## For each of the following sets, tell whether the set is countable or uncountable, then justify briefly.

Question For each of the following sets, tell whether the set is countable or uncountable, then justify briefly. (a) The power set of Q. (b) The set {x y | x, y ∈ Q } (that is, the set of all numbers that can be represented as one positive rational number to the power of another positive rational number). (c) The set of all finite strings consisting only of ‘a’s, ‘b’s, and ‘c’s (can repeat any number of times in any order; example elements: ‘a’, ‘bb’, ‘bcabc’, ‘cccb’). (d) The set of all ordered pairs (x,y) such that x and y are real-valued solutions to the equation y = x 2 − 5x 6. (e) The set { √n x | n ∈ Z , x ∈ Q } (that is, the set of all positive integer roots of positive rational numbers).

## I was asked to send a learning log for math final unit. It will be

Question I was asked to send a learning log for math final unit. It will be worth 15% of my final mark. The question went like this:Throughout the course you should have completed 4 submissions for your Learning Log and received feedback on each. This was to help you prepare for this culminating activity.Learning Log Requirements: -five (5) entries (it would make sense to polish your first 4 entries)I’m not quite sure what it was meant by entries. Am i supposed to write the log differently in 4 separate files , or write it in 1 file, but in four paragraphs/sections? I would like to be guided so i can understand what i am expected to do. Thank You.

## Find an equation in standard form to model the polynomial. (Hint:

Question Find an equation in standard form to model the polynomial. (Hint: Write the most general standard form of the polynomial, bearing in mind its degree. Then use a number of (x,y) values to obtain a set of simultaneous linear equations. Solve the equations – using technology if appropriate – to obtain the coefficients in the standard form. Table went like this – X = 1, Y= -2, X = 2, Y = -4, X = 3, Y = -6 etc. Standard Form looks something like this: f(x) = 1x^4 ax^3 bx^2 cx d

## Get Answer Watch the following videos: https://youtu.be/2dOCARQUV-Q?t=18 https://youtu.be/uPgEgPTm9n8?t=18 write and solve a probability question associated with this scenario. Explain

Question Get Answer Watch the following videos: https://youtu.be/2dOCARQUV-Q?t=18 https://youtu.be/uPgEgPTm9n8?t=18 write and solve a probability question associated with this scenario. Explain your steps in the solution and use correct notation. Include in your submission a tree diagram and use of the fundamental counting principle. Are the events independent or dependent? Justify. Using your feedback from Unit 1 Activity 2, resubmit your answer to the following question: Explain the Law of Large Numbers and how a casino benefits from it. Use the example of the Die Roller from the Games Fair to create your own very simple similar example involving money. Choose a non-mutually exclusive question created by a peer. Compare to your own non-mutually exclusive question, change your question and solution if required. Choose a compound event question created by a peer. Compare to your own compound event question, change your question and solution if required.

## Please type in fractions like 2/3 2/3 (you do not need to reduce).

Question Please type in fractions like 2/3 2/3 (you do not need to reduce). Two marbles are drawn, one after the other, randomly from a jar with 1616 red marbles and 1818 blue marbles (each marble can only be one color).During the draws, the first marble is not placed back in the jar.a) After the first marble is drawn, for the second draw, how many marbles are left in the jar? What is the probability of drawing:b) a red marble on the first draw? c) a blue marble on the first draw? d) a red marble on the second draw, given that a red marble was drawn first? Hint: be careful with the denominator. How many marbles are in the jar?e) a blue marble on the second draw, given that a red marble was drawn first? For the remaining parts of this problem, during the draws, the first marble is replaced (returned to the jar).f) After the first marble is drawn, for the second draw, how many marbles are left in the jar? What is the probability of drawing:g) a red marble on the second draw, given that a red marble was drawn first? h) a blue marble on the second draw, given that a red marble was drawn first?

## A deck consists of 22 22 cards with 2 2 suits labelled A A and B

Question A deck consists of 22 22 cards with 2 2 suits labelled A A and B B, and numbered ranks from 11 to 1111. That is, there are 1111 cards of each suit and 22 cards of each rank.A single card is drawn at random from this deck.a) What is the probability of it being suit B?b) What is the probability of it having rank 6?c) What is the probability of it having rank 6 given that it is suit B?Hint: Among the cards with suit B, how many of them have rank 6?d) What is the probability of it being suit B given that it has rank 6?Hint: Among the cards with rank 6, how many of them are suit B?e) The events, the card is suit B, and the card has rank 6, are IndependentNot independentWe can see this because the answers to part (a) and part (b),(c)or (d) are equalnot equal . A deck consists of 20 cards with 22 suits labelled A and B. Unlike the earlier deck, this deck has 11 cards with suit A numbered 1 to 11, but it only has 9 cards with suit B numbered 1 to 9. The number of cards in each suit is not the same.A single card is drawn at random from this deck.f) What is the probability of it being suit B?g) What is the probability of it having rank 6?h) What is the probability of it having rank 6 given that it is suit B?Hint: Among the cards with suit B, how many of them have rank 6?i) What is the probability of it being suit B given that it has rank 6?Hint: Among the cards with rank 6, how many of them are suit B?j) The events, the card is suit B, and the card has rank 6, are Independent Not independent We can see this because the answers to part (f) and part ??? (g), (h)or(i) are equal or not equalWe can also see this because the answers to part (g) and part (f),(h) or (i) are equal or not equal