i need help please hurry.

The solution to the given integral equation is: f(t) = e^t - 1 + t - te^t

To solve the given integral equation using Laplace transform, we first take the Laplace transform of both sides of the equation.

Using the linearity property of the Laplace transform, we have:
L{f(t)} + L{t(t - τ)f(τ)} = L{t}

where L denotes the Laplace transform operator.

We can simplify the second term on the left-hand side using the convolution property of the Laplace transform:
L{t(t - τ)f(τ)} = L{t} * L{(t - τ)f(τ)}

where * denotes convolution. The Laplace transform of (t - τ)f(τ) is:
L{(t - τ)f(τ)} = F(s) - sF(s)

where F(s) is the Laplace transform of f(t). Substituting this in the above equation, we get:
L{t(t - τ)f(τ)} = L{t} * (F(s) - sF(s)) = L{t}F(s) - sL{t}F(s)

Using the Laplace transform of t, we have:
L{t} = 1/s^2

Substituting this in the above equation, we get:
L{t(t - τ)f(τ)} = F(s)/s^2 - F(s)/s = F(s)(1/s^2 - 1/s) = F(s)(1 - s)/s^2

Substituting all these in the original equation and rearranging, we get:
F(s) = s^2/(s^3 - s^2)

To find the inverse Laplace transform of this expression, we can use partial fraction decomposition. Factoring the denominator, we get:
s^3 - s^2 = s^2(s - 1)

Therefore, we can write:
F(s) = s^2/(s^2(s - 1)) = 1/(s - 1) - 1/s + s/(s^2(s - 1))

Taking the inverse Laplace transform of each term using standard Laplace transform tables, we get:
f(t) = e^t - 1 + t - te^t

So the solution to the given integral equation is:
f(t) = e^t - 1 + t - te^t

Know more about the integral equation here:

https://brainly.com/question/22008756

#SPJ11

A definite integral is a numerical value that represents the area under a curve between two specific endpoints. It is calculated by evaluating the integral over a specific range of values.

True or false: Evaluating a definite integral is always a well-conditioned problem.

Answer: False.

Evaluating a definite integral is not always a well-conditioned problem. A well-conditioned problem refers to a problem in which small changes in the input produce small changes in the output, making the problem stable and easier to solve numerically. In the context of definite integrals, this means that slight variations in the integrand or the limits of integration should result in minor changes in the integral's value.

However, there are cases where evaluating a definite integral becomes an ill-conditioned problem. This occurs when the integrand function or the integration domain have particular features that make the problem sensitive to small changes in input, such as rapidly oscillating functions, singularities, or functions with high gradients. In these cases, small perturbations in the input can lead to significant changes in the output, making the problem ill-conditioned.

To deal with ill-conditioned problems, it is essential to use appropriate numerical methods, such as adaptive quadrature or specialized techniques like the Gauss-Kronrod or Clenshaw-Curtis methods. These methods can help improve the accuracy and stability of the definite integral evaluation in challenging cases.

In conclusion, evaluating a definite integral is not always a well-conditioned problem, as there are situations where the problem becomes ill-conditioned due to specific features in the integrand function or the integration domain.

To know more about definite integral visit:

https://brainly.com/question/29974649

#SPJ11

The given statement "the irregular variation component of a time series measures the over-all general directional movement over a long period of time." is true because the overall behavior of the series and make more accurate predictions about future trends.

The irregular variation component of a time series can be defined as the part of the series that is not explained by any of the other components, such as the trend, seasonal, or cyclical components. This means that it represents the random fluctuations in the series that are not due to any underlying pattern or trend. In other words, it measures the extent to which the series deviates from its expected value at any given point in time.

Mathematically, the irregular variation component can be expressed as the difference between the observed value of the time series at a particular point in time and the expected value of the series at that same point in time, given the other components of the series.

The irregular variation component is important because it can provide insight into the underlying causes of the random fluctuations in the time series.

To know more about variation here

https://brainly.com/question/28107529

#SPJ1

the probability that a randomly sampled individual is AS is 4/9.Let's first write out the possible combinations of alleles an individual can have from their parents: AA, AS, AC, SS, SC, and CC.

Since we know that an individual can be AS by getting A from one parent and S from the other OR S from one parent and A from the other, we need to consider both possibilities.

