#3 on the book b MATLAB: An Introduction with A XThomas W. Hungerford - Abstrac ×+O File | C:/Users/angel/Downloads/Thomas%20W.%20Hungerford%20-%20Abstract%20Algebra_%20AN%20lntroduction-Cengage%20Learning%20(2014).pdf- A) Read aloud V DrawF HighlightO Erase121of 621Proof - Adapt the proof of Corollary 1.3 to F[x].Polynomials f(x) and g(x) are said to be relatively prime if their greatest commondivisor is 1pTheorem 4.10Let F be a field and a(x), b(x), c(x)eF[x]. If a(x)| b(x)c(x) and a(x) and b(x) arerelatively prime, then a(x)|c(x).Proof Adapt the proof of Theorem 1.4 to F[x]. II ExercisesNOTE: F denotes a field.A. 1. If f(x) EF[x], show that every nonzero constant polynomial divides f(x).2. If f(x) = G + · · · + co with C, # Op, what is the gcd of f(x) and Op?3. If a, beFand a + b, show that x+a and x + b are relatively prime in F[x].4. (a) Let f(x), g(x)EF[x]. If f(x)|g(x) and g(x)\f(x), show that f(x) = cg(x) forsome nonzero cEF.(b) If f(x) and g(x) in part (a) are monic, show that f(x) = g(x).5. The Euclidean Algorithm for finding god's is described for integers in Exercise 15of Section 1.2. The process given there also works for polynomials over afield, with one minor adjustment. For integers, the last nonzero remainder isthe gcd. For polynomials the last nonzero remainder is a common divisor ofhighest degree, but it may not be monic. In that case, multiply it by the inverseof its leading coefficient to obtain the gcd. Use the Euclidean Algorithm tofind the gcd of the given polynomials:(a) x*-x - + 1 and x - 1 in Q[x](b) * +x + 2x -x- x- 2 and x* + 2x' + 5x? + 4x + 4 in Q[x](c) x* + 3x + 2x + 4 and x – 1 in Z[](d) 4x* + 2x + 6x² + 4x + 5 and 3x+ 5x? + 6x in Z,[x]Coprte 2012 O La AI Rig Rad May aot be copled t or te wae or in part D to leroic d,e rd perty eo y be fnte Bodk ndrC . Balvw bded that ny d dn at any ha he oaa ngmpera Cglaing ieomveddidonal tay te dghteinaguire i100 Chapter 4 Arithmetic in F[x]11:13 AMe Type here to searchEPICAiEPIC99+10/30/2020

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Answered: 3. If a, beFand ab, show that x + a…

3. If a, beFand ab, show that x + a andx+ bare relatively prime in FIx. 4 (a) Let fly) drle ETyl If (lof v) and of v showthat f(y) cef r) for

