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Chapter 11: Problem 21
Use the Binomial Theorem to expand each binomial and express the result in simplified form. $$ \left(2 x^{3}-1\right)^{4} $$
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Determine whether each statement makes sense or does not make sense, and explain your reasoning. I've noticed that the big difference between arithmetic and geometric sequences is that arithmetic sequences are based on addition and geometric sequences are based on multiplication.
Use the formula for the sum of the first n terms of a geometric sequence to solve Exercises \(71-76\). A pendulum swings through an arc of 16 inches. On each successive swing, the length of the arc is \(96 \%\) of the previous length. $$ \begin{array}{cccc} {16,} & {0.96(16),} & {(0.96)^{2}(16),} & {(0.96)^{3}(16)} \\ {\text { Ist }} & {2 \text { nd }} & {3 \text { rd }} & {4 \text { th }} \\ {\text { swing }} & {\text { swing }} & {\text { swing }} & {\text { swing }} \end{array} $$ After 10 swings, what is the total length of the distance the pendulum has swung?
A single die is rolled twice. Find the probability of rolling an odd number the first time and a number less than 3 the second time.
$$ \text { Solve: } \quad \log _{2}(x+9)-\log _{2} x=1 . \text { (Section } 4.4, \text { Example } 7 \text { ) } $$
Explaining the Concepts Write a probability word problem whose answer is one of the following fractions: \(\frac{1}{6}\) or \(\frac{1}{4}\) or \(\frac{1}{3}\)
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