Answer: -1
The negative value indicates a loss
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Explanation:
Define the three events
A = rolling a 7
B = rolling an 11
C = roll any other total (don't roll 7, don't roll 11)
There are 6 ways to roll a 7. They are
1+6 = 7
2+5 = 7
3+4 = 7
4+3 = 7
5+2 = 7
6+1 = 7
Use this to compute the probability of rolling a 7
P(A) = (number of ways to roll 7)/(number total rolls) = 6/36 = 1/6
Note: the 36 comes from 6*6 = 36 since there are 6 sides per die
There are only 2 ways to roll an 11. Those 2 ways are:
5+6 = 11
6+5 = 11
The probability for event B is P(B) = 2/36 = 1/18
Since there are 6 ways to roll a "7" and 2 ways to roll "11", there are 6+2 = 8 ways to roll either event.
This leaves 36-8 = 28 ways to roll anything else
P(C) = 28/36 = 7/9
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In summary so far,
P(A) = 1/6
P(B) = 1/18
P(C) = 7/9
The winnings for each event, let's call it W(X), represents the prize amounts.
Any losses are negative values
W(A) = amount of winnings if event A happens
W(B) = amount of winnings if event B happens
W(C) = amount of winnings if event C happens
W(A) = 18
W(B) = 54
W(C) = -9
Multiply the probability P(X) values with the corresponding W(X) values
P(A)*W(A) = (1/6)*(18) = 3
P(B)*W(B) = (1/18)*(54) = 3
P(C)*W(C) = (7/9)*(-9) = -7
Add up those results
3+3+(-7) = -1
The expected value for this game is -1.
The player is expected to lose on average 1 dollar per game played.
Note: because the expected value is not 0, this is not a fair game.
Answer: The tree was 27 feet tall
Step-by-step Explanation: First of all Sally was standing 30 feet away from the tree and she looks up at an angle of elevation of 38 degrees to the top of the tree. With this bit of information we can determine that a right angled triangle has been formed with the reference angle as 38 degrees, the side facing it as h (the height of the tree) and the adjacent side as 30. We shall apply the trigonometric ratio as follows;
Tan 38 = opposite/adjacent
Tan 38 = h/30
0.7813 = h/30
0.7813 x 30 = h
23.4 = h
We remember at this point that Sally’s eyes were 4 feet above the ground. What we have just calculated is the height of the tree from “4 feet above the ground” (where her eyes were). Hence the actual height of the tree is calculated as 23.4 plus 4 which gives us 27.4
Therefore the tree was 27 feet tall (approximately to the nearest foot)
Your answer would be 54 degrees since 90+36=126 so then you subtract 126 from 180 and get 54
