Another instance when you may face a cost-benefit analysis is if you frequently visit a café that serves coffee. yes, this example is near and dear to my heart. some cafés offer special refillable mugs in an effort to reduce waste. one such mug at a particular café costs $3.50 and holds 16 oz. of delicious coffee. refills of this mug are $0.50. if you elect to forgo this refillable coffee mug, you can buy a disposable cup of coffee that only holds 12 oz. for $1.00. at what volume of coffee does buying the refillable mug become cost-effective?

Refillable mug:

Fixed cost is $3.50 including 16 oz of coffee

Each additional 16 oz of coffee cost $0.50

Disposable cup:

Cost is $1.00 per 12 oz of coffee

We can build up a table showing number of purchases, cost, and amount of coffee for each type of purchase until we see the refillable cup becoming cheaper.

                Refillable Mug              Disposable cup

               Cost     Amount              Cost       Amount

1               3.50        16                    1.00                  12

2              4.00        32                   2.00                24

3              4.50         48                  3.00                 36

4              5.00         64                  4.00                 48

5              5.50         80                  5.00                 60

Notice that with 3 fill ups of the refillable cup, you have bought 48 oz of coffee for $4.50. With the disposable cup, the same 48 oz of coffee represent 4 cups, but at only $4.00, so up to the amount of 48 oz of coffee, you are better off buying the disposable cups.

When you spend $5.00, you can have 64 oz of coffee using the refillable cup or 60 oz of coffee using the disposable cup. When you spend $5.00 and up, then the refillable cup gives you the better price.

The refillable cup becomes cost effective at 64 oz.

graph b

step-by-step explanation:

one solution- graph a (clear intercepting point.)

no solution- graph b (they're parallel, there will never be a point of interception.)

infinite solutions- graph c (all points intercept.)

answer would be 8.64 or s = 11π/4 inches

step-by-step explanation:

s = r θ  

where s = arc length  

r = radius = 3 inches  

θ = central angle in radians = ( π /180)*165  

s = 3(π/180)*165  

= 8.64 inches