Which Statements Are Correct About The Table? Check All That Apply.$\[ \begin{tabular}{|c|c|} \hline Hours $(h)$ & Dollars $(d)$ \\ \hline 1 & 42 \\ \hline 2 & 84 \\ \hline 3 & 126 \\ \hline 4 & 168 \\ \hline 5 & $? $

Introduction

In this article, we will delve into a table that presents a relationship between hours and dollars. The table provides a clear pattern, and we will analyze it to determine which statements are correct. We will examine the table, identify the pattern, and then check all applicable statements.

The Table

Pattern Identification

Upon examining the table, we notice that the dollars increase by a fixed amount for each additional hour. To identify the pattern, let's calculate the difference between consecutive dollars.

• Between hours 1 and 2, the dollars increase by $84 - 42 = 42$.
• Between hours 2 and 3, the dollars increase by $126 - 84 = 42$.
• Between hours 3 and 4, the dollars increase by $168 - 126 = 42$.

We observe that the difference between consecutive dollars is always $42$. This indicates a linear relationship between hours and dollars.

Calculating the Missing Value

Now that we have identified the pattern, we can calculate the missing value for hours 5.

• The difference between consecutive dollars is $42$.
• To find the dollars for hours 5, we add $42$ to the dollars for hours 4: $168 + 42 = 210$.

Therefore, the missing value for hours 5 is $210$.

Checking the Statements

Now that we have analyzed the table and identified the pattern, we can check the statements.

Statement 1: The table represents a linear relationship between hours and dollars.

• Correct: The table presents a linear relationship between hours and dollars, as the difference between consecutive dollars is always $42$.

Statement 2: The dollars increase by $42$ for each additional hour.

• Correct: The dollars increase by $42$ for each additional hour, as observed in the table.

Statement 3: The missing value for hours 5 is $210$.

• Correct: We calculated the missing value for hours 5 as $210$, which is correct.

Statement 4: The table represents a non-linear relationship between hours and dollars.

• Incorrect: The table presents a linear relationship between hours and dollars, not a non-linear relationship.

Statement 5: The difference between consecutive dollars is not always $42$.

• Incorrect: The difference between consecutive dollars is always $42$, as observed in the table.

Conclusion

Q: What is the relationship between hours and dollars in the table?

A: The table presents a linear relationship between hours and dollars. This means that for each additional hour, the dollars increase by a fixed amount, which is $42$ in this case.

Q: How do I calculate the missing value for hours 5?

A: To calculate the missing value for hours 5, you can add $42$ to the dollars for hours 4. In this case, the missing value for hours 5 is $168 + 42 = 210$.

Q: Is the table a good example of a linear relationship?

A: Yes, the table is a good example of a linear relationship. The difference between consecutive dollars is always $42$, which indicates a consistent and predictable pattern.

Q: Can I use this table to make predictions about future values?

A: Yes, you can use this table to make predictions about future values. Since the relationship between hours and dollars is linear, you can continue to add $42$ to the dollars for each additional hour to make predictions.

Q: What if the difference between consecutive dollars is not always $42$?

A: If the difference between consecutive dollars is not always $42$, then the table does not represent a linear relationship. In this case, you would need to re-examine the table and identify a different pattern or relationship.

Q: Can I use this table to understand other relationships between variables?

A: Yes, you can use this table as a starting point to understand other relationships between variables. By analyzing the pattern and relationship between hours and dollars, you can develop a deeper understanding of how different variables interact and affect each other.

Q: Are there any limitations to using this table to make predictions?

A: Yes, there are limitations to using this table to make predictions. For example, if the relationship between hours and dollars changes over time, the table may not accurately reflect future values. Additionally, if there are external factors that affect the relationship between hours and dollars, the table may not account for these factors.

Q: How can I apply the concepts learned from this table to real-world scenarios?

A: You can apply the concepts learned from this table to real-world scenarios by analyzing relationships between variables and identifying patterns. For example, you can use this table to understand how different factors affect a business's revenue or how changes in one variable affect another variable.

Conclusion

In conclusion, the table presents a linear relationship between hours and dollars, and we can use this table to make predictions about future values. However, it's essential to consider the limitations of using this table and to re-examine the table if the relationship between hours and dollars changes over time. By applying the concepts learned from this table to real-world scenarios, you can develop a deeper understanding of how different variables interact and affect each other.