142 Chapter 2 Linear Equations and Inequalities in One Variable 76. Hong’s Psychology course grade is based on a weighted average. The weights are as follows: midterm (35%), papers (40%), and final exam (25%). If Hong earns a 75 on his midterm and 78 on his papers, what must he score on his final exam to maintain at least an 80 course average? 77. Amy rents a small fire hall for her family reunion for $400. She hires a caterer who charges $20 per person. If she has $2000 to spend on the reunion, how many family members and friends can attend? 78. Nam hires a maid service to clean her house biweekly. The company charges a one-time fee of $129 and $65 per cleaning visit. If Nam budgets $1800 for the maid service for the year, how many cleaning visits can she have? SECTION 2.5 Find the intersection or union of the two sets. Write each answer in interval notation when applicable. (See Objectives 1 and 2.) 79. (-∞, 0) ∩ (-4, ∞) 80. (-∞, 10 ∩ (10, ∞) 81. (-∞, 3.2) ∩ -1.8, 16.4) 82. ∩ 4, 12 83. ∩ (-2, 1) 84. -10, 3 ∪ (-4, 6) 85. (-∞, 4) ∪ 4, ∞) 86. (-∞, 8.6) ∪ -2.9, 13.8) 87. ∪ (-4, ∞) 88. ∪ 8, ∞) Solve each compound inequality. Write each answer in interval notation when applicable. (See Objectives 3 and 4.) 89. 6x - 7 ≥ 5 and 4x - 3 < 9 90. 2(1 - 5x) > 12 and 3x - 4 < 14 91. 6(2 - x)<-4 and 4x + 3 < 10 92. 3x - 5 > 7 and 2x + 6 < 1 93. 0.7x + 0.34 < 4.274 and 0.4x - 2.56>-1.7 94. 1.24x - 4.35≥-2.49 and 0.8x + 2.6 ≤ 2.4 95. 8x + 3 < 19 or 3x - 1 > 14 96. 4 - 3x ≤ 0 or 8x + 3>-5 97. 2 - 5x ≤ 1 or 4x - 3 > 5 98. 12x - 4 ≤ 8 or 3x + 2 > 8 Solve each problem using compound inequalities. (See Objective 5.) 99. Margie wants to maintain a test average between an 80 and 89. If Margie’s test scores thus far are 81, 70, 85, and 76, what must she score on her fifth test to make the desired grade? (Assume the highest grade possible is 100.) 100. Grace wants to make a quiz average between 70 and 79. If Grace’s quiz scores are 65, 72, 65, 71, and 68, then what must she score on her sixth quiz to get the desired grade? (Assume the highest grade possible is 100.) 101. Michael needs someone to trim two-thirds of his bamboo forest. He finds a company that charges $35 per hour plus $90 to haul the trees away. If Michael plans to spend between $195 and $500, how many hours can he afford to hire the tree-trimmer? 102. Patty hires a professional organizer to organize her home office. The professional organizer charges a flat fee of $80 plus $32 per hour. If Patty budgets $720 to $1000 to get her office organized, how many hours can she afford to hire the professional organizer? SECTION 2.6 Solve each equation. (See Objective 1.) 103. u12x - 5u = 25 104. u5x - 16u = 14 105. u7 - 2xu = 18 106. u9 - 4xu = 3 107. ` 8x - 4 2 ` - 1 = 6 108. ` 2x + 9 5 ` + 1 = 4 109. ` 2x 3 ` =-12 110. ` 15x 4 ` = 0 111. u3x + 2u = 0 112. u6x - 9u = 0 113. u0.6x - 2.5u = 7.1 114. u0.4x + 4.1u = 11.5 Solve each equation. (See Objective 2.) 115. ` 5x + 1 3 ` = ` x 6 ` 116. ` 3x - 1 4 ` = ` x 4 ` 117. u2x + 10u = u4x - 8u 118. u6x - 11u = u5 - 4xu Solve each problem using an absolute value equation. (See Objective 3.) 119. Suppose the actual length of an object is 6.245 m. If the length is approximated to be 6.512 m, what is the absolute error?
hendricks_intermediate_algebra_1e_ch1_3
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