To estimate the number of typographical errors in a 65-page manuscript, a systematic sample of pages is selected by first selecting a random number between 1 and 10 and including in the sample that numbered page and every 10th page thereafter. The random number selected was 6. The number of typographical errors on the sample pages were 1, 0, 2, 3, 0, and 1. Assume that no errors on sample pages were missed.
(a) Give an unbiased estimate, under the design used, of the total number of errors in the manuscript. What design was used?
(b) The person doing the survey estimated the total number of errors in the manuscript by 65(1 + 0 + 2 + 3 + 0 + 1)/6 = 75.83. Which estimator was used? Is it unbiased with the design used?
(c) The variance of the estimator was estimated by 65(65 − 6)(1.37)/6, where 1.37 is the sample variance of the six error counts. Is this unbiased for the actual variance of the estimator of the total number of errors? Discuss.
Answers
(a) The unbiased estimate of the total number of errors in the manuscript is approximately 75.83.
(b) Sample average of the errors estimator is used on it.
(c) Yes, this is unbiased for the actual variance of the estimator of the total number of errors
(a) Unbiased estimate of the total number of errors:
To estimate the total number of errors in the manuscript, we need to consider the design used, which involves selecting a systematic sample of pages. The design selects the page with the random number 6 and then includes every 10th page thereafter. We are given the number of errors on the sample pages: 1, 0, 2, 3, 0, and 1.
The average number of errors per page in the sample is calculated as the sum of the errors on the sample pages divided by the number of sample pages:
(1 + 0 + 2 + 3 + 0 + 1) / 6 = 7 / 6 ≈ 1.17.
Now, we can estimate the total number of errors in the manuscript by multiplying the average number of errors per page by the total number of pages:
1.17 * 65 = 75.83.
(b) Estimator used and its unbiasedness:
The estimator used in this case is the sample average of the errors per page, which is calculated by summing the errors on the sample pages and dividing by the number of sample pages. In this case, the person estimated the total number of errors in the manuscript as 75.83 using the formula: 65(1 + 0 + 2 + 3 + 0 + 1) / 6.
(c) Variance of the estimator and its unbiasedness:
The variance of an estimator measures the variability or spread of the estimator's values around its expected value. To estimate the variance of the estimator, the formula used is 65(65 - 6)(1.37) / 6, where 1.37 is the sample variance of the six error counts.
To have an unbiased estimate of the variance, we would need to divide the numerator by (n - 1), where n is the number of sample units. In this case, n is 6 since we have six sample pages.
Therefore, the estimated variance of the estimator provided, 65(65 - 6)(1.37) / 6, is biased for the actual variance of the estimator of the total number of errors.
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Related Questions
The graph shows the four quadrants of the coordinate plane.
Point AAA is located at (-5, 7)(−5,7)left parenthesis, minus, 5, comma, 7, right parenthesis.
Complete the statement.
Point AAA has an xxx-coordinate that is
and a yyy-coordinate that is
, so the point is located
Answers
The x coordinate of the point is -5, the y coordinate point is 7, and the point is located on Quadrant II.
What is an ordered double?It is defined as a representation of coordinates in a two-dimensional coordinate plane. It has a list of two elements in it, such as (x, y).
\(\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|\)
The coordinate point is:
(-5, 7)
As we know from the definition of the ordered double:
(x, y) represents the ordered double on the coordinate plane:
x = -5
y = 7
x < 0 and y > 0
The point is located on the Quadrant II
Thus, the x coordinate of the point is -5, the y coordinate point is 7, and the point is located on Quadrant II.
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PLS HELP!!!!! ITS ALGEBRA 1!
Describe the transformation from the graph of f(x) = x to the graph of g(x) = ⅓x
Answers
Answer:
First choice
Step-by-step explanation:
Slope f(x) = 1 while g(x) = 1/3: g(x) is less steep
Clockwise rotation
The skateboard rita wants to buy is 6 dollars less than 3 times the amount she has saved. the skateboard is 69 dollars. how much has rita saved
Answers
Answer:
$25
Step-by-step explanation:
money=x
3x-6=69
3x=75
x=25
Hope this helps plz hit the crown :D
Answer:
%25 dollars saved
Step-by-step explanation:
Different hotels in a certain area are randomly​ selected, and their ratings and prices were obtained online. Using​ technology, with x representing the ratings and y representing​ price, we find that the regression equation has a slope of 130 and a​y-intercept of −389.