The probability of getting A from one parent is 2/3 (since AA, AS, and AC all have at least one A allele), and the probability of getting S from the other parent is 1/3 (since SS and AS have an S allele). Thus, the probability of being AS from this scenario is (2/3) * (1/3) = 2/9.

Now, we also need to consider the opposite scenario, where an individual gets S from one parent and A from the other. The probabilities of getting S and A are the same as before, but we need to switch them around. Thus, the probability of being AS from this scenario is also (2/3) * (1/3) = 2/9.

Adding these two probabilities together, we get:

P(AS) = 2/9 + 2/9 = 4/9

Therefore, the probability that a randomly sampled individual is AS is 4/9.

To  learn  more about probability click here :brainly.com/question/32004014

#SPJ11

The angle of slope of the wire is approximately 12.34 degrees.

Now, To find the angle of slope of the wire, we can use trigonometry.

Let's the height of the taller pole H and the height of the shorter pole h.

We can also call the midpoint of the wire M, where it joins the two poles.

Now, Using the Pythagorean theorem, we can find the distance between the midpoint M and the ground:

d = √(12 - ((H-h)/2))

Now, we can use trigonometry to find the angle of slope of the wire:

tan(θ) = (H - h) / 2d

Substituting the values we have:

tan(θ) = (20 - 15) / (2 * √(12 - ((20-15)/2)))

Simplifying this expression gives us:

tan(θ) = 5 / (2 * √(12 - (2.5)))

tan(θ) = 5 / (2 * √(144 - 6.25))

tan(θ) = 5 / (2 * 11.644)

tan(θ) = 0.214

Taking the arctan of both sides, we get:

θ = arctan(0.214)

θ ≈ 12.34 degrees

Therefore, the angle of slope of the wire is approximately 12.34 degrees.

Learn more about the angle visit:;

https://brainly.com/question/25716982

#SPJ1

A data of cases of diabetes from the centers for disease control and prevention, the probability that the combined sample tests positive with at least 1 of the 10 people having diabetes is equals to 0.04218.

We have a data from the centers for disease control and prevention.

The rate of new cases of diabetes

= 4.3 per 1000

So, probability ( diabetes) =[tex] \frac{4.3}{1000}[/tex] = 0.0043

Using complement rule, Probability for no diabetes people, P( no diabetes)

= 1 - 0.0043 = 0.9957

Now, blood samples from 10 is randomly selected. It is assumed that each of these different people having diabetes is independent events. Using multiplcation rule for independent events, P( All 10 have no diabetes )

= P( no diabetes)× P( no diabetes)×....× P( no diabetes) ( 10 times)

= ( P( no diabetes))¹⁰ = 0.9957¹⁰

= 0.957823

Using complement rule, P ( atleast 1 the 10 people having diabetes) = 1 - P( All 10 have no diabetes ) = 1 - 0.957823

= 0.04218

Since, probability value is small so it is unlikely that a combined sample test. Hence, required probability is 0.04218.

For more information about probability, refer:

https://brainly.com/question/25870256

#SPJ4

To find h'(3) given h(x) = f(x) xg(x), we use the product rule of differentiation:

h'(x) = f'(x) xg(x) + f(x) g(x) + f(x) xg'(x)

We are not given the functions f(x) and g(x), but we can use the given graphs to estimate their values near x = 3. Let's say that f(3) = 2 and g(3) = 5. We also need to estimate f'(3) and g'(3) in order to calculate h'(3). We can estimate these values using the slopes of the tangent lines to the graphs at x = 3.

Let's say that the slope of the tangent line to the graph of f(x) at x = 3 is 1, and the slope of the tangent line to the graph of g(x) at x = 3 is 3. Then we have:

f'(3) ≈ 1

g'(3) ≈ 3

Substituting these values into the product rule for h'(x), we get:

h'(x) = f'(x) xg(x) + f(x) g(x) + f(x) xg'(x)

h'(3) = f'(3) 3 g(3) + f(3) g(3) + f(3) 3

h'(3) = (1)(3)(5) + (2)(5) + (2)(3)

h'(3) = 19

Therefore, h'(3) is approximately equal to 19, based on the given graphs and our estimates of f'(3) and g'(3).

