The edge roughness of slit paper products increases as knifeblades wear. only 1% of products slit with new blades have roughedges, 3% of products slit with blades of average sharpness exhibitroughness, and 5% of products slit with worn blades exhibitroughness. if 25% of the blades in manufacturing are new, 60%are average sharpness, and 15% are worn, what is the proportion ofproducts that exhibit edge roughness?

There is 2.8% of products that exhibit edge roughness.

Step-by-step explanation:

Let A₁ be the event that blades are new.

Let A₂ be the event that blades are average sharpness.

Let A₃ be the event that blades are worn.

P(A₁) = 25% = 0.25

P(A₂) = 60% = 0.60

P(A₃) = 15% = 0.15

Let the B be the event that selected blade is rough.

So, P(B|A₁) = 0.01

P(B|A₂) = 0.03

P(B|A₃) = 0.05

So, P(B) would be

Hence, there is 2.8% of products that exhibit edge roughness.

u = -(6/7)w

step-by-step explanation:

place all values with 'u' on one side of the equation.

4u + 8w = - 3u + 2w

4u + 3u = 2w - 8w

further simplify the equation by solving the addition and subtraction.

7u = - 6w

make 'u' the independent variable by placing its co-efficient on the right-hand side.

u = - (6/7)w