Below are two parallel lines with a third line intersecting them.

The complete proof of the theorem is

Statements                                     Reasons

1. p||q                                               1. Given

2. ∠1≅∠3                                         2. Alternate interior angles theorem

3. ∠1≅∠3                                        3. Definition of congruent angles

4. ∠3 + ∠2 ≅ 180°                          4. Definition of linear pair

5. m∠3 + m∠2 = 180°                      5. Linear pair theorem

6. m∠1 + m∠2 = 180°                     6. Substitution prop. of equality

7. ∠1 and ∠2 are supplementary  7. Consecutive interior angles theorem

From the question, we are to complete the given proof

The proof is completed as shown below

Statements                                     Reasons

1. p||q                                               1. Given

2. ∠1≅∠3                                         2. Alternate interior angles theorem

3. ∠1≅∠3                                        3. Definition of congruent angles

4. ∠3 + ∠2 ≅ 180°                          4. Definition of linear pair

5. m∠3 + m∠2 = 180°                      5. Linear pair theorem

6. m∠1 + m∠2 = 180°                     6. Substitution prop. of equality

7. ∠1 and ∠2 are supplementary  7. Consecutive interior angles theorem

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There are zero positive real roots for the given polynomial equation [tex]x^4 + x^3 + x^2 + x + 1 = 0[/tex]. This is explained by Descarte's rule of signs. So, the best choice is T (true).

The given polynomial equation is [tex]x^4 + x^3 + x^2 + x + 1 = 0[/tex]

On applying Descarte's rule of signs,

[tex]f(x)=x^4 + x^3 + x^2 + x + 1[/tex]

Since there are no changes in the signs of the coefficients of any of the terms in the above polynomial, the polynomial has no positive real roots.

[tex]f(-x)=(-x)^4+(-x)^3+(-x)^2+(-x)+1\\ = x^4-x^3+x^2-x+1[/tex]

Since there are four changes in the signs of the coefficients of the terms of the given polynomial when f(-x), the polynomial has 4 negative real roots.

Therefore, the given polynomial equation has zero positive real roots. So, the correct choice is T(true).

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Hello and Good Morning/Afternoon:

Let's take this problem step by step:

Let's consider what the problem wants:

⇒ the value of (f-g)(y)

Let's consider what the problem gives us:

⇒ the value of f(y) and g(y)

Let's consider the relationship between f(y), g(y) and (f-g)(y)

 ⇒ [tex](f-g)(y)=f(y)-g(y)[/tex]

Let's solve for (f - g)(y)

 [tex]\hookrightarrow(f-g)(y) = f(y)-g(y) = 5y^2-2y+1-(-3y^2-y-2)\\=5y^2-2y+1+3y^2+y+2=8y^2-y+3[/tex]

Answer: 8y²- y + 3

Hope that helps!

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Using proportions, it is found that she should walk at a speed of 8 mph to arrive at noon.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, considering the speeds of arrival at 11 am and at 1 pm, we have that for each 2 km slower, she arrives one hour later.

Walking at 10 mph she arrives at 11 am, hence she should walk at a speed of 8 mph to arrive at noon.

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The values of the triangles are as follows:

The triangle is an isosceles triangle because two sides and angles are equal. Therefore,

4x - 7 = 2x + 7

4x - 2x = 7 + 7

2x = 14

x = 14 / 2

x = 7 units

GH = 4(7) - 7 = 28 - 7 = 21

HI = 2(7) + 7 = 14 + 7 = 21

GI = 7 + 5 = 12

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Chantelle can use the following equation,

n = (Number of stickers) / (Number of friends)

or n = 56/8

Given Information

Chantelle has 56 stickers

⇒ Number of stickers = 56

She will distribute all of the stickers to 8 friends

⇒ Number of friends = 8

The number of stickers each friend will get = n

We have to form an equation for n.

Forming the Equation

Equation for  the number of stickers to be given to each friend is as follows,

n = (Number of stickers) / (Number of friends)

n = 56/8

n = 7

Therefore, Chantelle needs to give 7 stickers to each of her 8 friends. And, the equation used to find this count, n is n = (Number of stickers) / (Number of friends) or n =56/8

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(a) The Sample mean of each sample is 1, 2, 5, 1.5, 3, 3.5, 3, 1.5,3,3.5.

(b) The mean of the sample means from part (a) is 8/3.

(c) Yes, The mean of the sample distribution is always equal to the mean of the Population.

According to the questions,

Game number                          1      2        3      Total

Number of interceptions         1        2       5          8

a)   Element 1            Element 2

    1                              1

    2                            2

    5                            5

    1                             2

    1                            5

  2                             5

  2                              1

  5                               1

   5                              2

Sample mean of each sample is 1, 2, 5, 1.5, 3, 3.5, 3, 1.5,3,3.5.

b) The mean of the sample means from part a.

