Description
Show that if a, b (= Z such that a, b not= 0, then gcd(9a, 9b) = 9 · gcd(a, b).
[Hint: Let d = gcd(a, b). Then show that the product 9d satisfies the definition of the GCD of 9a and 9b
User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.
Explanation & Answer
d=gcd(a, b) if and only if then a = d*a' and b = d*b' where a' and b' are mutually prime integers.
Since 9a = (9d)*a' and 9b = (9d)*b', we conclude that 9d = gcd(9a, 9b).
Completion Status:
100%
Review
Review
Anonymous
Really great stuff, couldn't ask for more.
Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4
24/7 Homework Help
Stuck on a homework question? Our verified tutors can answer all questions, from basic math to advanced rocket science!
Most Popular Content
6 pages
Solution
A random sample of 5 year old children is evaluated for being left- or right-handed. The size n = 100 children of which 79 ...
Solution
A random sample of 5 year old children is evaluated for being left- or right-handed. The size n = 100 children of which 79 are right-handed, 15 are ...
MATH 160 CC Undergraduate Students Sleep Hours in Nighttime Lab Report
Progress CheckUse this activity to assess whether you and your peers can: Under appropriate conditions, conduct a hypothes ...
MATH 160 CC Undergraduate Students Sleep Hours in Nighttime Lab Report
Progress CheckUse this activity to assess whether you and your peers can: Under appropriate conditions, conduct a hypothesis experiment about a difference between two population means. State a conclusion in contextLearn by DoingIn this activity you will learn to use StatCrunch to perform a two-sample t-test.Some features of this activity may not work well on a cell phone or tablet. We highly recommend that you complete this activity on a computer.Use the rubric at the bottom of this page as a guide for completing this assignment.A list of StatCrunch directions is provided after the Prompt section below.DirectionsSubmit your work:Carefully read all sections below (beginning with the Context section and ending with the Prompt section).Commit a good-faith effort to address all items in the Prompt section below. Please be sure to number your responses.If directed to do so, embed all required StatCrunch output in your initial submission. Please do not submit StatCrunch output as an attachment.Complete your assigned peer reviews:After you submit your initial good-faith attempt, continue to the ANSWER(S) page and review your instructor's response. But please do not submit your corrected work yet.Within three days after the due date, return to this assignment and complete your assigned peer reviews (directions (Links to an external site.)).Submit your corrected work:We all learn from mistakes (our own and our classmates' mistakes). So please do not immediately correct your own mistakes. If possible, wait until you receive feedback from at least one of your peers. If necessary, correct your work and resubmit the entire assignment - including any required StatCrunch output. Your instructor will only review and grade your most recent submission, so please do not refer to a previous submission.ContextDo undergraduates sleep less than graduate students?A student conducted a study of sleep habits at a large state university. His hypothesis is that undergraduates will party more and sleep less than graduate students. He surveyed random samples of 75 undergraduate students and 50 graduate students. Subjects reported the hours they sleep in a typical night.For this hypothesis test, he defined the population means as follows:𝜇1μ1μ2 is the mean number of hours undergraduate students sleep in a typical night.𝜇2 is the mean number of hours graduate students sleep in a typical night.VariablesHours: typical number of hours a student sleeps each night Program: undergraduate or graduate Program is the explanatory variable, and the data is categorical. Hours is the response variable, and the data is quantitative.DataDownload the sleep2 (Links to an external site.) datafile, and upload the file in StatCrunch. PromptState the null and alternative hypotheses. Include a clear description of the populations and the variable.Explain why we can safely use the two-sample T-test in this case.Use StatCrunch to carry out the test. (directions)Copy and paste the content of in the StatCrunch output window (text and the table) in your initial post. State a conclusion in the context of this problem.List of StatCrunch DirectionsEach link will open in a new window. To return to this discussion, either close the new tab or select the tab for this discussion. Purchase StatCrunch (You only need to do this once.)Open StatCrunchDownload Excel FileUpload Excel Data File to StatCrunchDownload StatCrunch Output Window (no screenshots; please use these directions)Upload Files to Your Stats-Class Folder in CanvasEmbed Pictures in a Textbox (no attachments; please use these directions)Copy & Paste a StatCrunch Table Conduct a Hypothesis Test for a Difference in Two Population MeansContent by the Open Learning Initiative (Links to an external site.) and licensed under CC BY (Links to an external site.).RubricPeer Reviewed Assignment w/ StatCrunchPeer