A recent increase in sales of microchips has forced a computer company to buy a new processing machine to help keep up with demand. The builders of the new machine claim that it produces fewer defective microchips than the older machine. From a random sample of 90 microchips produced on the old machine, 5 were found to be defective. From a random sample of 83 microchips produced on the new machine, 3 were found to be defective. The quality control manager wants to construct a confidence interval to estimate the difference between the proportion of defective microchips from the older machine and the proportion of defective microchips from the new machine.


Why is it not appropriate to calculate a two-sample z-interval for a difference in proportions?




The microchips were not randomly assigned to a machine.


A

There is no guarantee that microchips are approximately normally distributed.


B

The normality of the sampling distribution of the difference in sample proportions cannot be established.


C

Both sample proportions are less than 0. 10.


D

The sample sizes are not the same

Answer:

10.5

Step-by-step explanation:

The equation that represents the total cost is  C(x)=13x +95​. (option d)

The problem tells us that it costs $95 to rent the cafeteria, which is a fixed cost that doesn't change based on the number of people attending. However, the cost per person is $13. So, if we have x number of people attending the banquet, the total cost would be $95 (for the cafeteria rental) plus $13x (for each person attending).

Now, we need to represent this relationship using an equation. An equation is a mathematical statement that shows the relationship between two quantities. In this case, the two quantities are the total cost and the number of people attending the banquet.

Using the third equation, C(x) = 95x + 13, we get:

C(0) = 95(0) + 13 = 13

This makes sense, because if there are 0 people attending, the total cost should just be the rental fee of $95.

Now, let's try the last equation, C(x) = 13x + 95:

C(0) = 13(0) + 95 = 95

This gives us the correct rental fee of $95, but it doesn't take into account the cost per person. This equation takes into account the rental fee of $95 as well as the $13 cost per person attending the banquet.

Hence the correct option is (d).

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An equation of this line in slope-intercept form is equal to y = -x + 4.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (0 - 4)/(4 - 0)

Slope (m) = -4/4

Slope (m) = -1

At data point (0, 4) and a slope of -1, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 4 = -1(x - 0)  

y - 4 = -x

y = -x + 4

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quadratic inequality

Answer:

3

Step-by-step explanation:

5x + 2(x-3) =5x + 2(3-x)

or，5x＋2x－6＝5x＋6－2x

or，7x－6＝3x＋6

or，4x＝12

or，×＝3

Answer: miss bailey bought 8 for 3 dollars each  

Step-by-step explanation:

so if a binder cost 12 subtract that form the $36 and you are left with $24. divided it by 8 and are left with 3

There are 4242 ways to select a committee of five members of the department with at least one woman on the committee.

Total faculty members: 7 women + 9 men = 16 members

Total ways to select 5 members without any restrictions: C(16, 5)

Now, let's find the ways to select a committee with no women (only men):

Total ways to select 5 men from 9: C(9, 5)

Using the principle of inclusion-exclusion, we can find the number of ways to select a committee with at least one

woman:

Ways with at least one woman = Total ways - Ways with no women

Ways with at least one woman = C(16, 5) - C(9, 5)

Now, calculate the values:

C(16, 5) = 16! / (5! × (16-5)!) = 4368

C(9, 5) = 9! / (5! × (9-5)!) = 126

Ways with at least one woman = 4368 - 126 = 4242

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If y is proportional to the square root of x and y = 60 when x = 36, then the value of x when y = 80 is 64

We are given that y is proportional to the square root of x, or y ∝ √x.

Using the constant of proportionality k, we can write this relationship as:

y = k√x

To solve for k, we can use the values given in the problem

y = 60, x = 36

60 = k√36

60 = k × 6

k = 60 / 6

Divide the numbers

k = 10

Now that we know k, we can use the same equation to find x when y = 80

80 = 10√x

Squaring both sides, we get

6400 = 100x

x = 64

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The given question is incomplete, the complete question is:

y ∝ √x If y = 60 when x = 36, find x when y = 80​.

Answer:

y int: (0, -23)

Step-by-step explanation:

first you find the slope by taking two points and substituting it in rise over run ([tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex])

I used 25-13/-72+54 which eventually simplified to -2/3

You then use point slope form and plug in one pair of points

I used (-36,1) since it seemed the easiest

y-1=[tex]\frac{-2}{3}[/tex](x+36)   point slope form: [tex]y-y_{1}=m(x-x_{1} )[/tex]

y-1= [tex]\frac{-2}{3} x-\frac{72}{3}[/tex]

y-1=[tex]\frac{-2}{3} x-24[/tex]

y=[tex]\frac{-2}{3} x-23[/tex]

the number without the variable is always y int regardless of the numbers in the equation

therefore, the y int is (0,-23)

The scale ratio for this map is 0.0000063.

