We know angle P is 90 degrees because of Thales Theorem, and angle N is 60 degrees. Because the angles in a triangle have to add up to 180 degrees, angle PMN has to be 30 degrees.
Angle QMO is half of angle PMN, so it's 15 degrees. Angle MQO is equal to angle QMO because the radii make Triangle OQM isosceles, so angle MQO is 15 degrees.
Mandy Increases her books by 2 per month.
Bill increases his books by 4 per month.
Month Mandy Bill
May 18 4
June 20 8
July 22 12
August 24 16
Sept 26 20
Oct 28 24
Nov 30 28
Dec 32 32
At the end of December they will have read the same amount of books.
1. Take out the constants
-(2 x 3 x 4 x 2)xxyy^3
2. Simplify 2 x 3 x 4 x 2 to 48
-48xxyy^3
3. Use Product Rule: x^ax^b = x^a+b
-48x^1+1y^1+3
4. Simplify 1 + 1 to 2
-48x^2y^1+3
5. Simplify 1 + 3 to 4
-48x^2y^4
Firstly, put Derek and Paul's collection together:
1950, 1952, 1908, 1902, 1955, 1954, 1901, 1910, 1929, 1935, 1928, 1930, 1925, 1932, 1933, 1920
1950+1952+1908+1902+1955+1954+ 1901+1910+1929+1935+1928+1930+ 1925+ 1932+1933+1920
=30864
=30864÷16
=1929
∴the mean is 1929.
Median:
1901, 1902, 1908, 1910, 1920, 1925, 1928, 1929, 1930, 1932, 1933, 1935,
1950, 1952, 1954, 1955
1930÷1929
=1.0005184
= Median
Range:
1955-1901
=54
∴the range is 54.
