Question

A third method, referred to as the “mid-parent rule,” uses a weighted average of the parents’ heights in inches in which the height of the opposite-gender parent is multiplied by a factor of 12/13 before it is averaged with the other parent’s height.Use the variable D, (which represents the height of dad) and M, (which represents the height of mom)Write the formula for a boy’s adult height.(6 points) Write the formula for a girl’s adult height.(6 points)

Answer 1

We have to write the formula of the height H of a boy in function of the father's height (D) and the mother's height (M) using the mid-parent rule.

The opposite gender for the boy will be its motehr gender. Then, the mother's height will be multiplied by the factor 12/13 before averaging with the father's height.

Then, we can write the corrected mothers height as:

`M^(\prime)=(12)/(13)M`

Then, averaging both heights (father's heigth D and corrected mother's height M'), we get:

`\begin{gathered} H=(D+M^(\prime))/(2) \\ H=(1)/(2)(D+(12)/(13)M) \\ H=(D)/(2)+(12)/(2\cdot13)M \\ H_{\text{boy}}=(D)/(2)+(6)/(13)M \end{gathered}`

In the case of a girl's adult height, we change the opposite gender so the father's heihgt is affected by the factor.

Then, the height of the girl will be:

`\begin{gathered} H=(1)/(2)(D^(\prime)+M) \\ H=(1)/(2)((12)/(13)D+M) \\ H_{\text{girl}}=(6)/(13)D+(M)/(2) \end{gathered}`

Answer:

a) The boy's height will be H = (1/2)*D + (6/13)*M

b) The girl's height will be H = (6/13)*D + (1/2)*M