Answer:
The length of AP will be 14 units.
Step-by-step explanation:
As P is the centroid of ΔABC as shown in question figure.
As the side AB of the triangle has the midpoint D, the side AC of the triangle has the midpoint F and the side BC of the triangle has the
midpoint E.
Hence, CD, BF and AE being medians of ΔABC.
The point of intersection of these medians will be the centroid of the triangle. Hence, P is the centroid of ΔABC
According to rule, the centroid point of the triangle ΔABC divides each median into two segments in the ratio 2 : 1.
So,

As the value of AE = 21
So,

AP = 14
So, the length of AP will be 14 units.
Keywords: centroid, triangle
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Answer:
3003
Step-by-step explanation:
We want to find out how many ways we can choose 10 players among 15 players (since the goalie is not interchangeable)
The number of different lineups you can have can be found by using combination:

There are 3003 different lineups that can be chosen.
243 counselors will be there
Answer:
$1,391.25
Step-by-step explanation:
Noon would be 12:00 PM which would be 4 hours ahead of 8:00 AM
We subtract $8,821 by $3,256 to get the amount earned between 8:00 AM and 12:00 PM
$8,821 - $3,256
= $5,565
The find the average taken in within those 4 hours we will have to divide the money earned by the hours
$5,565/4
= $1,391.25
Given:
Area of a right triangle = 18 sq. inches
Length of one leg = 6 inches
To find:
The length of another leg.
Solution:
We know that, the area of a triangle is

In a right angle triangle, the area of the triangle is

Putting A=18 and
, we get


Divide both sides by 3.


Both legs are equal so the given triangle is an isosceles right triangle.
If the triangle is not isosceles triangle, then the length of legs are factors of 36 because half of 36 is 18.
Therefore, the possible pairs of legs are 1 and 36, 2 and 18, 3 and 12, 4 and 9, 6 and 6, 9 and 4, 12 and 3, 18 and 2, 36 and 1.