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Our arguments in favor of the sum principle were quite intuitive. In fact the sum principle for n sets follows from the sum principle for two sets. Use induction to prove the sum principle for a union of n sets from the sum principle for a union of two sets.
A rectangular study plot is to be enclosed by 625 m of fencing. What are the dimensions of the study plot that will have the largest area?
A car rental agency rents 220 cars per day at a rate of 31 dollars per day. For each 1 dollar increase in the daily rate, 5 fewer cars are rented. At what rate should the cars be rented to produce the maximum income, and what is the maximum income..
For the problem given in Question 2, the probabilities are given by P(10000 miles) = 0.5, P(14000 miles) = 0.3 and P(18000 miles) = 0.2. Compute the expected value for each decision and select the best one. Compute the expected regret value for each..
If you drew all possible samples from some population, calculated the mean for each of the samples, and constructed a line graph (showing the shape of the distribution) based on all of those means, what would you have?
Out of 5000 policies for cell phones, a company received 585 claims. The average amount paid on the claims was $80. If the annual cost of the policy was $48, what was a customer's expected value of the cell phone insurance policy?
Round your answer to 4 decimal places. Remember to round your z-value to 2 decimal places.
Does this method find an augmenting path? Is there an augmenting path?
In lectures, we estimated the area under the graph of y = x2 over the interval [0, b] by partitioning [0, b] into n equal subintervals, estimating the area under the curve over each of these subintervals, and adding up the resulting estimates. The..
The trough is full of water (density 1000 kg/m^3 ). Find the amount of work in joules required to empty the trough by pumping the water over the top. (Note: Use g=9.8 m/s^2 as the acceleration due to gravity.)
Describe fractional parts. What are the two distinct requirements of fractional parts? Explain how children's concepts of partitioning need to be refined to produce a concept of fractional parts.
There is a formula that converts temperature in degrees Celsius to temperature in degrees Fahrenheit. You are given the following data points:
Compare your answer with that given by thePoisson approximation.
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