     (1+2+5+1.5+3+3.5+1.5+3+3.5)/9 = 8/3

The mean of the sample means from part (a) is 8/3

c) Mean of the populations = (1+2+5)/3 = 8/3

   The mean of the sample distribution from part b. is 8/3

Yes, The mean of the sample distribution is always equal to the mean of the Population

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Answer:

B. Every integer is also an irrational number.

The true statements are :

the average monthly temperatures of New Orleans are not as varied as that of Indianapolis.

The median of the average monthly temperatures of New Orleans is equal to the upper quartile of the average monthly temperature of Indianapolis.

A box plot is used to study the distribution and level of a set of scores. The box plot consists whiskers. The whiskers represents the minimum and maximum scores.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median.  The third line on the box represents the upper (third) quartile.

Range for New Orleans = 85 - 50 = 35

Range for Indianapolis = 75 - 25 = 50

Median for New Orleans = 70

Upper quartile for  Indianapolis = 70

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One landscaper's hourly rate is $15 lower than the other landscaper's. Casey is deciding which of two landscapers to hire. Each landscaper charges an hourly rate plus a fee for each job.

What is system of linear equations?

A set of two linear equations with two variables is a system of linear equations. Casey is deciding between hiring one of two landscapers. Each landscaper bills a fee for each job in addition to an hourly rate. A set of linear equations was appropriately written and solved by Casey using substitution. He solved for the other variable and substituted an expression for one in his work. The intersection of the lines that represent the linear equations is where a system of linear equations finds its solution. Each landscaper bills a fee for each job in addition to an hourly cost. Casey produced a system of linear equations that was correctly written and solved. The hourly rates for both landscapers are the same, however their rates for individual jobs vary.

Casey is deciding between hiring one of two landscapers. Each landscaper bills a fee for each job in addition to an hourly cost. By using substitution, Casey created and properly figured out a set of linear equations. He solved for the other variable and replaced an expression for one in his work, producing the equation 5 = 20.

equation 5=20

20-5 = 15

Therefore, One landscaper's hourly rate is $15 lower than the other landscaper's.

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The common ratio of the geometric sequence is 1.5

Common ratio can be described as difference between two numbers in a sequence.

The first term of the sequence is 10 and the second term is 15, the common ratio can be calculated by dividing the first term by the second term

= 15/10

= 1.5

Hence the common ratio of the sequence is 1.5

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Answer:

B

Step-by-step explanation:

The common ratio of the geometric sequence is 1.5

Common ratio can be described as difference between two numbers in a sequence.

The first term of the sequence is 10 and the second term is 15, the common ratio can be calculated by dividing the first term by the second term

= 15/10

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1.5

Sanjay and Felipe would take a time of 3.4 hours to do the puzzle if they were working together.

Time can be described in mathematics as an ongoing and continuous series of events that take place one after another, from the past through the present and into the future.

The amount of time that something exists or continues to happen as measured or measurable.

The duration of events or the gaps between them can be measured, compared, or even ordered using time.

Time taken by Sanjay= 6 hours

Time taken by Felipe= 8 hours

Time taken by both if they work together,

=[tex]\frac{1}{1/6+1/8}[/tex]

=[tex]\frac{1}{\frac{4+3}{24} }[/tex]

=24/7

=3.4 hours

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Answer:

the answer is C

Step-by-step explanation:

The total number of students in the school is calculated as; 600 students

Usually, some figures are expressed as a fraction of a whole as depicted in this case. Thus, when we are given a fraction of a whole to be equal to a particular figure, we will just cross multiply to get the total number.

We are told that;

Number of students that play a team sport at Lincoln high school = 225

Now, we are told that the number above represents a fraction of 3/8 of the total students in that school.

Thus, if the total number of students in the school is x, then we can say that;

(3/8)x = 225

Multiply both sides by 8 to get;

3x = 1800

x = 1800/3

x = 600 students

Thus, we can conclude that if two hundred and twenty five students play a team sport at Lincoln high school and these students represent 3/8 of the total, then we can say that the total number of students in the school is 600 students.

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Answer:

Step-by-step explanation:  use a square bracket [ when the set includes the endpoint and a parenthesis ( to indicate that the endpoint is either not included or the interval is unbounded.

Basado en la información, el valor de abc + bca + cab debe ser de 60.

El valor de la combinación de estás tres letras es de 20.

Según la propiedad conmutativa el orden de los factores sumados no debe afectar su resultado, por lo que:

20+20+20 = 60

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The solution of the system of equations contains one point

The system is given as:

x + y = 6

x - y = 0

Add both equations

2x = 6

Divide by 2

x = 3

Substitute x = 3 in x - y = 0

3 - y = 0

Solve for y

y = 3

So, we have x =3 and y = 3

Hence, the solution of the system of equations contains one point

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Answer:

-3/2

Step-by-step explanation:

Slope=rise/run

Pick any 2 points and you can see that for every increase in 2 increases for x, there are 3 decreases for y.

A random samples of ticket prices for concerts and the random samples of Coldplay ticket prices are independent . The answer is True.