To learn more about differentiation refer below

https://brainly.com/question/31492852

#SPJ11

The length of the pole corrected to three significant figures is L = 29.6 m

Given data ,

Let the length of the pole be represented as L

Now , the value of L is given by

L = 29.6 m

And , trailing zeros are only significant if the number contains a decimal point

where 29.60 has 4 significant figures

Hence , the length of the pole rounded to 3 figures is 29.6 m

To learn more about rounding up off numbers click :

https://brainly.com/question/4896544

#SPJ1

Answer:

A, C, D

Step-by-step explanation:

30/90 reduces to 1/3

A) reduces to 1/3

B) reduces to 1/2

C) reduces to 1/3

D) 1/3

E) reduces to 1/2

F) 2/3

Hope this helps! :) happy studies!

The values in cells A9 to E13 will give you the solution to the system of linear equations

To solve the system of linear equations using an Excel spreadsheet, we can use the matrix method. We'll set up the equations in matrix form and use Excel's matrix functions to find the solution.

1. Open a new Excel spreadsheet.

2. In cells A1 to E1, enter the variables: a, b, c, d, e.

3. In cells A2 to E6, enter the coefficients of the variables for each equation:

Equation 1: 2.5  -1    0    1.5  -2

Equation 2: 3     4    -2   2.5  -1

Equation 3: -4    3    1     -6    2

Equation 4: 2     3    1     -2.5  4

Equation 5: 1     2    5     -3    4

4. In cells A7 to E7, enter the constants on the right-hand side of each equation:

Equation 1: 57.1

Equation 2: 27.6

Equation 3: -81.2

Equation 4: -22.2

Equation 5: -12.2

5. In cells A9 to E13, use Excel's matrix formula `=MINVERSE(A2:E6)*A7:E7` to calculate the solution. This formula calculates the inverse of the coefficient matrix and multiplies it by the constant matrix.

6. The values in cells A9 to E13 will give you the solution to the system of linear equations. These values represent the variables a, b, c, d, and e, respectively.

That's it! Excel will calculate the solution for the system of linear equations using the matrix method.

Learn more about Equations here

https://brainly.com/question/29050831

#SPJ4

The area of the region bounded by the given curves, we need to first identify the points of intersection between the two curves. Setting y = 3x^2 ln x equal to y = 12 ln x, we get: 3x^2 ln x = 12 ln x 3x^2 = 12 x^2 = 4 x = ±2 So the two curves intersect at x = 2 and x = -2.

To find the area of the region bounded by the given curves y = 3x^2 ln(x) and y = 12 ln(x), we first need to determine the points of intersection between the two curves. To do this, set the two functions equal to each other:
3x^2 ln(x) = 12 ln(x)
Divide both sides by ln(x) and 3:
x^2 = 4
Take the square root of both sides:
x = ±2
Since ln(x) is only defined for positive x-values, we disregard the negative solution. Thus, the points of intersection occur at x = 2.
Now, we will set up an integral to calculate the area between the curves. Since the first curve is above the second curve in the given interval, we'll integrate their difference:
Area = ∫[3x^2 ln(x) - 12 ln(x)] dx from 1 to 2
To evaluate the integral, use integration by parts or a numeric method (such as a calculator or software) to find the approximate value.
Area ≈ 4.67 square units
In summary, the area of the region bounded by the given curves y = 3x^2 ln(x) and y = 12 ln(x) is approximately 4.67 square units.

To know more about integral visit:

https://brainly.com/question/31744185

#SPJ11

Given the fraction 3/10 and 1 coin earned, it's unclear what the question is asking. However, for the second question regarding the rectangle with a length of five-fourths meters and a width of two-thirds of a meter, the total area in square meters is 5/6 square meters.

Explanation:

To find the area of a rectangle, we simply need to multiply the length by the width. For the second question, the length of the rectangle is given as five-fourths meters and the width is given as two-thirds of a meter.

Multiplying these two values together, we get:

(5/4) x (2/3) = 10/12 = 5/6

Therefore, the total area of the rectangle is 5/6 square meters.

As for the first question, the fraction 3/10 and 1 coin earned doesn't provide enough information to answer a specific question. It's unclear what the question is asking and more information is needed to provide a solution.

To learn more about area click here, brainly.com/question/30307509

#SPJ11

Jennifer paid $2.27 for the bag of apples after using the coupon.

Jennifer bought a bag of apples and had to consider the tax and coupon discount in her final payment. Here's a breakdown of the calculation:

1. Jennifer initially bought the bag of apples for $2.50.
2. The tax on her purchase was 19 cents ($0.19).
3. She used a coupon to receive a 42-cent ($0.42) discount.

