GENETIC ENGINEERING - EXAMPLE 27.1 : In Mendelian genetics, yellow (Y) is dominant to green (y) and round (R) is dominant to wrinkled (r). (a) What is the probability P of Rr x Rr producing wrinkled seeds? (b) What is the probability P of Yy x yy producing green seeds? (c) What is the probability that RRYy x RrYy would produce RrYy?
GENETIC ENGINEERING - ANSWER 27.1 : (a) There are 3 types of seeds produced : RR, Rr, rR, rr where RR, Rr, rR (3) are dominantly round and rr (1) is recessively wrinkled. P (wrinkled) = 1 / (3 + 1) = 1 / 4. (b) There are 2 types of seeds produced : Yy, Yy, yy, yy where Yy (2) are dominantly yellow and yy (2) are recessively green. P (green) = 2 / (2 + 2) = 1 / 2. (c) Let RR x Rr produces RR, Rr, RR, Rr, then P (Rr) = 2 / 4 = 1 / 2. Let Yy x Yy produces YY, Yy, yY, yy, then P (Yy) = 2 / 4 = 1 / 2. P (RrYy) = P (Rr) x P (Yy) = 1 / 2 x 1 / 2 = 1 / 4. The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.13 (CORRECTION) : (i) In the Present Value Multiplication Rule, let PV = present value, Ra = interest rate for first discount, A = duration for first discount; Rc = interest rate for second discount, C = duration for second discount. Let PV = [ 1 / (1 + Ra) ^ A ] [ 1 / (1 + Rc) ^ C ] where ^ is the symbol of power : 3 ^ 2 = 3 x 3, 2 ^ 3 = 2 x 2 x 2. (a) For discounts involving 8 % / year for 3 years and 10 % / year for 9 years, find the value of PV. (b) If Re = interest rate for third discount, E = duration of third discount, form a mathematical equation of PV as a function of A, C, E, Ra, Rc, Re. Note : Discounts are available in the purchase of certain biochemical engineering instruments. (ii) Let R = nominal interest rate related to growth rate of money, r = real interest rate related to growth rate of purchase power. If I = inflation, where the unit of R, r and I is %, find the mathematical relationship of r as a function of R and I.
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ENGINEERING MATERIAL - EXAMPLE 12.1 : In crystal material, hexagonal crystal system could form 4-digit index in certain direction of solid. For [1(-1)0] direction in the hexagonal crystal systems of particular catalyst applied in fume removal of incinerator, what is the four-digit index for this direction? Hint : The transformation equations between the 3-digit [h'k'l'] and the 4-digit [hkil] indices are : h = (1/3) (2h'-k'); i = - (h + k); k = (1/3) (2k'-h'); l = l' A. [(-1)100] B. [1(-1)00] C. [(-1)000] D. [00(-1)(-1)] E. [(-1)0(-1)0]
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