Reviewed Assignment w/ StatCrunchCriteriaRatingsPtsThis criterion is linked to a Learning OutcomeAddressing the Prompt6 ptsFull MarksAll parts of the Prompt are addressed. Answers are correct. Statistical vocabulary is used appropriately. Writing is clear and thought process is easy to follow.4 ptsPartial CreditSome parts of the prompt are not addressed, are incorrect, or are unclear.0 ptsNo MarksThe prompt is not addressed.6 ptsThis criterion is linked to a Learning OutcomeStatCrunch Data2 ptsFull MarksAppropriate StatCrunch graphs and/or tables are provided as directed.1 ptsPartial CreditStatCrunch graphs and tables are inappropriate or missing important information.0 ptsNo MarksNo StatCrunch information is provided.2 ptsThis criterion is linked to a Learning OutcomeIndividual Penalty0 ptsNo individual penalty-1 ptsIndividual penalty.Please see the instructor comments for more information.0 ptsThis criterion is linked to a Learning OutcomePeer Reviews2 ptsFull MarksYou completed all assigned peer reviews (maximum of 2). For each peer review, the points you assigned in the rubric are appropriate. You included comments explaining the score you posted in the rubric. If you deducted points in the rubric, your comments explain what the author needs to do to earn a higher grade when the teacher grades the assignment.1 ptsPartial CreditCommitted a good-faith effort to provide a high-quality peer review, but many necessary instructive comments are missing.0 ptsNo MarksNo peer review provided or the comments are not instructive.2 ptsTotal Points: 10
MAC2105 College Algebra Week 4
Need assistance in completing week 4. There is multiple classwork that needs to be completed. This includes week 4 weekly ...
MAC2105 College Algebra Week 4
Need assistance in completing week 4. There is multiple classwork that needs to be completed. This includes week 4 weekly summary (10 Question answer with steps on how you found the answer). There is week 4 Summary as well as 3 other exams as well.All work has is found and completed on my student portal website. Access will be provided to you.Week 4 Weekly SummaryWhen posting here in the Weekly Summary section please do not post "answers only" but rather show how you obtained your answers in a step by step manner. If your solution is correct, it is in your best interest for us to see how you obtained the answer. If your solution is incorrect, showing your steps will help us to follow your process and we can then work together to find your mistake.No bonus points will be awarded for answers without explanations.A maximum of 5 bonus points will be awarded for 5 correct answers with step by step explanations.The weekly summary answers and explanations will be posted in the Announcement section by Friday of each week. Please try to work each problem without pasting and copying or you will defeat your purpose of learning. Credit will only be given for "original" work. Please feel free to study the explanations, learn the problem, and create your own step-by-step explanation for bonus points . You may post your explanations throughout the term (please remind your instructor in the General Questions thread to grade your problems if you have posted after Sunday).Solve the following equation for n:n/4 - 5/6 = 5/12Solve the following equation for x:2x/3 - 4x/5 = 1/15Solve the following equation for x: 9/(4x) + 1/3 = 5/(2x)Solve the following equation for x:|5x-7| = 14Hint: This absolute value equation will turn into 2 linear equations, so there will be two solutions!Solve the following system of linear equations: 2x + 3y = -5 -2x + y = 9 6. Solve for (x, y, z), if there is a solution to the given system of linear equations: - x + 2y + 3z = 0 3x - 2y - 2z = 5 4x + y - 3z = -9 7 . Solve: x2 - 4x + 5 = 0. 8, Add the complex numbers: (5 – 2i) + (1 + 6i) 9. Subtract the complex numbers: (4+3i) - (6+i). 10. Multiply the complex numbers (4+3i) (6+i).Week 4 Algebra Talk Many students have often asked questions such as: Why do I need to learn Mathematics? Where and when am I going to use it in my life?Now that you are almost done with this College Algebra class, can you now explain why it is important for everyone to learn Mathematics? Can you also give examples on when, where, and how you have used and are using Mathematics in your everyday life?Please give examples and feel free to include: budgeting, investing, traveling, locating, securing personal informations, spending, saving, investing, measuring, cooking, etc.EXAMPLE: Hello! Math is an everyday tool that I use in everything I do. Math is important because it helps me take care of everything I need to on a daily basis. I was able to calculate how much money I would save for the year after doing my monthly budgets. I was able to figure out the distance, mileage, time, and how much it would cost to drive from Florida to New York last month. Then I was able point out the exact location of my final destination on a map. "The great book of nature can be read only by those who know the language in which it was written. And that language is mathematics". Galileo
Similar Content
Functions equations x
the equation x-6+4y=4 is it a function ...
