<h3>
Answer: Choice D) -$22</h3>
You'll lose on average $22 per roll.
====================================================
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:

Step-by-step explanation:
a) 
b) 
c) 
d) 
e) 
f) 
The answer would be 44,800 if you want to round the hundreds place
I believe it is A and Yes
The bigger the price is on an item, the more tax you would have to pay, so both numbers increase. As for whether or not there is a line through the dots, you use a line when you could go inbetween the points. For example, with this question you can have 0.24, 0.86, or any other number as the price and it would make sense. If the question was sales tax on a certain number of shirts, well, you can't buy half a shirt so you don't need anywhere inbetween the dots.
Proportional in these kinds of problems means whether or not the line curves. If it doesn't and is a straight line, then it is proportional.