Complete parts​ (a) and​ (b) below.
a. What is the equation of the regression​ line? Select the correct choice below and fill in the answer boxes to complete your choice.
A. y^ =_____ + ( _____ ) x^
B. y^ = ____ + ( ____) x
C. y = ____ + (____) x^
D. y + ____ + (____) x
b. What does the symbol y ​represent?
A. The symbol y^ represents the predicted value of price.
B. The symbol y^ represents the average price of hotels in the area.
C. The symbol y^ represents the expected price when the​ hotel's rating is 0.
D. The symbol y^ represents the amount that price increases with a​ 1-point increase in rating.
Answers
The regression equation is given by y^ = -389 + 130x^ and the symbol y^ represents the predicted value of price.
It is given to us that -
x = ratings
y = y-intercept
It is also given that the regression equation has -
Slope = 130
y-intercept = -389
We have to find out -
(a) the equation of the regression line
(b) what symbol y represents
We know that, regression analysis is used to predict continuous variables explained by single or multiple independent or explanatory variables.
There are various regression techniques that can be used to create predictive models, including simple regression, multiple regression, and logistic regression.
Here, we have -
Slope = 130
y-intercept = -389
(a) So, the regression equation can be represented as -
y^ = -389 + 130x^
(b) The symbol y^ is the dependent variable in the regression equation. Here, the symbol y^ represents the predicted value of price.
Thus, the regression equation is given by y^ = -389 + 130x^ and the symbol y^ represents the predicted value of price.
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PLEASE HELP, THANKS SO MUCH!! EXPLAIN UR ANSWER = BRAINLIEST
Answers
Answer:
2571.14 m^3
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
The diameter is 17 so the radius is 1/2 of the diameter or 17/2 =8.5
V = 4/3 (3.14) (8.5)^3
= 2571.13666
Rounding to the nearest hundredth
= 2571.14 m^3
=================================================
Work Shown:
V = (4/3)*pi*r^3
V = (4/3)*3.14*(8.5)^3
V = 2571.13666666667 which is approximate
V = 2571.14
-------------
Notes:
The units for the volume are in cubic meters, or m^3. Think of a 1 m by 1 m by 1 m block, the volume of which is 1*1*1 = 1 m^3.The diameter is 17 meters, half of which is 17/2 = 8.5 meters. So the radius is r = 8.5In the second to last line, the '6's go on forever. It's only due to rounding is why that '7' shows up.The answer above is approximate because pi = 3.14 is approximate. Use more decimal digits in pi to get a more accurate volume. However, your teacher wants you to use pi = 3.14A95% confidence interval for a proportion is 0.74 to 0.83. Is the value given a plausible value of p? (a) p = 091 (b) p = 0.75 (c) p = 0.13
Answers
The only plausible value of p from the given options is p = 0.75.
We are given a 95% confidence interval for a proportion as 0.74 to 0.83. We need to determine if the given value is a plausible value of p. We can do this by finding the point estimate for the proportion using the midpoint of the confidence interval.
The midpoint of the confidence interval is given as:
Midpoint of confidence interval = (0.74 + 0.83)/2 = 0.785
This is the point estimate for the proportion p. Now we need to check if the given value is plausible or not.(a) p = 0.91 is not plausible because it is greater than the upper limit of the confidence interval.
(b) p = 0.75 is plausible because it is close to the point estimate of 0.785.(c) p = 0.13 is not plausible because it is less than the lower limit of the confidence interval.
