Mathematics practise english3 doc

49. c. Find the amount of interest. For the time period, use ᎏ 1 9 2 ᎏ , which equals ᎏ 3 4 ᎏ , or .75. Multiply. $1,500 × 0.04 × 0.75 = $45. Add to find the amount paid back. $1,500 + $45 = $1,545. 50. c. Multiply 3 lb. 12. oz. by 6 to get 18 lb. 72 oz. Divide 72 oz. by the number of oz. in a pound (16) to get 4 lbs. with a remainder of 8 oz. Therefore, 18 lb. + 4 lb. 8 oz. = 22 lb. 8 oz. 51. a. If 80% of the audience were adults, 100% − 80% = 20% were children. 20% = .20, and 0.20(650) = 130 52. b. Let x = number of inches between the towns on the map. Set up a proportion: ᎏ 6 1 0 i m n. i. ᎏ = ᎏ 22 x 5 in m . i. ᎏ 60x = 255 x = ᎏ 2 6 5 0 5 ᎏ = 4 ᎏ 1 4 ᎏ 53. b. 4 ft. 3 in. = 3 ft. 15 in. − 2 ft. 8 in. = 1 ft. 7 in. 54. d. v = lwh; the container is 5 ft. long × 3 ft. wide × 2 ft. high. 5 × 3 × 2 = 30 ft. 3 55. d. The top of the bar for Wednesday is at 6 on the vertical scale. 56. e. The top of the bar for Monday is halfway between 4 and 6, so 5 gal. were sold on Monday. The top of the bar for Saturday is halfway between 16 and 18, so 17 gal. were sold on Sat- urday. The difference between 17 gal. and 5 gal. is 12 gal. 57. d. The tops of the bars for Monday through Sun- day are at 5, 4, 6, 5, 14, 17, and 9. These add up to 60. 58. a. Let x = m∠OAB. OA ឈ ៮ ៬ = OB ឈ ៮ ៬ since radii of the same circle have equal measures. Therefore, m∠OAB = m∠OBA. x + x + 70 = 180 2x + 70 = 180 2x = 180 − 70 = 110 x = 110 ÷ 2 = 55 59. e. Let x = number of books on the small shelf, and x + 8 = number of books on the large shelf. Then, 4x = number of books on 4 small shelves, and 3(x + 8) = number of books on 3 large shelves. 4x + 3(x + 8) = 297 4x + 3x + 24 = 297 7x + 24 = 297 7x = 297 − 24 7x = 273 ÷ 7 = 39 60. a. 40 ft. = 40 × 12 = 480 in. 3 ft. 4 in. = 3(12) + 4 = 36 + 4 = 40 in. 480 ÷ 40 = 12 scarves. 61. b. $130,000 (catalog sales) − $65,000 (online sales) = $65,000 62. b. $130,000 + $65,000 + $100,000 = $295,000, which is about $300,000. Working with compat- ible numbers, $100,000 out of $300,000 is ᎏ 1 3 ᎏ . A B O 70° 20 Number of Gallons Days of the Week Paint Sales at Carolyn’s Hardware M T W Th F Sa Su 18 16 14 12 10 8 6 4 2 – GED MATHEMATICS PRACTICE QUESTIONS– 450 63. c. 22 feet = 264 inches; 264 ÷ 5.5 = 48. 64. ᎏ 1 3 ᎏ . The coordinates of point A are (−3,0). The coordinates of point B are (3,2). Use the slope formula: ᎏ x y 2 2 − − y x 1 1 ᎏ Substitute and solve: ᎏ 3 2 − − (− 0 3) ᎏ = ᎏ 2 6 ᎏ ,or ᎏ 1 3 ᎏ 65. 58. Substitute the values for x and y in the expres- sion. Then simplify. 3(2 × 4 − 5) + (3 + 4) 2 = 3(3) + 7 2 = 9 + 49 = 58 66. e. Since the dimensions of Box A are half of the dimensions of Box B, the side lengths must be 3, 2, and 1.5. Next, find the volumes of the two boxes. Use the formula V = lwh. The volume of Box B is 72, and the volume of Box A is 9. 72 is 8 times larger than 9. 67. d. Set up a proportion: ᎏ 1 5 00 ᎏ = ᎏ 1 x 2 ᎏ ,where x is the number of children enrolled in the program. 12 × 100 = 1,200, and 1,200 ÷ 5 = 240. 68. e. Add the number of marbles to get the total number in the bag; 12 + 3 + 6 + 4 = 25. There- fore, 25 is the number of possible outcomes. Seven marbles are either blue or yellow. Seven is the number of favorable outcomes; ᎏ 2 7 5 ᎏ × ᎏ 4 4 ᎏ = ᎏ 1 2 0 8 0 ᎏ = 28%. 69. a. Substitute 4 for b and 3 for n into the function. Then, solve the equation. C = $25.60(4) + $14(4)(3 − 1) = $102.40 + $112.00 = $214.40 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 6 7 8 9 0 • / 1 2 3 4 5 6 7 9 0 • 58 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 4 5 6 7 8 9 0 • 1/3 – GED MATHEMATICS PRACTICE QUESTIONS– 451 70. 375. Multiply $250 by 1.5, which equals $375. 71. 1,040. Set up the proportion and solve: x = the number of miles between the two landmarks. = 6 ᎏ 1 2 ᎏ × 120 = 780 and 380 ÷ ᎏ 3 4 ᎏ = 1,040 The answer is 1,040 miles. 72. d. Separate the two inequalities into two inequali- ties, x < 4 and −2 = x. Choice d is the only graph that represents the inequalities. There must be an open circle to represent that the 4 is not included and a shaded circle to represent that the −2 is included. 73. a. Angle 4 and the angle measuring 50° are corre- sponding angles. Therefore, m∠4 = 50°. 74. a. Angle 3 and the angle measuring 104° are sup- plementary; therefore, m∠3 = 180 − 104 = 76. As established in the previous problem, angle 4 and the angle measuring 50° are corresponding angles, so m∠4 = 50°. Angle 3, angle 4, and x are the interior angles of a triangle, so they equal 180°; 50 + 76 + x = 180, and so x = 54°. 6 ᎏ 1 2 ᎏ ᎏ x ᎏ 3 4 ᎏ ᎏ 120 1 2 3 4 5 6 7 8 9 • 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 • / 1 2 3 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 • 0140 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 8 9 0 • / 1 2 3 4 6 7 8 9 0 • 375 – GED MATHEMATICS PRACTICE QUESTIONS– 452 75. (−3, −1). The vertical line is parallel to the y-axis, and all of its points have the x-coordinate −3. The hori- zontal line is parallel to the x-axis, and all of its points have the y-coordinate −1. Therefore, the coordinates are −3 and −1. 76. c. Mean = average. Add the scores and divide by the number of scores. 78 + 86 + 82 + 81 + 82 + 77 = 486 486 ÷ 6 = 81 77. 10. Quadrilateral ABCD is a trapezoid because it has one pair of parallel sides. The bases are the parallel sides, AB and CD. The height is 2.5 cm. Use the formula for the area of a trapezoid. A = ᎏ 1 2 ᎏ × (b 1 + b 2 ) × h = ᎏ 1 2 ᎏ × (6 + 2) × 2.5 = ᎏ 1 2 ᎏ × 8 × 2.5 = 4 × 2.5 = 10 cm 2 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 • 10 1 2 −3 4 −5 −6 0 1 −2 3 4 5 6 −1 2 3 −4 5 −6 −1 −2−3−4 −5 6 – GED MATHEMATICS PRACTICE QUESTIONS– 453 78. 4.8 or 4.80. Set up the proportion ᎏ 5 3 ᎏ = ᎏ 8 x ᎏ ,where x is the cost of 8 cans of yams; 3 × 8 = 24, and 24 ÷ 5 = $4.80. 79. d. 5 ft. 9 in. = 69 inches. Divide by 3: 69 ÷ 3 = 23 inches. Convert feet to inches, 23 in. = 1 ft. 11 in. 80. d. Think of the space as two rectangles: 21 ft. by 14 ft. and 10 ft. by 7 ft. (You can find the length of the missing side of the smaller rectangle by sub- tracting: 24 − 14 = 10.) Use the formula A = lw to find the area of each rectangle, and then com- bine to find the total area of the floor to be car- peted: 21 × 14 = 294, and 7 × 10 = 70. Add the areas of the two rectangles: 294 + 70 = 364, so the Wrights will need to buy 364 square feet of carpeting. 81. e. x = one number and 3x + 12 = the other num- ber, for the equation: x + 3x + 12 = − 20 4x + 12 = −20 4x = −32 x = −8 3(−8) + 12 = −12 82. a. Find 24% of $2,500. ᎏ 2,5 x 00 ᎏ = ᎏ 1 2 0 4 0 ᎏ ᎏ 1 1 0 0 0 0 x ᎏ = ᎏ 60 1 , 0 0 0 00 ᎏ x = 600 83. ᎏ 2 1 0 ᎏ or ᎏ 1 5 00 ᎏ . Clothing expenses take 5% of the Wrights’ pay. Change 5% to a fraction to get ᎏ 1 5 00 ᎏ , which can also be reduced to ᎏ 2 1 0 ᎏ . 