Solve.

$$2 x ^ { 2 } - 2 = 48$$

State whether the molecular weight of a polymer that is synthesized by addition polymerization is relatively high, medium, or relatively low for the following situations: (a) Rapid initiation, slow propagation, and rapid termination (b) Slow initiation, rapid propagation, and slow termination (c) Rapid initiation, rapid propagation, and slow termination (d) Slow initiation, slow propagation, and rapid termination

Write the value of the underlined digit.

$$598,\underline{1}02$$

Graph the numbers in this sequence on a number line.

$$\ldots , - 15 , - 10 , - 5,0,5,10,15 , \dots$$

Write each expression without a fraction bar.

$$\frac { a ^ { 9 } b ^ { 3 } } { a ^ { 7 } b ^ { 8 } }$$

Find the following product. Show and justify each step.

$$(2a^2)(-3ab^3)$$

Which of the following actions would the Federal Reserve use to address inflation? A. make an open-market sale of Treasury bills B. increase the money supply C. lower the discount rate D. decrease money demand E. raise taxes

Consider a hypothetical reaction between A, B, and C that is first order in A, zero order in B, and second order in C. How does the rate change when [B] is tripled and the other reactant concentrations are held constant?

Find a polynomial with real coefficients of the specified degree that satisfies the given conditions. Prove that the equation

$$3 x ^ { 4 } + 5 x ^ { 2 } + 2 = 0$$

has no real root.

Translate the formula for calculating z-values into English instructions.

Two researchers are testing the null hypothesis that a population proportion p is .25 and the alternative hypothesis that p > .25. Both take a sample of 100 observations. Researcher A finds a sample proportion of .29, and Researcher B finds a sample proportion of .33. For which researcher will the p-value of the test be smaller? Explain without actually doing any computations.

If

$$f ( x ) = x + 2 , g ( x ) = - 4 x + 3 , \text { and } h ( x ) = x ^ { 2 } - 2 x + 1$$

find each value.

$$\left( f \cdot g \cdot h \right) ( 3 )$$

Randomly selected statistics students of the author participated in an experiment to test their ability to determine when 1 min (or 60 seconds) has passed. Forty students yielded a sample mean of 58.3 sec. Assuming that $\sigma=9.5 \mathrm{sec}$, construct a 95% confidence interval estimate of the population mean of all statistics students. Based on the result, is it likely that their estimates have a mean that is reasonably close to 60 sec?

(The information presented in this exercise comes from the Westview Blueberry Farm and National Oceanic and Atmospheric Administration Reports [NOAA].) For the following paired data, (x, y), x gives the Holland, Michigan, rainfall for June, and y gives the blueberry production in thousands of pounds from the Westview Blueberry Farm: (4.11, 56.2) (5.49, 45.3) (5.35, 31.0) (6.53, 30.1) (5.18, 40.0) (4.89, 38.5) (2.09, 50.0) (1.40, 45.8) (4.52, 45.9) (1.11, 32.4) (0.60, 18.2) (3.80, 56.1) The data are from 1971 to 1989 for those years in which the last frost occurred May 10 or earlier. a. Find the correlation coefficient for these data. b. Find the least squares regression line. c. Make a scatter plot of the data with the least squares regression line on the plot. d. Calculate and plot the residuals. Does linear regression seem to be appropriate? e. Find the least squares quadratic regression curve. f. Calculate and plot the residuals. Does quadratic regression seem to be appropriate? g. Give a short interpretation of your results.