Find the missing side of each triangle round your answers to the nearest 10th

Axes were labeled, then triangle ABC was drawn followed by a rotation of 90 degrees clockwise, and then it was translated three units down.

What are triangles?

Three vertices make up a triangle, a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a single point. The sum of all three angles of the triangle is equal to 180 degrees.

How rotation of a point by 90 degrees clockwise will take place?

When points will be rotated 90 degrees clockwise, the x will become y while y will become -x.

After rotation:

A (-3, 0) will become A' (0,3)

B (-2, 4) will become B'(4,2)

C (1, -1). will become C'(-1,-1)

After rotation of 90 degrees clockwise is performed, translation of three units down will be performed as follows:

A' (0,3) will become A'' (0,0)

B'(4,2) will become B''(4,-1)

C'(-1,-1) will become (-1,-4)

Thus, Axes were labeled, then triangle ABC was drawn followed by a rotation of 90 degrees clockwise, and then it was translated three units down.

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Answer: Gavin drank 2.25 quarts today.

Step-by-step explanation: First you need to find out how many quarts are in 8 ounces -the answer to that is 0.25. Then you will need to times that by 9.

The estimated annual income can be calculated using the equation above. If the data point is used to calculate the slope and y-intercept of the regression line, then the annual income can be estimated using the equation y = m(14) + b.

If the education level is 14 years,

To create a simple linear regression model using education level as the independent variable, you will need to input data for education level and annual income.

This data can be used to estimate the annual income for any given education level. The equation for this linear regression model is y = mx + b, where y represents the annual income, m is the slope of the line, x is the education level, and b is the y-intercept.

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The customers of Rhythm Time, an online music service, downloaded 397,970 songs last year.

Rhythm Time, an online music service, had 278,579 songs downloaded this year by its customers. That figure is 30% less than last year. Last year

We can begin by assuming that the total number of songs downloaded last year was x. According to the problem statement, 278,579 songs were downloaded this year, which is 30% less than last year. We can write it as an equation:x - 0.30x = 278,579 Simplifying, we get:0.70x = 278,579 Dividing both sides by 0.70, we get:x = 397,970Therefore, last year, Rhythm Time's customers downloaded 397,970 songs.

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Let's start by writing a differential equation for the rate of formation of chemical C. Since the rate is proportional to the product of the amounts of A and B not converted to C, we can write:

d[C]/dt = k[A](B - 2[C]/B)

where [A] and [B] are the amounts of A and B not converted to C at any time t, [C] is the amount of C formed at time t, and k is a proportionality constant. Note that the term 2[C]/B represents the amount of A that has been used up to form C, since 2 grams of A are used for every gram of B.

At t=0, [A]=40 g and [B]=50 g. We also know that 25 g of C is formed in 8 minutes, so at that time [C]=25 g.

d[C]/dt = k[A](B - 2[C]/B)

25/8 = k40(50 - 2*25/50)

k = 1/800

Now we can use this value of k to solve for [C] at t=16 minutes:

d[C]/dt = k[A](B - 2[C]/B)

C - C = ∫[0]^16 k[A](B - 2[C]/B) dt

C - 25 = ∫[0]^16 (1/800)40(50 - 2[C]/50) dt

C = 37.2 g

Therefore, 37.2 grams of C is formed in 16 minutes.

To find the limiting amount of C after a long time, we can set the derivative of [C] with respect to time to zero and solve for [C]:

d[C]/dt = k[A](B - 2[C]/B) = 0

[C] = B/2 = 25 g

So the limiting amount of C after a long time is 25 grams.

To find the amounts of A and B that remain after a long time, we can use the fact that the total amount of A used is twice the amount of B used. Therefore, the amount of A remaining after a long time is:

[A] = 40 g - 2*[C] = 40 g - 2*25 g = -10 g

This means that all of the A is used up in the reaction, and there is none remaining. The amount of B remaining can be found as:

[B] = 50 g - [C] = 50 g - 25 g = 25 g

So 25 grams of B remains after a long time. Note that this is the same as the limiting amount of C, since one gram of B is converted to one gram of C.

