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A univariate polynomial can be divided by another one to produce a polynomial quotient and a polynomial remainder. For example,
Division can be performed via long division. That is, divide the highest-order term of the dividend by the highest-order term of the divisor. The result is the first term of the quotient. Next, multiply the result by the divisor, subtract that from the dividend, and produce the rest of the answer by recursively dividing the difference by the divisor. Stop when the order of the divisor exceeds the order of the dividend and declare the dividend to be the remainder. Also, if the dividend ever becomes zero, return zero as both quotient and remainder. We can design a div-poly procedure on the model of add-poly and mul-poly. The procedure checks to see if the two polys have the same variable. If so, div-poly strips off the variable and passes the problem to div-terms, which performs the division operation on term lists. Div-poly finally reattaches the variable to the result supplied by div-terms. It is convenient to design div-terms to compute both the quotient and the remainder of a division. Div-terms can take two term lists as arguments and return a list of the quotient term list and the remainder term list. Complete the following definition of div-terms by filling in the missing expressions. Use this to implement div-poly, which takes two polys as arguments and returns a list of the quotient and remainder polys.
suppose x is a discrete random variable with probability distributionx01fx1-ppin other words x is a bernuolli random
discuss the issues a decision maker should consider when determining the significance level to use in a hypothesis
consider the following research eight hours of nightly sleep is not the health panacea you were brought up to believe
How many students would you include in a random sample to determine with 95% probability and to within 5% of the true value the proportion who arrive at 9am lectures without breakfast?
a nutritionist wants to determine how much time nationally people spend eating and drinking. suppose for a random
Perform a significance test to assess whether there is an association between mortality from cirrhosis of the liver and duration of employment in the group hired after 1945. Report a p-value.
suppose that x y and z are independent random variables each having a standard normal distribution. determine
Pulse rate is an important measure of the fitness of a person's cardiovascular system. The mean pulse rate for all U.S. adult males is approximately 72 heart beats per minute.
Choose, at random, a direction which will keep you on dry land, and walk 1 km in that direction. Let P denote your position. What is the expected distance from P to the river?
a selection of cereals was sampled and the number of calories was plotted against the number of grams of protein with
What is the minimal number of days a person must watch to be at least 96.8% sure of seeing one or more hawks migrating?
A student throws a deck of cards into the air and then counts the number of cards that, after landing, are showing the face of the card
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