methods‚ it may be a good idea to encourage students to know one method for these factorizations rather than have them memorize two separate formulas. First of all‚ the factorization is the product of a binomial and a trinomial. There is amnemonic device for remembering the signs that works when the binomial is put in front of the trinomial as above. The other two special factoring formulas are two sides of the same coin: the sum and difference of cubes. These are the formulas: a3 + b3 = (a + b)(a2 – ab + b2)
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essential question listed below. How can a Greatest Common Factor be separated from an expression? By simplifying the equation . By breaking them up by dividing them up What methods can be used to rewrite square trinomials and difference of squares binomials as separate factors? distribution in what conditions can a factored expression be factored further? Greatest Common Factor A greatest common factor of two or more terms is the largest factor that all terms have in common. The greatest common factor
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(continuously compounded returns in up step in binomial tree) 1.418 D (down step in binomial tree) 0.705 risk-free rate (based on 10yr US Treasury rate in 1992) 7.03% exp(r∆T) 1.006 q (risk-neutral probability of up move‚ using Lognormal model) 0.422 Avg Hypothetical Negative Cost of Sequel (discounted to Year 2) $19.79 Table of the parameters and values used to build the binomial trees and find the option price. Building the Binomial Tree for Asset Values The binomial model is used to see how the state variable
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Explain Why It Is Impossible to Derive An Analytical Formula For Valuing American Puts. Explain why it has proved impossible to derive an analytical formula for valuing American Puts‚ and outline the main techniques that are used to produce approximate valuations for such securities Investing in stock options is a way used by investors to hedge against risk. It is simply because all the investors could lose if the option is not exercised before the expiration rate is just the option price (that
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understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients). a. Explain how long division of a polynomial expression by a binomial expression of the form x − a‚ a∈ I ‚ is related to synthetic division. b. Divide a polynomial expression by a binomial expression of the form x − a‚ a∈ I ‚ using long division or synthetic division. c. Explain the relationship between the linear factors of a polynomial expression and the zeros of the
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Describe the properties of discrete probability distribution. 10. Given E(X) = 0.55‚ Var(X) = 1.55 and Y = 2X + 1. Find E(Y) and Var(Y). 11. Show that the mean of the binomial distribution (q + p)2 is 2p. 12. Show that mean is 2p and σ2 = 2pq for a binomial distribution in which n = 2. 13. A random variable X has a binomial distribution with E(X) = 2.4 and p = 0.3. Find the standard deviation of X. 14. Describe the normal distribution and write down its equation. 15. What is standard
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a2+b2=c2 is the formula for the Pythagorean Theorem. Let a=x‚ b=2x+4‚ c=2x+6 x2+ (2x+4)2=(2x+6)2 The binomials are plugged into the Pythagorean Theorem. The binomials are squared. x2+4x2+8x+16=4x2+12x+36 Notice the 4x2on both sides of the equation‚ I will subtract this from both
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probability out of a randomly selected group of five that exactly three will say they watch less T.V. this year than last. a. Not binomial. b. N/A c. n=5 p=0.70 q=0.30 r: (0‚ 3.5) 2. There are 20 m&m’s candies in a dish. 8 are brown‚ three red‚ five green and four yellow. Two candies are picked from the dish at random. What is the probability that both are red? a. Binomial b. P(Success) = 6/20 = 3/10 P(Failure) = 14/20 = 7/10 c. n=20 p=0.30 q=0.70 r: (0‚ 6) 3. A multiple choice test is
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ORGANIZATIONAL CLOTHING AND INDIVIDUAL EQUIPMENT (OCIE) GUIDE PHOTO CIF NOMENCLATURE LIN COMMONLY CALLED CHARACTERSITICS BODY ARMOR FRAG A92145 FRAG VEST‚ FLAK VEST BAG BARRACKS B13907 BARRACKS BAG‚ LAUNDRY BAG OD COTTON BAG‚ STRING CLOSURE BAG DUFFEL B14729 DUFFEL BAG NYLON BAG W/ GROMMET CLOSURE‚ SHOULDER STRAPS BAG CLTHING WTRPROOF B15825 WATER PROOF BAG RUBBERIZED NYLON BAG‚ STRING CLOSURE UNIVERSAL (ACU) CAMOUFLAUGE. INCLUDES THE BASE
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transition also includes a development from the distributive property of a monomial times a binomial to the product of two binomials. Finding the product of two binomials can be a daunting task‚ unless students are presented the material in connection with a learning strategy that they are able to master. The lesson‚ found in the appendix‚ is designed to facilitate the evolution of multiplication of monomials and binomials. It was taught to one struggling seventh grade student who is the product of social
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