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The ball reaches a maximum height of approximately 146 feet, to the nearest foot.

Maximum Height refers to the highest point of the structure or sign as measured from the average natural ground level at the base of the supporting structure.

The ball is thrown upward with an initial velocity of 75 feet per second, implying that v0 = 75. We are also told that the ball is thrown from a height of 4 feet, implying that h0 = 4.

The function: can be used to model the ball's vertical motion.

16t2 + v0t + h0 = h(t).

Substituting v0 and h0 values yields:

h(t) = -16t^2 + 75t + 4

To determine the maximum height of the ball, we must first locate the vertex of the parabolic function h. (t). The vertex of the parabola is given by the equation y = ax2 + bx + c:

x = -b / 2a

y = c - b^2 / 4a

a = -16, b = 75, and c = 4 in this case. Substituting these values into the above formulas yields:

t = -75 / 2(-16) = 2.34 sec

h(t) = 4 - (752) / (4(-16)) 146 ft.

As a result, the ball reaches a maximum height of about 146 feet to the nearest foot.

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If we are told that the counterfeit coin is too light, we can identify it with a minimum of ⌈log3(n)⌉ weighings.

First, we divide the n coins into three groups of equal size. We then weigh any two of these groups against each other. If the scale tips, the counterfeit coin is in the lighter group, and we repeat this process with that group of coins. If the scale is balanced, the counterfeit coin is in the remaining group, and we repeat the process with that group of coins.

We continue to divide the remaining coins into three groups of equal size and weigh two of them against each other until we are left with a single coin, which must be the counterfeit coin.

Since each weighing reduces the number of possible coins by a factor of 3, we need at most ⌈log3(n)⌉ weighings to identify the counterfeit coin.

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Answer:156 Yd ∧3

Step-by-step explanation:

lengthl = 8 ydwidthw = 6.5 ydheighth = 3 yddiagonald = 10.7354553 ydtotal surface areaStot = 191 yd2lateral surface areaSlat = 87 yd2top surface areaStop = 52 yd2bottom surface areaSbot = 52 yd2volumeV = 156 yd3

The completed table:

                                  Die

                     1          2          3         4          5        6

 Head      H - 1     H - 2    H - 3   H - 4   H - 5    H - 6

  Tail        T - 1      T - 2    T - 3    T - 4    T - 5   T - 6

We have,

The set of all possible outcomes when rolling the die and flipping the coin is the sample space.

The total number of outcomes.

= 6 x 2

= 12 outcomes.

Each cell in the table will represent one possible outcome.

Here's the completed table:

                                  Die

                     1          2          3         4          5        6

 Head      H - 1     H - 2    H - 3   H - 4   H - 5    H - 6

  Tail        T - 1      T - 2    T - 3    T - 4    T - 5   T - 6

Thus,

The completed table is given above.

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A dividend is the distribution of a company's earnings to its shareholders and is determined by the company's board of directors. Dividends are often distributed quarterly and may be paid out as cash or in the form of reinvestment in additional stock.

1. For a company that reports an increase in retained earnings of $1,560 and net income of $5,260, the amount of dividends is $3,700 .

2. For a company that reports beginning retained earnings of $2,110, net income of $1,610, and $320 dividends, the amount of ending retained earnings is $3,400.

3. For a company that reports an increase in retained earnings of $1,420 and dividends of $1,970, the amount of net income is $3,390.

4. For a company that reports ending retained earnings of $2,400, net income of $580, and dividends of $430, the amount of beginning retained earnings is $2,250.

5. For a company that reports an increase in retained earnings of $660 and net income of $1,270, the amount of dividends is $610 .

In each scenario, we can use the formula: Beginning retained earnings + net income - dividends = ending retained earningsWe can rearrange this formula to solve for any variable we need.

