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Chapter 9: Problem 3
Fill in the blanks. To determine the ______ of an event, you can use the formula \(P(E)=\frac{n(E)}{n(S)},\) where \(n(E)\) is the number of outcomes in the event and \(n(S)\) is the number of outcomes in the sample space.
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Finding a Sum In Exercises \(45-54\) , find the sum using the formulas for the sums of powers of integers. $$\sum_{j=1}^{10}\left(3-\frac{1}{2} j+\frac{1}{2} j^{2}\right)$$
Linear Model, Quadratic Model, or Neither? In Exercises \(61-68\) , write the first six terms of the sequence beginning with the given term. Then calculate the first and second differences of the sequence. State whether the sequence has a perfect linear model, a perfect quadratic model, or neither. $$a_{1}=2$$ $$a_{n}=n-a_{n-1}$$
Finding a Quadratic Model In Exercises \(69-74\) find a quadratic model for the sequence with the indicated terms. $$a_{0}=3, a_{1}=3, a_{4}=15$$
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 $$f(x)=\sqrt{x}$$
In Exercises \(75-82,\) solve for \(n\) $$_{n} P_{6}=12 \cdot_{n-1} P_{5}$$
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