A set of 1000 cards numbered 1 through 1000 is randomly distributed among 1000 people with each receiving one card. Compute the expected number of cards that are given to people whose age matches the number on the card.

Length of the shorter diagonal of the parallelogram will be 18.46 feet

Let the Parallelogram ABCD with BD and AC as it’s diagonal

According to the question,

AB = 17 feet

AD = 11 feet

As the opposite sides of a parallelogram are parallel and equal

Therefore, AB = CD = 17 feet

                AD = BC = 11 feet

Also the longer diagonal, BD = 22 feet

In triangle BCD, using cosine formula

[tex]BD^{2}[/tex] = [tex]CD^{2}[/tex] + [tex]BC^{2}[/tex]- 2BC.CD.CosC

[tex]22^{2}[/tex] = [tex]17^{2}[/tex] + [tex]11^{2}[/tex] - 2(11)(17)Cos C

484 = 289 + 121 - 374CosC

-0.197 = Cos C

C = arc Cos(-0.197)

Therefore, C = [tex]110^{0}[/tex]

Now ∠C + ∠D = [tex]180^{0}[/tex]

101+  ∠D = 180

∠D = [tex]79^{0}[/tex]

Now, in triangle ADC

[tex]AC^{2}[/tex] = [tex]AD^{2}[/tex] + [tex]CD^{2}[/tex] - 2AD.CD.CosD

 [tex]AC^{2}[/tex] = [tex]11^{2}[/tex] + [tex]17^{2}[/tex] - 2(11)(17)Cos79

[tex]AC^{2}[/tex] = 121 + 289 - 374Cos79

[tex]AC^{2}[/tex] = 410 -364(.19)

[tex]AC^{2}[/tex] = 340.84

AC = sqrt(340.84)

AC = 18.46

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The series is convergent with sum 5/8

A series is said to be convergent, if it converges to a value as the terms of series tends to infinity.

A series is said to divergent, it it does not converge to a value but keeps on either increasing or decreasing as the terms of series tends to infinity.

In the question ,

[tex]\frac{1}{3} +\frac{2}{9} + \frac{1}{27} +\frac{2}{81}+..[/tex] is given series

dividing the series into two parts ,

[tex](\frac{1}{3} +\frac{1}{27} +\frac{1}{243}+..)[/tex] + [tex](\frac{2}{9} + \frac{2}{81} + \frac{2}{729}+...)[/tex]

Using infinite geometric series formula both the side ,

=> [tex]\frac{\frac{1}{3}}{1- \frac{1}{9}} + \frac{\frac{1}{2}}{1- \frac{1}{9}}[/tex]

=> [tex]\frac{1/3}{8/9}+ \frac{1/2}{8/9}[/tex]

=>  [tex]\frac{3}{8} + \frac{1}{4}[/tex]

=> [tex]\frac{5}{8}[/tex]

Hence , the series is convergent.

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The value of c for the statement P(Z>c) = 0.1379 in the standard normal distribution is 1.09.

Φ is symbol for cumulative distribution function (CDF) for standard normal distribution with mean equal to 0 and standard deviation equal to 1.

Z follow standard normal distribution. So,

Z ∼ N(0,1)

Since,

P(Z>c) = 0.1379

1 - P(Z≤c) = 0.1379

P(Z≤c) = 1 - 0.1379

P(Z≤c) = 0.8621

or

Φ(c) = 0.8621

Next, we know Φ(Z) is equal to P(Z≤z) with z∈R is CDF for N(0,1). So,

P(Z≤z) = 0.8621

From standard normal distribution table or z table, we get z = 1.09. So,

P(Z≤1.09) =  0.8621

Φ(1.09) = 0.8621

Since, Φ(c) = 0.8621. So, c = 1.09

Thus, the value of c is 1.09 for statement P(Z>c) in standard normal distribution is equal to 0.1379.

Your question is incomplete, but most probably your full question is

Suppose Z follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of c so that the following is true.

P(Z>c)=0.1379

Round your answer to two decimal places.

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When the original two-digit number is equal to the sum of the number's digits plus the product of its digits, the number is said to be special two-digit number.

We are required to describe the 2-digit special number in the provided question.

When the original two-digit number is equal to the sum of the number's digits plus the product of its digits, the number is said to be special.

Remove the first and last digits of the number, then add and multiply each digit separately. The two-digit number should then be multiplied by the sum and product of its digits, and the output should be compared to the initial value. It is a special two-digit number if they coincide; if not, it is not.

