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The height of a rooted or binary tree with one vertex is 0; otherwise it is 1 plus the maximum of the heights of its subtrees. Based on Exercise 6.2-9, what is the minimum height of any binary tree on n vertices? (Please prove this.)
a farmer has 400 feet of fence with which to fence a rectangular plot of land. the plot lies along a river so that only three sides need to be fenced. estimate the largest area that can be fenced.
a pizza company claims that it puts 0.5 kg of cheese in its pizza of a certain size. the amount of cheese on a randomly selected pizza of this size is normally distributed with a mean of 0.5 kg and standard deviation of 0.025 kg.
Stonehenge in Salisbury Plains, England, was constructed using solid stone blocks weighing over 99,000 pounds each. Lifting a single stone required more than five hundred people, who pulled the stone up a ramp inclined at an angle of θ = 10° with the..
According to an article in the Maclean's magazine, "Cable, satellite and wireless companies may be charging illegal late fees. Companies may calculate a compounded late-fee rate of two percent a month. However, because they charge even if a customer ..
Now, in how many days will a total of 250 students in the residence hall get infected? Use a constant of propottionality accurate up to four decimal places.
Find the slope and intercepts. If necessary, round all answers to 2 decimal places.
What is the average speed for the round trip?
What should the outside dimensions be of this center for the construction cost to be minimum as possible?
An anchor weighing 105 lb in water is attached to a chain weighing 2 lb/ft in water. Find the work done to haul the anchor and chain to the surface of the water from a depth of 30 ft.
A poster is to have an area of 150 in2 with 3 inch margins at the bottom and sides and a 5 inch margin at the top. What dimensions will give the largest printed area? (Give your answers correct to one decimal place.)
Define the following predicate P(x,y,z) for naturals x and y and positive naturals z. If x = z, then P(x,y,z) is false.
What is the volume of the cuboid of the brick - Find the volume of the room and Find the volume of the cylinder.
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