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3.3. If in a ring R every x ∈ R satisfies x2 = x, prove that R
must be commutative
(A ring in which x2 = x for all elements is called a Boolean ring).
3.1. If R is a ring and a, b, c, d ∈ R, evaluate (a + b)(c + d).
3.2. Prove that if a, b ∈ R, then (a + b)2 = a2 + ab + ba + b2 where
by x2 we mean xx.
according to a study conducted by the grade 12 student, php 175 is the average monthly expenses for cell phone loads of high school students in their province.aA statistics students claim that this amount has increased since January of this year .do you think his claim is acceptable if a random sample of 50 students has an average monthly expense of php164 for cellphone loads ? using 5% level of significance , assume that a population standard deviation is 53
1. Let x be a nilpotent element of a ring A. Show that 1 + x is a unit of A. Deduce
that the sum of a nilpotent element and a unit is a unit.
Solve the system of linear equations using matrix inverse method.
x-y+z=1
2y-z=1
2x+3y=1
A medical centre reports that the average cost of rehabilitation for stroke victims is 24672 BD. To see if the average cost of rehabilitation is different at a particular hospital, a researcher selects 35 victims at random and find the average cost is 26343 BD. Standard deviation is 3251 BD. At α=0.01, can it be concluded that the average cost of rehabilitation at a particular hospital is different form 24672 BD
4. Number of calls coming to customer care of mobile company per minute is a poisson random variable with mean 5. Find the probability that no calls are in certain minute.
A nutritionist wants to know the populatiin proportion of grade 11 students who eat vegetables. Pegged at a confidence of 95% survey among 1200 respondents was conducted and 200 said that they eat vegetables.
a.What is the margin of error?
b.Construct the confidence interval
c.Find the length of the confidence interval
A nutritionist wants to know the population proportion of grade 11 students who eat vegetables . Pegged at a confidence of 95% survey among 1200 respondents was conducted and 200 said that they eat vegetables. What is the margin of error???
45* . Prove that if a, b, c are three different integers, then there exist in-
finitely many positive integers n such that a+n, b+n, c+n are pairwise rel-
atively prime.