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The slope of the line of best fit to the raw-score scatter plot is 0.98

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

The slope (b) of the line is calculated as

b = r * Sy/Sx

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

b = 0.75 * 2.45/1.88

Evaluate

b = 0.98

A linear equation is represented as

y = bx + c

Where

Slope = b

y-intercept = c

In (a), we have

b = 0.98

So, we have

y = 0.98x + c

Recall that the point (13, 9) is on the line of best fit.

So, we have

9 = 0.98 * 13 + c

This gives

9 = 12.74 + c

Evaluate

c = -3.74

So, we have

y = 0.98x - 3.74

Here, we have

x = 12

So, we have

y = 0.98 x 12 - 3.74

Evaluate

y = 8.02

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Therefore, the intensity pattern due to each single slit only extends over a finite region, and the double slit interference pattern can only be observed within this region.

In mathematics, interference is a phenomena that happens when two or more waves interact with one another. Depending on the waves' respective frequency  to reinforce or cancel. Interference can be constructive, where the waves combine to generate a bigger wave, or destructive, where the waves cancel each other out. This phenomena is widely observed in light waves, sound waves, and water waves. The superposition principle, which asserts that the total wave at any place in space equals the sum of all the individual waves existing at that point, is a mathematical concept that describes interference. In disciplines including physics, engineering, and signal processing, this idea is frequently applied.

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we are 99% confident that the population proportion lies between the confidence interval.

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time.

Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. Therefore, it can be concluded that there is a 95% probability that the true value falls within that range if a point estimate of 10.00 is produced from a statistical model with a 95% confidence interval of 9.50 - 10.50.

margin of error =E

=0.03p

=101/300

=0.337

For 95% CI, alpha is 5% and z=1.96

Sample size n=(z/E)² × (p(1-p)

=(1.96/0.03)² × (0.337(1-0.337))

=953.7

=954(approximately)

confidence interval is interpreted as that we are 99% confident that the population proportion lies between the confidence interval.

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Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an expression or equation made up of variables, constants, and exponents.

Find the x-intercepts in step one.

Solve the equation to obtain the x-intercepts.

Find the y-intercepts in step two.

Put x=0 in the equation to determine the y-intercepts.

STEP 3: Determine the final action

A polynomial's final behavior and the final behavior of a leading term are identical.

STEP 4: Locate the pivotal moments

We must locate the first derivative of p in order to identify the turning point (x)

The first derivative's zeros are where the turning point's x coordinate is situated.

Substituting the aforementioned value into p will yield the y coordinate (x).

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(4x² - 9)(4x² + 9) = 0 equation is equivalent to the given equation.

What is factorization?

Factorization in mathematics is the process of dividing a large number into smaller ones that, when multiplied together, give you the original number.

Here, we have

Given equation,

f(x) = 16x⁴ – 81 = 0

The difference of squares is used to solve this equation. There are three perfect squares: 16, x⁴, and 81. ( which means that it is a number multiplied by itself, 16 is 4 x4 for example).

We solve this equation by formula: (a² - b²) = (a - b)(a + b)

= 16x⁴ – 81 = 0

Now, we determine the square root of 16 which is 4, and of x⁴ which is x², and 81 which is 9.

Now we write the equation in the (a - b)(a + b) form :

⇒ (4x² - 9)(4x² + 9) = 0

Hence, the (4x² - 9)(4x² + 9) = 0 equation is equivalent to the given equation.

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The given equation's solution is x = 5i or x = i.

An equation has been provided.

x⁴+6x²+5 = 0

We to settle it utilizing replacement.

If u = x2, then u2 = x4 In the above equation, we find that u2+6u+5 = 0. Now, use the factorization method.

Divide the middle term of the previous equation as follows: u2+5u+u+5 = 0; u(u+5)+1(u+5) = 0; u(u+5)(u+1) = 0 Using the zero-product property, we can determine that u+5 or u+1 equals 0; u = -5 or u = -1; x2 equals -5 or x2 equals -1; taking the square root of both sides of.

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The probability of randomly selecting alphabet a is 1/26.

Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.

Statistics is the study of events that follow a probability distribution.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

So, the probability of the digit a:

We know that there are 26 digits in the alphabet.

Marcel selects 1 digit at random.

The probability of digit a will be:

The probability formula: P(E) = Favourable events/Total events

Put values and calculate:

P(E) = Favourable events/Total events

P(E) = 1/26

Therefore, the probability of randomly selecting alphabet a is 1/26.

