Section 1.2 Operations with Real Numbers and Algebraic Expressions 27 of years after 2002. According to the expression, what is the average retail price of regular gas in January 2013? (Source: www.eia.doe.gov) d. The volume of a sphere is given by 4 3 πr3, where r is the radius of the sphere. Find the volume of a basketball that has a radius of 4.7 in. Round answer to the nearest hundredth. Troubleshooting Common Errors Some common errors associated with exponents and order of operations are shown. Objective 7 ▶ Troubleshoot common errors. Objective 7 Examples A problem and an incorrect solution are given. Provide the correct solution and an explanation of the error. 7a. Simplify -102. Incorrect Solution Correct Solution and Explanation -102 = (-10)(-10) The base of the exponent is 10 not -10 since the negative sign is not in parentheses. So, we find the opposite of 10 squared. -102=-10 · 10 =-100 = 100 7b. Simplify 4 + 5(3)2. Incorrect Solution Correct Solution and Explanation 4 + 5(3)2 = 4 + 152 Exponents should be applied before multiplication. 4 + 5(3)2 = 4 + 5(9) = 4 + 45 = 49 = 4 + 225 = 229 ANSWERS TO STUDENT CHECKS Student Check 1 a. -1 b. -6 c. 2 7 d. -3.5 e. 8 f. - 4 35 g. 5 Student Check 2 a. 18 b. -1 c. 41.2 d. -16 e. 5 3 f. -27 g. undefined h. 0 i. 4 Student Check 3 a. 216 b. 125 8 c. -64 d. 64 e. -343 f. -343 Student Check 4 a. -2 b. 15 c. 10 d. -8 e. 1 5 Student Check 5 a. -6 b. 40 c. 3 d. 16 Student Check 6 a. -$150,000 b. i. Date Closing Price Daily Change in Price 6/06/2011 $47.36 n/a 6/07/2011 $47.06 -0.30 6/08/2011 $46.86 -0.20 6/09/2011 $47.16 0.30 6/10/2011 $46.70 -0.46 ii. The average daily change was a decrease of $0.165 per day. c. about $4.50 per gallon d. 434.89 in.3
hendricks_intermediate_algebra_1e_ch1_3
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