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Answer: 300 minuets

Step-by-step explanation:

Answer:

350

Step-by-step explanation:

60 miles is 1 hr. all it is, is a ratio.  multiply 60 by 5 to get your answer; 350

Suppose that [tex]A1 ∩ A2[/tex]is path-connected. If each of the subspaces A1, A2, and A1 ∩ A2 is simply connected, then the quotient space X / A1 ∼ A2 is simply connected too.

Given a quotient space et p which is obtained by identifying the north and south poles of two spheres s2 to a single point.

Let's find the value of p.The quotient space et p can be visualized as shown below:Quotient Space et pThis space et p has the structure of the cone C(A) over the 1-dimensional CW complex

A obtained from two 0-cells and one 1-cell connecting them with attaching maps

as shown below:

In our case, the spaces A1, A2, and A1 ∩ A2 are s2, s2, and S1, respectively. Both s2 and S1 are simply connected, since they are homotopy equivalent to a point. Since S1 is path-connected, we can apply the above proposition to conclude that et p is simply connected.Therefore, the value of p is 1 since the fundamental group of et p, π1(et p), is trivial.

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A ball is dropped from a height of 6 ft. assuming that on each bounce, the ball rebounds to one-third of its previous height, the total distance traveled by the ball is approximately 11.926 feet.

We have to calculate the distance traveled by the ball with the help of the given data, as shown below;The first height of the ball is 6 feet. Distance traveled by the ball at the first instance = 6 feet.The ball rebounds to one-third of its previous height, and the ball goes to a height of:6/3 = 2 feet.

Distance traveled by the ball after the first bounce = 6 + 2 + 2 = 10 feet.The ball rebounds again to one-third of its previous height, and the ball goes to a height of:2/3 = 0.6667 feet. Distance traveled by the ball after the second bounce = 10 + 0.6667 + 0.6667 = 11.3334 feet.

The ball rebounds again to one-third of its previous height, and the ball goes to a height of:0.6667/3 = 0.2222 feet. Distance traveled by the ball after the third bounce = 11.3334 + 0.2222 + 0.2222 = 11.7778 feet. The ball rebounds again to one-third of its previous height, and the ball goes to a height of:0.2222/3 = 0.0741 feet.

Distance traveled by the ball after the fourth bounce = 11.7778 + 0.0741 + 0.0741 = 11.926 feet. Therefore, the total distance traveled by the ball is approximately 11.926 feet.

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Answer:

Step-by-step explanation:

The answer is true

Answer 1: The solution to the equation is x = 4.

Answer 2:

The graph shows that the revenues for online ads have steadily increased since the paper started its online version, while the revenues for printed ads have been steadily decreasing.

Answer 3a:

Beach A is decreasing at a faster rate than Beach B, with its width decreasing from around 400 feet in 1995 to around 250 feet in 2015.

Answer 3b:

Between the years 2011 and 2012, the beaches have approximately the same width.

Answer 3c:

To get a better approximation of when the two beaches will have the same width, the rate of erosion of each beach should be calculated over time.

Equation is an statement that two expressions have the same value, and can be written using symbols, numbers and/or variables.

Answer 1: The equation 2.5x − 10.5 = 64(0.5x) can be solved by completing the table below:

x | 2.5x | 0.5x | 64(0.5x) | 2.5x - 10.5 | 2.5x - 64(0.5x)

--|------|------|-----------|--------------|-----------------

1 | 2.5  | 0.5  | 32        | -8.5         | -29.5

2 | 5    | 1    | 64        | -5.5         | -21.5

3 | 7.5  | 1.5  | 96        | -3.5         | -13.5

4 | 10   | 2    | 128       | -0.5         | -5.5

Answer 2:

The graph shows that the revenues for online ads were approximately equal to the revenues for printed ads around 2006, which is the 12th year after the online version of the paper was started.

Answer 3a:

Beach A is decreasing at a faster rate than Beach B, with its width decreasing from around 400 feet in 1995 to around 250 feet in 2015. Beach B's width is decreasing at a slower rate, from around 500 feet in 1995 to around 350 feet in 2015.

