Alice and Bob play a game involving a circle whose circumference is divided by 12 equally spaced pedals. The points are numbered clockwise, from 1 to 12. Both start on point 12. Alice moves clockwise and Bob, count clockwise. In a turn of the game, Alice moves 5 points clockwise and Bob moves 9 points count clockwise. The game ends when they stop on the same point. How many turns will this take?

6 turns

Step-by-step explanation:

Step    Bob     Alice

    1         3          5

    2        6          10

    3        9          3

    4        12         8

    5        3          1

    6        6          6

pakistan's principal natural resources are arable land and water. about 25% of pakistan's agriculture accounts for about 21% [1] of gdp and employs about 43% of the labour force. in pakistan, the most agricultural province is punjab where wheat and cotton are the most grown.

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b