Anew restaurant with 138 seats is being planned. studies show that 59% of the customers demand a smoke-free area. how many seats should be in the non-smoking area in order to be very sure (mu plus 3 sigma) of having enough seating there?

Step-by-step explanation:

Given that a new restaurant with 138 seats is being planned. Studies show that 59% of the customers demand a smoke-free area.

Non smoke area = 100-59=41%

mu for non smoke area = 0.41

Std  deviation =

mu-3sigma =

mu+3 sigma =

Thus 28.43 to 53.54 percent should be in non smoke area

Or 39.2334 to 73.8852 seats

74 seats should be in the non-smoking area in order to be very sure (mu plus 3 sigma) of having enough seating there

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .