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The equilateral triangle theorem states that in an equilateral triangle, all sides are equal in length and all angles are equal in measure (60 degrees).

The equilateral triangle theorem states that in an equilateral triangle, all sides are equal in length and all angles are equal in measure (60 degrees).

To prove this theorem, we can use the following steps:

1. Draw an equilateral triangle and label the sides as a, b, and c.

2. Use the definition of an equilateral triangle to state that all sides are equal in length, which means a = b = c.

3. Use the definition of an equilateral triangle to state that all angles are equal in measure, which means all angles are equal to 60 degrees.

4. Use the properties of a triangle to show that the sum of the interior angles of a triangle is 180 degrees.

5. Substitute the values for the sides and angles of the equilateral triangle into the formula for the sum of the interior angles of a triangle:

a + b + c = 180 degrees.

6. Simplify the equation by substituting the equal values of a, b, and c:

3a = 180 degrees.

7. Divide both sides of the equation by 3 to find the value of a:

a = 60 degrees.

8. Since a represents the measure of each angle in the equilateral triangle, this proves that the measure of each angle in an equilateral triangle is 60 degrees.

This proof demonstrates that the equilateral triangle theorem is true for all equilateral triangles.

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The three categories are interquartile range, standard deviation, and variance. The range of a distribution's middle quintile is known as the interquartile range.

The difference between the highest and lowest values for a certain data set's statistics is the range. Any real number between any two other numbers in the set is considered to be in the range, which is a set of real numbers.

here

The range is the space between the highest and lowest numbers.

The range of a distribution's middle quintile is known as the interquartile range.

Average separation from the mean is known as standard deviation. Variance is defined as the sum of squared deviations from the mean.

Therefore, the three categories are interquartile range, standard deviation, and variance.

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The perimeter of the triangle is 5x + 12 inches

From the question, we have the following parameters that can be used in our computation:

Lengths = 7 inches, 4x + 1 and x + 4

The perimeter of a triangle is the sum of the side lengths

so, we have

Perimeter = sum of side lengths

Substitute the known values in the above equation, so, we have the following representation

Perimeter = 7 + 4x + 1 + x + 4

Evaluate the sum

Perimeter = 5x + 12

Hence, the perimeter is 5x + 12

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Since the electrician charged $360 on a particular job, the number of hours that this electrician worked for is 4 hours.

In Mathematics, a linear function is sometimes referred to as an expression or the slope-intercept form of a straight line and it can be used to model (represent) the total amount of money that is being charged by this electrician;

T = mh + b

Where:

Therefore, the required linear function that represents the total amount of money that is being charged by this electrician per hour is given by this mathematical expression;

T = 80h + 40

When the total amount of money is $360, the number of hours worked by this electrician can be calculated as follows;

360 = 80h + 40

80h = 360 - 40

80h = 320

Time, h = 320/80

Time, h = 4 hours.

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The first step in solving the equation by distributing is represented by "negative 12 x plus 20 = negative 16".

The correct answer option is option A

-4(3x - 5) = -16

Step 1:

apply distributive property

-12x + 20 = -16

Apply Subtraction equality

-12x = -16 - 20

-12x = - 36

applying division equality

x = -36 / - 12

x = 3

In conclusion, the solution to the equation as solved by Melanie by distributing is x = 3

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With a 95 percent confidence interval, you have a 5 percent chance of being wrong.

You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% probability of being incorrect with a 90% confidence interval. A 95% confidence interval is narrower than a 99% confidence interval (for example, plus or minus 4.5 percent instead of 3.5 percent).

What is the correct calculation for a 95% confidence interval?

The 68-95-99.7 Rule states that 95% of values lie within two standard deviations of the mean, hence to get the 95% confidence interval, you add and subtract two standard deviations from the mean.

In statistics, confidence is another word for probability. If you create a confidence interval, for instance, with a 95% level of confidence, you can be sure that 95 out of 100 times, the estimate will fall between the upper and lower values indicated by the confidence interval.

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The statement is true that is root 2 over 2 is equal to 1 over root 2 is true we can write as √2/2=1/√2.

Given that,

We have to find is root 2 over 2 is equal to 1 over root 2.

We know that,

A number can be squared, but it can also be divided into its square root. The value we get from multiplying a number by itself yields its square value, whereas the value we get from finding a number that, when squared, yields the original value of the number yields its square root value.

Now,

Root 2 over 2 is equal to 1 over root 2 can write as

√2/2=1/√2

Taking multiplying √2 on both side.

√2/2×√2=1/√2×√2

(√2×√2)/2=(1×√2)/√2

2/2=√2/√2

1=1

Therefore, The statement is true that is root 2 over 2 is equal to 1 over root 2 is true we can write as √2/2=1/√2.