To calculate her final payment, we first need to add the tax to the initial price of the apples:

$2.50 (initial price) + $0.19 (tax) = $2.69 (price with tax)

Next, we subtract the coupon discount from the price with tax:

$2.69 (price with tax) - $0.42 (coupon discount) = $2.27

Therefore, Jennifer paid a total of $2.27 for the bag of apples after including the tax and applying her coupon discount.

Know more about Tax here :

https://brainly.com/question/30046826

#SPJ11

Answer: 74.8

Step-by-step explanation: If you add all of the students grades, you would get 748. If you divide that by 10, you get 74.8.

The t-score that should be used to find a 99% confidence interval estimate for the population mean is given as follows:

t = 2.6923.

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

The variables of the equation are listed as follows:

The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 45 - 1 = 44 df, is t = 2.6923.

More can be learned about the t-distribution at https://brainly.com/question/27701525

#SPJ1

It is likely that 975 players in the shipment of 1000 video players will have no defects.

To predict the number of players in the shipment that are likely to have no defects, we can use the proportion of defect-free players observed in the sample.

In the given sample of 200 video players, 195 of them have no defects. This means that the proportion of defect-free players in the sample is 195/200.

To estimate the number of defect-free players in the shipment of 1000 video players, we can use the same proportion. We multiply the proportion by the total number of video players in the shipment:

Number of defect-free players = Proportion of defect-free players * Total number of players

Number of defect-free players = (195/200) * 1000

Calculating this expression:

Number of defect-free players = (195/200) * 1000 = 975

Know more about proportion here:

https://brainly.com/question/30657439

#SPJ11

If speed is important and the array is large, the a. Binary search algorithm should be used. This algorithm is designed to efficiently search through sorted arrays by repeatedly dividing the search interval in half.

It has a time complexity of O(log n), which means that as the size of the array increases, the time it takes to search for an item will not increase at the same rate.
On the other hand, ascending bubble sort and other sorting algorithms such as selection sort and insertion sort have a time complexity of O(n^2), which means that as the size of the array increases, the time it takes to sort the array will increase exponentially. Therefore, these algorithms are not efficient for large arrays and should not be used if speed is important.
In summary, when dealing with large arrays and speed is important, binary search is the best algorithm to use for searching, while ascending bubble sort and other sorting algorithms with a time complexity of O(n^2) should be avoided.

To learn more about the Binary search algorithm, refer:-

https://brainly.com/question/29734003

#SPJ11

A) The density function is a horizontal line between x = 20 and x = 60. The height of the line is determined by the formula [tex]Height (density) = \frac{1}{ (maximum - minimum) }[/tex], which in this case is [tex]f(x)=\frac{1}{60-20} =\frac{1}{40}[/tex].B) P(35)=1/40 C) The density function is f(x) = 1/40, 20 <= x <= 60

A) The density function for a uniformly distributed random variable can be represented as a rectangle, with a constant height and defined minimum and maximum values. In this case, the minimum value is 20 and the maximum value is 60. The height of the rectangle (density) can be calculated as:
[tex]Height (density) = \frac{1}{ (maximum - minimum) }=\frac{1}{60-20} =\frac{1}{40}[/tex]
So, the density function is a rectangle with a constant height of 1/40, stretching from 20 to 60 on the x-axis.
B) To determine P(35), we first need to check if the value is within the range of our uniform distribution, which it is (20 ≤ 35 ≤ 60). Since the distribution is uniform, the probability density is constant across the entire range. Therefore, P(35) = density = 1/40.
C) Drawing the density function is the same as in part A, but now we also include the probability at x = 35. The density function is still a rectangle with a constant height of 1/40 from 20 to 60 on the x-axis. At x = 35, the probability P(35) is equal to the density, which is 1/40.

Learn more about probability here: https://brainly.com/question/32004014

#SPJ11

The quadratic regression equation that best fits the data set is [tex]y = -1.62x^2 + 34.89x - 5.57.[/tex]

To determine which quadratic regression equation best fits the data set, we can use a graphing calculator or other technology to perform a quadratic regression analysis on the given data.

Using a graphing calculator, we can enter the data set as follows:

Press the STAT button.

Press ENTER to select 1:Edit.

Enter the x-values in L1 and the y-values in L2.

Press STAT again and choose CALC.

Choose option 5:QuadReg.

