An article considered the use of a uniform distribution with a = 0.20 and b = 4.25 for the diameter x of a certain type of weld (mm).

Using the formula f(x) = 1/(b-a), where B is 4.25 and A is 0.20. Substituting these values to the formula, we get f(x) = 1/(4.25-0.2) = 0.24691358. Therefore, we get the answer f(x) = 0.24691358, 0.20<x<4.25. Otherwise, it is 0.

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