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Answer:

[tex]y=2x+11[/tex]

Step-by-step explanation:

[tex]m=\frac{3-(-1)}{-4-(-6)}=2 \\ \\ y+1=2(x+6) \\ \\ y+1=2x+12 \\ \\ y=2x+11[/tex]

Equation of the line that passes through (2, 0) and is parallel and perpendicular to the line shown is y = - x + 5

What is perpendicular?

Two geometric objects are perpendicular in simple geometry if they intersect at a right angle. The perpendicular symbol,, can be used to graphically depict the condition of perpendicularity. It can be defined between two planes, two lines, or two planes and another line.

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = x - 3 ← is in slope intercept form

with slope m = 1

Given a line with slope m then the slope of a line perpendicular to it is

= -  = -  = - 1, thus

y = - x + c ← is the partial equation of line j

To find c substitute (2, 0) into the partial equation

0 = - 2 + c ⇒ c = 0 + 2 = 2

y = - x + 2 ← equation of line j

Parallel lines have equal slopes, thus

y = - x + c ← is the partial equation of line k

To find c substitute (- 1, 6) into the partial equation

6 = 1 + c ⇒ c = 6 - 1 = 5

y = - x + 5 ← equation of line k

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There are a few different contexts in which the concept of continuity arises, and the specific conditions that must be satisfied for something to be considered continuous can vary depending on the context. Here are three common sets of conditions that are often used to define continuity:

In mathematics, a function is generally considered to be continuous if it satisfies the following three conditions:

In physics, a physical quantity is generally considered to be continuous if it can vary smoothly and continuously over a range of values, rather than taking on only discrete values.

In computer science, a function is generally considered to be continuous if it satisfies the following three conditions:

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There are a few different contexts in which the concept of continuity arises, and the specific conditions that must be satisfied for something to be considered continuous can vary depending on the context. Here are three common sets of conditions that are often used to define continuity:

In mathematics, a function is generally considered to be continuous if it satisfies the following three conditions:

In physics, a physical quantity is generally considered to be continuous if it can vary smoothly and continuously over a range of values, rather than taking on only discrete values.

In computer science, a function is generally considered to be continuous if it satisfies the following three conditions:

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The distance between Katie and Helicopter will be 5.774 miles approximately.

We will solve this problem with the help of Trignometry. So, what is Trignometry?

A branch of mathematics called trigonometry examines correlations between triangles' side lengths and angles. Three crucial trigonometric functions—sine, cosine, and tangent—are represented by the abbreviations sin, cos, and tan.

In this problem, it is given that Katie is watching a helicopter flying at an altitude of 5 miles and the angle of elevation is π/3.

From Sin Cos Tan, you know that:

Sin = opposite/Hypotenuse

sin(π/3) = (5 miles)/Hypotenuse

Hypotenuse = (5 miles) / Sin(π/3) = 5/ ([tex]\sqrt[]{3}[/tex]/2) miles = 5.774 miles.

So, the distance between Katie to the Helicopter is about 5.774 miles.

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In this problem, it is given that Katie is watching a helicopter flying at an altitude of 5 miles and the angle of elevation is π/3.

From Sin Cos Tan, you know that:

Sin = opposite/Hypotenuse

sin(π/3) = (5 miles)/Hypotenuse

Hypotenuse = (5 miles) / Sin(π/3) = 5/ (/2) miles = 5.774 miles.

So, the distance between Katie to the Helicopter is about 5.774 miles.

The equation for graphing y = 4 in slope-intercept form is y = 4x + 0. This equation can be graphed by plotting the point (0, 4) and then using the slope of 0 to draw a horizontal line that passes through that point.

1. Plot the point (0, 4)

2. Draw a horizontal line that passes through the point (0, 4). This line will have a slope of 0.

Start by plotting the point (0, 4). This point marks the y-intercept of the graph. Then, draw a horizontal line that passes through this point. The slope of this line will be 0, which is necessary for graphing the equation y = 4 in slope-intercept form. The equation for this graph is y = 4x + 0 and the graph should be a straight, horizontal line that passes through the point (0, 4).

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The binomial factors of x²-16 is (x+4) and (x-4).

Binomial refers to an algebraic expression that only has two terms. A polynomial with two terms, it. It is referred to as a sum or difference between two or more monomials as well. It is a polynomial's most straightforward form.

Having two terms makes a polynomial a binomial. Binomials include, for instance, x 2 x -2 x2 and x 6 x -6 x6. This article will go over multiplying these binomials.

An integer that may be derived by evaluating a homogeneous polynomial with two terms is known as a binomial number in mathematics, more specifically in number theory.

Here, x²-16=0

Rewrite 16 as 42, and the expression will be equal to 0 if any of the factors on the left side of the equation are equal to 0.

x+4=0 and locate x.