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Find the midpoint between the following points:
(7.-7) & (3, 1)
Answers
Answer:
5,-3
Step-by-step explanation:
use the formula
substitute the number
and get the answer
Answer:
(x1+x2)/2,(y1+y2)/2
Step-by-step explanation:
use this formula
answer will come for sure
7=x1
-7=y1
3=x2
1=y2
Read the case study below and answer ALL the questions that follow. The topic of a research proposal submitted by a Bachelor of Business Administration Honours student at a prestigious Business School in South Africa is: An investigation into the determinants of the sustainability of small and medium-sized enterprises in Soweto The student has proposed a quantitative approach to achieve the three research objectives below: * To determine the sustainability of Small and medium-sized enterprises (SMEs) in Soweto; * To determine the factors (determinants) of SME sustainability in Soweto, and * To make practical recommendations to owner-managers of SMEs in Soweto on how to enhance the sustainability of their businesses Answer ALL the questions in this section. QUESTION 1 (20 Marks) On the basis of the student's research topic and research objectives specified above, answer the following questions: 1.1 With reference to the 5W criteria (What? Who? Why? Where? When?), critically analyse the topic (10 marks) of the research proposal. 1.2 State the aim of the proposed study. (2 marks) 1.3 (3 marks) Formulate three (3) research questions for the proposed study (Hint: the research questions should be based on the student's research objectives ). 1.4 For the proposed study, choose an appropriate research design and motivate your choice. (5 marks) QUESTION 2 (20 Marks) Based on the design you have chosen above in question 1.4 above, discuss the methodology you would follow with regard to the following:
Answers
The research proposal focuses on investigating the determinants of the sustainability of small and medium-sized enterprises (SMEs) in Soweto. The research objectives are to determine the sustainability of SMEs, identify the factors that contribute to their sustainability, and provide practical recommendations to enhance their sustainability.
1.1 The research proposal addresses the "what" by examining the determinants of SME sustainability in Soweto. It focuses on "who" by targeting owner-managers of SMEs in Soweto. The "why" is to understand the factors that influence SME sustainability. The "where" is in Soweto, South Africa, and the "when" refers to the time period during which the research will be conducted.
1.2 The aim of the proposed study is to explore and analyze the determinants of sustainability for small and medium-sized enterprises in Soweto, with the ultimate goal of providing practical recommendations to enhance their sustainability.
1.3 Three research questions for the proposed study could be:
What are the key indicators of sustainability for SMEs in Soweto?
What factors contribute to the sustainability of SMEs in Soweto?
How can owner-managers of SMEs in Soweto improve the sustainability of their businesses?
1.4 An appropriate research design for the proposed study could be a mixed-methods approach. This design would involve both quantitative and qualitative data collection and analysis methods. Quantitative data could be collected through surveys or questionnaires to measure indicators of sustainability and assess the relationship between various factors. Qualitative data could be collected through interviews or focus groups to gain a deeper understanding of the experiences and perspectives of owner-managers. The mixed-methods approach would provide a comprehensive and holistic understanding of the determinants of SME sustainability in Soweto and enable practical recommendations to be formulated based on both quantitative and qualitative insights.
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g on average, a call center receives calls from customers every 7 minutes, and it takes 15 minutes to finish a call. the system assumes poisson arrivals and exponential service time. the manager's goal is to limit the average customer waiting time to 2 minutes. what is the minimum number of customer services the call center needs to have to achieve this goal
Answers
We would need a minimum of 8 customer service representatives to achieve an average waiting time of 2 minutes.
To determine the minimum number of customer service representatives needed to achieve an average waiting time of 2 minutes, we can use the M/M/1 queuing model formula:
L = λ * Wwhere L is the average number of customers waiting in the queue, λ is the arrival rate (calls per minute), and W is the average time a customer spends waiting in the queue.
First, we need to convert the arrival rate from every 7 minutes to arrivals per minute:
λ = 1/7 = 0.143Next, we need to find the service rate, which is the reciprocal of the service time:
μ = 1/15 = 0.067The utilization factor (ρ) is calculated as the ratio of arrival rate to service rate:
ρ = λ/μ = 0.143/0.067 = 2.134Using Little's Law, we can calculate the average number of customers in the system:
L = λ * WL = ρ/(1 - ρ)L = 2.134/(1 - 2.134) = 2.134/-1.134L ≈ -1.88This negative value implies that the system is unstable and would result in an infinite queue. Therefore, we need to increase the number of customer service representatives to reduce the average waiting time.
Assuming we want to achieve an average waiting time of 2 minutes, we can rearrange the formula to solve for the minimum number of customer service representatives (n):
n = (ρ² + ρ) / (2 * (1 - ρ) * (1 - 2 * ρ * \(e^{(-p/2)}\)))
n ≈ 7.89
Therefore, we would need a minimum of 8 customer service representatives to achieve an average waiting time of 2 minutes.
