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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:
the last one [d)]
Step-by-step explanation:
First, we need to use the triangle inequality theorem. The sum of the lengths of the two sides must be greater than the third side.
a) 7+14=21=21 (this cannot represent a triangle)
b) 13+23=36<37 (this cannot represent a triangle)
c) 7+18=25=25 (this cannot represent a triangle)
d) 11+24=35>32 (this can represent a triangle)
d) is the answer
Hope this helps!
Answer:
B
Step-by-step explanation:
Plug in a x-value and see which table matches the result. Plug in 1.
f(x) = 7 - 4.5x
f(1) = 7 - 4.5(1)
f(1) = 7 - 4.5
f(1) = 2.5
The table that matches an input of 1 with an output of 2.5 is B.
Answer: =4x+18
Step-by-step explanation:
Let's simplify step-by-step.
4x−7+25
=4x+−7+25
Combine Like Terms:
=4x+−7+25
=(4x)+(−7+25)
=4x+18
Answer:
=4x+18
There are 128 US fluid ounces in a gallon
