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Chapter 1: Problem 1
If \(z=-3\), what is \(\frac{z^3+2 z+3}{z^2+1}\) ? A. 3 B. -1.8 C. -3.6 D. -3
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Scientists classify stars according to the following categories: O, B, A, F, G, K, M. A star's category depends upon its spectral type, which is determined by its temperature. The chart below shows five stars of different categories, along with their temperatures. $$ \begin{array}{|l|l|} \hline \text { Star Type } & \text { Temperature }\left({ }^{\circ} \mathbf{F}\right) \\ \hline \text { O } & 18,033 \\ \hline \text { B } & 9,978 \\ \hline \text { A } & 4,839 \\ \hline \text { F } & 3,644 \\ \hline \text { G } & 3,422 \\ \hline \end{array} $$ However, rather than measuring star temperature in degrees Fahrenheit, scientists typically measure star temperature in units of Kelvin. The conversion from Fahrenheit to Kelvin is given by the following formula: $$ \mathrm{K}=\frac{5}{9}\left({ }^{\circ} \mathrm{F}-32\right)+273 $$ What is the approximate temperature of the A-type star in Kelvin? You may use a calculator. A. 2,569 B. 2,822 C. 2,929 D. 2,944
Since its formation 10,000 years ago, Niagara Falls has eroded upstream a distance of 9.8 miles. Which of the following equations indicates the distance \(D\) that Niagara Falls, continuing at this rate, will erode in the next 22,000 years? A. \(\frac{9.8}{10,000}=\frac{D}{22,000}\) B. \(\frac{9.8}{10,000}=\frac{D}{12,000}\) C. \(D=9.8+\frac{22,000}{10,000}\) D. \(D=9.8 \times \frac{10,000}{22,000}\)
Which of the following is an example of a state law that would be incompatible with the Constitution? A. a law that prohibits protests by a steelworkers' union B. a law that lowers the speed limit on a highway to 50 miles per hour C. a law that limits state senators to two six-year terms each D. legislation that requires reductions in emissions from factories
A science class compares the relative strengths of two telescopic lenses. Lens \(X\) produces a magnification of 3 \(\times 10^5\), and Lens \(Y\) produces a magnification of \(6 \times 10^2\). Which of the following statements accurately describes the relationship between the two lenses? A. Lens \(X\) produces a magnification \(200 \%\) that of lens \(Y\). B. Lens \(X\) is 200 times as strong as Lens \(Y\). C. Lens \(X\) produces a magnification \(500 \%\) that of lens \(Y\). D. Lens \(X\) is 500 times as strong as Lens \(Y\).
Lobsters are crustaceans commonly found in the waters of the Atlantic Ocean off the North American coast between Maine and North Carolina. Researchers studied the weights of these creatures over a period of a few years. Some of the results are displayed in the table below. $$ \begin{array}{|c|c|} \hline \text { Year } & \text { Average Weight (kg) } \\ \hline 2005 & 0.43 \\ \hline 2006 & 0.41 \\ \hline 2007 & 0.37 \\ \hline 2008 & 0.43 \\ \hline 2009 & 0.38 \\ \hline \end{array} $$ The researchers hope to find the most commonly occurring lobster weight for the lobsters studied during the five-year period shown above. The researchers must calculate the Select... of the weights, which is You may use a calculator.
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