Let S be the set of all integers k such that, if k is in S, then and are terminating decimals. What is the smallest integer in S that is greater than 2010?

  2079

Step-by-step explanation:

In order for the decimal equivalents to be terminating, the only factors that can remain in the denominators are 2 and 5.

Here, the given denominators are

  66 = 2·3·11

  105 = 5·3·7

So, the values of k must be multiples of 3, 7, and 11. The least common multiple of these numbers is 3·7·11 = 231, so ...

  S = {0, ±231, ±462, ±693, ...}

The smallest member of S that is greater than 2010 is ...

  ceiling(2010/231)·231 = 9·231 = 2079

_____

For k=2079, the terminating decimals are ...

well the answer to that is xoxoxo

step-by-step explanation:

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