In bowling, the distance from the foul line to the headpin is 60 feet. a bowling ball has a radius of about 4.3 inches. how many times must a ball rotate in order to strike the head pin

  about 26.6 times

Step-by-step explanation:

The circumference of the ball is found from ...

  C = 2πr = 2π(4.3 in) ≈ 27.02 in

There are 12 inches per foot, so the 60 foot distance of interest is ...

  (60 ft)×(12 in/ft) = 120 in

In terms of ball circumference, that distance is ...

  (120 in)/(27.02 in/rotation) ≈ 26.6 rotations

If the ball starts rotating at the foul line, it will turn about 26.6 times before reaching the head pin.

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt  that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes. 

step-by-step explanation:

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 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.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

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

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.