This likely has a pattern. Lets see if we can find it.
The sum of a triangle is 180
The sum of a 4 sided figure is 360
The sum of a 5 sided figure is 3*180 = 540
The sum of a 6 sided figure is 4*180 = 720
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The pattern looks like it it (( n-2 )*180) for any polygon where n is the number of sides of the polygon.
You can convince yourself (but this is not a formal proof) by starting with a 6 sided figure. Pick one point on the figure where 2 sides meet. Draw diagonals to all the points not connected to the point you've chosen. You should be able to get 4 such diagonals. You have created 4 triangles.
4*180 = 720 just what your estimate said.d
8 sides will give 6*180 = 1080 degrees and if you keep going on the above table you will see 1080 come up for 8. I'd post a diagram but I don't know how to upload it.
This procedure is extremely important. There is a new math around where these kinds of problems are solved by reducing them to much simpler questions, and getting an answer for them. The pattern is what you are looking for.
Now you can do the rest of the questions.
Pentagon: (5 - 2) * 180 =
Octagon: (8 - 2) * 180 =
dodecagon (12 - 2)*180=
40 sides 38*180 =
100 sides 98 * 180 =
Answer:
Clearly, the probability of drawing a heart out of the deck is 13/52, or 1/4. The probability of drawing an even number as card #2 (∈{2,4,6,8,10}) for any suit is 20/51, except when the first card drawn is an even heart, then the probability of the second draw is 19/51.
Answer: A. When it comes after the decimal point, as in 4.000
Step-by-step explanation: If there are no other numbers after the zeros, there is no reason for them to be place holders. Zeros in decimals act as place holders such as in 4.09 or 4.0009. This actually does change the value of the decimal but 4.000 is just the same as a regular old 4. Hope this helps!
So... hmmm if you check the first picture below, for 2)
we could use the proportions of those small, medium and large similar triangles like
now.. for 3) will be the second picture below
