Question 71879
These problems can be solved by using ratios. The first one is simply a ratio of 75 to 10 which can be written as 75:10. However it needs to be reduced, so it could be rewritten as 15:2, since each has a factor of 5. 
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The second one can be written as
{{{1/160=x/45}}}Where x is the length of the scale model. 
{{{x=45/160=9/32}}}So the scale model is 9/32 feet or 3.375 inches
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The 3rd problem can be expressed as
{{{1/20=x/240}}}Where x is the length of the line on the map
We need to convert everything to inches, so the units match up. Multiply the denominator on the left and right by (5280*12). This converts from miles to inches.
{{{1/1267200=x/15206399}}}Solve for x
{{{x=15206399/1267200=1}}}Even though these numbers look nasty, they divide to get 12(there are decimal roundoffs that I forgot to put in). So the length of the line is 12 inches. This makes sense because if 1 inch is 20 miles, then 12 inches is 240 miles (12*20=240)

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For the last one, the odds of choosing a green marble are the number of green marbles over the total number of marbles
       <pre>
                           # of green
                 P(green)= ------------
                             # total              </pre>
<pre>
                                6
                 P(green)= ------------
                               6+7+3             </pre>
<pre>
                                6
                 P(green)= ------------
                                16             </pre>
<pre>
                                3
                 P(green)= ------------
                                8             </pre>
P(green)=3/8
So the chances of picking a green marble are 3 of 8 or a 37.5% chance