Press ENTER to select the regression equation.

The calculator will display the quadratic regression equation in the form y = [tex]ax^2 + bx + c.[/tex]

After performing the quadratic regression analysis, we get the following equation:

y = [tex]-1.62x^2 + 34.89x - 5.57[/tex]

Therefore, the quadratic regression equation that best fits the data set is [tex]y = -1.62x^2 + 34.89x - 5.57.[/tex]

Learn more about quadratic regression equation

https://brainly.com/question/30738733

#SPJ4

Full Question: Use a graphing calculator or other technology to answer the question. 4.5 122 Which quadratic regression equation best fits the data set? 6.2 145 7.0 155 8.9 189 O Û = 1.62x2 + 34.89x +5.57 10.1 171 © = -5.5722 + 34.89x – 1.62 14.8 170 O Û = -1.62x2 + 34.89x 15.7 133 © y = -1.62x2 + 34.893 – 5.57

The equation of the blue line in the graph is y = -x - 1.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

From the graph, the line passes through the points (-1,0) and (0,-1).

First, find the slope of the line using the slope formula:

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( -1 - 0 ) / ( 0 - (-1) )

m = -1 / 1

m = -1

Next, using the point-slope form, plug in one of the given points and slope m = -1 to find the equation of the line.

Let's use the point (0,-1):

y - y₁ = m(x - x₁)

y - (-1) = -1(x - 0)

y + 1 = -x + 0

y + 1 = -x

y = -x - 1

Therefore, the equation of the line is y = -x - 1.

Learn more about equation of line here: brainly.com/question/2564656

#SPJ1

The equation that can be used to find r, the rate of growth per year of the world population, is [tex]r = (7.53 / 5.88 )^{(1/20)} - 1[/tex].

If we assume that the growth rate of the world population was constant from 1997 to 2017, then we can use the following equation:

Population in 2017 = Population in 1997 × (1 + r)²⁰

where r is the annual growth rate, and the exponent 20 represents the number of years between 1997 and 2017.

We can rewrite this equation to solve for r:

(7.53 ) = (5.88 ) × (1 + r)²⁰

Divide both sides by (5.88 ):

(7.53 ) / (5.88 ) = (1 + r)²⁰

Take the 20th root of both sides:

[tex](7.53 / 5.88 )^{(1/20)} = 1 + r[/tex]

Subtract 1 from both sides:

[tex]r = (7.53 / 5.88 )^{(1/20)} - 1[/tex]

Therefore, the equation that can be used to find r, the rate of growth per year of the world population, is [tex]r = (7.53 / 5.88 )^{(1/20)} - 1[/tex].

Learn more about the growth rate here:

https://brainly.com/question/29291084

#SPJ1

Answer:

Step-by-step explanation:

5x5=25

The ratio of male to female attendees was 1:1, then we can estimate that 100 ladies attended the party as well ([tex]$1000 / $5[/tex] per ticket).

A fraternity charged admission for two different categories of people to their finals week bash, and they made and sold tickets.

How many individuals attended the party in each category?
Given the information provided, it is clear that the fraternity charged different amounts for admission to their finals week bash based on the gender of the attendees.

They collected separate ticket sales for the two categories.
In order to calculate the number of attendees in each category, we need to know the total revenue generated by ticket sales, as well as the price of admission for each category.

Unfortunately, these details are not provided in the question.
If we make some assumptions, we can attempt to estimate the number of attendees.

If we assume that the price of admission for both categories was the same, then we can simply divide the total revenue by the price of admission to get the total number of attendees.
Alternatively, if we assume that the ratio of male to female attendees was equal, then we can use the information provided to calculate the number of female attendees.

If the fraternity charged [tex]$10[/tex] per ticket for dudes and [tex]$5[/tex] per ticket for ladies, and they collected [tex]$1000[/tex] in total ticket sales, then we can calculate the number of male attendees as 100 ([tex]$1000 / $10[/tex] per ticket).
It is important to note that these calculations are based on assumptions, and the actual number of attendees could be different depending on the actual price of admission and the actual ratio of male to female attendees.

For similar questions on attended the party

https://brainly.com/question/27666773

#SPJ11

Answer: You just have to multiply the percent and divide it by the weight.

