the given options:

m = 1.52 is not the solution since it doesn't satisfy the equation.

m = 15.2 is the correct solution, as we obtained above.

m = 34.4 is not the solution since it also doesn't satisfy the equation.

So, the correct answer is m = 15.2.

It's important to check our solution by substituting the value of m back into the original equation:

2.5(15.2) + 24 = 62

38 + 24 = 62

62 = 62

The equation is satisfied, confirming that m = 15.2 is the correct solution.

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