Question 1190748
<pre>
{{{a[1]+a[2] }}}+...+{{{a[n]}}} / n = 500    (1)

(a)
Adding 10 to each term gives

{{{ (a[1]+10)+(a[2]+10) }}}+...+{{{ (a[n]+10) }}} / n 
Notice we've add 'n' 10's:
= ( {{{ 10n + a[1]+a[2] }}}+...+{{{a[n]}}} ) / n

Writing it slightly different:
= ( {{{ 10n/n }}} ) + ({{{ a[1]+a[2] }}}+...+{{{a[n]}}} ) / n 

The second paren's is just 500  (from (1))
=    10 + 500  = {{{ highlight(510) }}}

(b)
Multiplying each term by  k  results in a new mean that is  k*(original_mean)

So the new mean if you multiply by -5   is   -5 * 500 = {{{highlight(-2500)}}}