If the range of X is the set {0,1,2,3,4,5,6,7,8} and P(X=x) as defined in the following table:
x 0 1 2 3 4 5 6 7 8
P(X=x) 0.06528 0.3870 0.03062 0.0968 0.06913 0.0968 0.04846 0.01252 0.1935
Determine the mean and variance of the random variable.
(a) mean
(b) variance

Answer:

7.57082 or its just 7.5

The client was charged $85 to get a job that earns $1500

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

Let y represent the total cost for the client.

A job hotline service charges $25 plus a 4% commission, c, on the first month of earnings, hence:

y = 4% of c + 25

y = 0.04c + 25

The client earns $1500 the first month, hence:

y = 0.04(1500) + 25 = $85

The client was charged $85

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Implementing an expansion strategy, attracting capital, lowering tax obligations, facilitating entry into a business, and utilizing limited liability are all options are correct.

In most cases, a corporation is set up to benefit from restricted liability. This indicates that the shareholders, who are the corporation's owners, are not personally liable for the debts and liabilities of the business. The additional reasons you have provided for forming a corporation are also viable possibilities, but they are not its main objective. Establishing a corporation might be one approach to carry out an expansion strategy, which is a company's plan for growth and expansion.

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P(x)=ax⁵+bx⁴+cx³+12 is the polynomial which has 4 terms and vertical axis at y=12 and the degree is 5

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

The standard form of a polynomial equation with a leading degree is 5 is expressed as P(x)=ax⁵+bx⁴+cx³+dx+e

Since the polynomial should have only 4 terms, the standard form of the equation will be P(x)=ax⁵+bx⁴+cx³+d

d is the constant

Since the graph of the Polynomial crosses the vertical axis at y = 12, hence the constant value "d" will be 12.

Substituting the constant value, the required equation of the polynomial will be expressed as P(x)=ax⁵+bx⁴+cx³+12

Hence, P(x)=ax⁵+bx⁴+cx³+12 is the polynomial which has 4 terms and vertical axis at y=12 and the degree is 5

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The interval for the proportion of 16- to 17- year old's who text while driving at 95% confidence (0.30717,0.37283).

a) The value of the point estimate is 0.34

b) The corresponding critical value [tex]$Z_{\alpha / 2}$[/tex] is 0.025

c) Margin of error is 0.016748134224444

d) The interval is (0.30717,0.37283)

As per the given data we have to obtain a 95% confidence interval for the proportion of 16- to 17- year olds who text while driving.

a)

[tex]\hat{p}=\frac{X}{N}=\frac{272}{800}[/tex]

= 0.34

b)

Calculate α:

α = 1 - Confidence Percentage

α = 1 - 0.95

α = 0.05

Find α spread range:

[tex]& \alpha=\frac{1}{2} (\alpha) \\[/tex]

[tex]& \alpha=\frac{1}{2} (0.05) \\[/tex]

α = 0.025

From the z-score table:

[tex]\text { z score }_{0.025}=1.96[/tex]

The z-score table is attached at the end of the solution.

c)

Calculate [tex]$\sigma_p$[/tex]

[tex]& \sigma_p=\frac{\sqrt{\hat{p}\left(1-\hat{p}\right)}}{\sqrt{N}} \\[/tex]

[tex]& \sigma_p=\frac{\sqrt{0.34(1-0.34)}}{\sqrt{800}} \\[/tex]

[tex]& \sigma_p=\frac{\sqrt{0.34(0.66)}}{\sqrt{800}} \\[/tex]

[tex]& \sigma_p=\frac{\sqrt{0.2244}}{\sqrt{800}} \\[/tex]

[tex]& \sigma_p =\sqrt{0.0002805} \\[/tex]

[tex]& \sigma_p[/tex] = 0.016748134224444

Calculate Margin of Error:

Margin of Error =[tex]\sigma_p[/tex] × z-Score

Margin of Error = 0.016748134224444 × 1.96

Margin of Error = 0.032826343079911

d)

Calculate high-end confidence interval total:

High End [tex]=\hat{p}+$ zscore $_a \times \sigma_p$[/tex]

