the scale factor or ratio of two similar figures, will be the same as the ratio of their perimeter, or even the ratio of two corresponding sides.

for example, we have say, an irregular octagon with a perimeter of say 13, and a similar octagon with a perimeter of 39, then

$\bf \cfrac{\textit{small octagon}}{\textit{large octagon}}~\hspace{5em}\cfrac{perimeter}{perimeter}\implies \cfrac{13}{39}\implies \stackrel{simplified}{\cfrac{1}{3}}~\hfill \stackrel{\textit{scale factor}}{1:3}$

which is another way to say, the smaller is 1/3 of the larger one, or the larger one is 3 times as the smaller one.

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2 years ago

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4. Thoughtful Politicians [This problem setting is due to Prof. James Norris of Cambridge University.] In a group of 100 politic

kirill [66]

Answer:

Step-by-step explanation:

The focus is on Party 2, because as already said, Party 1 members NEVER change their minds on anything!

There are 60 politicians in Party 2. They change their minds completely-randomly every day.

Tomorrow, the politicians will vote on a proposition: Proposition 88, but today, 10 are in favor of it while 50 are against it.

Each member changes their mind based on the toss of a coin (a fair/unbiased coin; since it was not stated that the coin is biased). A fair coin has a 0.5 probability of landing HEADS and same 0.5 probability of landing TAILS.

What is the distribution of the number of members in Party II who will favor Prop 88 tomorrow?

The number of figures in the distribution will depend on the number of times the coin is tossed, between today and tomorrow.

KEY: Assuming the coin is tossed 12 times between today and tomorrow AND assuming that half of the time - 6 times - it landed HEADS and half of the time, TAILS (Head and Tail simultaneously).

Beginning with HEADS, the distribution of the number of members who will favor the proposition tomorrow, is:

50, 10, 50, 10, 50, 10, 50, 10, 50, 10, 50, 10

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2 years ago