Step-by-step explanation:

90%*40%= 3600

3600/600= 6 grams

The correct ordered pairs are C (-5,27), (-1,15), (8,-12)

Given is an equation of a line y = 12-3x we need to find the points which on this line,

1) (-5,27)

y = 12 -3(-5)

y = 12 + 15

y = 27

27 = 27

Hence This is correct.

2) (-1,15)

y = 12 -3(-1)

y = 12 + 3 

y = 15 

15 = 15

Hence This is correct.

3) (8,-12)

y = 12 -3(8)

y = 12 - 24 

y = -12 

-12 = -12

Hence This is correct.

Hence the correct ordered pairs are C (-5,27), (-1,15), (8,-12)

Learn more about ordered pairs click;

https://brainly.com/question/30805001

#SPJ1

Answer:

Step-by-step explanation:

1,098,503

The system of equations that is represented in the graph is:

y > x² + 4x-5

y > x + 5

The system of equations represents two inequalities in two variables x and y. The first inequality is a quadratic function, y = x² + 4x - 5, which represents a parabola opening upwards.

The second inequality is a linear function, y = x + 5, which represents a straight line with a positive slope.

The solution set for the system of equations is the region above the intersection of the two functions. Since the parabola is above the line, the solution set is the region above the parabola. Therefore, the solution set is the region above the parabola y = x² + 4x - 5.

Learn more  about system of equations:
https://brainly.com/question/24065247
#SPJ1

The data provided by another lab group has been analyzed using a graph template. The graph shows a trend similar to the expected pattern, but there is a significant deviation in one data point that suggests an experimental error.

Explanation:

Upon analyzing the data, it appears that the overall trend of the graph is similar to what we would expect. However, there is a significant deviation in one of the data points. This deviation suggests that there was an experimental error during that particular measurement. It could be due to various reasons such as equipment malfunction, human error, or sample contamination.

To identify the source of the error, the lab group should investigate their methods and procedures for that particular measurement. They should check the calibration of their equipment and the accuracy of their measurements. Additionally, they should review their lab notes and compare their results with those obtained by other lab groups to see if there were any inconsistencies. Once the source of the error is identified, they can take corrective action and repeat the measurement to obtain accurate results. Overall, the identification and correction of experimental errors are crucial to ensure the validity and reliability of scientific data.

To learn more about measurement click here, brainly.com/question/28913275

#SPJ11

Answer:  A + B is orthogonally diagonalizable and A’ is also orthogonally diagonalisable.

Step-by-step explanation:

(a) Let A and B be orthogonally diagonalizable matrices, then there exist orthogonal matrices P and Q such that A = PDP’ and B = QDQ’, where D and D’ are diagonal matrices.

Then, A + B = PDP’ + QDQ’. Since P and Q are orthogonal, their product PQ is also orthogonal.

Therefore, we can write:

A + B = PDP’ + QDQ’

= PQDP’Q’ + PQD’P’Q’

= (PQ)D(PQ)’

where (PQ) is also an orthogonal matrix.

Thus, A + B is orthogonally diagonalizable.

(b) Let A and B be orthogonally diagonalizable matrices, then there exist orthogonal matrices P and Q such that A = PDP’ and B = QDQ’, where D and D’ are diagonal matrices.

The transpose of A is A’ = (PDP’)’ = (P’)’D’P’. Since the transpose of an orthogonal matrix is also orthogonal, we have: A’ = (PDP’)’ = (P’)’D’P’ = (P’)’DP’(P’)’which shows that A’ is also orthogonally diagonalisable.

Learn more about matrices here, https://brainly.com/question/11989522

#SPJ11

Answer: The angle sum theorem states that the sum of the three angles in any triangle is always 180 degrees. Therefore, we can use this theorem to find the value of y in the given triangle.

We know that angle A = x, angle B = 120 degrees, and angle C = 20 degrees.

The sum of the three angles in this triangle is:

A + B + C = x + 120 + 20 = x + 140

Since y is outside the triangle on a line to the left of x, we can see that the angle formed by the line containing y and the line containing side AC is a straight angle, which has a measure of 180 degrees.

Therefore, we have:

A + C + y = 180

Substituting the values we know, we get:

x + 20 + y = 180

Solving for y, we get:

y = 160 - x

Therefore, the value of y is 160 degrees minus the measure of angle A (which is x).

Answer:

C. (The purple/third table)

Step-by-step explanation:

x always multiplies by 2 to get y.

TIP: In a proportional relationship x always multiplies by the same number in every column.