Final_Exam_Review_Solutions - *REVIEW FOR THE FINAL The...

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*REVIEW FOR THE FINAL * The hope is that this will prepare you for the final. If you work out the problems diligently, bring up questions as necessary and review daily, the final will seem like just another exercise. Here we go: Fractions 1) 1/3 + 2/5 * 2/9 – 2/7 = Multiply the 2/5 by 2/9 1/3 + 4/45 – 2/7 = Find a common denominator Denominator = 315 The first fraction of 1/3 converts to 105/315 The second fraction of 4/45 converts to 28/315 and The last fraction converts to 90/315. You now have: 105 + 28 – 90 = 43 315 315 Answer: 43/315 2) 7/16 divided by 1/8 = Answer: 7/2 or 3 ½ 7/16 * 8/1 = 56/16 = 7/2 or 3 1/2 Conversion of fractions, decimals and percents Express as a percent: 3) 2.045 Answer: 204.5% 4) 2/225 = Answer: .888% 5) .876 = Answer: 87.6%
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6) .00456 = Answer: .456% Express as a decimal: (Round to at least two decimals) 7) 3/125 = Answer: .024 8) 6/57 = Answer: .10526 Express as a fraction: 9) 2.075 = Answer: 2 3/40 10) .0035% = Answer: 7/200,000 Order of Operation 11) (-4) + (-6)(-8) divided by [16 – (-1)] = (-4) + (-6)(-8) = (-4) + 48 = 44 16 – (-1) 16 + 1 17 Answer: 44/17 12) (-7)(5)(+2) divided by (10 +7) = (-7)(5)(+2) = (-35)(2) = -70 10 +7 17 17 Answer: -70 17 Evaluation Problems 13) Given the equation X = Y 3 + Z/2 divided by [K - 3] , Find X when K = (-7), Y = 3 and Z = 6 (3) 3 + 6/2 = 27 + 3 = 30 = -3 -7 – 3 -10 -10
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Answer: -3 Solve for "x": 14) 3x + 7 = 2(4x –5) –2x = 3x + 7 = 8x –10 – 2x 3x + 7 = 6x – 10 -3x = -17 x = 17/3 Answer: x = 17/3 or 5 2/3 15) 7(y –2) +4 = 3(8y + 7) = 7y – 14 + 4 = 24y + 21 7y – 10 = 24y + 21 -17y = 31 y = 31/-17 Answer: y = - 31/17 or – 1 14/17 Counting Techniques 16) Interpret the following: (BA II PLUS usage) 12! /7! = {12, 2 nd , X! / 7, 2 nd , X!, =}, = 95,040 (12 x 11 x 10 x 9 x 8) 8! /(8 - 4)! = {8, 2 nd , X! / 4, 2 nd , X!, =}, = 1,680 (8 x 7 x 6 x 5) Intersection % Union of Sets, Venn diagrams 17) In the rolling of a fair die, what is the probability of rolling an even number or a number that is less than 3? Solution: Let A be the event that consists of observing an even number, and B a number that is less than 3. P (A) = P (Even #) = P (2, 4, 6) = ½ and P (B) = P (# < 3) = P (1, 2) = 2/6 or 1/3, thus P (A U B ) = P (A) + P (B) – P (A ∩ B) = ½ + – 1/6 = 4/6 o 2/3 18) Given X = {2, 5, 7} and Y = {3, 4, 5} depict these two sets as a union and an intersection, i.e., (x U y) =? and (x y) =? Solution: Union: = {2, 3, 4, 5, 7} Intersection: = {5} Depreciation Expense
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A Widget maker was purchased at a cost of $225,000. Depreciation will be calculated on the Straight-line method over a period of 20 years. The salvage value of this machine is $25,000. Answer the following question: 19) What is the annual depreciation expense? Answer: Depreciation = $10,000 per year 20) What is the value of the equipment after 11 ½ years? Answer: The value formula after T years is: V = $225,000 - $10,000 * T. When T = 11.5, Value = V = $225,000 - $10,000 * 11.5 = $225,000 - $115,000 = $110,000 21) Give me the depreciation expense for a piece of machinery purchased on April 17 th . Assume that the end of this company’s fiscal year is December 31 st . If the yearly depreciation is $1,500, how much can be depreciated in this first year? Since the purchase of this machinery was after the 15 th , that month, April cannot be depreciated thus, 8 months remain that can or 2/3rds of the $1,500 or $1,000.
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