p1. From the measurement of the height of nine trees obtained data as following.
a) There are three different measurement results (in meters)
b) All data are positive numbers
c) Mean= median = mode =3
d) The sum of the squares of all data is 87.
Determine all possible heights of the nine trees.
p2. If x and y are integers, find the number of pairs (x,y) that satisfy ∣x∣+∣y∣≤50.
p3. The plane figure ABCD on the side is a trapezoid with AB parallel to CD. Points E and F lie on CD so that AD is parallel to BE and AF is parallel to BC. Point H is the intersection of AF with BE and point G is the intersection of AC with BE. If the length of AB is 4 cm and the length of CD is 10 cm, calculate the ratio of the area of the triangle AGH to the area of the trapezoid ABCD.
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p4. A prospective doctor is required to intern in a hospital for five days in July 2011.
The hospital leadership gave the following rules:
a) Internships may not be conducted on two consecutive days.
b) The fifth day of internship can only be done after four days counted since the fourth day of internship. Suppose the fourth day of internship is the date 20, then the fifth day of internship can only be carried out at least the date 24.
Determine the many possible schedule options for the prospective doctor.
p5. Consider the following sequences of natural numbers:
5, 55, 555, 5555, 55555, ... ,nnumbers5555...555555... .
The above sequence has a rule: the nth term consists of n numbers (digits) 5.
Show that any of the terms of the sequence is divisible by 2011. algebrageometrycombinatoricsnumber theoryindonesia juniors