In order to prove
Let's write both sides in terms of 
only.
Let's start with the left hand side: we can use the formula for sum and subtraction of the sine to write
and
So, their multiplication is
So, the left hand side simplifies to
Now, on with the right hand side. We have
Now simply make this expression one fraction:
And as you can see, the two sides are equal.
There are several information's already given in the question. Based on the given information's the answer can be easily deduced.
Base of the parallelogram = 3 1/2 feet
= 7/2 feet
Altitude of the parallelogram = 3/4 feet
Area of the parallelogram = base * Altitude
= (7/2) * (3/4)
= 21/8
= 2 5/8 square feet
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There are nine possible combinations as follows: bb, bc, bt, cb, cc, ct, tb, tc, tt, each having a probability of 1/9. The four combinations with a cab exactly one time are: bc, cb, ct, tc. Therefore the probability that she'll use a cab exactly one time is: 4/9.
Let x = hours taken by William to assemble a computer.
Let y = hours taken by Douglas to assemble a computer
Because William takes 2 hours less than Douglas to assemble a computer, therefore
x = y - 2
When working together, they assemble 25 computers in 60 hours. Therefore
(x + y hours/computer)*(25 computers) = (60 hours)
25(x + y) = 60
x + y = 2.4
Because x = y - 2, obtain
y - 2 + y = 2.4
2y = 4.4
y = 2.2
x = y - 2 = 2.2 - 2 = 0.2
William takes 0.2 hours (12 minutes) to assemble a computer.
Douglas takes 2.2 hours (or 2 hours, 12 minutes) to assemble a computer.
Answer: 2.2
