53 if 3 f x x and 2 6 g x x what is the value of f g

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53. If ( ) 3 f x x = + and 2 ( ) 6 g x x = , what is the value of f ( g (2))? 54. A pitcher contains 4 1 2 cups of water. A 1 3 -cup scoop is used to transfer water from the pitcher to a bowl. How many scoops are needed until the bowl has more water than the pitcher? 55. Grandma gave Bryce and Carter some raisins. Bryce received 6 more raisins than Carter, and Carter received half the number of raisins Bryce received. How many raisins did Bryce receive? 56. Kyle has 112 unit cubes. If no unit cube may be cut into smaller pieces, what is the minimum number of additional unit cubes he needs in order to build a solid cube using all the unit cubes? 57. When a positive number is multiplied by the sum of twice the number and half the number, the result is the original number. What is the number? Express your answer as a common fraction. 58. Given that 0.5 liters is approximately 1.05 pints, how many pints are in one liter? Express your answer as a decimal to the nearest tenth. 59. How many common fractions with a value between 0 and 1 have 6 as their denominator? 60. The product of three different positive integers is equal to 7³. What is the sum of the three integers? 61. How many inches are in 1 6 2 yards? 62. A ferry trip departs from the ferry dock every 15 minutes. Yesterday the first ferry trip left at 8 a.m. and the last ferry trip left at 5 p.m. How many ferry trips left from the ferry dock yesterday? 63. The ones digit of the product of four consecutive positive integers is 4. If this product is greater than 1000, what is the sum of the four smallest such integers? 64. A rectangular box has a volume of 108 cubic feet. How many cubic yards is the volume of this box? 65. What is the positive difference between the greatest and the least member of the set { 3 6 4 11 7 3 8 16 , , , }? Express your answer in simplest form. 52. ________________ 53. ________________ 54. ________________ 55. ________________ 56. ________________ 57. ________________ 58. ________________ 59. ________________ 60. ________________ 61. ________________ 62. ________________ 63. ________________ 64. ________________ 65. ________________
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Copyright MATHCOUNTS, Inc. 2006. All rights reserved. 2007 Chapter Countdown Round 66. A 2 inch by 2 inch square has its area increased by 21 square inches producing a new square. How many inches long is a side of the new square? 67. The radius of a circle is decreased by 10%. By what percent will the area be decreased? 68. What is 3 4 16 8 4 expressed as a positive integer? 69. What is the ratio of the volume of a cube with edge length six inches to the volume of a cube with edge length one foot? Express your answer as a common fraction. 70. Anne donates 4% of her total income each year to charity. If her 2005 donations totaled $1,308, what was her total 2005 income, in dollars? 71. An exhibit hall in a convention center measures 20 by 30 yards. A square area of 9 square yards must be reserved in one corner for registration. How many square yards will remain for exhibit space? 72. Carla spent two-fifths of her savings on a bracelet and had $9 left over. How many dollars did Carla’s bracelet cost?
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