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Question 1180852: TV weather forecasters use satellite and radar data to predict where storms will move in order to help viewers know what weather to expect. The map below shows a storm off the eastern coast of the United States. The arrows show the path the heart of the storm traveled over the last 48 hours. If you were a forecaster in the northeast, use the map to answer the following questions.
https://api.agilixbuzz.com/Resz/~0.6NT8GFszQyEepNgJ.U8Pc_1Jw6w7bKhdBO1lgK6sThuzD160XdxwpKkVzzWg/48780464,FA7,11,3/Assets/Media/Images/41.2-HOT3-Weather.jpg
a. What would you tell your Northeast coast audience? Which type of reasoning—inductive or deductive—did you use? Explain.
b. Write an if-then statement to describe your conjecture.
c. Write the inverse of the statement.
d. Write the converse and contrapositive of the statement.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's an analysis of the storm's path and how a forecaster might present the information:
**a. What to tell the Northeast coast audience:**
"Good evening, everyone. As you can see on the map, a storm is currently located off the East Coast. Over the past 48 hours, it has followed a generally westward track, as indicated by these arrows. Based on this observed pattern, we can *induce* that the storm is likely to continue moving in a westerly direction. This means it *could* potentially impact the Northeast coast in the coming days. However, it's important to note that storm tracks can change, so we'll continue to monitor the situation closely and provide updates as they become available. We urge everyone in coastal areas to stay informed and prepare for possible severe weather."
* **Type of reasoning:** Inductive reasoning was used. Inductive reasoning involves making generalizations based on observed patterns or specific instances. The forecaster observed the storm's past track and *induced* that it would likely continue on a similar path. It's important to emphasize the uncertainty inherent in inductive reasoning ("could," "possibly") as the observed pattern doesn't *guarantee* future behavior.
**b. If-then statement (Conjecture):**
If a storm has moved westward for the past 48 hours, then it will continue to move westward.
**c. Inverse of the statement:**
If a storm has *not* moved westward for the past 48 hours, then it will *not* continue to move westward.
**d. Converse and Contrapositive:**
* **Converse:** If a storm continues to move westward, then it has moved westward for the past 48 hours.
* **Contrapositive:** If a storm does *not* continue to move westward, then it has *not* moved westward for the past 48 hours.
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