Consumers in a certain state can choose between three long-distance telephone services: gtt, ncj, and dash. aggressive marketing by all three companies results in continual shift of customers among the three services. each year, gtt loses 30% of its customers to ncj and 15% to dash, ncj loses 10% of its customers to gtt and 5% to dash, and dash loses 30% of its customers to gtt and 30% to ncj. assuming that these percentages remain valid over a long period of time, what is each company's expected market share in the long run?

cut 138 centimeters off

step-by-step explanation:

250-112 = 138

$650 per month plus utilities

step-by-step explanation:

just based on the info you gave, it would seem more cost effective to rent at $650 per month plus utilities.   if utilities are, in fact, $150 per month, your monthly living costs would be $800 as opposed to the other option of $825.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for