84. d. Either locate each point on the grid and com- pare it to the line, or substitute the x and y val- ues from each ordered pair into the equation: y = − ᎏ 3 4 ᎏ x + 1 −5 = − ᎏ 3 4 ᎏ (8) + 1 −5 = −6 + 1 −5 = −5 85. d. The three numbers can be represented by x, x + 2, and x + 4. Solve the equation: x + x + 2 + x + 4 = 90 3x + 6 = 90 3x = 84 x = 28 The three numbers are 28, 30, 32. The question asks for the largest of these. 1 2 3 4 5 6 7 8 9 • 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 • /120 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 / 1 2 3 4 5 6 7 9 0 • 4.8 – GED MATHEMATICS PRACTICE QUESTIONS– 454 86. e. Similar triangles have the same angle measures. Congruent triangles have the same angle meas- ures and the same side lengths. From the given information, you cannot know if the side lengths are the same, so you can conclude only that the triangles are similar. 87. (1,1). Plot the points given in the problem and com- pete the parallelogram. Remember that in a par- allelogram, both pairs of opposite sides are equal and parallel. 88. e. The median time is the middle time. There is no way of knowing how far behind the median the slowest runner was. 89. b. The steepest rise on the graph was from April 23 to April 30. The symbol indicates that it was in the Midwest. 90. d. The prices for the West Coast have been rising steadily by 2 or 3 cents each week. On May 7, the price on the West Coast is a little beneath $1.80. If it rises 2 or 3 cents, it should be at about $1.82 by the following week. The question gives no reason to expect a sudden decline in price or a sharp increase. 91. b. Add the times and multiply by 9 cents: 19 + 24 + 8 = 51 minutes; 51 × .09 = $4.59. 92. 56. Let x represents the amount that Christian put in and 2x − 20 represents Maggie’s contribution. Solve the equation. x + 2x − 20 = 94 3x = 114 x = 38 Christian put in $38 and Maggie put in 94 − 38 = $56. 93. d. The number of games played is the total of the wins and losses, (20 + 15 = 35). Write the ratio and simplify. ᎏ 2 3 0 5 ᎏ = ᎏ 4 7 ᎏ . 94. b. Use the Pythagorean theorem: 25 2 + 9 2 = c 2 : c = ͙25 2 + 9 ෆ 2 ෆ = ͙625 + ෆ 81 ෆ = ͙706 ෆ 95. b. Use the order of operations. −3 × 5 2 + 2(4 − 18) + 3 3 −3 × 25 + 2(−14) + 27 −75 + (−28) + 27 −76 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 6 7 8 9 0 • / 1 2 3 4 5 7 8 9 0 • 56 1 2 −3 4 −5 −6 0 1 −2 3 4 5 6 −1 2 3 −4 5 −6 −1 −2−3−4 −5 6 – GED MATHEMATICS PRACTICE QUESTIONS– 455 . Gallons Days of the Week Paint Sales at Carolyn’s Hardware M T W Th F Sa Su 18 16 14 12 10 8 6 4 2 – GED MATHEMATICS PRACTICE QUESTIONS– 450 63. c. 22 feet = 264 inches; 264 ÷ 5.5 = 48. 64. ᎏ 1 3 ᎏ . The. $214.40 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 6 7 8 9 0 • / 1 2 3 4 5 6 7 9 0 • 58 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • 1 2 4 5 6 7 8 9 0 • 1/3 – GED MATHEMATICS PRACTICE QUESTIONS– 451 70. 375. Multiply $250 by 1.5, which equals $375. 71. 1,040. Set. 54°. 6 ᎏ 1 2 ᎏ ᎏ x ᎏ 3 4 ᎏ ᎏ 120 1 2 3 4 5 6 7 8 9 • 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 • / 1 2 3 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 • 0140 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 8 9 0 • / 1 2 3 4 6 7 8 9 0 • 375 – GED MATHEMATICS PRACTICE QUESTIONS– 452 75. (−3, −1). The vertical line is parallel to the y-axis, and