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Mathematics for Business, Science, and Technology, Third Edition Copyright © Orchard Publications 1−35 Chapter 1 Elementary Algebra 1. a. R + 50 = 150 , R + 50 – 50 = 150 – 50 , R = 50 b. V – 25 = 15 , V – 25 + 25 = 15 + 25 , V = 40 c. 1 = R , R = 10 d. --R e. R 5P = 10 , ( 5P ) f. ( 100 + R )10 4. = 10 , ( 5P ) = 1 , ( 100 + R )10 (1 ⁄ 2) × 2 –3 2 = 10 , 5P = 100 , ( 5P ) ⁄ 5 = 100 ⁄ 5 , P = 20 3 3 0 × 10 = 1 × 10 , ( 100 + R )10 = 1000 , ( 100 + R ) × 1 = 1000 , 100 + R – 100 = 1000 – 100 , R = 900 2.

6. 6. 13 Proportions A proportion is defined as two ratios being equal to each other. 70) Consider a line segment with a length of one unit. Let us divide this segment into two unequal segments and let x = shorter segment 1 – x = longer segment The golden proportion is the one where the ratio of the shorter segment to the longer segment, that is, x ⁄ ( 1 – x ) is equal to the ratio of the longer segment to the whole segment, that is, ( 1 – x ) ⁄ 1 . 382 . 7. 7. 14 Summary • Algebra is the branch of mathematics in which letters of the alphabet represent numbers or a set of numbers.

2 volts. 08 volts. 08 volts. Hence, the name moving average. However, a more meaningful moving average can be obtained if we assign weights to each reading where the most recent reading carries the most weight. Thus, using a 5−day moving average we could take the reading obtained on the 5th day and multiply it by 5, the 4th day by 4, the 3rd day by 3, the 2nd day by 2, and the 1st day by 1. , 5+4+3+2+1=15. 09 is referred to as the Weighted Moving Average (WMA). An Exponential Moving Average (EMA) takes a percentage of the most recent value and adds in the previous value’s exponential moving average times 1 minus that percentage.