High End = 0.34 + 1.96 × 0.016748134224444

High End = 0.34 + 0.032826343079911

High End =0.3728

Calculate low-end confidence interval total:

Low End [tex]=\hat{p}-$ Zscore $_{\mathrm{a}} \times \sigma_{\mathrm{p}}$[/tex]

Low End =0.34-1.96 × 0.016748134224444

Low End = 0.34 - 0.032826343079911

Low End =0.3072

Now we have everything, display our 95 % confidence interval:

0.3072 < p < 0.3728

This means that if we use the same sampling method to select different Samples and computed an interval estimate for each sample, our true population proportion (b) will fall between our confidence Interval (0.30717,0.37283) 95 % of the time.

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In the 2009 Parent-Teen Cell Phone Survey conducted by Princeton Survey Research Associates International, 800 randomly sampled 16- to 17- year olds living in the United States were asked whether they have ever used their cell phone to text while driving. Of the 800 teenagers surveyed, 272 indicated that they text while driving. Obtain a 95% confidence interval for the proportion of 16- to 17- year olds who text while driving.

A) Determine the point estimate: [tex]$\hat{p}=\frac{x}{n^{\prime}}$[/tex] and [tex]$\hat{q}=1-\hat{p}$[/tex]

B) Find the corresponding critical value [tex]$Z_{\alpha / 2}$[/tex]

Confidence Level            Critical Value([tex]$\mathbf{Z}_{\boldsymbol{\alpha} / \mathbf{2}}$ \\[/tex])

           90 %                                 1.645

           95 %                                 1.96

           98 %                                 2.33

           99 %                                 2.575

C) Determine the Error

[tex]$$E=Z_{a / 2} \sqrt{\frac{\hat{p} \hat{q}}{n}}$$[/tex]

D) Construct the interval

[tex]\hat{p}-E < p < \hat{p}+E[/tex]

The probability of having a total of more than 180 arrivals at the toll in the next two hours is 0.84.

The time taken to assemble follows the normal distribution.

Given mean i.e. μ = 100

Given standard deviation i.e. σ = 40

The normal random variable of a standard normal distribution is called a standard score or a z-score. Every normal random variable X can be transformed into a z score via the following equation:

z=(X−μ)/σ

where X is a normal random variable, μ is the mean of X, and σ is the standard deviation of X.

For X=180

Z=(180−100)/40= 2

For X=2

Z=(2-2)/2=0

P(a<X<b)=P(X<b)–P(X<a)

P(20<X<22)=P(X<180)−P(X<2)

                   =P(Z<2)−P(Z<0)

                    =0.8413

Thus, The probability of having a total of more than 180 arrivals at the toll in the next two hours is 0.84.

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As per the given standard deviation, the probability of having a total of more than 180 arrivals at the toll in the next two hours is written as 0.84.

Here we have given that the number of arrive at a highway toll in an hour is independent of other hours and is well-estimated by a Normal distribution with an average of 100 cars per hour and standard deviation 40 cars.

Which means that

mean  = 100

And the value of standard deviation = 40

Now, we have to use the normal random variable of a standard normal distribution is called a standard score or a z-score.

Then the value of z score is calculated as

=> z=(X−μ)/σ

Apply the values on it then we get

=> z = (180−100)/40= 2

Therefore, the probability is calculated as

=> P(20 < x <22) = P(X<180)−P(X<2)

When we apply the value on it then we get,

=> P(Z<2) − P(Z<0)

=> P = 0.8413

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Swim practice will be no more than 35 laps is P≤35.

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Complete Question is: Write an inequality for each sentence.

1. Swim practice will be no more than 35 laps.

Using sine and cosine law, the value of x is 7.2 unit

Cosine law is a mathematical formula used to calculate the sides and angles of a triangle when the lengths of all three sides are known. It states that the square of a side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of those sides and the cosine of their included angle.

