Acompany in south dakota manufactures hard hats used in the mining industry. they record measurements on all the hats they produce for quality control and planning purposes. the measurements they collect include hat size, circumference, and lengths of the major and minor axes. meaning the company wants to predicts size of hat given the circumference. what is the response variable?

a. the size of hat, because it is the variable being predicted
b. the circumference, becauase it is the variable being predicted
c. the size of hat, because it is being used to predict circumference
d. the circumference, because it is being used to predict the size of hat.

a. The size of hat, because it is the variable being predicted

Step-by-step explanation:

The response variable, or the dependent variable, is the one whose value depends on the variation of another variable. In this case, the size of the hat is predicted based on the circumference, and lengths of the major and minor axes. Therefore, the size of the hat is the response variable.

The answer is alternative a.

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form