Bluffton University People of Color and Odds Over Workplace Equity Essay
Hello , In this projected there is 6 parts of it. I did part 1-5 and I attracted I also attracted the rubric of the whole ...
Applied Analysis Continuous Function & Differentiable Function Worksheet
Please send me type work, and I want it by the end of Nov 22. (Not very far from now) Thank you!!...
Related Tags
Book Guides
One Flew Over the Cuckoos Nest
by Ken Kesey
Little Women
by Louisa May Alcott
Homo Deus
by Yuval Noah Harari
Dracula
by Bram Stoker
Uncle Tom's Cabin
by Harriet Beecher Stowe
A Passage to India
by E. M. Forster
Salt To The Sea
by Ruta Sepetys
Harry Potter and the Sorcerers Stone
by J. K. Rowling
12 Rules for Life
by Jordan Peterson
Get 24/7
Homework help
Our tutors provide high quality explanations & answers.
Post question
Most Popular Content
6 pages
Solution
A random sample of 5 year old children is evaluated for being left- or right-handed. The size n = 100 children of which 79 ...
Solution
A random sample of 5 year old children is evaluated for being left- or right-handed. The size n = 100 children of which 79 are right-handed, 15 are ...
MATH 160 CC Undergraduate Students Sleep Hours in Nighttime Lab Report
Progress CheckUse this activity to assess whether you and your peers can: Under appropriate conditions, conduct a hypothes ...
MATH 160 CC Undergraduate Students Sleep Hours in Nighttime Lab Report
Progress CheckUse this activity to assess whether you and your peers can: Under appropriate conditions, conduct a hypothesis experiment about a difference between two population means. State a conclusion in contextLearn by DoingIn this activity you will learn to use StatCrunch to perform a two-sample t-test.Some features of this activity may not work well on a cell phone or tablet. We highly recommend that you complete this activity on a computer.Use the rubric at the bottom of this page as a guide for completing this assignment.A list of StatCrunch directions is provided after the Prompt section below.DirectionsSubmit your work:Carefully read all sections below (beginning with the Context section and ending with the Prompt section).Commit a good-faith effort to address all items in the Prompt section below. Please be sure to number your responses.If directed to do so, embed all required StatCrunch output in your initial submission. Please do not submit StatCrunch output as an attachment.Complete your assigned peer reviews:After you submit your initial good-faith attempt, continue to the ANSWER(S) page and review your instructor's response. But please do not submit your corrected work yet.Within three days after the due date, return to this assignment and complete your assigned peer reviews (directions (Links to an external site.)).Submit your corrected work:We all learn from mistakes (our own and our classmates' mistakes). So please do not immediately correct your own mistakes. If possible, wait until you receive feedback from at least one of your peers. If necessary, correct your work and resubmit the entire assignment - including any required StatCrunch output. Your instructor will only review and grade your most recent submission, so please do not refer to a previous submission.ContextDo undergraduates sleep less than graduate students?A student conducted a study of sleep habits at a large state university. His hypothesis is that undergraduates will party more and sleep less than graduate students. He surveyed random samples of 75 undergraduate students and 50 graduate students. Subjects reported the hours they sleep in a typical night.For this hypothesis test, he defined the population means as follows:𝜇1μ1μ2 is the mean number of hours undergraduate students sleep in a typical night.𝜇2 is the mean number of hours graduate students sleep in a typical night.VariablesHours: typical number of hours a student sleeps each night Program: undergraduate or graduate Program is the explanatory variable, and the data is categorical. Hours is the response variable, and the data is quantitative.DataDownload the sleep2 (Links to an external site.) datafile, and upload the file in StatCrunch. PromptState the null and alternative hypotheses. Include a clear description of the populations and the variable.Explain why we can safely use the two-sample T-test in this case.Use StatCrunch to carry out the test. (directions)Copy and paste the content of in the StatCrunch output window (text and the table) in your initial post. State a conclusion in the context of this problem.List of StatCrunch DirectionsEach link will open in a new window. To return to this discussion, either close the new tab or select the tab for this discussion. Purchase StatCrunch (You only need to do this once.)Open StatCrunchDownload Excel FileUpload Excel Data File to StatCrunchDownload StatCrunch Output Window (no screenshots; please use these directions)Upload Files to Your Stats-Class Folder in CanvasEmbed Pictures in a Textbox (no attachments; please use these directions)Copy & Paste a StatCrunch Table Conduct a Hypothesis Test for a Difference in Two Population MeansContent by the Open Learning Initiative (Links to an external site.) and licensed under CC BY (Links to