Aking in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess board. on the second square the king would place two grains of wheat, on the third square, four grains of wheat, and on the fourth square eight grains of wheat. if the amount of wheat is doubled in this way on each of the remaining squares, what is the total weight in tons of all the wheat that will be placed on the first 51 squares? (assume that each grain of wheat weighs 1/7000 pound. remember that 1 ton equals 2000 lbs.)

Step-by-step explanation:

The number of grains of wheat on the n(th) square is 2^(n-1), or 2 to  

the power of n-1.  This is because the first square has 2^0 = 1 grain,  

the second has 2^1 = 2, and the n(th) square has twice as many as the  

previous. Thus the total number of grains of wheat is

    S = 1 + 2 + 4 + 8 + ... + 2^63.

Since this is a geometric sequence with common ratio 2, the sum is

        2^64 - 1

    S = = 2^64 - 1 = 18446744073709551615.

          2 - 1

need more info

step-by-step explanation:

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)