Using cosine law, we can find the length of A which will in turn assist us in finding the value of x

a² = 12² + 10² -2(12)(10) cos80

a² = 202.32

a = √202.32

a = 14.22

Using sine law;

a / sin A = x / sin X

Substituting the values into the formula

14.22 / sin 80 = x / sin 30

x = 14.22sin30 / sin80

x = 7.2

The value of x is 7.2

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We generally use scatter plots to observe the relationship between variables. Dots are used in a scatter plot to represent values for two different numeric variables.

Values for an individual data point are indicated by the position of each dot on the horizontal and vertical axis.  A scatter plot represents data points on a two-dimensional plane or on a Cartesian system.

On the X-axis, the independent variable is marked and the dependent variable is marked on the Y-axis. We call these plots as scatter plots or scatter diagrams. Scatter plots can be defined as one of the most useful inventions in statistical graphs. In 1833, it was presented by an English Scientist, John Frederick W. Herschel.

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Answer: standard form: 2.3x 10⁴

               expanded form: 23.082

Answer:

Step-by-step explanation:

Answer: Obtuse

Step-by-step explanation:

A right angle is an angle that is aqual to 90°. A 90° angle looks something like this: ∟. An obtuse angle is an angle tha mesures larger than that, like this: ⦦. An Acute angle is an angle that has a smaller angle mesaure than 90°. An acute angle looks smething like this: ⦟. Hope this helps, good luck.

The score 3 months ago is 2.31 If The team's engagement score was 4. 6 this month and The score has been improving at a rate of 11% per month.

Simple Interest (S.I) is the method of calculating the interest amount for some principal amount of money. Have you ever borrowed money from your siblings when your pocket money is exhausted? Or lent him maybe? What happens when you borrow money? You use that money for the purpose you had borrowed it in the first place. After that, you return the money whenever you get the next month’s pocket money from your parents. This is how borrowing and lending work at home.

given,

employee engagement score this month= 4.6

rate of improvement = 1%

to find,

the employee engagement score 3 months ago

solution,

to find the employee engagement score 5 months ago, we can use the formula given below :

A= P [tex]( 1 + \frac{R}{100} ) ^{n}[/tex]

where:

A = current employee engagement score

P = initial employee engagement score

n = time period

4.6 = P [tex](1+\frac{11}{100} )^{3}[/tex]

4.6 = P [tex](\frac{111}{100} )^{3}[/tex]

P= 2.31

therefore, 3 months ago, the employee engagement score was 2.31.

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If the team's engagement score was 4. 6 this month, then with a improving rate of 11% per month, the score 3 months ago is approximately 3.46.

Therefore, the engagement score 3 months ago was approximately 3.46.

To find the engagement score 3 months ago, we need to first find the rate of improvement over 3 months. We can do this by multiplying the monthly rate of improvement by 3. So the rate of improvement over 3 months is

11% × 3 = 33%

If rate of improvement over 3 months is 33%, then

((current engagement score) - (score 3 months ago))/(score 3 months ago) × 100 = 33

that is

[tex]\frac{(current\ engagement\ score) - (score\ 3\ months\ ago)}{score\ 3\ months\ ago} \ 100 = 33[/tex]

Let score 3 months ago be a, then

(4.6 - a)/ a × 100 = 33, that is

[tex]\frac{4.6\ -\ a}{a} \ 100 = 33[/tex]

Multiplying by a and dividing by 100 on both sides

4.6 - a = 0.33a

Adding a on both sides

1.33a = 4.6

Dividing by 1.33

a = 4.6/ 1.33

a ≈ 3.46

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Answer:

3 1/3+2 3/4 = 73/12=6 1/12

Step-by-step explanation:

1.Conversion a mixed number 3  1/3 to a improper fraction: 3 1/3 = 3  1/3 = 3 · 3 + 1/3 = 9 + 1/3= 10

2.Conversion a mixed number 2  3/4 to a improper fraction: 2 3/4 = 2  3/4 = 2 · 4 + 3/4 = 8 + 3/4= 11

3.Add: 10/3 + 11/4 = 10 · 4/3 · 4 + 11 · 3/4 · 3 = 40/12 + 33/12 = 40 + 33/12 = 73/12

Answer: 42

Step-by-step explanation: you have to find the rule, which is 4, which means b X 4 = 168, and 168 divided by 4 = 42.

