name is who they are. The name is who they are because in their first game‚ four players and their head coach were Native Americans. The name according to A1‚ was never a label. Instead‚ according to Dan Snyder‚ is a badge of honor. The redskin name is also everything they stand for. It is the same values that guide Native Americans. According to A1‚ the values are strength‚ courage‚ pride‚ and respect. According to A2‚ Daniel Snyder said that by staying true to their history and honoring the deep and
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written as for all of n∈N‚ ()‚ ()‚ ()+… +(n = =+ +(n a. Proof: ==(2n+1)+(2n+1)(2n+2)/2=+( 4.2 5. Give a recursive definition for the intersection of the sets A1‚ A2‚ . . . ‚ An‚ An+1 ⊆ _‚ n ≥ 1. Use the result in part (a) to show that for all n‚ r ∈ Z+ with n ≥ 3 and 1 ≤ r < n‚(A1 ∩ A2 ∩ ・ ・ ・ ∩ Ar ) ∩ (Ar+1 ∩ ・ ・ ・ ∩ An) _ A1 ∩ A2 ∩ ・ ・ ・ ∩ Ar ∩ Ar+1 ∩ ・ ・ ・ ∩ An. Solution a) The intersection of ‚ is ∩ . The intersection of ‚ ‚ … ‚
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two 4-bit binary words (A1 – A4‚ B 1 – B4) and a Carry Input (C0). It generates the binary Sum outputs ∑1 – ∑4) and the Carry Output (C4) from the most significant bit. The LS83A operates with either active HIGH or active LOW operands (positive or negative logic). The SN54 / 74LS283 is recommended for new designs since it is identical in function with this device and features standard corner power pins. CONNECTION DIAGRAM DIP (TOP VIEW) B4 16 Σ4 15 C4 14 C0 13 GND 12 B1 11 A1 10 Σ1 9 NOTE: The Flatpak
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7166M01.qxd_lb 6/3/09 09:38 AM Page 1 1 BASIC CONCEPTS 1.1 INTRODUCTION Concrete is strong in compression‚ but weak in tension: its tensile strength varies from 8 to 14 percent of its compressive strength. Due to such a low tensile capacity‚ flexural cracks develop at early stages of loading. In order to reduce or prevent such cracks from developing‚ a concentric or eccentric force is imposed in the longitudinal direction of the structural element. This force prevents the cracks
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theorem (described in [2]) gives the expansion of a multinomial to an integer power p > 0‚ (a1 + a2 + ⋅⋅⋅ + an ) p = p k1 k2 kn a1 a2 ⋅⋅⋅ an . k1 ‚ k2 ‚ ⋅⋅⋅‚ kn k1 + k2 +⋅⋅⋅+ kn = p ∑ (1) Here the multinomial coefficient is calculated by p p! . = k1 ‚ k2 ‚ ⋅⋅⋅‚ kn k1 !k2 !⋅⋅⋅ kn ! (2) This is a generalization of the familiar binomial theorem to the case where the sum of n terms ( a1 + a2 + + an ) is raised to the power p. In (1)‚ the sum is taken over all ‚ kn such that
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possible to rearrange the letters in “MISSISSAUGA”? Hint: Consider in how many ways the letter “M” can be placed‚ and then in how many ways the letters “I” can be placed‚ etc (b) Consider a string using only letters A1 ‚ . . . ‚ An . Let S be the family of strings with exactly i1 letters A1 ; i2 letters A2 ; . . . ; in letters An (where i1 ‚ . . . ‚ in are some non-negative integers). Find a formula for the cardinality of S. Hint: This generalizes the problem in part (a)‚ the proof is similar. Solution:
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“Midterm test”. [0.25 mark] B. Problem [ 8.75 mark ] In the “Midterm test” worksheet‚ create one model to solve the following problem: As of Jan 1st‚ 2011‚ you want to buy a car and are given two payment methods as follow: A1. Pay now: to pay VND 500 million A2. Pay by annuity: to pay for 5 years‚ each year pays 3 times at the beginning of each period. The amount paid each time is VND 44 million. Regardless of your choice‚ the first payment will occur today
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Big-M method The Big-M method of handling instances with artificial variables is the “common sense approach”. Essentially‚ the notion is to make the artificial variables‚ through their coefficients in the objective function‚ so costly or unprofitable that any feasible solution to the real problem would be preferred....unless the original instance possessed no feasible solutions at all. But this means that we need to assign‚ in the objective function‚ coefficients to the artificial variables that
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Exercise 7.3 (Solutions) MathCity.org Calculus and Analytic Geometry‚ MATHEMATICS 12 Merging man and maths Available online @ http://www.mathcity.org‚ Version: 1.0.0 Question # 1 ˆ j ˆ (i) u = 3i + ˆ − k ‚ ˆ j ˆ v = 2i − ˆ + k u = (3)2 + (1) 2 + (−1)2 = 9 + 1 + 1 = 11 v = (2) 2 + (−1)2 + (1)2 = 4 + 1 + 1 = 6 ˆ j ˆ u ⋅ v = 3iˆ + ˆ − k ⋅ 2i − ˆ + k j ˆ ( )( ) = (3)(2) + (1)(−1) + (−1)(1) = 6 − 1 − 1 = 4 u ⋅ v = u v cosθ Now ⇒ cosθ = u⋅v u v 4
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Compensation structure for FastCat Executive summary In Phase I we looked at the descriptions of sample jobs at FastCat and proposed a structure for the jobs based on the concepts of internal equity and organizational objectives of innovative product design‚ improved marketing and cost competitiveness. Based on the content and value of the job descriptions available we had created a tailored and hierarchical structure‚ which supported the organization strategy‚ work flow and motivates
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