Answer 3b:

Between the years 2011 and 2012, the beaches have approximately the same width.

Answer 3c:

To get a better approximation of when the two beaches will have the same width, the rate of erosion of each beach should be calculated over time. This can be done by plotting the width of each beach over time and calculating the slope of the line, which will give an indication of the rate of erosion.

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1: The solution to the equation is x = 4.

2: The graph shows that the revenues for online ads have steadily increased since the paper started its online version, while the revenues for printed ads have been steadily decreasing.

3a: Beach A is decreasing at a faster rate than Beach B, with its width decreasing from around 400 feet in 1995 to around 250 feet in 2015.

3b: Between the years 2011 and 2012, the beaches have approximately the same width.

3c: To get a better approximation of when the two beaches will have the same width, the rate of erosion of each beach should be calculated over time.

Equation is an statement that two expressions have the same value, and can be written using symbols, numbers and/or variables.

1: The equation 2.5x − 10.5 = 64(0.5x) can be solved by completing the table below:

x | 2.5x | 0.5x | 64(0.5x) | 2.5x - 10.5 | 2.5x - 64(0.5x)

--|------|------|-----------|--------------|-----------------

1 | 2.5  | 0.5  | 32        | -8.5         | -29.5

2 | 5    | 1    | 64        | -5.5         | -21.5

3 | 7.5  | 1.5  | 96        | -3.5         | -13.5

4 | 10   | 2    | 128       | -0.5         | -5.5

2: The graph shows that the revenues for online ads were approximately equal to the revenues for printed ads around 2006, which is the 12th year after the online version of the paper was started.

3a: Beach A is decreasing at a faster rate than Beach B, with its width decreasing from around 400 feet in 1995 to around 250 feet in 2015. Beach B's width is decreasing at a slower rate, from around 500 feet in 1995 to around 350 feet in 2015.

3b: Between the years 2011 and 2012, the beaches have approximately the same width.

3c: To get a better approximation of when the two beaches will have the same width, the rate of erosion of each beach should be calculated over time. This can be done by plotting the width of each beach over time and calculating the slope of the line, which will give an indication of the rate of erosion.

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Answer:

B

Step-by-step explanation:

x² + 4x - 21 = 0 ← in standard form

(x + 7)(x - 3) = 0 ← in factored form

equate each factor to zero and solve for x

x + 7 = 0 ⇒ x = - 7

x - 3 = 0 ⇒ x = 3

Answer:

x= -7, 3

Step-by-step explanation:

x^2 +4x-21=0

You need to extract the factors for the equation. Two factors that multiplied give the result -21 and added give +4, with the form:

x^2 +4x-21=0

(x+7)(x-3)=0

You obtain:

x+7=0

x=-7

and,

x-3=0

x=3

the length of chord in the circle is 13.5 units.

According to Pythagoras' Theorem, the square of the hypotenuse side of a right-angled triangle equals the sum of the squares of the other two sides.The Perpendicular, Base, and Hypotenuse are the three angles that make up this triangle.

The Pythagoras Theorem formula is as follows from the definition:

Hypotenuse² = Perpendicular² + Base²

c² = a² + b²

From the figure, the hypotenuse, x of both triangle are same as both of them are radius of circle.

According to Pythagoras theorem,

x²=6.3²+11.9²

x²=181.3

x=√181.3

x=13.5

Hence, the length of chord in the circle is 13.5 units.

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Adding and subtracting polynomials worksheets assist pupils in becoming acquainted with the idea of polynomial addition and subtraction.

Adding and subtracting polynomial worksheets provide pupils with a platform to access a variety of well-structured problems. Because these worksheets progress in complexity, they are simple to use and allow pupils to reinforce their concepts.

Children must study in accordance with their learning curve, and these worksheets are designed to allow young brains to work at their own speed. These math worksheets also address the logical and reasoning aspects of arithmetic, assisting pupils in real-life situations.