What is scale ratio?

Scale ratio is the ratio between the measurements of an object or distance on a map or drawing and the actual measurements of the object or distance it represents in real life. It allows us to compare and relate the sizes or distances of objects in a drawing or map to their actual sizes or distances in the real world.

The scale ratio can be found by dividing the distance on the map by the corresponding distance in reality:

scale ratio = distance on map / distance in reality

In this case, the distance from Wellspring to Red Creek is 4 inches on the map and 10 miles in reality. So the scale ratio is:

scale ratio = 4 inches / 10 miles

To simplify this ratio, we need to convert the units so that they are the same. Let's convert inches to miles:

1 mile = 63,360 inches

So, we can convert the inches on the map to miles as follows:

4 inches * (1 mile / 63,360 inches) = 0.000063 miles

Now we can rewrite the scale ratio as:

scale ratio = 0.000063 miles / 10 miles

Simplifying this ratio by canceling out the units of miles, we get:

scale ratio = 0.0000063

Therefore, the scale ratio for this map is 0.0000063.

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the proportion of men and women under 30 that use online dating sites.

The null hypothesis, H0, is that there is no difference in the proportion of men and women under 30 that use online dating sites.

The alternative hypothesis, Ha, is that there is a difference in the proportion of men and women under 30 that use online dating sites.

We can use a two-sample z-test for proportions to test this hypothesis.

First, we calculate the pooled sample proportion:

[tex]\^p = (67 + 62) / (96 + 88) = 0.648[/tex]

Next, we calculate the standard error of the difference between the two sample proportions:

[tex]SE =\sqrt{(\^p(1 - \^p) (1/96 + 1/88))} = 0.079[/tex]

The test statistic is:

[tex]z = (\^p1 - \^p2) / SE = (0.698 - 0.705) / 0.079 = -0.886[/tex]

[tex]\^p1 = 67/96 = 0.698[/tex] is the sample proportion of women who use online dating sites, and [tex]\^p2 = 62/88 = 0.705[/tex] is the sample proportion of men who use online dating sites.

Using a two-tailed test with a significance level of [tex]\alpha = 0.05[/tex], we can find the critical value of [tex]z as \±1.96.[/tex]

Since the absolute value of the test statistic, 0.886, is less than the critical value, 1.96, we fail to reject the null hypothesis.

The p-value for this test can also be calculated. Since this is a two-tailed test, we need to find the area under the standard normal distribution curve that is beyond the absolute value of the test statistic:

[tex]p-value = P(|z| > 0.886) = 2P(z < -0.886) = 2(0.187) = 0.374[/tex]

the p-value is greater than the significance level of α = 0.05, we again fail to reject the null hypothesis.

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The Poisson distribution is applied to events where the probability of occurrence of a certain number of events in a fixed interval of time, space, or distance is small but not necessarily "very small". False.

The Poisson distribution is used to model events that occur randomly and independently over a continuous or discrete interval of time, space, or distance, such as the number of phone calls received at a call center in an hour, the number of cars passing through a toll booth in a given time period, or the number of emails received per day. The Poisson distribution is characterized by a discrete probability mass function that describes the probability of a certain number of events occurring in a given interval, and it is widely used in probability theory and statistics for modeling events with low to moderate occurrence rates.

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The poisson distribution is applied to events for which the probability of occurrence over a given span of time, space, or distance is very small.

Given statement is False.

Because, The Poisson distribution is applied to events for which the probability of occurrence over a given span of time, space, or distance is not necessarily very small, but rather where the events occur randomly and independently at a constant average rate.

The Poisson distribution models the number of events that occur in a fixed time interval or within a certain area or volume of space, assuming that the events occur independently of each other and at a constant average rate. It is used in many fields, such as biology, physics, economics, and engineering, to model the occurrence of rare or common events.

The Poisson distribution has several important properties, including:

Its mean is equal to λ, and its variance is also equal to λ.

It is a discrete distribution, meaning that it models only whole numbers of events.

