the gross earnings • group health insurance (assuming 15% of gross earnings) pension deduction (assuming 6.5% of gross earnings)
• total deductions • net pay Earnings Deductions Description Rate Hours Current fed tax 55.00 Regular 7.75 40.0 state tax 15.50 SOC sec 21.25 health insr pension IN TOTAL DEDUCTIONS NET PAY
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In the given figure we can determine the coordinate of point M from the graph, we get:
We can also determine the coordinates of point N as:
Now, to determine the length of segment MN, we need to subtract the x-coordinate of M from the coordinates of N, we get:
Subtracting the fractions we get:
Now, to obtain the length of AB we need to subtract the x-coordinate of A from the x-coordinate of B.
The coordinates of A are determined from the graph:
The coordinates of B are:
Therefore, the length of segment AB is:
Now we do the same procedure to determine the segment of CD. The coordinates of C are:
The coordinates of D are:
Therefore, CD is:
Now, we determine MN as half the sum of the bases. The bases are AB and CD, therefore:
Therefore, we have proven that the median of a trapezoid equals half the sum of its bases.