The edge roughness of a slit paper products increases as knife blades wear. only 1% of products slit with new blades have rough edges, 3% of products shot with blades of average sharpness exhibit roughness, and 5% of the products slit with worn blades exhibit roughness. if 25% of the blades in manufacturing are new, 60% are of average sharpness, and 15% are worn blades.

a. what is the proportion of products that exhibit edge roughness?

b. if a paper was selected at random and found that it has rough edges, what is the probability that it was slit by a new knife blades?

c. if a paper was selected at random and found that it has rough edges, what is the probability that it was slit with a blade of average sharpness blades or worn blades?

a) 2.8% of products exhibit edge roughness.

b) If a paper has rough edges, there is an 8.93% probability that it was slit by a new knife blades.

c) If it has rough edges, there is a 91.07% probability that it was slit with a blade of average sharpness blades or worn blades.

Step-by-step explanation:

We have these following probabilities:

A 25% probability that the blade is new

A 60% probability that the blade is of average sharpness.

A 15% probability that the blade is worn.

If a blade is new, a 1% probability that it has rough edges.

If a blade is of average sharpness, a 3% probability it has rough edges.

If a blade is worn, a 5% probability it has rough edges.

a. What is the proportion of products that exhibit edge roughness?

This is

are those that are new and exhibit edge roughness. So

are those of average sharpness that exhibit rough edges. So

are those that are worn and exhibit rough edges. So

So

2.8% of products exhibit edge roughness.

b. If a paper was selected at random and found that it has rough edges, what is the probability that it was slit by a new knife blades?

From a), we found that there is a 0.028 probability that it has rough edges.

Also, there is a 0.0025 probability that it was slit by a new knife blades and have rough edges. So

If a paper has rough edges, there is an 8.93% probability that it was slit by a new knife blades.

c) If a paper was selected at random and found that it has rough edges, what is the probability that it was slit with a blade of average sharpness blades or worn blades

From a), we found that there is a 0.028 probability that it has rough edges.

Also, there is a 0.018 probability that it was sliced with a blade of average sharpness and has rough edges and an 0.0075 probability that it was slices with worn blades and has rough edges. So

If it has rough edges, there is a 91.07% probability that it was slit with a blade of average sharpness blades or worn blades.

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)

answ5

step-by-step explanation:

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