Question

the threshold weight t for a person is the weight above which the risk of death increases greatly. one researcher found that the threshold weight in pounds for men aged 40 - 49 is related to height in inches by the equation h = 12.3t^{1/3}. what height corresponds to a threshold of 257 pounds for a man in this age group? what does the value of 257 represent in the given equation? a. t b. 12.3t^{1/3} c. t^{1/3} d. h

Explanation:

Step1: Identify the given values

We are given $T = 257$ pounds and the formula $h=12.3T^{\frac{1}{3}}$.

Step2: Substitute the value of T

Substitute $T = 257$ into the formula: $h = 12.3\times257^{\frac{1}{3}}$.
First, find $257^{\frac{1}{3}}=\sqrt[3]{257}\approx6.36$.
Then, $h=12.3\times6.36 = 78.228\approx78.2$ inches.

For the multiple - choice part:
The value 257 represents the threshold weight $T$ in the equation $h = 12.3T^{\frac{1}{3}}$. So the answer to the multiple - choice is A. T.

Answer:

The height corresponding to a threshold of 257 pounds is approximately 78.2 inches.
A. T