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1. Consider the closed interval [0,1]. Remove the open interval 11 I which has center at 1/ 2and length 1/ 2 . 2 Then remove 12 I and 22 I from 11 I ? I so that their centers coincide with the center of closed interval of 11 [0,1]? I and their length 1/ 2 . 4 Continuing in this way, construct 1/ 2 K in a similar way we constructed the Cantor set K in class, as an intersection of all remaining closed intervals. And show that length of the complement of 1/ 2 K is 1/ 2. 2.Use the induction to prove Bernoulli's inequality: If 1+x>o, then (1+x)^n≥1+nx for all n in N 3.Let S be a nonenpty bounded subset of R and let m=sup S. Prove that m∈S iff m=max S
Using the graph, how much should be spent on advertising to maximize sales? What is the maximum sales level?
Test the instructor's claim at a five percent level of significance. Write your conclusion?
how many commuters must be randomly selected to estimate the mean driving time of chicago commuters? we want 98
a car rents for $35 per day plus .18 per mile you are on a daily budget of $71. what mileage will allow you to stay within your budget?
Probability density function sample question, Let E be the event that the number which comes up when a single die is tossed is divisible by 3. Let X be the number of times that event E occurs in 3 tosses of the die
Assume that d=sa+tb is a linear combination of integers a and b. Find infinitely many pairs of integers ( s sub k, t sub k ) with d=s sub k a + t sub k b
What will the value of the investment be after 12 years? If the deposits were made at the beginning of each period, what would the value of the deposits be after 12 years?
Find the linear equation that relates value (V) in dollars to time (t) in years. What would be the value of the equipment after 6 years?
I want to prove that a population mean is not 150. Use an alpha of 5 percent & set up the full, detailed, five step hypothesis test. Suppose when the sample 200 is taken the sample standard deviation is ten & the sample mean is 151.77.
Show that the greedy algorithm for making change for n cents using quarters, dimes, nickels and pennies has O(n) complexity measured in terms of comparisons needed.
If q is the number of quarts of lemonade, than 1/4 q can be used to find the number of cups of lemonade mix needed to make the lemonade. How much mix is needed to make each amount of lemonade?
The upper left-hand corner of a piece of paper 8 in. wide by 12 in. long is folded over to the righthand edge as in the figure. How would you fold it so as to minimize the length of the fold? In other words, how would you choose x to minimize y?
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