Fernando built a robot to filter air and water efficiently. He expects the robot to filter more than 512 liters of air and water while using less than 9 Joules of energy. A represents the number of minutes the robot filters air, and W represents the number of minutes the robot filters water.

21A+14W > 21A+14W>51, A, plus, 14, W, is greater than, 512 represents the number of minutes the robot filters air and water to filter more than 512512512 liters of air and water.

0.36A+0.6W < 90.36A+0.6W<90, point, 36, A, plus, 0, point, 6, W, is less than, 9 represents the number of minutes the robot filters air and water while using less than 9 Joules of energy.

there is no

the total estimated nappy use.=10,500,000

step-by-step explanation:

given that on an average the average baby uses 3528 napkins.

in a particular year 2014, the number of births were 299697 in new south wales.

rounding off the number of births to the nearest hundred thousand we have

no of birtsh = 300000

also rounding off the average usage to nearst thousand we get

average use of a baby = 3500

hence total number of nappy estimated to be used = 3500x300000

= 10,500,000

answer is 10,500,000 nappies

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt