Help me please with this math word problem and there is graphing needed. It is urgent!
8. This table shows the time it takes a skateboarder to reach the bottom floor f a ramp when starting from various points along the ramp.
a) Identify the independent variable and the dependent variable. Explain your reasoning.
b) Make a scatter plot of the data.
c)Describe the relationship between the variables.
d) Identify any outliers. Explain whether you would include any of these outliers in the data set.
e)Estimate the time it would take the skater-boarder to reach the bottom of the ramp from a starting height of 3.6 m. Explain how you made your estimate.
Ответы на вопрос
Ответ:
a) The independent variable is the initial height of the skateboarder on the ramp, and the dependent variable is the time it takes for the skateboarder to reach the bottom of the ramp. This is because the time it takes to reach the bottom of the ramp depends on the initial height of the skateboarder.
b) Here is a scatter plot of the data:
without b((
c) The scatter plot shows that there is a generally positive relationship between the initial height of the skateboarder and the time it takes to reach the bottom of the ramp. As the initial height increases, the time to reach the bottom also tends to increase. However, there are a few outliers where the skateboarder took longer than expected to reach the bottom, despite having a lower initial height.
d) The outlier with an initial height of 4.7 meters seems to be significantly higher than the other data points, so it may be reasonable to consider removing it from the dataset. However, the outlier with an initial height of 4.5 meters appears to be within a reasonable range of the other data points, so it may be reasonable to keep it in the dataset.
e) To estimate the time it would take the skateboarder to reach the bottom of the ramp from a starting height of 3.6 meters, we can use interpolation. We can draw a line between the two data points that bracket 3.6 meters on the x-axis (3.4 m and 3.8 m), and estimate the corresponding y-value (time) using the equation of the line. Alternatively, we can use a curve-fitting technique, such as a quadratic regression, to find a more accurate estimate. Based on visual inspection of the scatter plot, it seems like a quadratic regression may fit the data reasonably well.
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