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Prove that if R is commutative ring and N=(a1,a2,..am) where each ai is a nilpotent element, then N is a nilpotent ideal, i.e N^n=0 for some positive integer n. Deduce that if the nilradical of R is finitely generated then it is a nilpotent ideal.
P.S. the set of nilpotent elements form an ideal which is called nilradical of R for a commutative ring R
if you assume returns follow a normal distribution, which investment has a better chance of giving you $40 million in returns.
How variable is the number of service calls with which Sam's department must deal?
The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals:
What is the probability that the mean weight for a sample of 40 trout exceeds 405.5 grams?
Four components of a time series are secular trend, cyclical variation, seasonal variation, and irregular variation (Lind, 2005). Briefly describe each of these components and provide a real-world example of one component.
If the sides of a square are lengthened bt 5cm, the area becomes 169cm2. Find the length of a side of the original square.
Assume that the cost for this type of hospital emergency room visit is normally distributed with a standard deviation of $92. Assume that the following questions about the cost of a hospital emergency room visit for this medical service.
Which of the following does not explain a possible relationship between variables when the null hypothesis is rejected
A poll found that 38% of male voters and 46% of female voters support a particular candidate. To test whether this candidate has equal levels of support between male and female voters, the null hypothesis should be:
Horizon Wireless, a cellular telephone company, is expanding into a new era. Relay towers are necessary to provide wireless telephone coverage to the different areas of the city.
A man is in the process of buying a new car. He has a choice of 3 engine makes, 7 body styles and 10 colors. How many different cars does he have to choose from?
Based on a survey of over 10,000 households, the number of televisions in the home was recorded as given in the table below. Based on the data, find the expected number of televisions in a home.
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