Once x=-4 x-4=0 and x=4 are found.

As a result, the final solution is x = 4, 4 and all choices that lead to (x + 4) (x 4) = 0 are true.

Hence, The binomial factors of x²-16 is (x+4) and (x-4).

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AS per the given details, the system of linear inequalities for each ticket is  x + y ≥ 30, 7.5x + 12.5y ≤ 400

The term inequation is a claim that one quantity or algebraic expression has a value that is not equal to another.

Here we have given that Cian is buying movie tickets for a group. He wants to have at least 30 tickets and spend no more than $400. Adult tickets cost $12. 50 and child tickets cost $7. 50.

And we need to find the system of inequalities can be used to find the number of each type of ticket can could buy.

According to the given information, here we are given that,

The adult tickets cost $12.50 and the child tickets cost $7.50.

Let us consider the number of adult tickets be y and the number of child tickets be x.

Here we also given that, that Cian wants to spend no more than $400.

So, the system of inequations is written as

=> x + y  ≥ 30,

And the other inequality is written as,

=> 7.5x + 12.5y ≤ 400

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There is no mode in the data set 1, 2, 3, 4, 5,6,7,8,9.

A mode is defined as the value that has a higher frequency in a given set of values. It is the value that appears the most number of times.

Given that,

Data set= 1, 2, 3, 4, 5,6,7,8,9

By the definition of mode, it is clear that the most observed data in a data set will be the mode of that data set. And this can be zero also. And it can be more than zero.

In statistics, the mode is the most commonly observed value in a set of data. And for the normal distribution, the mode is always the same as the mean and median. But in many cases, the modal value of a data set will differ from the average value in the data.

If we take our question then 1, 2, 3, 4, 5, 6,7,8,9.

Here, no term is repeated more than once.

So, there is no most observed term.

So, there is no mode in this data.

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The chi-squared statistic can be used to determine whether there is a significant association between the two variables.

What is chi-squared statistic?

When the sample sizes are large, a chi-squared test is a statistical hypothesis test used in the study of contingency tables. To put it another way, the main purpose of this test is to determine whether two category factors have independent effects on the test statistic.

To test whether people who kiss more than ten times a day wear brighter colors to work than those who do not, the appropriate test statistic to use would be the chi-squared statistic.

The chi-squared statistic is a measure of the difference between observed and expected frequencies in a contingency table.

Once we have the contingency table, we can calculate the chi-squared statistic using the following formula:

     [tex]chi-squared = ((observed - expected)^2 / expected)[/tex]

In this case, the null hypothesis is that there is no association between kissing more than ten times a day and wearing bright colors to work. To calculate the expected frequency of each cell, we need to use the formula:

    expected = (row total * column total) / sample size)

Plugging in the values from our contingency table, we can calculate the chi-squared statistic as follows:

     [tex]chi-squared = (10 - 15)^2 / 15 + (20 - 15)^2 / 15\\\\= 25 / 15 + 25 / 15\\\\= 2[/tex]

The chi-squared statistic can be used to determine whether there is a significant association between the two variables.

Refer following diagram.

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The required average of Will's bowling average after 8 games is 126.

Given the information, Willis’s bowling average after 5 games was 120. In his next 3 games, Willis scored 118,124, and 142.

The average of the values is the ratio of the total sum of values to the number of values.

here,
An average of 8 games is given as,
As an average of 5 games is 120, taking this average as 1 term
Now,
Average = 120 + 118 + 124 + 142 / 4 = 504 / 4
Average = 126

Thus, Will's required bowling average after eight games is 126.

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Answer:

x=5/6

Step-by-step explanation:

5/6+1/6=1

Answer: x= 5/6

Step-by-step explanation:

x + 1/6 = 1

Change 1 to an improper fraction = 6/6

x + 1/6 = 6/6

1/6 - 1/6 = 0

6/6 - 1/6 =5/6

 x = 5/6

Answer: ΔDEB ≅ ΔCEA; SAS

Step-by-step explanation:

          Using the diagram below, we can see that these two triangles share an angle, meaning that angle in both triangles is congruent. Next, we see dashed lines representing congruence for two of the other sides. This means these two triangles are proved congruent by SAS;

    S = Side

    A = Angle

    S = Side

          See attached for a visual.

Epidemiological process is used to determine the who had contacted with the measles and to identify those with immunity and assesses the probability of containing the measles .

The term "Epidemiology" is the study of the determinants, occurrence, and distribution of health and disease in a defined population. Infection is the replication of organisms in host tissue, which may cause disease. A carrier is an individual with no overt disease who harbors infectious organisms. Dissemination is the spread of the organism in the environment. Epidemiology process utilizes an organized approach to problem solving by:

(1) confirming the existence of an epidemic and verifying the diagnosis.