Students may have a better grasp and explore these worksheets more quickly with the aid of pictures. These worksheets' step-by-step approach helps pupils better comprehend ideas and reinforce their comprehension.

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Answer:

Step-by-step explanation:

The mixed number for 3.6 is 3 6/10.

What is a Mixed Fraction?

Improper fractions and mixed numbers have the same value but are written differently. Whole numbers are displayed separately from fractions in mixed numbers. The numerator is larger than the denominator and complete numbers are not displayed separately in improper fractions.

Given:

We have to write 3.6 into a mixed number

So, the decimal 3.6 into a fraction

= 3.6

= 36/10

Then, the division is

                           10 | 36| 3

                                  30

                                 _____

                                    6  

So, the mixed number is 3 6/10.

Answer:

Step-by-step explanation:

Hi there! Just multiply by x and find the value of f=p. Good luck!

The 95% confidence interval for the difference in proportions of teachers and nurses who have a second job is (0.014, 0.206).

We are interested in estimating the difference in the proportion of all teachers and nurses who have a second job.

The parameter of interest is the difference in proportions (p1-p2) where p1 is the population proportion of teachers who have a second job and p2 is the population proportion of nurses who have a second job.

We want to construct a 95% confidence interval for the parameter.

The general formula for a confidence interval for the difference in proportions is

(point estimate) ± (critical value) x (standard error)

where the point estimate is the difference in sample proportions, the critical value is based on the desired level of confidence, and the standard error is a measure of the variability in the sampling distribution.

The specific formula for a confidence interval for the difference in proportions between two independent samples is:

(point estimate) ± (critical value) x (standard error)

where

(point estimate) = p1 - p2

(critical value) = the z-value corresponding to a 95% confidence level, which is 1.96

(standard error) = sqrt[(p1(1-p1)/n1) + (p2(1-p2)/n2)]

where n1 and n2 are the sample sizes for the two groups.

Now, we can plug in the given values to find the confidence interval.

(point estimate) = 0.32 - 0.21 = 0.11

(standard error) = sqrt[(0.32(0.68)/150) + (0.21(0.79)/100)] = 0.049

(critical value) = 1.96

Therefore, the 95% confidence interval for the difference in proportions is

0.11 ± (1.96)(0.049)

0.11 ± 0.096

The lower limit of the confidence interval is 0.014 and the upper limit is 0.206.

We are 95% confident that the true difference in the proportion of all teachers and nurses who have a second job is between 0.014 and 0.206. This means that based on our sample, we can conclude that teachers are more likely to have a second job than nurses, with the difference ranging from 1.4% to 20.6%.

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Using the Unique factorization theorem for the following integers the standard factored form of 504 is 2³ x 3²x 7 , for 819 is 3² ×7×13 and for  5,445 is 3²×5×7².

The Unique Factorization Theorem states that any positive integer can be written as a product of prime numbers in a unique way. To write each of the integers in standard factored form.

Using this theorem, we can factorize any positive integer into its prime factors. Here are the steps to factorize a number:

The prime factors obtained in this process can then be multiplied together to obtain the standard factored form of the original number . Therefore,

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Smallest number in the data set that is not an outlier is 15, Median of the first half is 17, Median of the entire data set is 20.5. Median of the second half is 22. Largest number in the data set that is not an outlier is 35.

Give a short note on Median?

In statistics, the median is a measure of central tendency that represents the middle value in a dataset. To find the median, the data must first be sorted in ascending or descending order. If the dataset contains an odd number of values, the median is the middle value. If the dataset contains an even number of values, the median is the average of the two middle values.

The median is a useful measure of central tendency in datasets that are skewed or have outliers, as it is less sensitive to extreme values than the mean. It is also useful in datasets with non-numeric values, such as rankings or survey responses.