It is often used to model rare or unusual events, but can also be used for events that occur frequently, as long as they occur independently at a constant average rate.

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Natalie used for constructing the bar graph is type of writing utensil.

The representation of numerical data using rectangles (or bars) of equal width and varying height is known as a bar graph.

Depending on the distribution and nature of the data, various types of charts or graphs, such as scatter plots, histograms, or box plots, would typically be used to represent the mentioned quantitative variables, such as the price, volume, and weight of each writing utensil.

Natalie probably used the variable "type of writing utensil" for the bar graph based on the information provided. This is due to the fact that a bar graph is a type of chart that uses rectangular bars to represent categorical data. Each bar represents a distinct category or group.

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the new club sent out 50 coupons to existing members and 150 coupons to potential members to boost sales for next year's memberships.

How to solve the question?

Let x be the number of coupons sent to existing members. Then the number of coupons sent to potential members is 3x, as they provided 3 times as many coupons to potential members than to existing members.

According to the problem, the total number of coupons sent is 200. Therefore, we can write the following equation:

x + 3x = 200

Simplifying this equation, we get:

4x = 200

Dividing both sides by 4, we get:

x = 50

Therefore, the number of coupons sent to existing members is 50, and the number of coupons sent to potential members is 3 times as many, or 150.

In conclusion, the new club sent out 50 coupons to existing members and 150 coupons to potential members to boost sales for next year's memberships.

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The answer is   X = 10

⇒ Given [tex]\frac{2x}{3} + 1 = \frac{7x}{15} + 3[/tex]

⇒  [tex]\frac{2x+3}{3} = \frac{7x+45}{15}[/tex]

⇒ 15(2x + 3) = 3(7x + 45)

⇒ 30x + 45 = 21x + 135

⇒ 30x - 21x = 135 - 45

⇒ 9x = 90

⇒ x = [tex]\frac{90}{9}[/tex]

⇒ Therefore X = 10

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A basis for Col A is (-2,2,0,0) and (4,-6,0,0). A basis for Nul A is (2,1,0,0), (-1,0,1,1/2), and (-2,0,0,1). These bases were found using the row reduced form of A.

Since A is row equivalent to B, they have the same row space, null space, and column space. Thus, we can find the bases for Nul A and Col A using the row reduced form of A, which is

[tex]\left[\begin{array}{cccc}1&-2&1&2\\0&1&1/2&-1\\0&0&0&0\\0&0&0&0\end{array}\right][/tex]

To find a basis for Col A, we can take the columns of A that correspond to the pivot columns in the row reduced form. In this case, the pivot columns are the first and second columns. Therefore, a basis for Col A is

(-2, 2, 0, 0), (4, -6, 0, 0)

To find a basis for Nul A, we need to solve the system of homogeneous linear equations Ax = 0, which is equivalent to solving the system of equations corresponding to the row reduced form. Letting the free variable be t, we have

x¹ - 2x² + x³ + 2x⁴ = 0

x² + (1/2)x³ - x⁴ = 0

Expressing x¹ and x⁴ in terms of x² and x³, we get

x¹ = 2x² - x³ - 2x⁴

x⁴ = (1/2)x³ - x²

Thus, any solution to Ax = 0 can be written as

x = (2x² - x³ - 2x⁴, x², x³, (1/2)x³ - x²) = x²(2, 1, 0, 0) + x³(-1, 0, 1, 1/2) + x⁴(-2, 0, 0, 1)

Therefore, a basis for Nul A is

(2, 1, 0, 0), (-1, 0, 1, 1/2), (-2, 0, 0, 1)

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The Pythagorean theorem to make problem-solving more accessible and efficient.

By incorporating technology into mathematical problem-solving, these tools help students and professionals alike in understanding and applying the theorem in various scenarios.

The Pythagorean theorem or provide a workaround. Here are a few tools that you might find useful:
GeoGebra:

GeoGebra is a dynamic geometry software that allows users to create, manipulate, and visualize geometric constructions.

It heavily relies on the Pythagorean theorem to explore and prove various geometric relationships.

GeoGebra can be accessed online or through its app, making it convenient and easy to use.
Desmos Graphing Calculator:

Desmos is an advanced graphing calculator that helps visualize and solve problems involving the Pythagorean theorem.

By plotting points, lines, and curves, you can explore the theorem's applications in various contexts, such as distances, vectors, and trigonometry.
Microsoft Math Solver:

This app allows you to input a math problem and receive step-by-step solutions.

