Athief steals a number of rare plants from a nursery. on the way out, the thief meets three security guards, one after another. to each security guard, the thief is forced to give one dash half of the plants that he still had, plus 2 more. finally, the thief leaves the nursery with 15 plants. how many plants were originally stolen?

181 plants were originally stolen.

Step-by-step explanation:

To get the solution to this problem, We must go from the end to the beginning.

When the thief left the nursery, he had 15 plants left. That is equivalent to half of the plants he gave to the third guard plus two more plants. That's:

Where X3 is the amount of plants given to the 3rd. guard

Isolating x3

X3= 26 plants

When the thief met the third guard, he had 26 plants. From this amount we can calculate the amount of plants that the thief had when he met the second guard.

Where X2 is the amount of plants given to the 2nd. guard

Isolating x2

X2= 48 plants

When the thief met the second guard, he had 48 plants. From this amount we can calculate the amount of plants that the thief had when he met the first guard.

Where X1 is the amount of plants given to the 1st. guard

Isolating x1

X1= 92 plants

So, if we already know the amount of plants that the thief gave each guard, and also knowing that when he left the nursery he had 15 plants left, we can calculate the initial amount.

Where Xi is the initial amount of plants.

Isolating Xi from the equation:

So, 181 plants were originally stolen.

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:

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above