An assembly line is manufacturing gears that have a circumference of 8 cm. the tolerance for the circumference of the gears is 0.03 cm. to check the quality of the gears, the foreman has pulled 19 off the line and measured their circumferences. what percentage of the gears fall outside of the tolerance? round your answer up to the nearest percentage. {7.96, 7.965, 7.97, 7.982, 7.99, 7.99, 8, 8, 8, 8, 8, 8, 8.01, 8.01, 8.012, 8.02, 8.025, 8.029, 8.031} %

16% (rounded)

Step-by-step explanation:

8 cm with a tolerance of 0.03 means:

8 - 0.03 = 7.97

and

8 + 0.03 = 8.03

Hence, all should fall between 7.97 and 8.03

Let's check:

7.96 Outside

7.965 Outside

7.97 within

7.982 within

7.99 within

8 within

8.01 within

8.012 within

8.02 within

8.025 within

8.029 within

8.031 Outside

So 3 of them fall outside the tolerance from 19. The percentage is thus:

3/19 * 100 = 15.79%

To the nearest percentage, that's 16%

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11