It can solve problems related to the Pythagorean theorem, including finding side lengths and proving whether a triangle is a right triangle.
Wolfram Alpha:

Wolfram Alpha is a computational knowledge engine that can process queries and provide answers.

It is particularly helpful for solving problems based on the Pythagorean theorem. \

A problem, and Wolfram Alpha will provide a step-by-step solution, helping you understand the process better.

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There are indeed modern tools that help solve problems related to the Pythagorean theorem. Some of these tools include computer software, smartphone applications, and online calculators. These tools often provide a workaround or rely heavily on the Pythagorean theorem to solve various geometric and trigonometric problems, such as finding the length of a side in a right-angled triangle or determining the distance between two points in a coordinate system. By using these tools, users can easily and accurately apply the Pythagorean theorem to solve real-life problems or mathematical challenges.

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Mason's friends do not play video games are 4.

Mason asked some classmates whether they play video games.

The ratio of friends who play video games to everyone he asked is given as some fraction or decimal value.
Let's assume that the ratio is in the form of "x:y",

"x" represents the number of friends who play video games, and "y" represents the total number of friends that Mason asked.
To find out how many of his friends do not play video games,

To subtract the number of friends who play video games from the total number of friends that Mason asked.

This is because the remaining friends who were not counted in the "x" value of the ratio must be those who do not play video games.
So, the number of friends who do not play video games can be calculated as:
Total number of friends - Number of friends who play video games = y - x
The ratio of friends who play video games to everyone he asked is 3:7,

It means that out of 7 friends, 3 play video games, and 4 do not play video games.

The number of friends who do not play video games can be calculated as:
y - x = 7 - 3 = 4  

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1) The common denominators of 2/3 and 7/9 are: 9, 18, 27, 36, 45, 54, 63, ...

2) The common denominators of 1/9 and 1/2 are: 18, 36, 54, 72, 90, 108, ...

To find the common denominators of 2/3 and 7/9, we need to find the least common multiple (LCM) of the denominators 3 and 9.

Prime factorization of 3: 3 = 3^1

Prime factorization of 9: 9 = 3^2

To find the LCM, we take the highest power of each prime factor that appears in either factorization. So, LCM(3, 9) = 3^2 = 9.

Therefore, the common denominators of 2/3 and 7/9 are all multiples of 9.

2) To find the common denominators of 1/9 and 1/2, we need to find the LCM of the denominators 9 and 2.

Prime factorization of 9: 9 = 3^2

Prime factorization of 2: 2 = 2^1

To find the LCM, we take the highest power of each prime factor that appears in either factorization. So, LCM(9, 2) = 2 x 3^2 = 18.

Therefore, the common denominators of 1/9 and 1/2 are all multiples of 18.

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The probability that a 120 square foot roll will contain more than one flaw is approximately 0.0001, or 0.01%.

The number of flaws per square foot, denoted by X, as a Poisson distribution with parameter lambda = 1/40 (since there is an average of one flaw per 40 square feet).

To find the probability that a 120 square foot roll will contain more than one flaw, we need to calculate the probability of X > 1, where X is Poisson distributed with parameter lambda = 1/40.

Using the Poisson distribution formula, we have:

[tex]P(X > 1) = 1 - P(X < = 1)[/tex]

= [tex]1 - [P(X = 0) + P(X = 1)][/tex]

We can calculate P(X = 0) and P(X = 1) using the Poisson distribution formula:

P(X = k) = (e^(-lambda) * lambda^k) / k!

where k is the number of flaws and lambda = 1/40.

[tex]P(X = 0) = (e^(-1/40) * (1/40)^0) / 0! = e^(-1/40) = 0.9756[/tex]

[tex]P(X = 1) = (e^(-1/40) * (1/40)^1) / 1! = (1/40) * e^(-1/40) = 0.0244[/tex]

[tex]P(X > 1) = 1 - [P(X = 0) + P(X = 1)][/tex]

[tex]= 1 - (0.9756 + 0.0244)[/tex]

[tex]= 0.0001[/tex]

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a. A best-fit line is close to most of the data points.

Best-fit lines help show trends or correlations in data

Best-fit Lines

Best-fit lines attempt to create a line that is close to most data points. This line is a function that can be used to estimate data points that are not a part of the original data set. Additionally, best-fit lines will show the trend of the data. For example, if the slope of the best-fit line is constant, then the data points are directly proportional.

Common Misconceptions

Although best-fit lines can be extremely accurate and helpful, they are not perfect. A best-fit line will attempt to minimize the distance between the line and data points, but it will rarely be perfect. In most cases, there is no way to write a line that will perfectly describe the exact coordinates of each data point.

Additionally, data sets can have any type of correlation. It does not need to be proportional or positive. This means that the slope of a best-fit line can be anything.

Finally, as aforementioned, best-fit lines try to fit the data as much as possible. However, this does not mean that the line has to go through any data points. It is possible for best-fit lines to not go through any data points at all.

Answer:

y = -4.3x + 23.8

Step-by-step explanation:

To find the equation for g(x), we need to first understand what it means for g(x) to be parallel to f(x). Two lines are parallel if they have the same slope, but different y-intercepts. The slope of f(x) is -4 3/10, which can be written as -43/10 in fraction form and -4.3 in decimal form. Therefore, the slope of g(x) is also -4.3.

Now we need to use the fact that g(x) passes through the point (6, -2) to find its y-intercept. We can use the point-slope form of a linear equation to do this: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Plugging in our values, we get:

y - (-2) = (-4.3)(x - 6)

Simplify the left side

y + 2 = (-4.3)(x - 6)

Next, simplify the right side

y + 2 = -4.3x + 25.8

Subtracting 2 from both sides, we get:

y = -4.3x + 23.8

Therefore, the equation for g(x) is y = -4.3x + 23.8 in simplified slope-intercept form.

The availability of this repairable product is approximately 0.762, or 76.2%.

In order to find the availability of a repairable product, we need to consider its failure rate and mean time to repair. The formula for availability (A) is:

A = MTBF / (MTBF + MTTR)

Where MTBF is Mean Time Between Failures and MTTR is Mean Time To Repair.

Since we have a constant failure rate (λ), we can calculate the MTBF as the inverse of the failure rate:

MTBF = 1 / λ

In this case, the failure rate (λ) is 0.0078 failures per hour. Let's calculate the MTBF:

MTBF = 1 / 0.0078 = 128.205 hours

Now, we know the MTTR is 40 hours. We can use the availability formula to find the answer:

A = MTBF / (MTBF + MTTR)
A = 128.205 / (128.205 + 40)
A = 128.205 / 168.205
A ≈ 0.762

So, the availability of this repairable product is approximately 0.762, or 76.2%.

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The set of constraints that represents all possible number of bracelets and necklaces is: 4b + 7n ≥ 150, b ≤ 36, and n ≤ 12.

Constraints are limitations and boundaries that must be applied to variables in equations used to simulate real-world scenarios.

It's possible that some answers, while theoretically proving an equation correct, may not make sense in the context of a real-world word problem. In order for the mathematical model to accurately depict the situation, constraints are then required.

An equation's related x-values (the independent variable) or y-values (the dependent variable) may be subject to restrictions.

Let us suppose number of bracelets = b.

Let us suppose the number of necklaces sold = n.

Thus, for profit we have:

4b + 7n ≥ 150

Also, according to the given constraints:

b ≤ 36

n ≤ 12

Hence, the set of constraints that represents all possible number of bracelets and necklaces is: 4b + 7n ≥ 150, b ≤ 36, and n ≤ 12.

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The correct answer is c, 4b+7n≥150 and b≤36, n≤12.

The total profit P made by selling b bracelets and n necklaces can be expressed as:

P = 4b + 7n

To make a profit of at least $150, we need:

4b + 7n ≥ 150

Also, we cannot sell a negative number of bracelets or necklaces, so we have the constraints:

b ≥ 0

n ≥ 0

And since they have already made 36 bracelets and 12 necklaces, we have:

b ≤ 36

n ≤ 12

So the correct set of constraints is:

4b + 7n ≥ 150

b ≥ 0

n ≥ 0

b ≤ 36

n ≤ 12

Therefore, option c is the correct answer.

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The calculated value of the length of the segment EG is 54 units.

Since J is the midpoint of EG, we know that EJ = JG.

So, we can set the two expressions equal to each other and solve for x:

5x - 3 = 3x + 9

Subtracting 3x from both sides, we get:

2x - 3 = 9

Adding 3 to both sides, we get:

2x = 12

Dividing both sides by 2, we get:

x = 6

Now that we have x, we can substitute it back into either EJ or JG to find its value:

EJ = 5x - 3 = 5(6) - 3 = 27

JG = 3x + 9 = 3(6) + 9 = 27

Therefore, EG = EJ + JG = 27 + 27 = 54.

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The sales tax rate is 6%

If the sales-tax rate is 6%, the tax paid on an $8.50 purchase would be:

Tax = 0.06 x $8.50

Tax = $0.51

Therefore, the total cost of the purchase including sales tax would be:

Total cost = $8.50 + $0.51

Total cost = $9.01

The sales tax rate is 6%.

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The expression 0.8p+1 and 1 + 0.8p are equivalent to (0.5p + 7) + (0.3p-6).

We can simplify the given expression by combining like terms:

(0.5p + 7) + (0.3p-6) = 0.5p + 0.3p + 7 - 6

= 0.8p + 1

Therefore, 0.8p + 1 is equivalent to (0.5p + 7) + (0.3p-6).

Similarly, we can simplify the given expression in another way:

(0.5p + 7) + (0.3p-6) = 0.5p + 0.3p + 7 - 6

= 0.8p + 1

The other options (1 + 0.8p, 7.5p-5.7) are not equivalent to the given expression.

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The solution is A, which is $13.50 as a two-day bike rental normally costs $7 each day multiplied by two days for a total of $14.

The term "amount" designates a sum or number, typically expressed in terms of monetary value or a tangible good. It can also be used to describe the whole amount of anything, such as the total time that is spent on a work or the total amount of rain that falls in a specific location. "Amount" is frequently used synonymously with "amount" or "total."

given

A two-day bike rental normally costs $7 each day multiplied by two days for a total of $14.

Joanna paid $7/2 ($3.50) on Friday thanks to a voucher she utilised to pay half the price.

The normal Saturday bike rental fee should be "x." Then, according to the issue, Joanna paid $4 less than double what renting a bike normally costs during the workweek. As a result, she spent $10 on Saturday (2($7) - $4).

As a result, she spent the following sum overall to rent the bike:

$3.50 + $10 = $13.50

The solution is A, which is $13.50 as a two-day bike rental normally costs $7 each day multiplied by two days for a total of $14.

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Euler's method with step size [tex]$h = 0.2$[/tex], we estimate [tex]$y(1.4) \approx 0.32$[/tex].

Euler's method with step size[tex]$h = 0.1$[/tex], we estimate [tex]$y(1.4) \approx 0.343$[/tex].

Euler's method to approximate the solution of the initial-value problem:

[tex]y \prime =x - xy,y(1)=0[/tex]

with step size [tex]$h = 0.2$[/tex]and [tex]$h =0.1[/tex]

Euler's method with step size [tex]$h = 0.2$[/tex], we have:

[tex]x_0 &= 1 \y_0 &= 0 \x_1 &= 1 + h = 1.2 \y_1 &= y_0 + hf(x_0, y_0) = 0 + 0.2(1-1\cdot 0) = 0.2 \x_2 &= 1.2 + h = 1.4 \y_2 &= y_1 + hf(x_1, y_1) = 0.2 + 0.2(1.2 - 1.2\cdot 0.2) = 0.32 \[/tex]

Euler's method with step size [tex]$h = 0.2$[/tex], we estimate.

[tex]$y(1.4) \approx 0.32$[/tex].

Euler's method with step size[tex]$h = 0.1$[/tex], we have:

[tex]x_0 &= 1[/tex]

[tex]y_0 &= 0[/tex]

[tex]x_1 &= 1 + h = 1.1[/tex]

[tex]y_1 &= y_0 + hf(x_0, y_0) = 0 + 0.1(1-1\cdot 0) = 0.1[/tex]

[tex]x_2 &= 1.1 + h = 1.2[/tex]

[tex]y_2 &= y_1 + hf(x_1, y_1) = 0.1 + 0.1(1.1 - 1.1\cdot 0.1) = 0.19[/tex]

[tex]x_3 &= 1.2 + h = 1.3[/tex]

[tex]y_3 &= y_2 + hf(x_2, y_2) = 0.19 + 0.1(1.2 - 1.2\cdot 0.19) = 0.266[/tex]

[tex]x_4 &= 1.3 + h = 1.4[/tex]

[tex]y_4 &= y_3 + hf(x_3, y_3) = 0.266 + 0.1(1.3 - 1.3\cdot 0.266) = 0.343 \\end {align}[/tex]

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