Pairs of shoes are manufactured for $24. They are sold to a warehouse with a mark-up of 15%. The warehouse sells the shoes to a distributor after charging a holding fee of $10 per pair. The distributor sells them to ‘Fine Shoes’ for a percentage profit of 12%. The store then marks them up by 30%. a. Determine the price of a pair of shoes if you buy it from one of the ‘Fine Shoes’ stores (round to the nearest 5 cents). Show working out.

‭$54.75

Step-by-step explanation:

The price the shoes are sold to the warehouse is:

= 24 * ( 1 + 15%)

= 24 * 1.15

= $27.60

The price the warehouse sells it is:

= 27.60 + 10

= $37.60

Price distributor sells is:

= 37.60 * 1.12

= $42.112

Fine shoes will then sell at 30% profit:

= 42.112 * 1.3

= $‭54.7456‬

= ‭$54.75

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}