Find the vertical, horizontal, and oblique asymptotes, if any, of the given rational function. \( H(x)=\frac{x^{3}-1}{x^{2}-3 x+2} \) Find the vertical asymptotes. Select the correct choice and, if necessary, fill in the answer box(es) to complete your choice. A. The function has one vertical asymptote, \( \square \). (Type an equation. Use integers or fractions for any numbers in the equation.) B. The function has two vertical asymptotes. The leftmost asymptote is \( \square \) and the rightmost asymptote is (Type equations. Use integers or fractions for any numbers in the equations.)

Solve the following inequality. \[ (x-3)(x-6)(x-7) \geq 0 \]

\begin{tabular}{|l} Solve the following:, \\ \( \begin{array}{ll}\text { (i) } 2^{3 x} \cdot 4^{x+1}=128 & \text { (ii) } 3^{x+1} \cdot 9^{2-2}=\frac{1}{2}\end{array} \)\end{tabular}

Let \( I_{0} \) be the intensity of sound at the threshold of human hearing. The decibel level of a sound with intensity I is given by \( \mathrm{dB}=10 \log _{10}\left(\frac{1}{I_{0}}\right) \). If the intensity of a sound increases by a factor of 50 , how is the decibel level affected? Round your answer to the nearest tenth.

B. (9pts) List the first 10 multiples of each fraction. a. Then write the equivalent form for any whole and improper fraction b. Tell the method you used. SHOW ALL WORK 6. \( \frac{3}{4} \) \( \frac{1}{4} \)

A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment, 18 subjects had a mean wake time of 103.0 min. After treatment, the 18 subjects had a mean wake time of 74.9 min and a standard deviation of 24.6 min. Assume that the 18 sample values appear to be from a normally distributed population and construct a \( 99 \% \) confidence interval estimate of the mean wake time for a population with drug treatments. What does the result suggest about the mean wake time of 103.0 min before the treatment? Does the drug appear to be effective? Construct the \( 99 \% \) confidence interval estimate of the mean wake time for a population with the treatment. \( \square \min <\mu<\square \mathrm{min} \) (Round to one decimal place as needed.)