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Mathematical Formulae
(a + b)2 = a2 + b2 + 2ab
(a - b)2 = a2 + b2 - 2ab
(a + b)2 + (a - b)2 = 2(a2 + b2)
(a + b)2 - (a - b)2 = 4ab
a2 - b2 = (a + b) (a - b)
(a + b)3 = a3 + b3 + 3ab (a + b)
(a - b)3 = a3 - b3 - 3ab (a - b)
a3 + b3 = (a + b) (a2 - ab + b2)
a3 - b3 = (a - b) (a2 + ab + b2)
logax = y →ay = x
logaxp = p logax
logaxy = loga x + logay
A retired couple has up to $30000 to invest in fixed-income securities. Their broker recommends investing in two bonds: one a AAA bond yielding 8%; the other a B+ bond paying 12%.
Example of Adding signed numbers: Example: (2) + (-4) = Solution: Start with 2 and count 4 whole numbers to the left. Thus: (2) + (-4) = -2 Adding
Theorem If {a n } is bounded and monotonic then { a n } is convergent. Be cautious to not misuse this theorem. It does not state that if a sequence is not bounded and/or
In a certain class, one half of the male students and two thirds of the female students speak French. If there are three fourths as many girls as boys in the class. What fraction o
Series - Convergence/Divergence In the earlier section we spent some time getting familiar with series and we briefly explained convergence and divergence. Previous to worryin
A critical dimension of the service quality of a call center is the wait time of a caller to get to a sales representative. Periodically, random samples of 6 customer calls are mea
7(y + 3) - 2(x + 2) = 14, 4 (y - 2) + 3(x - 3) = 2 Ans: 7(y + 3) - 2 (x+ 2) = 14 --------- (1) 4(y- 2) + 3(x - 3) = 2 ----------(2) From (1) 7y +21 -
Explain how we Converting Fractions to Percents ? To convert a fraction to a percent: 1. Convert the fraction to a decimal using long division. 2. Move the decimal point two p
suresh invested rs.1080 in shares of face value rs.50 at rs.54.After receiving dividend on them at 8% he sold them at 52.In each of the transaction he paid 2 % brokerage.Hpw much d
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