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:
<h2>f(x - k) = (x - k)²⇒ k = 5</h2>
Step-by-step explanation:
f(x) + n - shift the graph n units up
f(x) - n - shift the graph n units down
f(x - n) - shift the graph n units to the right
f(x + n) - shift the graph n units to the left
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Look at the picture.
The graph has been shifted 5 units to the right.
Therefore we have f(x - 5).
Length = x
width = y
y = 16
x = 2y
x = 2(16)
x = 32
perimeter = 2x + 2y
= 2(32) + 2(16)
= 64 + 32
= 96
Hello there!
|b| > 2
Solve for the absolute value
We know either b > 2 or b < -2
b > 2
b < -2
Thus,
The correct answer is option A
b < -2 or b > 2
Answer:
Correct answer: (2 x - 1) (x + 2)
Step-by-step explanation:
Given:
2 x² + 3 x - 2 = ( ) · ( )
2 x² + 3 x - 2 = 2 · ( x² + (3/2) x - 1) = 2 ( x² + 2 · x · (3/4) + (3/4)² - (3/4)² - 1)
2 x² + 3 x - 2 = 2 · ( (x + (3/4))² - (9/16) - 1) = 2 · ((x + (3/4))² - (9/16) - (16/16))
2 x² + 3 x - 2 = 2 · ((x + (3/4))² - (25/16)) = 2 · ((x + (3/4))² - (5/4)²)
2 x² + 3 x - 2 = 2 · (x + (3/4) - (5/4)) · (x + (3/4) + (5/4)) =
2 · (x - (2/4)) (x + (8/4))
2 x² + 3 x - 2 = 2 · (x - (1/2)) (x + 2) = (2 x - 1) · (x + 2)
2 x² + 3 x - 2 = (2 x - 1) · (x + 2)
God is with you!!!