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The system of inequalities to represent this scenario for Barry will be:

x + y = 12

5x + 6y ≤ 50

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Let x represents the number of hens.

Let y represents the number of roosters.

The inequality will be:

5(x) + 6(y) ≤ 50

5x + 6y ≤ 50

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the limit will go to infinity or negative infinity (depending on the sign of the function).

How do you know if a limit is infinity or negative infinity?

The limit as x approaches zero would be negative infinity, since the graph goes down forever as you approach zero from either side: As a general rule, when you are taking a limit and the denominator equals zero, the limit will go to infinity or negative infinity (depending on the sign of the function).

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The number of ways to select a simple random sample of size 5 from a population of 7 children in a family is equal to 21ways.

As given in the question,

Number of children in the family 'n' = 7

Number of simple random sample of size  = 5  ( without replacement )

Number of ways to select the children defines a population

= ⁷C₅

= ( 7! ) / ( 7 - 5 )! ( 5! )

= ( 7 × 6 × 5! )/ ( 2! ) ( 5! )

= 7 × 3

= 21 ways

Therefore, the number of ways to select children of simple random sample of size 5 is equal to 21ways.

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a)The 95% confidence interval are

0-44,44-88

b))Yes, we can claim significant reduction in the rate of intrusion attempts

We have firewall change of 14 people.

We need to compute total sum before firewall change which can be done by

(56+47+49+37+38+60+50+43+59+50+56+54+58)/14

=657/14

=46.92

Now, similarly, after firewall change total sum is

(53+21+32+49+45+38+44+33+32+43+53+46+36+48+39+35+37+36+39+45)/20

=756/20

=37.8

Now the difference between average number of intrusion attempts before and after firewall change is

(46.92-37.8)

=9.12

Now, we need to make confidence interval to only 95% of this difference=

(95×9.12)/100

=44.196=44(approx)

It means our interval range varies from 0-44,44-88 with a difference of 44.

b)Yes, we can easily claim that rate of intrusion attempts decreases.

Before firewall change, we can see average number of intrusion attempt is =46.92

After firewall change, we can see average number of intrusion attempt is

37.8

So, we can see rate of intrusion decreases on increasing the number of blocked intrusions.

For computing z-value, we just need to take square root of the difference of average number of intrusions attempst

=>Z-value= √9.12=3.01

Using the z-table, we get that for the above z-value, corresponding p-value is 0.067

Hence, the interval range is 0-44,44-88 and b)Yes we can claim, p-value is 0.067.No, this assumption does not make a difference.

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Answer:

Shelly walked 1/15 km farther

Step-by-step explanation:

We need to get a common denominator.

1/3 * 5/5 =5/15

Shelly walked 5/15 km

Kelly walked 4/15 km

Shelly walked farther

5/15 - 4/15 = 1/15

She walked 1/15 farther

Answer:

Shelly walked the furthest by 0.06 km.

Step-by-step explanation:

On a calculator (you can do it on paper, but it will take longer), take 1/3 and divide 1 by 3:

1 divided by 3 = 0.33

Then, do the same with 4/15:

4 divided by 15 = 0.27

So, Shelly walked the furthest.

To find out how much farther Shelly walked then Kelly, we simply subtract the 2 answers:

0.33 - 0.27 = 0.06

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According to the given information for the normal distribution, we can expect that the corresponding z-score may be negative.

It is given to us that -

The normal distribution has mean 11

The normal distribution has data value of 9

We have to find out if the corresponding z-score is to be positive or negative.

The z-score calculates the number of standard deviations higher or lower the mean, the data point is present.

The formula for z-score is given by -

[tex]z=\frac{data point - mean}{standard deviation}[/tex]

Although we do not have the value of standard deviation in the question, we can see that the value of

data point - mean = 9-11 = -2

So, we can see that the numerator of the z-value formula is already negative.

Thus, we can expect that the corresponding z-score may be negative according to the information provided for the normal distribution.

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The ratio of the larger circle's circumference to the smaller circle's circumference is  8π : π.

Given info;

There are two circles, one with a radius of 1/4 and the other with a radius of 2.

To know the ratio of the larger circle's circumference to the smaller circle's circumference,

Let,

Circle's circumference = π * diameter

The circumference of the smaller circle = π/2

The diameter of the larger circle = 4π

Now,

The ratio of the circumference of the larger circle to the circumference of the smaller circle is,

⇒ 4π : π/2

    8π : π

Hence, the ratio is  8π : π.

