Numercy 1 The Ontario Lottery Group has recently started allowing betting on the outcomes of games of the CanadianCalvinball League. It costs $10 to purchase a ticket, and you must successfully determine the outcome of the night'sgames. Tonight the games areOakville OwlbearsBrampton BeholdersWhitby WyvernsVSVsVsMississauga Mind FlayersGuelph GithyankiKitchener Kuo-ToaYou will win 3* – 1 dollars for correctly determining the outcome of k matches.Question 1 Assuming all teams are equally matched, what are your expected net winnings? Note that your netwinnings are the difference between what you paid to play and what you won. Hence your winnings can be negativeif you lose money.Question 2 Per the rules of Calvinball, the team whose name occurs first alphabetically has an advantage and istwice as likely to win their game. Assuming you bet on the more likely winner in each game, what are your expectedvalue net winnings?Question 3 You have a friend who plays for the Whitby Wyverns. The team found a ringer from the Europeanleagues, and the likelihood that the Wyverns win their next game is now 100%. Assuming that you bet for theWyverns and that the other two games still favour the alphabetical team, what are your expected net winnings?1. Suppose f is a function which satisfies f(x + y)Numeracy 1value of f(0)?f(x) + f(y) for all , y E R. What is the%3D2. Let f(x) = e + r3 + x-3. This function is invertible. What is the value of f-1(-2)?3. Consider the function f, defined on R, whose graph on the interval [-3, 3] is given below:-2-112Assuming that the function maintains this pattern of behaviour on all of R, give an algebraic description of thefunction f; that is, write down f(x) in such a way that we can compute the value of f for any given x E R.1

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1. Suppose f is a function which satisfies f(r + y) = f(x) + f(y) for all r, y E R. What is the Numeracy 1 value of f(0)?

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

Numercy 1

The Ontario Lottery Group has recently started allowing betting on the outcomes of games of the Canadian
Calvinball League. It costs $10 to purchase a ticket, and you must successfully determine the outcome of the night's
games. Tonight the games are
Oakville Owlbears
Brampton Beholders
Whitby Wyverns
VS
Vs
Vs
Mississauga Mind Flayers
Guelph Githyanki
Kitchener Kuo-Toa
You will win 3* – 1 dollars for correctly determining the outcome of k matches.
Question 1 Assuming all teams are equally matched, what are your expected net winnings? Note that your net
winnings are the difference between what you paid to play and what you won. Hence your winnings can be negative
if you lose money.
Question 2 Per the rules of Calvinball, the team whose name occurs first alphabetically has an advantage and is
twice as likely to win their game. Assuming you bet on the more likely winner in each game, what are your expected
value net winnings?
Question 3 You have a friend who plays for the Whitby Wyverns. The team found a ringer from the European
leagues, and the likelihood that the Wyverns win their next game is now 100%. Assuming that you bet for the
Wyverns and that the other two games still favour the alphabetical team, what are your expected net winnings?
1. Suppose f is a function which satisfies f(x + y)
Numeracy 1
value of f(0)?
f(x) + f(y) for all , y E R. What is the
%3D
2. Let f(x) = e + r3 + x-3. This function is invertible. What is the value of f-1(-2)?
3. Consider the function f, defined on R, whose graph on the interval [-3, 3] is given below:
-2
-1
1
2
Assuming that the function maintains this pattern of behaviour on all of R, give an algebraic description of the
function f; that is, write down f(x) in such a way that we can compute the value of f for any given x E R.
1

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