Answer: C) 127, 152.4, 182.88, 219.456,...
Step-by-step explanation:
You can only find the sum of an infinite geometric sequence if it converges.
One criterion to see if the series converges is if:
aₙ < aₙ₋₁
This means that, as n increases, the value of the terms decreases.
This means that as n tends to infinity, aₙ tends to zero.
Then we only can find the sum of those series where the terms are decreasing.
in A, B and D the terms are decreasing, then we can find the sum of those 3 series.
Now in the case of C, the terms are increasing, then we can not find the sum of that series.
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.
Please see the attached image for a visual representation of our scale factor. We can set up this proportion by taking the DVD cover and poster values and placing them in fractions. Cross multiply and divide to solve for x.
Given:
Consider the line segment YZ with endpoints Y(-3,-6) and Z(7,4).
To find:
The y-coordinate of the midpoint of line segment YZ.
Solution:
Midpoint formula:
The endpoints of the line segment YZ are Y(-3,-6) and Z(7,4). So, the midpoint of YZ is:
Therefore, the y-coordinate of the midpoint of line segment YZ is -1.
