2: Answer this question **Transcription and Explanation for Educational Website**The line graph shown depicts average gasoline prices in a country from 1985 through 2010. ### Key StatementsLet p, q, and r represent the following simple statements:- **p:** Prices peaked in 2005.- **q:** Prices remained steady from 1990 through 1995.- **r:** Prices were more than $2.75 per gallon in 2000.**Problem Statement:**Write the symbolic statement $ \sim p \land r $ in words. Use the information from the graph to determine the truth value of the statement.**Answer Choices:**- **A:** Prices did not peak in 2005, and prices were more than $2.75 per gallon in 2000.- **B:** Prices peaked in 2005 and were less than $2.75 per gallon in 2000.- **C:** Prices peaked in 2005 and prices were more than $2.75 per gallon in 2000.- **D:** Prices did not peak in 2005, and prices were less than $2.75 per gallon in 2000.### Graph ExplanationThe graph titled “Average Gasoline Prices” has the vertical axis labeled as “Average Price per Gallon (unleaded regular)” ranging from $0.00 to $4.00. The horizontal axis is labeled “Year,” spanning from 1985 to 2010. The line trend shows a general increase in prices, peaking around 2005 at over $3.00 per gallon and decreasing toward 2010.- Prices in 2000 appear to be around $1.50 per gallon, which is less than $2.75.- The peak in 2005 is evident, confirming statement $ p $.### ConclusionThe graph suggests that statement $ \sim p \land r $: "Prices did not peak in 2005, and prices were more than $2.75 per gallon in 2000" is false, as prices did peak in 2005 and were not more than $2.75 in 2000. The section contains information on the average gasoline prices in a country from 1985 through 2010, interpreting a line graph. ### Statements and Variables- **p**: Prices peaked in 2005.- **q**: Prices remained steady from 1990 through 1995.- **r**: Prices were more than $2.75 per gallon in 2000.### Task- Write the symbolic statement $\sim p \land r$ in words.- Use the graph to determine the truth value of the statement.### Graph ExplanationThe graph titled "Average Gasoline Prices" depicts the fluctuating average price per gallon (unleaded regular) over the years 1985 to 2010. The y-axis ranges from $0.00 to $4.00, while the x-axis spans the years from 1985 to 2010.#### Observations:- Prices increase significantly from 1985 to 2005.- A noticeable peak appears around 2005.- Prices show a decline after 2005.### Options for Interpretation- **Option B**: Prices peaked in 2005 and were less than $2.75 per gallon in 2000.- **Option C**: Prices peaked in 2005 and prices were more than $2.75 per gallon in 2000.- **Option D**: Prices did not peak in 2005 and prices were less than $2.75 per gallon in 2000.Using the information from the graph, determine which options are true or false based on the statement $\sim p \land r$.

Answered: Image /qna-images/answer/1af1efdc-3077-4c77-a318-87a50885bbe1.jpg

The line graph to the right shows the average gasoline prices of a country from 1985 through 2010. Let p, q, and r represent the following simple statements. p: Prices peaked in 2005. q: Prices remained steady from 1990 through 1995. r: Prices were more than $2.75 per gallon in 2000. 2 Write the symbolic statement par in words. Then use the information given by the graph to determine the truth value of the statement. 6--- Average Price per Gallon (unleaded regular) Average Gasoline Prices $4.00- $3.00- $2.00- $1.00 50.00- 1990 OA. Prices did not peak in 2005 and prices were more than $2.75 per gallon in 2000. OB. Prices peaked in 2005 and were less than $2.75 per gallon in 2000. OC. Prices peaked in 2005 and prices were more than $2.75 per gallon in 2000. OD. Prices did not peak in 2005 and prices were less than $2.75 per gallon in 2000. 2000 2010 Year 73°F Clear Q 40

The line graph to the right shows the average gasoline prices of a country from 1985 through 2010. Let p, q, and r represent the following simple statements. p: Prices peaked in 2005. q: Prices remained steady from 1990 through 1995. r: Prices were more than $2.75 per gallon in 2000. 2 Write the symbolic statement par in words. Then use the information given by the graph to determine the truth value of the statement. 6--- Average Price per Gallon (unleaded regular) Average Gasoline Prices $4.00- $3.00- $2.00- $1.00 50.00- 1990 OA. Prices did not peak in 2005 and prices were more than $2.75 per gallon in 2000. OB. Prices peaked in 2005 and were less than $2.75 per gallon in 2000. OC. Prices peaked in 2005 and prices were more than $2.75 per gallon in 2000. OD. Prices did not peak in 2005 and prices were less than $2.75 per gallon in 2000. 2000 2010 Year 73°F Clear Q 40

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

2: Answer this question

**Transcription and Explanation for Educational Website**

The line graph shown depicts average gasoline prices in a country from 1985 through 2010.

### Key Statements

Let p, q, and r represent the following simple statements:

- **p:** Prices peaked in 2005.
- **q:** Prices remained steady from 1990 through 1995.
- **r:** Prices were more than $2.75 per gallon in 2000.

**Problem Statement:**

Write the symbolic statement $ \sim p \land r $ in words. Use the information from the graph to determine the truth value of the statement.

**Answer Choices:**

- **A:** Prices did not peak in 2005, and prices were more than $2.75 per gallon in 2000.
- **B:** Prices peaked in 2005 and were less than $2.75 per gallon in 2000.
- **C:** Prices peaked in 2005 and prices were more than $2.75 per gallon in 2000.
- **D:** Prices did not peak in 2005, and prices were less than $2.75 per gallon in 2000.

### Graph Explanation

The graph titled “Average Gasoline Prices” has the vertical axis labeled as “Average Price per Gallon (unleaded regular)” ranging from $0.00 to $4.00. The horizontal axis is labeled “Year,” spanning from 1985 to 2010. The line trend shows a general increase in prices, peaking around 2005 at over $3.00 per gallon and decreasing toward 2010.

- Prices in 2000 appear to be around $1.50 per gallon, which is less than $2.75.
- The peak in 2005 is evident, confirming statement $ p $.

### Conclusion

The graph suggests that statement $ \sim p \land r $: "Prices did not peak in 2005, and prices were more than $2.75 per gallon in 2000" is false, as prices did peak in 2005 and were not more than $2.75 in 2000.

The section contains information on the average gasoline prices in a country from 1985 through 2010, interpreting a line graph.

### Statements and Variables
- **p**: Prices peaked in 2005.
- **q**: Prices remained steady from 1990 through 1995.
- **r**: Prices were more than $2.75 per gallon in 2000.

### Task
- Write the symbolic statement $\sim p \land r$ in words.
- Use the graph to determine the truth value of the statement.

### Graph Explanation
The graph titled "Average Gasoline Prices" depicts the fluctuating average price per gallon (unleaded regular) over the years 1985 to 2010. The y-axis ranges from $0.00 to $4.00, while the x-axis spans the years from 1985 to 2010.

#### Observations:
- Prices increase significantly from 1985 to 2005.
- A noticeable peak appears around 2005.
- Prices show a decline after 2005.

### Options for Interpretation
- **Option B**: Prices peaked in 2005 and were less than $2.75 per gallon in 2000.
- **Option C**: Prices peaked in 2005 and prices were more than $2.75 per gallon in 2000.
- **Option D**: Prices did not peak in 2005 and prices were less than $2.75 per gallon in 2000.

Using the information from the graph, determine which options are true or false based on the statement $\sim p \land r$.

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