a person with a head circumference of 21 1/2 inches has a hat size of 6 7/8 while a person with a head circumference of 21 7/8 inches has a hat size of 7 find hat size as a function of head circumference
assuming that the head size is a function of the head's circumference,
treat it as having two ordered pairs
(21.5,6.875) and ( 21.875,7) -- >(c,h)
"slope" = (6.875-7)/(21.5 - 21.875)
= 1/3
using the point( 21.5, 6.875)
h = 1/3c + b
6.875 = 1/3(21.5) + b
b = -.2917
Headsize = (1/3)circumf - .2917
To find the hat size as a function of head circumference, we can analyze the given data points and create a formula. Let's break it down step by step:
1. Start by comparing the two data points we have:
- Person A has a head circumference of 21 1/2 inches and a hat size of 6 7/8.
- Person B has a head circumference of 21 7/8 inches and a hat size of 7.
2. Observe the pattern between the head circumference and hat size. By comparing the two data points, we can see that as the head circumference increases, the hat size also increases slightly.
3. Subtract the head circumferences of the two people: 21 7/8 - 21 1/2 = 3/8.
4. Subtract the hat sizes of the two people: 7 - 6 7/8 = 1/8.
5. Determine the change in hat size for every 1/8 inch change in head circumference. In this case, the hat size changes by 1/8 for every 3/8 inch increase in head circumference.
6. To find the hat size for a given head circumference, multiply the change in hat size per 1/8 inch by the change in head circumference:
- Hat size change per 1/8 inch of head circumference: 1/8 / (3/8) = 1/3.
- Hat size = (Head circumference difference in inches) * (Hat size change per 1/8 inch) + Initial hat size.
7. In the given example, we have an initial hat size of 6 7/8 and a head circumference of 21 1/2 inches. Let's use the formula to find the hat size for any given head circumference:
- Hat size = ((head circumference - 21 1/2) * (1/3)) + 6 7/8.
By using this formula, you can calculate the hat size for any head circumference. Keep in mind that this is an approximation based on the given data points, and different manufacturers might have slight variations in their hat size measurements.