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Chapter 9: Problem 73
Three points that are not collinear determine three lines. How many lines are determined by nine points, no three of which are collinear?
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Simplifying a Difference Quotient In Exercises \(67-72\) , simplify the difference quotient, using the Binomial Theorem if necessary. $$\frac{f(x+h)-f(x)}{b} \quad$$ Difference quotient $$f(x)=x^{4}$$
Expanding a Complex Number In Exercises \(73-78\) , use the Binomial Theorem to expand the complex number. Simplify your result. $$\left(-\frac{1}{2}+\frac{\sqrt{3}}{2} i\right)^{3}$$
American roulette is a game in which a wheel turns on a spindle and is divided into 38 pockets. Thirty-six of the pockets are numbered \(1-36,\) of which half are red and half are black. Two of the pockets are green and are numbered 0 and 00 (see figure). The dealer spins the wheel and a small ball in opposite directions. As the ball slows to a stop, it has an equal probability of landing in any of the numbered pockets. (a) Find the probability of landing in the number 00 pocket. (b) Find the probability of landing in a red pocket. (c) Find the probability of landing in a green pocket or a black pocket. (d) Find the probability of landing in the number 14 pocket on two consecutive spins. (e) Find the probability of landing in a red pocket on \(\quad\) three consecutive spins.
Finding a Sum In Exercises \(45-54\) , find the sum using the formulas for the sums of powers of integers. $$\sum_{n=1}^{10} n^{3}$$
In Exercises \(75-82,\) solve for \(n\) $$_{n} P_{5}=18 \cdot_{n-2} P_{4}$$
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