According to the questions,

A random samples of ticket prices for concerts by the Rolling Stones was obtained. For comparison purposes another random samples of Coldplay ticket prices was obtained.

The two groups of data are independent samples.

Hence, a random samples of ticket prices for concerts and the random samples of Coldplay ticket prices are independent . The answer is True.

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Stronger evidence against the null hypothesis is indicated by: smaller p-values.

A statistical conjecture known as a null hypothesis asserts that certain features of a population or data-generating process are not different from one another.

A mechanism to reject the null hypothesis with a predetermined level of confidence is provided by hypothesis testing.

The alternative hypothesis is supported if the null hypothesis can be rejected.

The foundation of the scientific falsification principle is null hypothesis testing. The null hypothesis presupposes that any variation in the selected characteristics you observe in a set of data is the result of chance.

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Answer:

B. (-6)(-6)

Step-by-step explanation:

-  X - = +

and 6 x 6 = 36.

A = 7M is the equation that might be used to find the unknown side length, M, of the rectangular logo.

We can determine the following details from the query:

Logo= rectangle with a

Length ,L= 7-foot

'A' stands for the logo's area, and 'M' for the side that isn't recognized.

The rectangle's area (A) is computed using:

A = L*W

⇒A = 7*M

(As per query, length, L=7 & W= M)

Consequently, the formula 'A = 7M' might be used to calculate the logo's undetermined side length, M.

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Collect data on a representative selection of patients for two weeks.

is the best data collection plan for this project.

According to the statement

we have a given that the surgical unit that receives 87 new patients per week.

and we have to tell the data plan to collect the baseline data before testing your change to control the pain across the unit.

And We know that the Data collection is A representative sample is one technique that can be used for obtaining insights and observations about a targeted population group

So,

Collecting data on a representative portion of your population — that is, sampling — allows you to collect baseline data and start making improvements faster, using fewer resources, than would be possible if you tried to look at every patient. Baseline data is important so that you can see if the changes you are testing are leading to improvement. Collecting data about a non representative sample of your population, such as by looking only at patients with the most severe pain, won't show the broad impact of your project on your unit.

So, Collect data on a representative selection of patients for two weeks.

is the best data collection plan for this project.

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Disclaimer: This question is incomplete. Please read the full content below.

Question:

You work on a surgical unit that receives 87 new patients per week. In your spare time, you are trying to improve pain control across the unit. As you prepare to collect your baseline data before testing your change, you consider your plan to gather this information. Which of the following would be the best data collection plan for this project, and why?

(A) Collect data on the pain level of every patient for at least a year.

(B) Collect data for at least a year, focusing only on patients who have undergone especially painful surgeries.

(C) Collect data on a representative selection of patients for two weeks.

(D) There is no reason to collect baseline data.

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The length of the measure of YZ is 80cm

Perpendicular lines are lines that are at angle 90 degrees to each other. From the given diagram;

WX = 82cm

Required

Length. of YZ

Using the pythagoras theorem

YV = VZ = √41²-9²

YV = VZ = √1600

YV = VZ = 40

Since YZ = YV + VZ

YZ = 40cm + 40cm

YZ= 80cm

Hence the length of the measure of YZ is 80cm

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Answer:

(D). 6.

Step-by-step explanation:

The number of parts = 1 + 10 = 11.

So 10/11 of the alloy is copper and 1/11 is aluminium.

So the answer is 1/11 * 66

= 66/11= 6 pound,s

A certain journey by train takes 5 hours at the speed of 45 km/h. What will be the speed of the train to complete the same journey in 3 hours?

Answer:

Journey taken time 5 hour at speed of 45km/hr

So,

 1 hour=45/5=9km/hr

Therefore,3 hour=(9x3)km/hr.

(please mark me brainliest if my answer was good)

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A function for the described sequence is; f(n) = 6• 3^(n-1) and the sixth term is; 1458.

Since, it follows that the first term of the sequence is; 6 and the common ratio is 3, it follows that the recursive function that represents the sequence is; f(n) = 6• 3^(n-1).

Additionally, by substitution of 6 for n; f(6) = 1,458.

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Fencer X attacks. Fencer Y makes a parry, and scores a riposte to the valid target of Fencer X. During the parry, Fencer Y strikes Fencer Xs mask with the bell guard. annual the touch fencer Y recieves  a RED CARD.

what are the fencing rules ?

Penalty cards or flags are also used in modern fencing. Each card has a unique meaning. A fencer who receives a yellow card is warned, but no further action is taken. A fencer who receives a red card is warned, and their opponent receives a touch. A fencer who receives a black card is disqualified from the competition and may be disqualified from the tournament, expelled from the venue, or suspended from future tournaments if the offence is serious. However, black cards are rarely given to fencers. It should be noted that spectators can (and occasionally are) carded or expelled.

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Answer:  12.56

Step-by-step explanation:

4 x 3.14

pi = 3.14