To create a modified box plot, we need the following values:

The smallest number in the data set that is not an outlier: 15

The median of the first half of the data set: 17

The median of the entire data set: 20.5

The median of the second half of the data set: 22

The largest number in the data set that is not an outlier: 35

So the values needed to create a modified box plot for this data set are: 15, 17, 20.5, 22, 35.

No, the given question is not a statistical question. The statistical form of the given question is: "What is the distribution of the number of people who tried out for the Volleyball team over a certain period of time?"

A statistical question is one that can be answered by collecting data and analyzing it. In this case, the original question was “How many people tried out for the Volleyball team?” which can be answered with a specific number. However, to make it a statistical question, we derived a new question: “What is the distribution of the number of people who tried out for the Volleyball team over a certain period of time?” This question asks about the pattern or spread of the data over time and can be answered by collecting data on the number of people who tried out for the Volleyball team at different points in time and analyzing it to see how it changes.

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The complete question is:

"How many people tried out for the Volleyball team?" - Is this a statistical question?

If not, then rewrite it accordingly.

Therefore , the solution of the given problem of graphs comes out to be step is not parallel to the border if the top edge's slope differs.  

Theoretical physicists use graphs to analytically and visually show claims rather than variables. A graph point typically depicts the connection between several different items. A specific type of pas de carrier structure made up of groups along with lines is known as a graph. Glue should be used to connect the boundaries, which are additionally referred to as the channels. Within the boundaries of this network, the digits 1 through 4 and the characters 2.5, 3.5, or 4.5 were all present.

Here,

These values allow us to determine the step's slope in the following manner:

=> incline means rise / run

where "run" denotes the step's horizontal depth and "rise" the step's height.

The slope for the lowest step is 8 inches for rise and 10 inches for run.

=> slope = 8 / 10 = 0.8

The slope of the top edge of the step should match the slope we just computed if the bottom step is parallel to the floor.

We can infer that the lowest stair is parallel to the floor if the slope of the top edge is also 0.8.

The step is not parallel to the border if the top edge's slope differs.

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Answer:

10

Step-by-step explanation:

Based on the given conditions, formulate: 40x16 divided by 64

Cross out the common factor: 40/4

Cross out common factor: 10

Get the result

Answer: 10

The sum of the two coefficients will be the effect of D1 on Y when D2=0.

The sum of the regression coefficients on D1 and I1 will be the effect of D1 on Y when D2=0. In other words, it is the effect of a change of D1 on Y when D2=0, holding all other variables constant.

This can be better understood by understanding what interaction variable I1 represents. I1 is the interaction between D1 and D2 and is equal to D1*D2. So, the coefficient of I1 is the effect of D1 when D2=1 and the coefficient of D1 is the effect of D1 when D2=0. Therefore, the sum of the two coefficients will be the effect of D1 on Y when D2=0.

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The correct answer is option b.24.

The given options are Meat: beef, chicken, pork vegetables: baked beans, corn, potatoes, tomatoesDessert: brownies, chocolate cake, chocolate pudding, ice creamThe order of food items is not important, so we need to find the number of combinations we can form by selecting one type of meat, two types of vegetables, and one dessert from the given options.

In selecting the meat, we have three choices, i.e. beef, chicken, and pork. We need to choose one of these three types. So, the number of ways to choose meat is 3. In selecting the vegetables, we have four choices, i.e. baked beans, corn, potatoes, and tomatoes. We need to choose two of these four types.

So, the number of ways to choose two vegetables is,4C2 = 6 (We can select any two vegetables out of four, and the order of vegetables does not matter)In selecting the dessert, we have four choices, i.e. brownies, chocolate cake, chocolate pudding, ice cream. We need to choose one of these four types. So, the number of ways to choose the dessert is 4. So, by the rule of multiplication, we can select a meal in 3 × 6 × 4= 72ways.

However, as the order of food items is not important, we need to divide the total number of combinations by the number of ways to arrange the selected items, i.e. 2! (since we have selected two types of vegetables), and 1! (for meat and dessert). So, the total number of possible meals that Tyler can choose is,72/2! = 36/2 = 18 meals (arranging 2 items from 4),18 × 4! = 18 × 24 = 432 total possible arrangements.

