8/17/2019 JHMC
1/2
Eric McCarthy
1. Sally and Angela are jogging around a 400 meter track. Sally
is ¾ of the way around the
track and Angela is !0 meters "ehind her. After half a minute
Angela com#letes her first
la# around the track and Sally is 100 meters through her second
la#. $ow much longer
does it take Angela to com#lete one la# around the track than
Sally%
&. 'our cards are drawn from a standard !& card deck.
(hat is the #ro"a"ility that at least
three of the four cards are face cards%). Amy dri*es at an
a*erage rate of +0 m#h and then sto#s 40 minutes to eat. After the
sto#
she dri*es at an a*erage rate of ,0 m#h. Altogether she dri*es
1+0 miles in a total time of
) hours including the sto#. $ow many minutes did -elly dri*e
"efore she sto##ed to eat%
4. ernardo randomly #icks ) distinct num"ers from the set
/1&)4! and arranges them
in descending order to form a )digit num"er. Sil*ia randomly
#icks ) distinct num"ers
from the set /1&)4 and also arranges them in descending
order to form a )digit
num"er. (hat is the #ro"a"ility that ernardo2s num"er is larger
than Sil*ia2s num"er%
!. 'or each #ositi*e integer n the mean of the first
n terms of a se3uence is n. (hat is the
&01+th term of this se3uence%
+. n 5orth -orea 6 soldiers stand in line with 1! ci*ilians. f
there is a soldier at each end
of the line and no soldier stands ne7t to each other how many
ways can the soldiers
stand throughout the line%
6. 8he *ertices of a regular decagon are la"eled 1 through 10.
$ow many num"as r there
Answer: 9ust mine :+)0;
