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uestion here's a roughly linear relationship between the length of someone's femur (the long leg- one in your thigh) and their expected height. Within a certain population, this relationship an be expressed using the formula \( h=2.36 f+55.4 \), where \( h \) represents the expected neight in centimeters and \( f \) represents the length of the femur in centimeters. What could he number 2.36 represent in the equation?

Ask by Boyd Burgess. in the United States
Jan 24,2025

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Answer

The number 2.36 represents how much the expected height increases for each additional centimeter of femur length.

Solution

In the equation \( h = 2.36f + 55.4 \), where \( h \) represents the expected height in centimeters and \( f \) represents the length of the femur in centimeters, the number 2.36 represents the slope of the linear relationship between the length of the femur and the expected height. ### Explanation: 1. **Slope Interpretation**: The slope (2.36) indicates how much the expected height \( h \) increases for each additional centimeter of femur length \( f \). Specifically, for every 1 cm increase in femur length, the expected height increases by 2.36 cm. 2. **Linear Relationship**: This linear relationship suggests that there is a consistent and proportional increase in height with respect to femur length within the population being studied. In summary, the number 2.36 represents the rate of change of height with respect to femur length, indicating that taller individuals tend to have longer femurs.

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The number 2.36 in the equation \( h=2.36 f+55.4 \) represents the slope of the line when considering the relationship between femur length and expected height. Essentially, it indicates that for each additional centimeter increase in femur length, the expected height increases by 2.36 centimeters. This is a vital piece of information when predicting height based on femur length, highlighting the linear nature of this relationship. To further understand this relationship, think about growth patterns: athletes often have longer femurs, which can correlate with their height and performance in sports. This formula can be particularly useful in fields like forensic anthropology where estimating a person's height from skeletal remains is crucial. It's a prime example of how biological measurements can help in real-world scenarios!

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