Use Venn Diagram To Solve The Following Problem To Estimate

Question

Use Venn Diagram To Solve Following Problemto Estimate The Number Of P Use Venn diagram to solve following problem To estimate the number of persons interested in recycling aluminum cans, glass, and newspapers, a company conducts a survey of 1000 people and finds that 200 recycles glass 300 recycles paper 450 recycles cans 50 recycles cans and glass 15 recycles paper and glass 60 recycle cans and paper 10 recycle all three Q1. How many people do not recycle at all? Q2. How many people recycle cans only? Q3. How many people recycle paper only? Please also show your work.

Dr. Jack HW Helper · Accepted Answer

The problem involves analyzing data from a survey to determine recycling behaviors among individuals, specifically focusing on aluminum cans, glass, and newspapers. The data provided include the total number of recyclers for each category, as well as overlaps among them. Using a Venn diagram approach allows us to visualize and calculate the number of individuals in each specific segment of recycling habits, including those who do not recycle at all. Introduction Recycling is a critical aspect of environmental sustainability. Understanding the distribution of recycling behaviors helps in designing better waste management policies. This problem employs set theory and Venn diagrams to analyze survey data, providing insights into how many individuals participate exclusively in recycling certain items, participate in multiple categories, or do not participate in recycling at all. Data Breakdown The survey of 1000 people yields the following data: - Total people surveyed: 1000 - Number of people who recycle glass (G): 200 - Number who recycle paper (P): 300 - Number who recycle cans (C): 450 Overlap areas include: - C and G: 50 - P and G: 15 - C and P: 60 - All three (C, P, G): 10 Step 1: Define the Variables and Venn Diagram Sections Let’s denote: - $ c $ = number who recycle cans only - $ p $ = number who recycle paper only - $ g $ = number who recycle glass only - $ cp $ = number who recycle cans and paper, but not glass - $ cg $ = number who recycle cans and glass, but not paper - $ pg $ = number who recycle paper and glass, but not cans - $ cpg $ = number who recycle all three From the data: - $ cpg = 10 $ - $ cg + cpg = 50 $, hence $ cg = 50 - 10 = 40 $ - $ pg + cpg = 15 $, so $ pg = 15 - 10 = 5 $ - $ cp + cpg = 60 $, giving $ cp = 60 - 10 = 50 $ Step 2: Calculate the Unknowns Using the totals for each category: - For cans: $$ c + cp + cg + cpg = 450 $$ $$ c + 50 + 40 + 10 = 450 $$ $$ c = 450 - 100 = 350 $$ - For paper: \[ p + cp + pg + c

Use Venn Diagram To Solve The Following Problem To Estimate

Use Venn Diagram To Solve Following Problemto Estimate The Number Of P

Paper For Above instruction

Introduction

Data Breakdown

Step 1: Define the Variables and Venn Diagram Sections

Step 2: Calculate the Unknowns

Step 3: Calculate the Number of People Who Do Not Recycle at All

Step 4: Answer the Specific Questions

Conclusion

References