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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From time to time, the UTM Human Resource (UTMHR) department observes various employees fortheir work productivity. Recently UTMHR wanted to check whether the four employees at theDepartment XYZ counters, serve on average the same number of customers per hour. The HR managerobserved each of the four employees for a certain number of hours. The following Table 5 gives thenumber of customers served by the four employees during each of the observed hours. employee a employee b employee c employee d 19 14 11 24 21 16 14 19 26 14 21 21 24 13 13 26 18 17 16 20 employee a employee b employee c employee d mean 21.6 14.8 15.0 22.0 s 3.4 ? 3.8 ? c) Find variance between sample,d) Find variance within sample, e) Calculate the test statistic, F.f) Determine the numerator and denominator.g) Find the critical value of F at the 5% significance level, and test the claim that the mean numberof customers served per hour by each of these four employees is…
From time to time, the UTM Human Resource (UTMHR) department observes various employees fortheir work productivity. Recently UTMHR wanted to check whether the four employees at theDepartment XYZ counters, serve on average the same number of customers per hour. The HR managerobserved each of the four employees for a certain number of hours. The following Table 5 gives thenumber of customers served by the four employees during each of the observed hours. employee a employee b employee c employee d 19 14 11 24 21 16 14 19 26 14 21 21 24 13 13 26 18 17 16 20 a) Define the hypothesis null, H0 and hypothesis alternative, H1.b) Given below are means and standard deviation for some of the employees. Calculate thestandard deviation for Employee B and D.
In the construction process for solid-state flash memory drives (thumb drives), nearly all drives areconstructed with a large potential amount of storage space, and are sold base on the actual amountof memory that forms correctly during the process (For example, drives that are designed to store 64gb but contain a large number of bad sectors will instead be formated and sold as 32 gb). Consider amanufacturing process where every chip has a 21% of having enough bad sectors to be downgraded,and these errors are random and independent.(a) If we wish to compute the probability thatxnumber of chips out of a production run of sizenaredowngraded, do we have a probability distribution that will work for that? Are the assumptionsfor that met? Explain. (b) Compute the probability that 5 chips out of a production run of 40 are downgraded. (c) Compute the probability that between 3 and 5 (inclusive)orbetween 2 and 8 (inclusive) aredowngraded. (d) Graph the probability mass function forxnumber of…
In the construction process for solid-state flash memory drives (thumb drives), nearly all drives areconstructed with a large potential amount of storage space, and are sold base on the actual amountof memory that forms correctly during the process (For example, drives that are designed to store 64gb but contain a large number of bad sectors will instead be formated and sold as 32 gb). Consider amanufacturing process where every chip has a 21% of having enough bad sectors to be downgraded,and these errors are random and independent. (a) If we wish to compute the probability that x number of chips out of a production run of size n are downgraded, do we have a probability distribution that will work for that? Are the assumptionsfor that met? Explain. (b) Compute the probability that between 3 and 5 (inclusive)or between 2 and 8 (inclusive) are downgraded. (c) Graph the probability mass function for x number of chips out of a production run of 10 aredowngraded.
Three components are connected to form a system asshown in the accompanying diagram. Because the componentsin the 2–3 subsystem are connected in parallel, thatsubsystem will function if at least one of the two individualcomponents functions. For the entire system to function,component 1 must function and so must the 2–3 subsystem. The experiment consists of determining the condition ofeach component [S (success) for a functioning componentand F (failure) for a nonfunctioning component].a. Which outcomes are contained in the event A thatexactly two out of the three components function?b. Which outcomes are contained in the event B that atleast two of the components function?c. Which outcomes are contained in the event C that thesystem functions?d. List outcomes in C9, A ø C, A ù C, B ø C, andB ù C.
A political strategist claims that 58% of voters in Madison County support his candidate. In a poll of 500 randomly selected voters, 260 of them support the strategist's candidate. At alpha = .05, is the political strategist's claim warranted?
Data on the 4000 largest mutual funds shows which funds provided a high 5-year return and a high 10-year return. Of the 4000 mutualfunds surveyed, 3000 funds had a high 5-year return, 2000 had a high 10-yearreturn, and 1500 had both a high 5-year return and a high 10-year return Given that a mutual fund had a high 5-year return, what is theprobability of a mutual fund having a high 10-year return?
High school seniors with strong academic records apply to the nation’s mostselective colleges in greater numbers each year. Because the number of slotsremains relatively stable, some colleges reject more early applicants. Suppose thatfor a recent admissions class, an Ivy League college received 2851 applications forearly admission. Of this group, it admitted 1033 students early, rejected 854outright, and deferred 964 to the regular admission pool for further consideration.In the past, this school has admitted 18% of the deferred early admission applicantsduring the regular admission process. Counting the students admitted early andthe students admitted during the regular admission process, the total class sizewas 2375. Let ?, ?, and ? represent the events that a student who applies for earlyadmission is admitted early, rejected outright, or deferred to the regularadmissions pool.a. Are events E and D mutually exclusive? Find (? ∩ ?)b. Suppose a student applies for early admission. What…
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If a study determines the difference in average salary for subpopulations of people with blue eyes and people with brown eyes is NOT significant, then the populations of blue-eyed people and brown-eyed people are ________ different salaries. a) unlikely to have b) very unlikely to have c) guaranteed to have d) guaranteed to not have