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)=
Premium Addition Natural number
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
Premium Normal distribution Answer
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
Premium Pythagorean theorem Triangle Law of cosines
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
Premium Multiplication Algebra Mathematics
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
Free Medicine Nursing Epidemiology
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
Premium Statistics Normal distribution Standard deviation
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
Premium Obesity Body mass index Mass
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:
Premium Addition Question Division
Lab 2 – Water Quality and Contamination Experiment 1: Effects of Groundwater Contamination Table 1: Water Observations (Smell‚ Color‚ Etc.) Beaker Observations 1 This beaker has water only‚ clear with no smell 2 I mixed oil in the water‚ the oil then started to settle at the top of the water. (oil is not a soluble) 3 Beaker contained vinegar and water‚ the water got a little cloudy and the vinegar smell is very strong. 4 The water and laundry detergent mix had a soapy look to it‚ water also
Premium Drinking water Water pollution Water
This archive file of SCI 207 Week 2 Answer to Lab Question 2 shows the solutions to the following problems: In the lab questions below‚ report your answers in the format of a scientific report: introduction‚ methods‚ results‚ discussion‚ conclusions and management recommendations. Introduction 1. What is the question that this study aimed to answer? State the hypothesis that you tested. 2. Briefly describe the methods of data collection and analysis you used to test your hypothesis
Free Question Answer Water supply