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Let K be a compact Hausdorff space and suppose for some k there are k continuous functions f1,..., fk from K into R such that x i→ ( f1(x ),..., fk (x )) is one-to-one from K into Rk . Let F be the smallest algebra of functions containing f1, f2,..., fk and 1. (a) Show that F is dense in C (K ) for dsup. (b) Let K := S1 := {(cos θ, sin θ ): 0 ≤ θ ≤ 2π } be the unit circle in R2 with relative topology. Part (a) applies easily for k = 2. Show that it does not apply for k = 1: there is no 1-1 continuous function f from S1 into R. Hint: Apply the intermediate value theorem, Problem 14(d) of Section 2.2. For θ consider the intervals [0, π ] and [π, 2π ].
Make a scatter plot of Y and X1 using Word. To do this click on insert and then chart. Click on X Y (Scatter). Enter the data from the table.
When the names of all the students at Omega University were dropped to a fishbowl, they would include:
Qoestion 1: A researcher is interested in the effects of gender on alcohol use. What is the independent variable(s)? Question 2: A researcher is interested in the effects of gender on alcohol use. What is the dependent variable(s)?
Pick a random sample of 50 homes from the enclosed 90 cases. Double the asking price and selling price and use this data to develop three predictive models:
a class of first graders includes 7 girls and 14 boys 2 students are selected at random for the teacher to help on a
the manager of a supermarket found that 72 of the shoppers who taste a free sample of a food item will buy the item.
Estimate the population mean
Discuss an example where you would use a test of hypothesis with three or more population means (that can be analyzed using ANOVA technique) at your employment or personal life.
4. Why is a 99% confidence interval wider than a 95% confidence interval?
you conducted a chi-square goodness of fit test in your asci 691 capstone project. unfortunately you did not get the
Write a problem for a classmate to solve that can be translated to a system of two (2) or more equations in a least two (2) variables. Explain your answer.
Should the conclusions between the two tests consistent? Why or why not? If the conclusions are not consistent, which one would you agree with and why?
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