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Let R be a principal ideal domain and let M be a torsion R-module. Prove that M is irreducible iff M=Rm for any nonzero element m in M where the annihilator of m is a nonzero prime ideal (p)
Statistics and Probability, Statistics
Amy currently has $500 in an account with an annual rate of return of 4.3%. She wants to have $3000 for a trip to Florida when she graduates in 2 years. How much will she have to save each month to afford her trip?
A statistics student has collected data from a random sample of 20 college students at his school. He collected data on many variables including GPA (grade point average) and how many hours per week they play video games ...
Jane must get at least three out of four problems on the exam correct to get an A. She has been able to do 60% of the problems on old exams, so she assumes that the probability she gets a given problem correct is 0.6. Sh ...
In the game of? roulette, a player can place a ?$7 bet on the number 18 and have a 1/38 probability of winning. If the metal ball lands on 18?, the player gets to keep the ?$7 paid to play the game and the player is awar ...
Boxes of sugar are filled by machine with considerable accuracy. The distribution of box weights is normal and has a mean of 32 ounces with a standard deviation of only 2 ounces. A quality control inspector takes a sampl ...
A school newspaper reporter decides to randomly survey 12 students to see if they will attend Tet (Vietnamese New Year) festivities this year. Based on past years, she knows that 24% of students attend Tet festivities. W ...
Is the following an example of a binomial experiment? At a campus activities board event, an entertainer gives tickets with sequential numbers to every attendee (i.e. 1, 2, 3, 4, 5... n). Throughout the event, the entert ...
We choose a number from the set {1, 2, ..., 100} uniformly at random and denote this number by X . For each of the following choices, determine whether the events in question are independent or not. A = {X is even}, B = ...
Discuss if you think policy makers truly represent the citizenry or are they pressured by third party special interest groups that support their campaigns. Should they represent both?
During a certain week the mean price of gasoline was $2.719 a gallon. A ronadom sample of 32 stations is drwn. What is the probability that the mean price was between $2.695 and $2.716. Assume o=$0.048.
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Why might a bank avoid the use of interest rate swaps, even when the institution is exposed to significant interest rate
Describe the difference between zero coupon bonds and coupon bonds. Under what conditions will a coupon bond sell at a p
Compute the present value of an annuity of $ 880 per year for 16 years, given a discount rate of 6 percent per annum. As
Compute the present value of an $1,150 payment made in ten years when the discount rate is 12 percent. (Do not round int
Compute the present value of an annuity of $ 699 per year for 19 years, given a discount rate of 6 percent per annum. As