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If n pigeons are divided among k pigeonholes and k<n, then some pigeonholes contain at least two pigeons.

Pigeonhole principle- It's given a list of 89 items, 50 are available. we have to show there are at least 2 available items in the list with exactly 9 items apart.

Let's number the items in the list from 1 to 115.

Let "Ai" represents the i th available number.

Let the pigeons be the numbers in the two sequences: a1, a2, a3,...... a50 and a1 + 9, a2 + 9, ...... a50 +9.

Now, pigeonholes be the possible numbers of the items in the sequences, there are k = 89+9 = 98 possible numbers for the items in the sequence and n= 50+50=100 numbers in the two sequences.

n= 100, k=98

Since, k<n ,there are at least 2 numbers in the two sequences that are the same number by the pigeonhole principle. Then need to be some number aj in the sequence a1, a2, a3,...... a50 and some number ai + 9 in the sequence a1 + 9, a2 + 9, ...... a50 +9.

ai + 9 = aj

Thus, there are at least 2 available items ( ai and aj ) that are exactly 9 items apart.

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If you want a method to be able to alter the value of a variable that is supplied to it as an argument. The variable must be pass by reference.

Given that,

If you want a method to be able to alter the value of a variable that is supplied to it as an argument. The variable must be------.

We have to fill the blank.

We know that,

A variable is an alphabet used to represent an unknown quantity in algebra. It embodies the value. In mathematics, a variable is a value that can be changed depending on the problem. Numerous algebraic expressions and equations use the generic letters x, y, and z. Or to put it another way, a variable is a symbol for a number whose value is unknown.

Therefore, If you want a method to be able to alter the value of a variable that is supplied to it as an argument. The variable must be pass by reference.

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The correct statement that describes variance inflationary factor (VIF) is option (a) the correlation of the x variable with each other  

The variance inflationary factor ( VIF ) defined as the  measure of the amount of multicollinearity in regression analysis.

When there is a correlation between multiple independent variable in multiple regression model, then there will be multicollinearity, therefore it will adversely affect the regression result

Correlation is defined as the extend to which the two variables are linearly connected. Therefore it will change at a constant rate together

Hence, the variance inflationary factor( VIF ) measures option (a) the correlation of the x variable with each other

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Since the lengths of both diagonals are given by the square root of the sum of the squares of their coordinates, they have the same length. Therefore, the diagonals of a b c d are congruent.

Triangles with the same size, form, and arrangement are said to be congruent. This indicates that all three of the triangle' side lengths are congruent, or equal in size. Congruent triangles can be rotated or reversed, yet their congruence remains constant.

The Side-Side-Side (SSS) Congruence Postulate argues that if three sides of one triangle are identical in length to the corresponding sides of another triangle, the halves of are congruent.

If two angles and a side of one triangle are congruent to the corresponding angles and sides of another triangle, then the two triangles are congruent. As an alternative, one can apply the Angle-Side-Angle (ASA) Congruence Postulate.

How to solve?

The distance formula is given by d = √((x2 - x1)^2 + (y2 - y1)^2), where d is the distance between the two points, (x1, y1) and (x2, y2).

To find the length of diagonal a c, we plug in the coordinates of points a and c into the distance formula: d = √((c - 0)^2 + (d - 0)^2) = √(c^2 + d^2)

To find the length of diagonal b d, we plug in the coordinates of points b and d into the distance formula: d = √((a - 0)^2 + (b - 0)^2) = √(a^2 + b^2)

Since the lengths of both diagonals are given by the square root of the sum of the squares of their coordinates, they have the same length. Therefore, the diagonals of a b c d are congruent.

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There is a 2.1% chance that a random sample of 40 expectant mothers will have a mean weight increase of 16 pounds or greater if the mean second trimester weight gain for all expectant mothers is 14 pounds

Given:

In the question;

Suppose that CHDS finds the average weight increase in the second trimester is 14 pounds. Suppose also that, in 2015, a random sample of 40 expectant mothers have mean weight increase of 16 pounds in the second trimester, with a standard deviation of 6 pounds. At the 5% significance level, we can conduct a one-sided T-test to see if the mean weight increase in 2015 is greater than 14 pounds. Statistical software tells us that the p-value = 0.021.

Now, According to the question:

Since we have to test that whether the mean weight is greater than 14 pounds, so test is right tailed and if ta is the value of test static then p-value is P(t> t_a ) . Where t_a={16-14\over 6/\sqrt {40}} .

Now p-value is 0.021.

