1 2. Establish each of the following for all n ≥ 1 by the Principle of Mathematical Induction. Solution a) S(n): ==‚ S(1): = = =1‚ So S(1) is true. Assume S(k): = Consider S(k+1) = = +=-1+= -1. Hence‚ it follows that S(k)⇒S(k + 1) is true for all n ∈ Z+ by the Principle of Mathematical Induction. b) S( n) for n=1‚ = 2 = 2+(1-1). So S(1) is true. Inductive Step: assume S(k)is true‚ for some (particular) k ∈ Z+—that is‚ assume that =2+(k-1). For n=k+1‚ = + (k+1) = 2+ (k-1)+(k+1)=
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Math 221 **** Example Format **** Week 6 Lab Submitted by: (Insert Name Here **REMOVE THIS NOTE PRIOR TO SUBMITTING**) (Note: Your labs should be well organized‚ with results clearly identified and in the proper order. When answering questions‚ be sure to use complete sentences and proper grammar. It is also important for you to fully explain your answers! Please do not answer “yes” (or “no”); you should explain why the answer
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Treasure Hunt: Finding the Values of Right Angle Triangles This final weeks course asks us to find a treasure with two pieces of a map. Now this may not be a common use of the Pythagorean Theorem to solve the distances for a right angled triangle but it is a fun exercise to find the values of the right angle triangle. Buried treasure: Ahmed has half of a treasure map‚which indicates that the treasure is buried in the desert 2x + 6 paces from Castle Rock. Vanessa has the other half of the map
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Formulas Read the following instructions in order to complete this discussion‚ and review the example of how to complete the math required for this assignment: • Read about Cowling’s Rule for child sized doses of medication (number 92 on page 119 of Elementary and Intermediate Algebra). • Solve parts (a) and (b) of the problem using the following details indicated for the first letter of your last name: |If your last |For part (a) of problem 92 use this information to
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Elementary Statistics iLab Week 6 Statistical Concepts: * Data Simulation * Discrete Probability Distribution * Confidence Intervals Calculations for a set of variables Mean Median 3.2 3.5 4.5 5.0 3.7 4.0 3.7 3.0 3.1 3.5 3.6 3.5 3.1 3.0 3.6 3.0 3.8 4.0 2.6 2.0 4.3 4.0 3.5 3.5 3.3 3.5 4.1 4.5 4.2 5.0 2.9 2.5 3.5 4.0 3.7 3.5 3.5 3.0 3.3 4.0 Calculating Descriptive Statistics Descriptive Statistics: Mean‚ Median Variable N N* Mean SE Mean StDev
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Caring for Populations through Community Outreach Chamberlain College of Nursing NR 443: Community Health Nursing Caring for Populations through Community Outreach I selected my work setting as the Health Department‚ functioning as a Health Promotion Nurse. The identified problem in Atlanta‚ Georgia was prevalence in cardiovascular disease and cancer. According to world heart foundation‚ a person has 50% risk of developing heart disease if that individual’s parents have suffered from heart
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Assignment: Inequalities Math 221: Introduction to Algebra Instructor Jonah Mutua June 16‚ 2013 Inequalities This assignment involves the use of inequalities in mathematical equations. The formula for finding Body Mass Index (BMI) is BMI =703W/H^2. In this formula W = weight in pounds In this formula H = height in inches. For this assignment four intervals based on our own personal heights must be calculated. I am 6 feet 4 inches tall
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c = 86 The INTEGERS above are needed to solve each given expressions. A) A^3 – B^3 (7^3) – (-2^3) 343-(-6859) =7‚202 This is the given expression with VARIABLES A and B and raised to the EXPONENTS of 3 on each of them. By substituting the integers in the variables and raising them to the 3rd power gives the answer of B) (a – b)(a2 + ab + b2) (7-(-19) (7^2+(7)(-19)+(-19^2) (26) (49-133) + 361 (26)(277) =7202 C) ( b-c )/ (2b- a) :-This expression uses all three variables:
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MINITAB Applications in Six Sigma Agenda 13:00-13:30 Registration 13:30-14:20 MSA-MINITAB 14:20-14:30 Break 14:30-15:20 SPC-MINITAB 15:20-15:30 Break 15:30-16:20 Case study (Healthcare & Banking) 16:20-16:30 Q&A July 14‚ 2006 in Taipei MSA-MINITAB Application in (Measurement Systems Analysis‚ MSA) Measuring System. What is a Measuring System? •The measuring device (Repeatability) •The person who is taking the measurement (Reproducibility) 3 Measurement Process The ideal measurement
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Lab for Chemistry 221 Lab: How much sugar is in a Can of Coke? Abstract: A 50mL (we used 100mL) volumetric flask was used to determine the amount of sugar in a can of Coke per mL in 5 different solutions. Using the calibration curve we determine the amount of sugar per mL in a can of coke. This experiment concluded that there is 43.83g of sugar in a 12oz can of Coke. Introduction: This experiment was conducted to determine the amount of sugar in a can of Coke and to and use a calibration
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