Hence the answer is option b.24.

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The order from smallest to largest is: 500 cm², 45,000 cm², 54,000 cm².

What is the area?

Area is a mathematical concept that describes the size or extent of a two-dimensional shape or surface, such as a rectangle, circle, or triangle. It is usually measured in square units, such as square meters, square centimeters, or square inches. The area of a shape is equal to the amount of space enclosed by the shape, and can be calculated by multiplying the length and width of a rectangle, by using a formula specific to the shape (such as the area of a circle = πr²), or by dividing the shape into smaller, regular shapes and summing their areas.

According to the given information:

compare the given areas, we need to convert all of them to the same unit.

45,000 cm²: This is already in square centimeters, so we don't need to convert it.

5.4 m²: This is in square meters, which is a larger unit than square centimeters. We can convert it to square centimeters by multiplying by the conversion factor [tex](100 cm/m)^2:[/tex]

[tex]5.4 m² = 5.4 x (100 cm/m)^2 = 54,000 cm²[/tex]

5 x 10⁶ mm²: This is in square millimeters, which is a smaller unit than square centimeters. We can convert it to square centimeters by dividing by the conversion factor [tex](10 mm/cm)^2:[/tex]

[tex]5 x 10⁶ mm² = 5 x 10⁶ / (10 mm/cm)^2 = 500 cm²[/tex]

Now that we have all the areas in square centimeters, we can compare them directly:

45,000 cm²

54,000 cm²

500 cm²

Therefore, the order from smallest to largest is: 500 cm², 45,000 cm², 54,000 cm².

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Write the areas in size order, starting with the smallest: 45,000 cm² < 5.4 m² < 5 x 10⁶ mm².

What is mathematical conversions?

Mathematical conversions refer to the process of changing one unit of measurement to another unit of measurement that is equivalent in value. This is done by using conversion factors, which are ratios that relate the two units of measurement.

For example, to convert 5 meters to centimeters, you can use the conversion factor 1 meter = 100 centimeters, and multiply 5 meters by 100 centimeters/meter to get 500 centimeters.

1. Convert 5.4m² to square millimeters:

1 m² = 1,000,000 mm² (since 1 meter = 1000 millimeters)

5.4 m² = 5.4 x 1,000,000 = 5,400,000 mm².

2.Compare 45,000 cm² and 5,400,000 mm² directly:

1 cm² = 100 mm² (since 1 centimeter = 10 millimeters, and 1 cm² = 10 mm x 10 mm = 100 mm²)

45,000 cm² = 45,000 x 100 = 4,500,000 mm²

4,500,000 mm² < 5,400,000 mm².

3.Therefore, write the areas in size order, starting with the smallest:

45,000 cm² < 5.4 m² < 5 x 10⁶ mm².

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The number of distinct elements of AB = m n.

Given that G is a group with subgroups A and B of orders m and n, respectively, where m and n are prime, we need to prove that the subset of G, AB = {abla E Ab E B}, has m n distinct elements. Step-by-step. Let, G is a group with subgroups A and B of orders m and n, respectively. Since, m and n are relatively prime, then we have gcd(m, n) = 1.By Lagrange's Theorem, the order of any subgroup of G divides the order of G.

Hence, the order of G is equal to the product of the orders of A and B, i.e. |G| = |A| * |B| = m * n Let, a and a' be two distinct elements of A and b and b' be two distinct elements of B. Thus, a and a' generate distinct subgroups of G, i.e.  ≠  and b and b' generate distinct subgroups of G, i.e.  ≠ .Now, the number of distinct elements of AB = {abla E Ab E B} is equal to |A||B| since any two elements ab and a'b' of AB will be distinct if either a and a' are distinct or b and b' are distinct or both are distinct. Hence, the number of distinct elements of AB = m n.

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