The missing value for the letter B is 42.

Given is that a teacher gives pens and pencils to elementary students at an equal rate.

Since the rate is equal, we can write -

(140 - 72)/(35 - 18) = (168 - 140)/(B - 35)

68/17 = 28/(B - 35)

68(B - 35) = 28 x 17

B - 35 = 7

B = 42

Therefore, the missing value for the letter B is 42.

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The expression startroot 64 r superscript 8 baseline endroot can be written as (64)1/8r8.

This expression is asking for us to take the eighth root of 64, and then multiply it by 8. To solve this we can use the formula for radicals, which states that the nth root of a number a is equal to a1/n. In this case, n is equal to 8, and a is equal to 64. Therefore, the expression can be rewritten as 641/8 x 8. This simplifies to 8r2.

To calculate this, we first need to calculate the eighth root of 64, which can be done by raising the number to the power of the reciprocal of the root. In this case, we need to calculate 64^1/8. We can use a scientific calculator to find that the eighth root of 64 is 2. To finish the calculation, we simply multiply 2 by 8, which gives us 16. We can rewrite 16 as 8r2, which is the answer to the expression.

Therefore, the simplified expression is 8r2.

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The simplified form of expression √(64r^8) is  8r^4

The correct answer is an option (b)

In this question we have been given an expression startroot 64 r superscript 8 baseline endroot.

i.e., √(64r^8)

We need to simplify this expresison.

We know that 64 is square of 8.

8^2 = 64

So, we can write given expression as,

√(64r^8)

= √(8^2r^8)

= √[8^2r^(2 * 4)]

We know that for the properties of exponents i.e., non-zero numbers a, m,n

(a^m)^n = a^(m * n)                    ............(1)

So, √[8^2r^(2 * 4)]

= √[8^2(r^4)^2]            

= √((8r^4)^2)

Square-root is nothing but the 1/2 power of number/expression.

i.e., √((8r^4)^2)

= [(8r^4)^2]^1/2

=  (8r^4)^(2 * 1/2)                  ...........(from (1))

= (8r^4)^1

= 8r^4

Therefore, √(64r^8)  =  8r^4

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The relationship is proportional when John works for the hour allocated.

Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportional relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of that constant.

Because the rate of change in a proportional relationship is constant (and equal to the constant of proportionality), it is a linear relationship.

In this case, when John works for an hour, he is paid $15, when he works for 2 hours, he's paid $30.

The constant will be:

= 15 / 1 or 30/2

= $15 per hour.

Therefore, it's a proportional relationship.

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When John works for an hour, he is paid $15, when he works for 2 hours, he's paid $30. Is the relationship proportional?

Since Elena's distances and times for a training run are given by the equation y = 8.5x, Tyler’s pace per minute is equal to 8.2 miles per minute.

In order to determine Tyler’s pace per minute, we would have to determine the rate of change (slope).

Mathematically, the rate of change is also referred to as slope and it can be calculated by using this formula;

Rate of change (slope), m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change (slope), m = (y₂ - y₁)/(x₂ - x₁)

Next, we would determine the rate of change with respect to Tyler’s pace per minute, with the following data points (0, 0) and (1, 8.2):

Rate of change (slope), m = (0 - 8.2)/(0 - 1)

Rate of change (slope), m = -8.2/-1

Rate of change (slope), m = 8.2.

Therefore, Tyler’s pace per minute is 8.2 miles per minute.

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Complete Question:

Tyler and Elena are on the cross country team. Tyler’s distances and times for a training run are shown on the graph. Elena's distances and times for a training run are given by the equation y = 8.5x, calculate Tyler’s pace per minute.

The solution is Option B.

The transformation of the function is a reflection along the vertical y axis

Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.

The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Given data ,

Let the function be represented as f ( x )

Now , the transformed function is given as g ( x )

The function g ( x ) has the x coordinates as the additive inverse

So , it must be a reflection transformation

And , the axis of transformation is y axis

So , when you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y)

Therefore , it is a vertical reflection

Hence , the transformation of the function f ( x ) is a reflection

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Answer:

a² + 5

Step-by-step explanation:

a² = The square of a number.

