Answer:
0.0009
Step-by-step explanation:
Triangle A B C is shown as the path of a ferry. Side A B is 3.5 miles long. The ferry turns 75 degrees to side B C. Side B C is
1 answer:
The length of C from A is 3.5 miles if AB=3.5 miles and BC is 6 miles .
Given The length of triangle ABC AB=3.5 miles , BC=6miles and AC=d
We have to find the value of d
First of all we have to draw a perpendicular from point A on side BC .
It forms two triangles ABE and AEC if E is the point where perpendicular stands on BC.
In triangle BEA
AE=
=
=
=1.8
Now in triangle AEC
AC=
=
=
=
=3.49 MILES
By rounding off to the nearest tenth we will get 3.4 miles
Hence the value of d is 3.4 miles.
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2) We can calculate the expected value of the game with the following: E=
3) We can adjust the value v of the winning event and since we want to have a fair game, the expecation at the end must be 0 (he must neither win or lose on average). Thus, we need to solve the equation for v:
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4) So, we have that the probability that you get a red or purple or yellow sector is 2/7. We have that the probability for the blue sector is only 1/7 since there are 7 vectors and only one is blue. Similarly, the 2nd row of the table needs to be filled with the product of probability and expectations. Hence, for the red sector we have 2/7*(-1)=-2/7, for the yellow sector we have 2/7*1=2/7, for the purple sector it is 2/7*0=0, for the blue sector 1/7*3=3/7. The average payoff is given by adding all these, hence it is 3/7.
5) We can approach the problem just like above and set up an equation the value of one sector as an unknown. But here, we can be smarter and notice that the average outcome is equal to the average outcome of the blue sector. Hence, we can get a fair game if we make the value of the blue sector 0. If this is the case, the sum of the other sectors is 0 too (-2/7+0+2/7) and the expected value is also zero.
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7) Let us use the expections formula we mentioned in 1. Substituting the possibilities and the values for all 4 events (each event is the different profit of the business at the end of the year).
E=0.2*(-10000)+0.4*0+0.3*5000+0.1*8000=-2000+0+1500+800=300$
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