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Can someone could explain the part of simplifying rational expressions where it is x is not equal to a number. I've had a hard time understanding how to get that answer. The picture is an example in my notes.
Answers
Answer:
yeah it is bcoz if x is -1 then x+1 will be
-1+1 which is 0 and ur whole equation will say
now thats a lot of damage
You start at (8, 6). You move left 6 units and right 8 units. Where do you end?
Answers
Answer:
(10,6)
Step-by-step explanation:
of you start at (8,6) X is left and right and Y is up and down so yoy move left 6 unites meaning your now at (2,6) then you move right so you go back again and now you have (10,6) Hope this helps
Code: (B+C) - (D+A)
Help me it’s a puzzle
Answers
Answer:
-A+B+C-D or B+C-D-A
Step-by-step explanation:
Simplify the expression
No, louise is incorrect because using the order of pemdas i know that (5x3+3)2 is 36. i also know that (5x3)2+(3)2 is 36 using the order of pemdas. however the 3rd problem is 25x6+9 and using pemdas i know that this would equal 234 which is not equal to 36 therefore louise is incorrect.
Answers
Based on the calculations, we can conclude that Louise is incorrect in assuming that all three expressions are equal to 36. The correct values for the expressions are 324, 234, and 159, respectively.
The given question involves evaluating expressions using the order of operations, also known as PEMDAS. Let's break down each expression step by step:
Expression 1: (5x3+3)2
According to PEMDAS, we first perform the multiplication (5x3), which equals 15.
Then, we add 3 to get 18. Finally, we square the result, which gives us 324. Therefore, (5x3+3)2 equals 324.
Expression 2: (5x3)2+(3)2
Again, applying PEMDAS, we start with the multiplication (5x3), which equals 15. Then, we square this result, which gives us 225.
Next, we square 3, resulting in 9. Finally, we add 225 and 9, which equals 234. Therefore, (5x3)2+(3)2 equals 234.
Expression 3: 25x6+9
Using PEMDAS, we first perform the multiplication (25x6), which equals 150.
Then, we add 9 to get the final result, which is 159. Therefore, 25x6+9 equals 159.
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What is the equation for the line of the slope intercept
Answers
Answer:
y = (1/7)x - 3
Step-by-step explanation:
By inspection the y-intercept is found to be (0, -3). The slope is
increase in y - 3 - (-4)
m = --------------------- = --------------- = 1/7
increase in x 0 - (-7)
Thus, the slope-intercept form of the equation of this line is
y = mx + b, or y = (1/7)x - 3
math help please 2 questions
Answers
Answer:
first one is the second choice
question 2 is correct, the answer is the 4th option
Step-by-step explanation:
no other words
Annie is
picking apples with her sister.
The number of apples in her
basket is described by n =
22t + 12, where t is the number
of minutes Annie spends picking
apples. What do the numbers 22
and 12 tell you about Annie's
apple picking? What is the
domain of this function?
Answers
The indications of the numbers in the linear equations that produces the number of apples in Annie's basket, n = 22·t + 12, are as follows;
22 is the number of apples Annie picks each minute12 is the initial number of apples in Annie's basket at the startThe domain of the function n = 22·t + 12 is R⁺ which is the set of positive real numbers, including zero, [0, ∞)
What is a linear equation and what is the domain of a function?A linear equation is a equation of the line of a straight line graph. The domain of a function is the set of the input values of the function.
The equation that describes the number of apples in Annie's basket, n = 22·t + 12
The number of minutes Annie spends picking apples = t
The number of apples in Annie's basket = n
The number 22 which is the coefficient of the variable t in the linear equation, which is the slope or the rate of change of the number of apples in Annie's, which indicates the number of apples Annie picks per minute.
The number 22 indicates that Annie picks 22 apples every minuteThe number 12 is the y-intercept of the equation y = 22·t + 12
The y-intercept is the value of the function where t = 0, which is the initial value of the function.
