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Chapter 10: Problem 92
What is an annuity?
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Use mathematical induction to prove that each statement is true for every positive integer \(n\). 3 is a factor of \(n(n+1)(n-1)\)
Use mathematical induction to prove that each statement is true for every positive integer \(n\). $$\sum_{i=1}^{n} 7 \cdot 8^{i}=8\left(8^{n}-1\right)$$
Mega Millions is a multi-state lottery played in most U.S. states. As of this writing, the top cash prize was \(\$ 656\) million, going to three lucky winners in three states. Players pick five different numbers from 1 to 56 and one number from 1 to \(46 .\) Use this information to solve Exercises \(27-30 .\) Express all probabilities as fractions. A player wins the jackpot by matching all five numbers drawn from white balls ( 1 through 56 ) and matching the number on the gold Mega Ball \(^{\oplus}\) ( 1 through 46 ). What is the probability of winning the jackpot?
If \(f(x)=4 x^{2}-5 x-2,\) find $$ \begin{aligned} \frac{f(x+h)-f(x)}{h}, h \neq 0 & \end{aligned} $$
Graph the hyperbola whose equation is $$ 25 x^{2}-16 y^{2}-100 x-96 y-444=0 $$ Where are the foci located? What are the equations of the asymptotes?
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