Question 1134560
Let {{{ k }}} = the constant of proportionality
Let {{{ s }}} = the number of students
Let {{{ n }}} = the number of lectures
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{{{ s = k*( 1/sqrt(n) ) }}}
{{{ k = s*sqrt(n) }}}
{{{ s = 30 }}}
{{{ n = 25 }}}
{{{ k = 30*sqrt(25) }}}
{{{ k = 30*5 }}}
{{{ k = 150 }}}
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{{{ s = 50 }}}
{{{ s = k*( 1/sqrt(n) ) }}}
{{{50 = 150*( 1/sqrt(n) ) }}}
Multiply both sides by {{{ sqrt(n) }}}
{{{ 50*sqrt(n) = 150 }}}
{{{ sqrt(n) = 3 }}}
{{{ n = 9 }}}
There are 9 lectures