You can divide the figure as follows:
- A vertical rectangle, 5 meters tall and 2 meters wide, on the top right.
- A horizontal rectangle, 2 meters tall and 5 meters wide, on the bottom left
- A 2x2 meters square on the bottom right, where the two rectangles meet.
The area of the rectangles is 5x2=10 meters squared, while the area of the square is 2x2=4 meters squared.
So, the total area is 10+4=14 meters squared.
Well I don't know.
Let's think about it:
-- There are 6 possibilities for each role.
So 36 possibilities for 2 rolls.
Doesn't take us anywhere.
New direction:
-- If the first roll is odd, then you need another odd on the second one.
-- If the first roll is even, then you need another even on the second one.
This may be the key, right here !
-- The die has 3 odds and 3 evens.
-- Probability of an odd followed by another odd = (1/2) x (1/2) = 1/4
-- Probability of an even followed by another even = (1/2) x (1/2) = 1/4
I'm sure this is it. I'm a little shaky on how to combine those 2 probs.
Ah hah !
Try this:
Probability of either 1 sequence or the other one is (1/4) + (1/4) = 1/2 .
That means ... Regardless of what the first roll is, the probability of
the second roll matching it in oddness or evenness is 1/2 .
So the probability of 2 rolls that sum to an even number is 1/2 = 50% .
Is this reasonable, or sleazy ?
Answer:
cot theta = -√3
Step-by-step explanation:
we are given that cos theta = - √3/2 within the range 180° < theta < 270° and
since cos theta = adj/hyp
adj = - √3
hyp = 2
Get the opposite using the pythagoras theorem
hyp^2 = opp^2 + adj^2
2² = opp² + (-√3)²
4 = opp² + 3
opp² = 4-3
opp² = 1
opp = 1
tan theta = opp/adj
tan theta = - 1/√3
Recall that cot theta = 1/tan theta
cot theta = 1/(-1/√3)
cot theta = -√3
He will have a fourth of a cup raisins left over<span />
