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Three couples arrive at the bank of a river. Each of the wives is jealous and does not trust her husband when he is with one of the other wives (and perhaps with other people), but not with her. How can six people cross to the other side of the river using a boat that can hold no more than two people so that no husband is alone with a woman other than his wife? Use a graph theory model.
The director of a summer day camp estimates that 120 children will join if the camp fee is $250, but for each $25 decrease in the fee, five more children will enroll.
A matching M in a graph is of maximum size if and only if M has no augmenting path. Further, if a matching M has an augmenting path P with edge set E(P), then we can create a larger matching by deleting the edges in M ∩ E(P) from M and adding in t..
An expensive fencing along the lots length costs $20 per fott and an inexpensive fencing along the two side widths costs only $8 per foot. the total cost of the fencing along the three sides comes to $3280. What is the area of the lot?
When 311 college students are randomly selected and surveyed, it is found that 116 own a car. Find a 99% confidence interval for the true proportion of all college students who own a car.
Suppose that each member of a set of people has a list of k books which he or she wishes to borrow from a library. SUppose also that each book appears on exactly k lists. Show that it is possible for everyone to borrow one of the books on his or h..
assume that adults have iq scores that are normally distributed with a mean of 102 and a standard deviation of 15. find the third quartile Q3 which is the iq score separating the top 25% from the others.
What makes a sequence an arithmetic sequence? Can the constant in an arithmetic sequence be a fraction less than 1? Why? In your own words, explain how using a sequence might be helpful when doing a real world calculation that you personally encount..
At least one of the three employees is lying when all are telling the truth?
Coordinate integration
Let S be a set with an associative binary operation but with no identity. Choose an element 1 not belonging to S, write M = {1} or S, and define an operation on M by using the operation of S and 1s=s=s1 for all s belonging to S.
From a group of 10 boys and 12 girls, a committee of 4 students is chosen at random. What is the probablility that a. all 4 members of the committee will be boys?
Two vertical,cylindrical tanks,each 10 m high are installed side by side in a tank farm,their bottom by a horizontal pipe 2 meters long,with pipe inside diameter 0,03 m.The first tanks(1) is full of oil and the second tank(2) is empty.Moreever,tanks ..
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