Find the best solutions to your problems with the help of IDNLearn.com's experts. Ask your questions and receive reliable and comprehensive answers from our dedicated community of professionals.
Sagot :
Certainly! Let's go through the problem step by step to determine the annual trend in tornado counts.
### Step 1: Organize Data
First, we have the following data for the number of tornadoes over different years:
[tex]\[ \begin{array}{|c|c|} \hline \text{Year} & \text{Number of Tornadoes} \\ \hline 1350 & 200 \\ \hline 1360 & 600 \\ \hline 1370 & 660 \\ \hline 1300 & 180 \\ \hline 1000 & 1150 \\ \hline 2000 & 1350 \\ \hline 2010 & 1300 \\ \hline \end{array} \][/tex]
### Step 2: Determine the Trend
To find the trend in the number of tornadoes over the years, we use linear regression. In linear regression, we fit a line of the form [tex]\( y = mx + c \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( c \)[/tex] is the intercept.
- Slope (m): Indicates the rate of change in the number of tornadoes per year.
- Intercept (c): Represents the baseline number of tornadoes when the year is zero.
Based on the calculations, we have obtained the following parameters:
- Slope ([tex]\( m \)[/tex]): [tex]\( 0.7146 \)[/tex]
- Intercept ([tex]\( c \)[/tex]): [tex]\( -283.5417 \)[/tex]
### Step 3: Trend Interpretation
The slope and intercept allow us to predict the number of tornadoes for any given year. The linear equation based on the slope and intercept is:
[tex]\[ \text{Number of Tornadoes} = 0.7146 \times (\text{Year}) - 283.5417 \][/tex]
### Step 4: Predicted Tornado Counts
Using the above linear equation, we compute the predicted tornado counts for each given year:
1. For year 1350:
[tex]\[ \text{Predicted Tornadoes} = 0.7146 \times 1350 - 283.5417 = 681.18 \][/tex]
2. For year 1360:
[tex]\[ \text{Predicted Tornadoes} = 0.7146 \times 1360 - 283.5417 = 688.33 \][/tex]
3. For year 1370:
[tex]\[ \text{Predicted Tornadoes} = 0.7146 \times 1370 - 283.5417 = 695.47 \][/tex]
4. For year 1300:
[tex]\[ \text{Predicted Tornadoes} = 0.7146 \times 1300 - 283.5417 = 645.45 \][/tex]
5. For year 1000:
[tex]\[ \text{Predicted Tornadoes} = 0.7146 \times 1000 - 283.5417 = 431.07 \][/tex]
6. For year 2000:
[tex]\[ \text{Predicted Tornadoes} = 0.7146 \times 2000 - 283.5417 = 1145.68 \][/tex]
7. For year 2010:
[tex]\[ \text{Predicted Tornadoes} = 0.7146 \times 2010 - 283.5417 = 1152.82 \][/tex]
### Conclusion
The linear equation [tex]\( 0.7146 \times \text{Year} - 283.5417 \)[/tex] provides a way to predict the number of tornadoes for any given year. The trend indicates that the number of tornadoes increases at a rate of approximately [tex]\( 0.7146 \)[/tex] tornadoes per year.
Here are the predicted tornado counts for the specified years:
[tex]\[ \begin{array}{|c|c|} \hline \text{Year} & \text{Predicted Tornadoes} \\ \hline 1350 & 681.18 \\ \hline 1360 & 688.33 \\ \hline 1370 & 695.47 \\ \hline 1300 & 645.45 \\ \hline 1000 & 431.07 \\ \hline 2000 & 1145.68 \\ \hline 2010 & 1152.82 \\ \hline \end{array} \][/tex]
Understanding the trend helps predict future occurrences and prepare accordingly.
### Step 1: Organize Data
First, we have the following data for the number of tornadoes over different years:
[tex]\[ \begin{array}{|c|c|} \hline \text{Year} & \text{Number of Tornadoes} \\ \hline 1350 & 200 \\ \hline 1360 & 600 \\ \hline 1370 & 660 \\ \hline 1300 & 180 \\ \hline 1000 & 1150 \\ \hline 2000 & 1350 \\ \hline 2010 & 1300 \\ \hline \end{array} \][/tex]
### Step 2: Determine the Trend
To find the trend in the number of tornadoes over the years, we use linear regression. In linear regression, we fit a line of the form [tex]\( y = mx + c \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( c \)[/tex] is the intercept.
- Slope (m): Indicates the rate of change in the number of tornadoes per year.
- Intercept (c): Represents the baseline number of tornadoes when the year is zero.
Based on the calculations, we have obtained the following parameters:
- Slope ([tex]\( m \)[/tex]): [tex]\( 0.7146 \)[/tex]
- Intercept ([tex]\( c \)[/tex]): [tex]\( -283.5417 \)[/tex]
### Step 3: Trend Interpretation
The slope and intercept allow us to predict the number of tornadoes for any given year. The linear equation based on the slope and intercept is:
[tex]\[ \text{Number of Tornadoes} = 0.7146 \times (\text{Year}) - 283.5417 \][/tex]
### Step 4: Predicted Tornado Counts
Using the above linear equation, we compute the predicted tornado counts for each given year:
1. For year 1350:
[tex]\[ \text{Predicted Tornadoes} = 0.7146 \times 1350 - 283.5417 = 681.18 \][/tex]
2. For year 1360:
[tex]\[ \text{Predicted Tornadoes} = 0.7146 \times 1360 - 283.5417 = 688.33 \][/tex]
3. For year 1370:
[tex]\[ \text{Predicted Tornadoes} = 0.7146 \times 1370 - 283.5417 = 695.47 \][/tex]
4. For year 1300:
[tex]\[ \text{Predicted Tornadoes} = 0.7146 \times 1300 - 283.5417 = 645.45 \][/tex]
5. For year 1000:
[tex]\[ \text{Predicted Tornadoes} = 0.7146 \times 1000 - 283.5417 = 431.07 \][/tex]
6. For year 2000:
[tex]\[ \text{Predicted Tornadoes} = 0.7146 \times 2000 - 283.5417 = 1145.68 \][/tex]
7. For year 2010:
[tex]\[ \text{Predicted Tornadoes} = 0.7146 \times 2010 - 283.5417 = 1152.82 \][/tex]
### Conclusion
The linear equation [tex]\( 0.7146 \times \text{Year} - 283.5417 \)[/tex] provides a way to predict the number of tornadoes for any given year. The trend indicates that the number of tornadoes increases at a rate of approximately [tex]\( 0.7146 \)[/tex] tornadoes per year.
Here are the predicted tornado counts for the specified years:
[tex]\[ \begin{array}{|c|c|} \hline \text{Year} & \text{Predicted Tornadoes} \\ \hline 1350 & 681.18 \\ \hline 1360 & 688.33 \\ \hline 1370 & 695.47 \\ \hline 1300 & 645.45 \\ \hline 1000 & 431.07 \\ \hline 2000 & 1145.68 \\ \hline 2010 & 1152.82 \\ \hline \end{array} \][/tex]
Understanding the trend helps predict future occurrences and prepare accordingly.
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. Your questions deserve precise answers. Thank you for visiting IDNLearn.com, and see you again soon for more helpful information.