(2) developing a case definition and collating data on cases.

(3) analyzing data by time, place, and person.

(4) developing a hypothesis.

(5) conducting further studies if necessary.

(6) developing and implementing control and prevention measures.

(7) preparing and distributing a public report.

(8) evaluating control and preventive measures.

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Answer:

Bonjour

h(x) = x² - 6x + 5 définie sur [0 ; 5 ]

1)

L' oiseau a commencé son vol à

h(0) =(0)² - 6(0) + 5 = 5 donc 5 mètres

3)

h(x) atteint son maximum pour x = -b/2a = 6 / 2 = 3

h(3) = 9 - 18 + 5 = -4 mètres

4)

(x-1)(x-5) = x² - 5x - x + 5 = h(x) ce qu'il fallait démontrer

5)

h(x) = 0 revient à

(x-1)(x-5) = 0 pour x = 1 et pour x = 5

L' oiseau est entré dans l'eau à 1 mètre et en est ressorti à 5 mètres

Bonne fin de journée

Answer:

6' = 12" with a scale of 1

8'= 20" with a scale of 1

6" = 12' with a scale of 1

48" = 146' with a scale of 1

-------------------------------------------

6' = 18" with a scale of 0.5

8' = 25" with a scale of 0.5

6" = 24' with a scale of 0.5

48" = 58' with a scale of 0.5

Step-by-step explanation:

Should be right.

A permit is a legal document that enables a person or a business to utilize a specific area for a project or other activity.

To obtain permission to use a specific location for a project, you may need to submit a request in writing or fill out a permission form. The exact document that you need to obtain permission will depend on the specific location and the requirements of the owner or manager of the location.

You may also need to provide information about your project, including the purpose, duration, and any potential impact on the location. Depending on the location and the nature of your project, you may also need to obtain other approvals or permits, such as building permits or environmental permits.

It is a good idea to research the requirements for using the specific location that you are interested in and to contact the appropriate authorities or individuals to find out what documents you need to obtain permission.

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The system of linear equations 2x – y = 7 and y = 2x + 3, has no solution.

Linear equations are those with a degree of 1. ax + by = c is the formula for linear equations in two variables, where a, b, and c are constants. We shall substitute the value of y in order to solve the system of linear equations.

Let equation (1) be 2x - y = 7 and equation (2) be y = 2x + 3

Enter the value of the equation y = 2x + 3 in equation (1).

2x - (2x+3) = 7

2x - 2x - 3 = 7

             -3 = 7

which is not true.

Therefore, there is no solution.

Correct Question:

What is the solution to the system of equations 2x – y = 7 and y = 2x + 3?

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There might be 200 votes cast overall. Given that a certain club has 50 members, 4 of those individuals are running for president, and every club member—including those running for president—votes for one of the four candidates, Understanding the provided conditions will help you get this.

We can discuss the probabilities of different outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events with a probability distribution.

given

There are 50 members in one club.

Each club member, including those vying for president, votes for one of the four candidates. There are four people standing for president.

We can write that based on the statements provided.

those who voted for these 4 members,

n = 50 Because the candidates have the option to vote for themselves or someone else,

There are x = 4 options available for each club member.

Thus, there are several distinct vote totals that could occur:

n ×4 = number of distinct votes possible

= 50 × 4

= 200

As a result, 200 votes are conceivably cast..

There might be 200 votes cast overall. Given that a certain club has 50 members.

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Answer:

To find the quotient of 3/4 and 5/6, divide each number by 2: 3/4 = 1/2 and 5/6 = 3/4. Therefore, the quotient is 1 1/9.

Step-by-step explanation:

The age of Ally and Burke is

1/2    [1   1 ]   [6 ]  -   [16]

     [  -1    1]   [  26]   [ 10]

A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers.

Algebraic expressions fall into three main kinds, including: Numeral Expression.

Binary Expression

Expression of a polynomial.

Let the age of Ally be x years

Then age of Burke will be x+6 years

Given, Sum of their age is 26

Therefore x+x+6=26

2x=26 - 6

x = 10

Thus the age of Burke is 10 years

Now age of Ally will be x + 6= 10 + 6 = 16

That is

1/2[1   1 ] [6 ]  - [16]6

  [  -1    1] [  26]   [ 10]

Therefore the age is of ally is 16 and burke is 10

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1. 4y

2. 2b

3. 3r

4. -1c

5. 5/3d+3b

6. 3x+2y^3 -4y

7. -2x+3y

8. 1/3

9. 27

10. 4

11. 12

Step-by-step explanation:

that means we need to transform the equation, so that it is in the form of

b = ...

b - c + d/8 = a | add c to both sides

b + d/8 = a + c | subtract d/8 from both sides

b = a + c - d/8

that's it.