Answer:
the answer is Y=(6/17)X + (285/17)
Step-by-step explanation:
1. Identify the X and Y coordinate of each point.
for example, the first point could be (12,21), therefore X1 = 12 and Y1 = 21 and the second point is then (46,33), therefore X2 = 46 and Y2 = 33
2. to find the equation of the line it is necessary to find the slope.
knowing that the equiation of the slope is M = Y2-Y1/X2-X1 we replace
and then we simplify the result to 
3. Using the Point-slope equation which is Y-Y1=M(X-X1) we replace
Don't hold me to it, but I think the answer is D.) 4 cups
<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.
Step by step explanation
Cost of one hotdog =140/56=2.5
To find the number of hot dogs =total cost so the cost of one hotdog is =175/2.5=70
So the numbers of hot dogs he had to sell more of =70-56=14
To find the median we put the numbers from least to greatest, and cross out the smallest number with the biggest number, until we can't any longer.
54/96, 55/95, 60/89, 66/88, 69/83, 72/82, 73/75, 74/75.
Since we ended with 74 and 75, pick the decimal number that's in between those two numbers, 74.5.
74.5 is your median.
The mode is the number that's most frequent.
There are two 75's, so 75 is your mode.
Range is the difference of the highest number and the lowest number.
96-54=42.
The range is 42.
