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1 answer:
<h3>Answer: A) gain of $0.45</h3>
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Explanation:
Let x be the net winnings the customer gets
Saying something like x = 24 means you've walked away with $24. This occurs when you pay $1, and get $25 back in prizes, so 25-1 = 24 dollars overall.
The probability of this event occurring is 1/100 since there's only one ticket with the $25 prize
Make a table as shown below. It represents all the possible x values which are all the possible net winnings. Note how 1/100 = 0.01, 3/100 = 0.03 and 95/100 = 0.95
The third column is x*p(x) which is the product of the first two columns. Adding everything in the third column (that isn't highlighted in yellow) gets us the value -0.45 which is the expected value for the customer.
This represents a loss of $0.45, aka a loss of 45 cents. This is from the perspective of the customer.
Flipping things around, the pizza company will see this is as a gain of $0.45 or a gain of 45 cents.
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Here's another way to see why this works:
The pizza company earns $100 in revenue since 100 tickets are sold for a dollar each. The company pays out 25+15+3*5 = 55 dollars in prizes overall. That means the company will make a profit of 100-55 = 45 dollars. So the average profit per ticket is 45/100 = $0.45 aka 45 cents and this is from the viewpoint of the pizza company (not the customer). The positive average profit represents a gain.
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Answer:
The area of polygon MNOPQR = Area of a rectangle that is 15 square units + Area of a rectangle that is <u>2</u> square units.
Step-by-step explanation:
We are given that a polygon MNOPQR is shown. The top vertex on the left is labeled M, and the rest of the vertices are labeled clockwise starting from the top-left vertex labeled, M. The side MN is parallel to side QR. The side MR is parallel to side PQ.
The side MN is labeled as 5 units. The side QR is labeled as 7 units. The side MR is labeled as 3 units, and the side NO is labeled as 2 units.
Firstly, we will draw a perpendicular line from point O which meets the line RQ at point T. Now, the polygon MNOPQR is divided into two rectangles MNTR and OPQT.
As we know that the area of the rectangle =
In the rectangle MNTR, the length (MN) = 5 units and the breadth (MR) = 3 units.
So, the area of the rectangle MNTR =
= = 15 square units
Now, as we know that in rectangle MNTR, the side NT = 3 units and the side NO is labeled as 2 units. This means that the side OT = NT - NO = 3 units - 2 units = 1 unit
Similarly, the side QR is labeled as 7 units and the side RT is labeled as 5 units. This means that the side TQ = QR - RT = 7 - 5 = 2 units
Now, in the rectangle OPQT, the length (TQ) = 2 unit and the breadth (OT) = 2 units.
So, the area of the rectangle OPTQ =
= = 2 square units
Hence, the area of polygon MNOPQR = Area of a rectangle that is 15 square units + Area of a rectangle that is <u>_2_</u> square units.