So, the correct conclusion is:

There is a 2.1% chance that a random sample of 40 expectant mothers will have a mean weight increase of 16 pounds or greater if the mean second trimester weight gain for all expectant mothers is 14 pounds

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The fundamental niche is the entire niche that an organism is capable of occupying if there was no competition. whereas, the realized niche is the niche occupied by the organism in the presence of competitors.

What is a niche?

This refers to the role an organism plays in an ecosystem/community.

Types of  niches

.The fundamental niche: This refers to the organism that is capable of occupying if there were no competitors.

. The realized niche:  This refers to organisms that exist in the presence of competitors. They are perceived to be less effective due to the presence of competitors.

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The residuals which are associated with the given x values are as follows;

A residual is the difference between what is plotted on a scatter plot at a specific point, and what the regression equation (straight line) predicts "should be plotted" at this specific point.

Consequently, the residuals in each case are;

1). For x = 1; Residual = 1 - 1 = 0.

2). For x = 2; Residual = 3 - 2 = 1.

3). For x = 3; Residual = 2 - 3 = -1.

4). For x = 4; Residual = 4.5 - 4 = 0.5.

5). For x = 5; Residual = 5 - 5 = 0.

Ultimately, the residual values are as listed above.

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Answer:

No, it is not possible to create a triangle with these measurements.

Step-by-step explanation:

It must follow these rules:

a + b > c

b + c > a

a + c > b

The average rate of change of function is 10.2 inches per day

The equation to show the height of the flower is

g(n) = 10(1.02)n

Where g(n) is the height of the flower

n is the number of days

The value of n is from n = 1 to n = 5

The average rate of change of the function = f(5) - f(1) / 5 -1

Then,

f(5) = 10(1.02)(5)

= 51 inches

f(1) = 10(1.02)(1)

= 10.2 inches

Substitute the values in the equation

The average rate of change of function = 51 - 10.2 / 5 - 1

= 40.8 / 4

= 10.2 inches per day

Hence, the average rate of change of function is 10.2 inches per day

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For the given a sample of 80 students further divided in subgroups like 20 freshman, 20 juniors ,20 sophomores and 20 senior on the basis of how much time they spent to complete their maths homework last night. This is random sampling, the method which used here is Stratified Sampling.

A sample is a specific group of people from whom we collect data.

Stratified Sampling:

In statistics, a simple random sample is a subset of people selected from a larger set in which subsets of people are randomly selected, all with equal probability. This is the process of randomly selecting samples.

In stratified sampling, a population is divided into subpopulations that may differ in important ways. By ensuring that each subgroup is well represented in your sample, you can draw more precise conclusions.

To use this sampling method, divide the population into subgroups (called strata) based on relevant characteristics (gender identity, age group, income class, occupational role, etc.).

Calculate how many people to sample from each subgroup based on the total population percentage. Then use random or systematic sampling to select one sample from each subgroup.

Using the same sampling technique, subsample of students based on the amount of time they spent completing their math homework.

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The solution of 1234 x 4321 using Karatsuba  multiplication is 5332114

Given,

1234 x 4321

We have to find the solution using Karatsuba  multiplication;

Karatsuba multiplication;

The first multiplication algorithm that was asymptotically quicker than the quadratic "grade school" technique was the Karatsuba algorithm. For sufficiently big n, the Schönhage-Strassen algorithm (1971) is even faster than the Toom-Cook algorithm (1963), which is a faster generalisation of Karatsuba's approach.

Here,

1234 x 4321

Lets see,

12      +      34       =      46

×                 ×                 ×

43     +      21       =       64

                                 2944 -

516    +   714      =      1230

                                 1714

Now,

516 × 100² + 714 + 1714 x 100 = 5332114

That is,

The solution of 1234 x 4321 using Karatsuba  multiplication is 5332114

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The three properties of parallel lines are transitive property of parallel lines, symmetric properties of parallel lines and properties cut by transversal.

Properties of parallel lines when cut by a transversal

Two lines when cut by a transversal line are parallel if the corresponding angles so formed are equal. Generally, the corresponding angles are in relative positions and lie along the same side of the transversal.

Two lines cut by a transversal line are said to be parallel if the alternate interior angles so formed are equal. In general, the pairs of the alternate interior are found in the inner side but lie on the opposite sides of the transversal.

Two lines cut by a transversal line are said to be parallell if the alternate exterior angles so formed are equal. In general, the pairs of alternate exterior angles are found on the outer side but lie opposite each other.

The above mentioned are 3 properties of parallel lines.

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