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Evolutionary theories often emphasize that humans have adapted to their physical environment. One such theory hypothesizes that people should spontaneously follow a 24-hour cycle of sleeping and waking-even if they are not exposed to the usual pattern of sunlight. To test this notion, eight paid volunteers were placed (individually) in a room in which there was no light from the outside and no clocks or other indications of time. They could turn the lights on and off as they wished. After a month in the room, each individual tended to develop a steady cycle. Their cycles at the end of the study were as follows: 25, 27, 25, 23, 24, 25, 26, and 25.
Using the .05 level of significance, what should we conclude about the theory that 24 hours is the natural cycle? (That is, does the average cycle length under these conditions differ significantly from 24 hours?) (a) Use the steps of hypothesis testing. (b) Sketch the distributions involved, (c) Explain your answer to someone who has never taken a course in statistics.
Define, in your own words, a rational expression. Describe the process for finding an equivalent rational expression. Explain why it might be necessary to find an equivalent rational expression, and give an example.
water is leaking out of an inverted conical tank. the tank has a height of 6 meters and the diameter at the top is 4 meters. write the volume of the tank as a function of its height h of the water.
The radius of a circular disk is given as 26cm with a maximum error in measurement of 0.2cm. Use differentials to estimate the maximum possible error in the calculated area of the disk.
As we know, a set is just a collection of objects that are similar in some way, like a gaggle of geese, pride of lions, or an army of ants. To further classify our world, we can create subsets from a larger set. Let's consider the idea of a subset..
In an inventory study it was determined that on average demands for a particular item at a warehouse were made four times per day. What is the probability that on a given day an item is requested.
Then find a particular solution to the non-homogeneous equation.
Find the slope and the equation of the horizontal line that passes through (-325, 185) Find the slope and the equation of the vertical line that passes through (-325, 185) Find the difference quotient of f(x) = 1/x^2
A car is moving at a rate of 76 miles per hour, and the diameter of its wheels is 2.9 feet.
A twin engined aircraft can fly 1520 miles from city A to city B in 5 hours with the wind and make the return trip in 8 hours against the wind. What is the speed of the wind?
Construct a Green's function for the given boundary conditions.
Under plan B, Giselle would pay the first $140, but only 20% of the rest. For what amount of medical bills will plan B save Giselle money? Assume she has over $140 in bills.
Use a finite sum to estimate the average value of the function on the given interval by partitioning the interval and evaluating the function at the midpoints of the subintervals.
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