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Easy expected value problem
Kempu33334 6
N
by aidan0626
Source: Me
Bob takes two real numbers,
and 
, independently at random from the range 
to 
. He then selects an operation out of 
, 
, and 
and performs that operation on them. Find the expected value of the answer.
Bob takes two real numbers,
and 
, independently at random from the range 
to 
. He then selects an operation out of 
, 
, and 
and performs that operation on them. Find the expected value of the answer.
6 replies
Challenge Problem in Similar Triangles
yes45 0
has a right angle at 
. 
and 
. Point 
lies on 
such that 
and point 
lies on 
such that 
= 
. Find the perimeter of 
.
.
.
.
.
.
from base 
shares angles 
with 
through AA Postulate. 
,
and 
.
,
(as both are right angles), and 
,
through SAS postulate. 
,
.
.0 replies
Interesting Geometry
captainmath99 0
Let ABC be a right triangle such that 
. A circle O with center C has a radius of 2. Let P be a point on the circle O.
a)What is the minimum value of
?
b) What is the minimum value of
?
. A circle O with center C has a radius of 2. Let P be a point on the circle O.a)What is the minimum value of
?b) What is the minimum value of
?
0 replies
[PMO27 Qualis] III. 1 Binary Counting
tapilyoca 5
N
by Magdalo
John wrote down all of the numbers from 1 to 128 in binary. How many 1's did he write?
5 replies
22nd PMO Qualifying Stage #11
pensive 3
N
by Magdalo
Let and be positive real numbers such that
![\[
\log_x 64 + \log_{y^2} 16 = \frac{5}{3} \quad \text{and} \quad \log_y 64 + \log_{x^2} 16 = 1
\]](//latex.artofproblemsolving.com/d/7/9/d79facd90d9c5b53cdc4df9db18923ad34f472df.png)
What is the value of 
?
and be positive real numbers such that![\[
\log_x 64 + \log_{y^2} 16 = \frac{5}{3} \quad \text{and} \quad \log_y 64 + \log_{x^2} 16 = 1
\]](http://latex.artofproblemsolving.com/d/7/9/d79facd90d9c5b53cdc4df9db18923ad34f472df.png)
What is the value of 
?
3 replies
[PMO22 Qualifying] I.11
Magdalo 3
N
by Magdalo
Let and be positive real numbers such that
![\[\log_x64+\log_{y^2}16=\dfrac{5}{3}\text{ and }\log_y64+\log_{x^2}16=1 \]](//latex.artofproblemsolving.com/6/6/6/666e220af0dd4e1f77283dc5109a59d796c81bda.png)
Find 
and be positive real numbers such that![\[\log_x64+\log_{y^2}16=\dfrac{5}{3}\text{ and }\log_y64+\log_{x^2}16=1 \]](http://latex.artofproblemsolving.com/6/6/6/666e220af0dd4e1f77283dc5109a59d796c81bda.png)
Find 
3 replies
Log Rationality
Magdalo 1
N
by Magdalo
Let 
be positive integers. How many pairs of 
are there such that 
is rational?
be positive integers. How many pairs of 
are there such that 
is rational?
1 reply
Original Problem U1
NeoAzure 1
N
by NeoAzure
How many three-digit positive integers are divisible by 4 and have exactly two even digits?
1 reply
[Sipnayan 2017 JHS] Semifinals A, Difficult, P2
NeoAzure 1
N
by NeoAzure
Akira fills an urn with 10 chips such that 1 chip is labeled “1”, 2 chips are labeled “2”, 3
chips are labeled “3”, and 4 chips are labeled “4”. She draws 4 chips from the box without
replacement. What is the probability the sum of the numbers labeled on the 4 chips is divisible
by 3
chips are labeled “3”, and 4 chips are labeled “4”. She draws 4 chips from the box without
replacement. What is the probability the sum of the numbers labeled on the 4 chips is divisible
by 3
1 reply
be positive reals such that 
,
of 
.