an external site.).RubricPeer Reviewed Assignment w/ StatCrunchPeer Reviewed Assignment w/ StatCrunchCriteriaRatingsPtsThis criterion is linked to a Learning OutcomeAddressing the Prompt6 ptsFull MarksAll parts of the Prompt are addressed. Answers are correct. Statistical vocabulary is used appropriately. Writing is clear and thought process is easy to follow.4 ptsPartial CreditSome parts of the prompt are not addressed, are incorrect, or are unclear.0 ptsNo MarksThe prompt is not addressed.6 ptsThis criterion is linked to a Learning OutcomeStatCrunch Data2 ptsFull MarksAppropriate StatCrunch graphs and/or tables are provided as directed.1 ptsPartial CreditStatCrunch graphs and tables are inappropriate or missing important information.0 ptsNo MarksNo StatCrunch information is provided.2 ptsThis criterion is linked to a Learning OutcomeIndividual Penalty0 ptsNo individual penalty-1 ptsIndividual penalty.Please see the instructor comments for more information.0 ptsThis criterion is linked to a Learning OutcomePeer Reviews2 ptsFull MarksYou completed all assigned peer reviews (maximum of 2). For each peer review, the points you assigned in the rubric are appropriate. You included comments explaining the score you posted in the rubric. If you deducted points in the rubric, your comments explain what the author needs to do to earn a higher grade when the teacher grades the assignment.1 ptsPartial CreditCommitted a good-faith effort to provide a high-quality peer review, but many necessary instructive comments are missing.0 ptsNo MarksNo peer review provided or the comments are not instructive.2 ptsTotal Points: 10
MAC2105 College Algebra Week 4
Need assistance in completing week 4. There is multiple classwork that needs to be completed. This includes week 4 weekly ...
MAC2105 College Algebra Week 4
Need assistance in completing week 4. There is multiple classwork that needs to be completed. This includes week 4 weekly summary (10 Question answer with steps on how you found the answer). There is week 4 Summary as well as 3 other exams as well.All work has is found and completed on my student portal website. Access will be provided to you.Week 4 Weekly SummaryWhen posting here in the Weekly Summary section please do not post "answers only" but rather show how you obtained your answers in a step by step manner. If your solution is correct, it is in your best interest for us to see how you obtained the answer. If your solution is incorrect, showing your steps will help us to follow your process and we can then work together to find your mistake.No bonus points will be awarded for answers without explanations.A maximum of 5 bonus points will be awarded for 5 correct answers with step by step explanations.The weekly summary answers and explanations will be posted in the Announcement section by Friday of each week. Please try to work each problem without pasting and copying or you will defeat your purpose of learning. Credit will only be given for "original" work. Please feel free to study the explanations, learn the problem, and create your own step-by-step explanation for bonus points . You may post your explanations throughout the term (please remind your instructor in the General Questions thread to grade your problems if you have posted after Sunday).Solve the following equation for n:n/4 - 5/6 = 5/12Solve the following equation for x:2x/3 - 4x/5 = 1/15Solve the following equation for x: 9/(4x) + 1/3 = 5/(2x)Solve the following equation for x:|5x-7| = 14Hint: This absolute value equation will turn into 2 linear equations, so there will be two solutions!Solve the following system of linear equations: 2x + 3y = -5 -2x + y = 9 6. Solve for (x, y, z), if there is a solution to the given system of linear equations: - x + 2y + 3z = 0 3x - 2y - 2z = 5 4x + y - 3z = -9 7 . Solve: x2 - 4x + 5 = 0. 8, Add the complex numbers: (5 – 2i) + (1 + 6i) 9. Subtract the complex numbers: (4+3i) - (6+i). 10. Multiply the complex numbers (4+3i) (6+i).Week 4 Algebra Talk Many students have often asked questions such as: Why do I need to learn Mathematics? Where and when am I going to use it in my life?Now that you are almost done with this College Algebra class, can you now explain why it is important for everyone to learn Mathematics? Can you also give examples on when, where, and how you have used and are using Mathematics in your everyday life?Please give examples and feel free to include: budgeting, investing, traveling, locating, securing personal informations, spending, saving, investing, measuring, cooking, etc.EXAMPLE: Hello! Math is an everyday tool that I use in everything I do. Math is important because it helps me take care of everything I need to on a daily basis. I was able to calculate how much money I would save for the year after doing my monthly budgets. I was able to figure out the distance, mileage, time, and how much it would cost to drive from Florida to New York last month. Then I was able point out the exact location of my final destination on a map. "The great book of nature can be read only by those who know the language in which it was written. And that language is mathematics". Galileo
Earn money selling
your Study Documents