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40 Chapter 1 Real Numbers and Algebraic Expressions 97. The expression P(1 + r)t represents the amount of money in an account when P dollars is invested at an annual interest rate of r (in decimal form) for t yr. Find the amount of money that will be in an account at the end of 5 yr if $1000 is invested at 5% annual interest. (Hint: Convert 5% to a decimal value before substituting this value in the expression.) 98. The expression P(1 + r) t represents the amount of money in an account when P dollars is invested at an annual interest rate of r (in decimal form) for t yr. Find the amount of money that will be in an account at the end of 3 yr if $5000 is invested at 3% annual interest. (Hint: Convert 3% to a decimal value before substituting this value in the expression.) 99. In 2011, the U.S. News & World Report Guide to America’s Best Colleges ranked Princeton University as one of the top national universities. Yearly tuition and fees at Princeton University is represented by the expression 1100c + 9200, where c is the number of credit hours taken in a year. What is the yearly tuition and fees if 30 credit hours are taken in a year? 100. In 2011, the U.S. News & World Report Guide to America’s Best Colleges ranked the University of Pennsylvania as the top Business School in the United States. Yearly tuition and fees at University of Pennsylvania is represented by the expression 3105c + 9804, where c is the number of credit units taken each year. What is the yearly tuition and fees if 11 credit units are taken in 1 yr? 101. According to the Bureau of Labor Statistics, the average hourly rate of registered nurses in the state of Illinois is $25. The expression 25x + 37.5y represents the average weekly earnings of a registered nurse in Illinois, where x is the number of regular hours worked in a week and y is the number of overtime hours worked in a week. Find the weekly salary of a registered nurse if a nurse works 36 regular hours and 10 overtime hours. 102. According to the Bureau of Labor Statistics, airplane pilots and navigators earned an average of $95.80 per hour. The expression 95.80x represents the average weekly earnings of an airplane pilot and navigator, where x is the number of hours worked in a week. What are the weekly earnings for an airplane pilot who works 30 hr per week? 103. The height of a baseball hit upward with an initial velocity of 100 ft/sec from an initial height of 2.5 ft is represented by the expression -16t2 + 100t + 2.5, where t is the number of seconds after the ball has been hit. What is the height of the ball after 4 sec? 104. The USS Constitution is the oldest commissioned warship afloat in the world. The height of a cannonball fired from the USS Constitution with an initial velocity of 388 ft/sec from a height of 24 ft is represented by the expression -16t2 + 388t + 24, where t is the number of seconds after the cannonball has been fired. What is the height of the cannonball after 12 sec? Mix ’Em Up! Use the order of operations to simplify each expression. 105. 63 106. -32 107. u-12(7) + 8(4)u 108. u-6(-13) + 8(-7)u 109. 1.43 110. -a3 4 b 3 111. 520 - u3 · 8 - 2(11 - 7)u 112. 618 - 7u4 · 3 - 2(6 - 1)u 25 + 1252 - 4(16)(9) 113. 2 · 9 114. 25 - 1252 - 4(8)(18) 2 · 18 115. 1 15 (45) - 1 7 15 116. 1 19 (76) - 2 17 19 117. 21 - 13 3 · 4 - 7 118. 18 ÷ 3 + 9 27 + 13 119. 10 · 32 - 28 ÷ 4 · 7 + 1 120. 3 · 52 - 32 ÷ 4 · 8 + 6 121. 1 6 (14 - 11)3 - 12 ÷ 3 122. (1 · 3)2 + 6 · 4 ÷ 2 + 10 Evaluate each expression for the given values of the variables. When multiple values are given, organize the information in a chart. 123. 5x - 3 for x = 1, 2, 3, and 4 124. 3x + 2 x + 1 for x = 0, 1, 2, and 3 125. 7x - 6y for x = 3 and y = 2 126. y2 - y1 x2 - x1 for x1 = 2, x2 = 14, y1 = 13, and y2 = 22 127. 1 2 (b1 + b2)h for b1 = 10, b2 = 6, h = 3 128. 2l + 2w for l = 9 and w = 17 129. 1(x1 - x2)2 + (y1 - y2)2 for x1 = 2, x2 = 14, y1 = 17, y2 = 22 130. b2 - 4ac for a = 2, b = 10, c = 5 Determine if the given value is a solution of the equation. 131. x2 + 3x - 6 = x + 9; x = -3 132. 6y + 2(5y - 3) = y + 9; y = 1 Translate each phrase into an algebraic expression. Let x represent the unknown number. 133. Five times the sum of a number and 11 134. Three times the sum of a number and 6


hendricks_beginning_algebra_1e_ch1_3
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