Then:

Five plus the square of a number is:

a² + 5

The system does appear to have a solution after the changes.

The equation of the orange line after the changes is y = -x - 3. The system appears to have a solution after the changes because the equations for both lines are in the same form. The blue line has a slope of -5 and the orange line has a slope of -1. This means that the lines have the same slope and the same y-intercept. This means that the two lines are parallel and will intersect at the point (-3,3).

To calculate the point of intersection, we can plug in -3 for x in both equations and solve for y.

For the blue line: y = -(-3)^5 = 3

For the orange line: y = -(-3) - 3 = 3

This means that the point of intersection for these two lines is (-3,3). Therefore, the system does appear to have a solution after the changes.

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The total amount of cash = $247. The total deposit = $248.22.The dollars received in cash = $247. The cents received in coins = 22 cents.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

For the first check for $223.47, you will receive 2 ten-dollar bills, 2 one-dollar bills, and 47 cents in coins. The total amount in cash received for this check is $223.

For the second check for $24.75, you will receive 3 one-dollar bills, 10 quarters, and 10 dimes. The total amount in cash received for this check is $24.

The total amount of cash received for both checks is $223 + $24 = $247.

The total deposit for both checks is $223.47 + $24.75 = $248.22.

The dollars received in cash for both checks is $247.

The cents received in coins for both checks is 22 cents.

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The simple interest gained on $1050 deposited at an interest rate of 2% for 9 months = $ 15.75.

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time.

The formula for simple interest is given by

Simple interest = PRT/100  

Where, P = Principal amount

R = Rate of interest

T = Time period

Here we have

$1050 deposited at an interest rate of 2% for 9 months.  

=> Principal amount, P = $ 1050

=> Time period, T = 9 months = 9/12 years

=> Rate of interest, R = 2 %

By the given formula,

Simple interest = 1050(2)(9/12)/100  

= 105(9/6)/10  

= 105(3/2)/10  

= 105(1.5)/10

= 15.75

Therefore,

The simple interest gained = $ 15.75.

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Answer:

1 or 21

Step-by-step explanation:

Answer:

Step-by-step explanation:

14

Answer:

14 will be your answer for that question

The sum of first square number and the first cube number would be 2.

What is the cube of a number?

A cube of a number is the number multiplied by itself three times. For example, the cube of 2 is 2 x 2 x 2 = 8. It can also be represented mathematically by raising the number to the power of 3, such as x^3 where x is the number you want to find the cube of.

The first square number is 1^2 = 1 and the first cube number is 1^3 = 1. Therefore, the sum of the first square number and the first cube number is 1 + 1 = 2.

Hence, the sum of first square number and the first cube number would be 2.

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a) The linear function to find the annual excess fuel as a function of the number of years since 2000 is given as follows: y = 2.4x + 35.

b) The estimate for the consumption in 2011 is given as follows: 61.4 gallons.

The yearly increase in the consumption is constant, meaning that a linear function is used to model this situation.

The slope-intercept definition for the linear function is given as follows:

y = mx + b.

In which:

The consumption increases by about 2.4 gallons per person each year, hence the slope is of:

m = 2.4.

In 2005, which is five years after 2000, the excess consumption was of 47 gallons, hence the intercept b is calculated as follows:

47 = 2.4(5) + b

b = 47 - 2.4(5)

b = 35.

Meaning that the function is defined as follows:

y = 2.4x + 35.

2011 is 11 years after 2000, hence the estimate is obtained as follows:

y = 2.4(11) + 35

y = 61.4 gallons.

