<h3>
Answer: Choice D) -$22</h3>
You'll lose on average $22 per roll.
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Explanation:
Normally there is a 1/6 chance to land on any given side of a standard die, but your friend has loaded the die in a way to make it have a 40% chance to land on "1" and an equal chance to land on anything else. Since there's a 40% chance to land on "1", this leaves 100% - 40% = 60% for everything else.
Let's define two events
- A = event of landing on "1".
- B = event of landing on anything else (2 through 6).
So far we know that P(A) = 0.40 and P(B) = 0.60; I'm using the decimal form of each percentage.
The net value of event A, which I'll denote as V(A), is -100 since you pay $100 when event A occurs. So we'll write V(A) = -100. Also, we know that V(B) = 30 and this value is positive because you receive $30 if event B occurs.
To recap things so far, we have the following:
- P(A) = 0.40
- P(B) = 0.60
- V(A) = -100
- V(B) = 30
Multiply the corresponding probability and net value items together
- P(A)*V(A) = 0.40*(-100) = -40
- P(B)*V(B) = 0.60*30 = 18
Then add up those products:
-40+18 = -22
This is the expected value, and it represents the average amount of money you earn for each dice roll. So you'll lose on average about $22. Because the expected value is not zero, this means this game is not mathematically fair.
This does not mean that any single die roll you would lose $22; instead it means that if you played the game say 1000 or 10,000 times, then averaging out the wins and losses will get you close to a loss of $22.
Answer:
rise= -16
Step-by-step explanation:
Please see the attached picture for the full solution.
Answer:
No Solution.
Step-by-step explanation:
-6(x-7)+6(x+5)=73
-6x+42+6x+30=73
72=73
no solution
The value of F(G(x)) is 2x^2 - 13
<h3>How to solve the composite functions?</h3>
The functions are given as:
F(x)=2x+1
G(x)=x^2-7
To find (FxG)(x), we make use of
(FxG)(x) = F(G(x))
So, we have:
F(G(x))=2G(x)+1
Substitute G(x)=x^2-7
F(G(x))=2(x^2-7)+1
Expand
F(G(x))=2x^2 - 14 + 1
Evaluate the like terms
F(G(x))=2x^2 - 13
Hence, the value of F(G(x)) is 2x^2 - 13
Read more about composite functions at:
brainly.com/question/20379727
#SPJ1
Answer:
There is no sufficient evidence to support the claim that wedding cost is less than $30000.
Step-by-step explanation:
Values (x) ∑(Xi-X)^2
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29.1 0.1702
28.5 1.0252
28.8 0.5077
29.4 0.0127
29.8 0.0827
29.8 0.0827
30.1 0.3452
30.6 1.1827
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236.1 3.4088
Mean = 236.1 / 8 = 29.51
Statement of the null hypothesis:
H0: u ≥ 30 the mean wedding cost is not less than $30,000
H1: u < 30 the mean wedding cost is less than $30,000
Test Statistic:
Test criteria:
SIgnificance level = 0.05
Degrees of freedom = df = n - 1 = 8 - 1 = 7
Reject null hypothesis (H0) if
Finding in the t distribution table α=0.05 with df=7, we have
= -1.9861 > -2.365
Result: Fail to reject null hypothesis
Conclusion: Do no reject the null hypothesis
u ≥ 30 the mean wedding cost is not less than $30,000
There is no sufficient evidence to support the claim that wedding cost is less than $30000.
Hope this helps!
