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Chapter 5: Problem 43
Express each terminating decimal as a quotient of integers. If possible, reduce to lowest terms. \(0.82\)
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Express each number in scientific notation. 32,000
A person is investigating two employment opportunities. They both have a beginning salary of $$\$ 20,000$$ per year. Company A offers an increase of $$\$ 1000$$ per year. Company B offers \(5 \%\) more than during the preceding year. Which company will pay more in the sixth year?
Shown in the figure is a 7-hour clock and the table for clock addition in the 7-hour clock system. $$ \begin{array}{|l|l|l|l|l|l|l|l|} \hline \oplus & \mathbf{0} & \mathbf{1} & \mathbf{2} & \mathbf{3} & \mathbf{4} & \mathbf{5} & \mathbf{6} \\ \hline \mathbf{0} & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \mathbf{1} & 1 & 2 & 3 & 4 & 5 & 6 & 0 \\ \hline \mathbf{2} & 2 & 3 & 4 & 5 & 6 & 0 & 1 \\ \hline \mathbf{3} & 3 & 4 & 5 & 6 & 0 & 1 & 2 \\ \hline \mathbf{4} & 4 & 5 & 6 & 0 & 1 & 2 & 3 \\ \hline \mathbf{5} & 5 & 6 & 0 & 1 & 2 & 3 & 4 \\ \hline \mathbf{6} & 6 & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline \end{array} $$ a. How can you tell that the set \(\\{0,1,2,3,4,5,6\\}\) is close under the operation of clock addition? b. Verify the associative property: \((3 \oplus 5) \oplus 6=3 \oplus(5 \oplus 6)\) c. What is the identity element in the 7-hour clock system? d. Find the inverse of each element in the 7-hour clocl system. e. Verify two cases of the commutative property: \(4 \oplus 5=5 \oplus 4\) and \(6 \oplus 1=1 \oplus 6\).
Some companies pay people extra when they work more than a regular 40-hour work week. The overtime pay is often \(1 \frac{1}{2}\) times the regular hourly rate. This is called time and a half. A summer job for students pays \(\$ 12\) an hour and offers time and a half for the hours worked over \(40 .\) If a student works 46 hours during one week, what is the student's total pay before taxes?
Police use the formula \(v=2 \sqrt{5 L}\) to estimate the speed of a car, \(v\), in miles per hour, based on the length, \(L\), in feet, of its skid marks upon sudden braking on a dry asphalt road. Use the formula to solve A motorist is involved in an accident. A police officer measures the car's skid marks to be 245 feet long. Estimate the speed at which the motorist was traveling before braking. If the posted speed limit is 50 miles per hour and the motorist tells the officer he was not speeding, should the officer believe him? Explain.
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