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On solving the provided question, we can say that - in the equation 2x + 5 the value of the equation is = 11

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

here, we have

2x + 5

and given that x= 5

so answer is 11

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The function an = -4 + 5(n - 1) in slope intercept form is an = 5n - 9

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

an = -4 + 5(n - 1)

The slope-intercept form of a linear equation is represented as

an = mn + c

Where the variable m is the slope and the variable c is the y-intercept

So, the first step in solving the question is to open the bracket in an = -4 + 5(n - 1)

This gives

an = -4 + 5n - 5

Add -5 and -9

an = 5n - 9

Hence, the representation of the equation is an = 5n - 9

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When [tex]$a < 1$[/tex][tex]$\delta=-1 \pm j \sqrt{2 a} \rightarrow$[/tex] Here two solutions oscillate when a is negative, the system has repeated eigen value when [tex]$a=0$[/tex], when [tex]$a=0$\\[/tex], then both solutions decay exponentially without oscillating,

The given Vector equation, When a is negative real number then both solutions grow exponentially with system oscillating.

[tex]$$\left.\begin{array}{l}y^{\prime}=\text { Ay } \\A=\left(\begin{array}{cc}-1 & a \\2 & -1\end{array}\right)\end{array}\right\}[/tex]

Now we will solve 2-

           [tex]$$|A-\delta I|=\left|\begin{array}{cc}-1-\lambda & a \\2 & -1-\lambda\end{array}\right|=0$$[/tex]

Now multiply, we get.

[tex]$$\begin{aligned}& (-1-\lambda)(-1-\lambda)-2 a=0 \\& 1+2 \lambda^2-2 a=0 \\& s^2+2 \lambda+1-2 a=0 \text { (1) }\end{aligned}$$[/tex]

Now we will find both 2 values of d.

[tex]$\left(\begin{array}{c}\text { if } a x^2+b x+c=0 \\ d=\frac{-2 \pm \sqrt{(2)^2-(4)(1)(1-2 a)}}{2(1)} \leftarrow\left(x=\frac{-b \pm \sqrt{b^2-4-a c}}{2 a}\right.\end{array}\right)$$$[/tex]

[tex]& =-1 \pm \frac{1}{2} \sqrt{4-4+8 a} \\\lambda & =-1 \pm \sqrt{2 a} .\end{aligned}$$[/tex]

(a) when [tex]$a < 1$[/tex][tex]$\delta=-1 \pm j \sqrt{2 a} \rightarrow$[/tex] Here two solutions oscillate when a is negative.

(b) put [tex]$a=0$[/tex]

[tex]$$\begin{aligned}& d=-1 \pm \sqrt{2 a} \\& d=-1 \pm \sqrt{2 \times 0} \\& d=-1 \pm 0 \\& r=-1\end{aligned}$$[/tex]

mean [tex]$s_1=\sqrt{2}_2=-1$[/tex], here system has repeated eigen value when [tex]$a=0$[/tex]

(c) when [tex]$a=0$\\[/tex], then both solutions decay exponentially without oscillating.

(d) Now, when use put [tex]$a=2$.[/tex]

[tex]$$\begin{aligned}& \delta=-1 \pm \sqrt{2 a} \\& \text { when } \\& a=2 \\& \delta=-1 \pm \sqrt{2 \times 2} \\& s_1=-1 \pm 2 \\& \delta_1=1\end{aligned}$$[/tex]

In the one of the solution decay exponentially and the other Grow exponentially.

(e). When a is negative real number then both solutions grow exponentially with system oscillating.

Therefore,When [tex]$a < 1$[/tex][tex]$\delta=-1 \pm j \sqrt{2 a} \rightarrow$[/tex] Here two solutions oscillate when a is negative, the system has repeated eigen value when [tex]$a=0$[/tex], when [tex]$a=0$\\[/tex], then both solutions decay exponentially without oscillating,

The given Vector equation, When a is negative real number then both solutions grow exponentially with system oscillating.

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The value of n in the vertical angles is 5 4 / 5.

Vertical angles are angles that are opposite of each other when two lines intersect each other.

Vertical angles share the same vertex. Vertically opposite angles are congruent to each other.

The measures of the two angles are 2n + 18 and 7n - 11. They are vertical angles.

Therefore, the two vertically opposite angles are congruent to each other. We will use the congruency to find the value of n in the equation.

2n + 18 = 7n - 11

2n - 7n = -11 - 18

-5n = -29

divide both sides by -5

n = -29 / -5

n = 29 / 5

Therefore,

n = 5 4 / 5

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