He diameters of apples from a certain farm follow the normal distribution with mean 4 inches and standard deviation 0.4 inch. apples can be size-sorted by being made to roll over mesh screens. first the apples are rolled over a screen with mesh size 3.5 inches. this separates out all the apples with diameters less than 3.5 inches. second, the remaining apples are rolled over a screen with mesh size 4.3 inches. find the proportion of apples with diameters less than 3.5 inches. round your answer to four decimal places.

10.56% of apples  are with diameters less than 3.5 inches.  

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 4 inches

Standard Deviation, σ = 0.4 inches

We are given that the distribution of apple size is a bell shaped distribution that is a normal distribution.

Formula:

a) P(apples with diameter less than 3.5 inches)

P(x < 3.5)

Calculation the value from standard normal z table, we have,  

10.56% of the apples will fall through a screen with mesh size of 3.5 inches that 10.56% of apples  are with diameters less than 3.5 inches.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

14

step-by-step explanation:

14 x 3 = 42