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A wooden artifact from an ancient tomb contains 20 percent of the carbon-14 that is present in living trees. How long age was the artifact made? (The half-life of carbon-14 is 5730 years.)
Let R be a commutative ring. Recall that an element x in R is nilpotent if x^n=0 for some positive integer n. Prove that the set of nilpotent elements form an ideal.
A farmer plans to use 21 m of fencing to enclose a rectangular pen having an area of 55 m². Only three sides of the pen need fencing because of an existing wall. Find the dimensions of the pen.
Find all lines through the point (2,1) that are tangent to parabola y=xsquared. What properties of parabolas and formulas do you use to solve this problem?
If I treat the upper block as a 2x2 matrix, I can find P = [1 0; 1 1] (Note: Using Matlab notation here). This correctly results in INV(P)AP = [3 1; 0 3] which is in the form needed.
What is the probability that at least 50 customers pay in cash? What is the probability that no more than 15 customers pay in cash? What is the probability that more than 20 and less than 40 customers pay in cash?
Use Method of undetermined coefficient to find a particular solution. Then write the general solution.
In R2, let triangle ABC be a right triangle with right angle at angle C. Consider the altitude CH (it meets AB perpendicularly). Prove that |CH|^2 = |AH| * |BH|.
Pages in a book are numbered in typical fashion, starting with 1. The folio for page 10 will contain the tenth and eleventh digits necessary to paginate the book. On what page will the 2009th digit occur?
Give examples to show that the finiteness of the collections in parts c and d is essential. For any finite collection G1, G2, ...., Gn of open sets, intersection (at the top of the intersection sign is n and at the bottom is i=1) of Gi is open.
Now verify that the subgame-perfect equilibrium is for the crook not to confess and for the policeman to go back on his threat. That is, explain why the policeman's threat is actually not credible.
Let f be a function that is differentiable for all real numbers. The table gives the values of f and its derivative f' for selected points x in the closed interval -1.5 0 for -1.5
What effect does changing the level of con?dence have on the sample size? Explain.
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