Therefore;
The number 12 indicates the initial number of apples in Annie's basket.The domain of the function n = 22·t + 12, are the possible values of the independent or input variable, t, which is the set of positive integers including 0
Therefore, the domain of the function is; [0, ∞), or the set of positive real numbers, R⁺ including zero R⁺ ∪ {0}.Learn more about linear equations here:
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David is making rice for his guests based on a recipe that requires rice, water, and a special blend of spice, where the rice-to-spice ratio is 15 : 1 15:1.He currently has 40 grams of the spice blend, and he can go buy more if necessary. He wants to make 10 servings, where each serving has 75 grams of rice. Overall, David spends 4.50 dollars on rice. What is the price of rice per gram?
Answers
Answer: Price of rice per gram = $ 0.006 per gram or 0.6 cents per gram .
Step-by-step explanation:
Given: David wants to make 10 servings, where each serving has 75 grams of rice.
Total quantity of rice required = 10 x 75 = 750 grams
Overall, David spends 4.50 dollars on rice.
i.e. cost of 750 grams of rice = 4.50 dollars
Price of rice per gram =(cost of 750 grams of rice ) ÷ 750
= (4.50 dollars ) ÷ 750
= $ 0.006 per gram.
Price of rice per gram = $ 0.006 per gram.
Answer:
0.006
Step-by-step explanation:
ehgfdcgmkmvnnrebsbhbnjrfjgnjkae
Position 3 Value of Term 8 20 Com
Answers
grade 8 unit rate pls add explanation
Franklin needs 2.75 cups of flour for every 1.5 cups of sugar in his cookie recipe. This will yield 3.5 dozen cookies. What is the unit rate for sugar per cookie? Round your answer to the tenths place.
Answers
Answer:
Is it .04
Step-by-step explanation:
What is a force of attraction between an object and the earth due to gravity?
Answers
Newton's law of gravitation says that the force due to gravitation between two objects with masses m₁ and m₁ is given by the formula
\(F=G\dfrac{m_1m_2}{r^2}\)
Where r is the distance between the objects, and G is the gravitational constant (about 6.674×10⁻¹¹ m³⋅kg⁻¹⋅s⁻²)
What is the slope of L=70-14t
Answers
Answer: m=-14
Step-by-step explanation: Use the slope-intercept form y=mx+b to find the slope m.
Graph down below.
I hope this helps you out. If not, I am so sorry.
In solving quadratic equation, if the constant term is missing what is the best method to
use?
Answers
Step-by-step explanation:
If you are looking for its roots, try completing the square method, and factoring out the common terms. These two is what I usually use.How to find the length of the segment indicated?
Answers
Answer:
Step-by-step explanation:
it is 2x
What is One-half of Seven-eighths ?
a.Six-sixteenths
b.Seven-sixteenths
c.Eight-tenths
d.Nine-tenths
Answers
Answer:
Seven-sixteenths
Step-by-step explanation:
(1/2)*(7/8)=7/16
find the distance between the two points (2,-1) and (2,5)
Answers
Answer:
the answer would be 6
Step-by-step explanation:
the way i got my answer is by adding on to the negative on the 2,-1 then i add 5 to the over all to get 1 plus 5 and get 6.
The distance between the two points (2,-1) and (2,5) is 6 units.
What is the distance between two pints?The distance between two points \((x_1,y_1),(x_2,y_2)\) is,
\(d=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2} }\)
For given example,
Let \((x_1,y_1)=(2,-1),(x_2,y_2)=(2,5)\)
Let 'd' be the distance between two points (2,-1) and (2,5).
Using distance formula,
⇒ \(d=\sqrt{(2-2)^{2}+(5-(-1))^{2} }\)
⇒ \(d=\sqrt{(0)+(5+1)^{2} }\)
⇒ \(d=\sqrt{6^{2} }\)
⇒ \(d=6\) units.
Therefore, the distance between two points (2,-1) and (2,5) is 6 units.
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there are 100 sample bottles of cough medicine in the cupboard. if you give 25 bottles away, what percentage is left in the cupboard?
Answers
Answer: 75%
Step-by-step explanation:
common sense
Please answer I’ll mark you brainlist!! :)
Answers
Answer:
The answer is 8
Step-by-step explanation:
4^3 = 64
2^3 = 8
64/8= 8
4^3 = 4 x 4 x 4
4 x 4 = 16
16 x 4 = 64
So, now you have 64/2^3. Now for the second part of the expression.
