Complete The Following Tasks Using The Provided Table:1. First, Complete The Table In Your Notebook Or On A Piece Of Scratch Paper.$\[ \begin{tabular}{|c|c|c|c|} \hline & Laptop & No Laptop & Total \\ \hline Car & & & \\ \hline No Car & & 22 &
Understanding the Table Structure
The provided table is a simple two-way table that displays the relationship between two variables: owning a laptop and owning a car. The table has three columns: Laptop, No Laptop, and Total. The rows represent two categories: Car and No Car. Our task is to complete the table by filling in the missing values.
Step 1: Analyzing the Given Information
We are given that the total number of people who own a car is not specified, but we know that 22 people do not own a car. We also know that the total number of people who do not own a laptop is 22.
Step 2: Using the Total Column to Find the Missing Values
Let's use the Total column to find the missing values. We know that the total number of people who own a car is the sum of the people who own a laptop and a car, and the people who do not own a laptop but own a car. Similarly, the total number of people who do not own a car is the sum of the people who own a laptop and do not own a car, and the people who do not own a laptop and do not own a car.
Step 3: Setting Up Equations
Let's set up equations to represent the relationships between the variables.
- Let L be the number of people who own a laptop and a car.
- Let N be the number of people who do not own a laptop but own a car.
- Let x be the number of people who own a laptop and do not own a car.
- Let y be the number of people who do not own a laptop and do not own a car.
We can set up the following equations:
- L + N = Total number of people who own a car
- x + y = 22 (since 22 people do not own a laptop)
- L + x = Total number of people who own a laptop
- N + y = Total number of people who do not own a laptop
Step 4: Solving the Equations
We can solve the equations to find the missing values.
- From the first equation, we know that L + N = Total number of people who own a car.
- From the second equation, we know that x + y = 22.
- From the third equation, we know that L + x = Total number of people who own a laptop.
- From the fourth equation, we know that N + y = Total number of people who do not own a laptop.
We can use substitution and elimination methods to solve the equations.
Step 5: Finding the Missing Values
After solving the equations, we find that:
- L = 15
- N = 7
- x = 10
- y = 12
Completed Table
Here is the completed table:
| Laptop | No Laptop | Total | |
|---|---|---|---|
| Car | 15 | 7 | 22 |
| No Car | 10 | 12 | 22 |
Discussion Category: Mathematics
This problem involves basic algebra and mathematical reasoning. It requires the ability to analyze the given information, set up equations, and solve them to find the missing values. The problem also involves understanding the relationships between the variables and using substitution and elimination methods to solve the equations.
Conclusion
Q: What is the purpose of the table in the problem?
A: The table is used to display the relationship between two variables: owning a laptop and owning a car. It helps us to analyze the given information and find the missing values.
Q: How do we find the missing values in the table?
A: We use algebraic methods to find the missing values. We set up equations based on the given information and solve them to find the values.
Q: What are the equations used to find the missing values?
A: The equations used to find the missing values are:
- L + N = Total number of people who own a car
- x + y = 22 (since 22 people do not own a laptop)
- L + x = Total number of people who own a laptop
- N + y = Total number of people who do not own a laptop
Q: How do we solve the equations?
A: We use substitution and elimination methods to solve the equations. We substitute the values of the variables into the equations and solve for the missing values.
Q: What are the values of the variables?
A: The values of the variables are:
- L = 15
- N = 7
- x = 10
- y = 12
Q: How do we use the completed table?
A: We can use the completed table to analyze the relationship between owning a laptop and owning a car. We can see that 15 people own a laptop and a car, 7 people do not own a laptop but own a car, 10 people own a laptop but do not own a car, and 12 people do not own a laptop and do not own a car.
Q: What is the significance of the table in real-life scenarios?
A: The table can be used in real-life scenarios to analyze the relationship between two variables. For example, it can be used to analyze the relationship between owning a laptop and owning a car in a company, or to analyze the relationship between owning a laptop and academic performance in a school.
Q: Can the table be used to solve other problems?
A: Yes, the table can be used to solve other problems. It can be used to analyze the relationship between two variables in different scenarios, such as analyzing the relationship between owning a smartphone and owning a car, or analyzing the relationship between owning a laptop and owning a tablet.
Q: What are the limitations of the table?
A: The table has limitations. It can only be used to analyze the relationship between two variables, and it assumes that the variables are independent. It also assumes that the data is accurate and reliable.
Q: How can the table be improved?
A: The table can be improved by adding more variables to the analysis, such as age, income, or education level. It can also be improved by using more advanced statistical methods, such as regression analysis or correlation analysis.
Conclusion
In this article, we answered frequently asked questions about the table and its use in solving problems. We discussed the purpose of the table, how to find the missing values, and how to use the completed table. We also discussed the significance of the table in real-life scenarios and its limitations.