Let A represent the total amount of money
r represent the registration fee.
There were 124 new members. Since 50 had their initial registration fee waived, 74 paid the registration fee.
---> Amount earned at registration: A = 74·r
Assuming that no-one dropped out, 6 months later:
Let m represent the monthly fee
---> Total amount earned for the first 6 months: A = 74·r + 124·m·6
Must the point have integer coordinates?
If so, list all the possible points, count how many are not above the x-axis and count the total number of points, and divide the answers.
If not, there are an infinite number of points possible. The number of points on the x-axis can be can be added to those below the x-axis without increasing the (infinite) number. Then, there will be as many points below the x-axis as above the x-axis, so the answer will be 1/2.
The possible ways to toss coin B: The possible ways to toss coin A:
H H H H H H T T
H T H H T T H T
T H H T H T T H
T T T H H T T T
The probability of getting two Heads with coin B and three Heads with coin A: (1/4)(1/8) = 1/32.
The probability of getting one Head with coin B and two or three Heads with coin A: (2/4)(4/8) = 8/32.
The probability of getting no Heads with coin B and at least one Head with coin A: (1/4)(7/8) = 7/32.
Adding together these possibilities: 1/32 + 8/32 + 7/32 = 16/32 = 1/2.
Call the intersection of BE with CH point X. Then the triangle BCX is a right isosceles right triangle.
This means that angle CBE is a 45 degree angle.
And, both BX and CX are equal to 6·sqrt(2).
CX is a height of the trapezoid and equals 6·sqrt(2).
CD is one base of the trapezoid and equals 12.
BE is the other base of the trapezoid and equals 6·sqrt(2) + 12 + 6·sqrt(2) = 12 + 12·sqrt(2).
The area of the trapezoid is (1/2) · height · (base #1 + base #2)
= (1/2) · 6·sqrt(2) · ( 12 + 12·sqrt(2) )
= 3 ·sqrt(2) · ( 12 + 12·sqrt(2) )
= 36·sqrt(2) + 72
Simplify: sqrt( 4x2 / 3y )
sqrt( 4x2 / 3y ) = sqrt( 4x2 ) / sqrt( 3y )
But sqrt( 4x2 ) = 2·| x | Technically, you need to use absolute value bars.
sqrt( 4x2 / 3y ) = 2·| x | / sqrt( 3y )
Now, multiply both the numerator and the denominator by sqrt( 3y )
sqrt( 4x2 / 3y ) = [ 2·| x | · sqrt( 3y) ] / [ sqrt( 3y ) · sqrt( 3y) ]
Since [ sqrt( 3y ) · sqrt( 3y) ] = 3y
sqrt( 4x2 / 3y ) = [ 2·| x | · sqrt( 3y) ] / ( 3y )