2^3 = 2 x 2 x 2
2 x 2 = 4
4 x 2 = 8
So, 64/8.
64/8 = 8
So, the answer would be 64/8 or 8. You should probably write 64/8 though because you're using Khan Academy and it's sensitive
In a regression study, a 95% confidence interval for β1 was given as: (-5.65, 2.61). What would a test for H0: β1=0 vs Ha: β1 ≠0 conclude? Select one:a. fail to reject the null hypothesis at null=0.05 and all larger nullb. reject the null hypothesis at null=0.05 and all smaller nullc. fail to reject the null hypothesis at null=0.05 and all smaller nulld. reject the null hypothesis at null=0.05 and all larger null
Answers
The correct answer is (a). fail to reject the null hypothesis at null= 0.05 and all larger null.
The null hypothesis (H0) in this case is that β1=0, meaning that there is no relationship between the independent and dependent variables in the regression study.
The alternative hypothesis (Ha) is that β1≠0, meaning that there is a relationship between the independent and dependent variables.
The 95% confidence interval for β1 is (-5.65, 2.61). This means that we are 95% confident that the true value of β1 falls within this range. Since the range includes 0, we cannot reject the null hypothesis that β1=0.
Therefore, we fail to reject the null hypothesis at a significance level of 0.05 (null=0.05) and all larger significance levels.
In other words, there is not enough evidence to suggest that there is a relationship between the independent and dependent variables in the regression study, so we cannot reject the null hypothesis.
Hence, fail to reject the null hypothesis at null=0.05 and all larger null is the correct answer, i.e., option (a)
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Factor the following expression
24g2 - 18g
Answers
Answer:
6g(4g - 3)
Step-by-step explanation:
24g² - 18g
Common factor:
6g
Factored equation:
6g(4g - 3)
Find an orthogonal matrix A where the first row is a multiple of (3,3,0). A=
Answers
Putting it all together, we get:
A:
[-3 0 0]
[ 0 1 0]
[ 0 0 -1]
which is an orthogonal matrix with the first row being a multiple of (3, 3, 0).
An orthogonal matrix is a square matrix whose columns and rows are orthonormal vectors, i.e., each column and row has unit length and is orthogonal to the other columns and rows.
Let's start by finding a vector that is orthogonal to (3, 3, 0). We can take the cross product of (3, 3, 0) and (0, 0, 1) to get such a vector:
(3, 3, 0) x (0, 0, 1) = (3*(-1), 3*(0), 3*(0)) = (-3, 0, 0)
Note that this vector has length 3, so we can divide it by 3 to get a unit vector:
(-3/3, 0/3, 0/3) = (-1, 0, 0)
So, the first row of the orthogonal matrix A can be (-3, 0, 0) or a multiple of it. For simplicity, we'll take it to be (-3, 0, 0).
To find the remaining two rows, we need to find two more orthonormal vectors that are orthogonal to each other and to (-3, 0, 0). One way to do this is to use the Gram-Schmidt process.
Let's start with the vector (0, 1, 0). We subtract its projection onto (-3, 0, 0) to get a vector that is orthogonal to (-3, 0, 0):
v1 = (0, 1, 0) - ((0, 1, 0) dot (-3, 0, 0)) / ||(-3, 0, 0)||^2 * (-3, 0, 0)
= (0, 1, 0) - 0 / 9 * (-3, 0, 0)
= (0, 1, 0)
We can then normalize this vector to get a unit vector:
v1' = (0, 1, 0) / ||(0, 1, 0)|| = (0, 1, 0)
So, the second row of the orthogonal matrix A is (0, 1, 0).
To find the third row, we take the cross product of (-3, 0, 0) and (0, 1, 0) to get a vector that is orthogonal to both:
(-3, 0, 0) x (0, 1, 0) = (0, 0, -3)
We normalize this vector to get a unit vector:
v2' = (0, 0, -3) / ||(0, 0, -3)|| = (0, 0, -1)
So, the third row of the orthogonal matrix A is (0, 0, -1).
Putting it all together, we get:
A:
[-3 0 0]
[ 0 1 0]
[ 0 0 -1]
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