Math 110/003 - Group 3
Members:	Daisy Gobina
	Jonathan Rothwell
	Supreet Saran
	Ghita Youssefi

Homework 3

Questions 1-10 Yuri Tomura

1. There is actually no time difference. It is just the fact that the time is written differently. It says the time it took for the bus to travel from the terminal to the airport was an hour and 20 mins which is the same as 60min + 20min = 80 mins, hence the same time duration it took for the bus to travel back to the terminal from the airport.

2. Although the question mentions a driver's license, we should not assume that this lady was driving a car. She could have been walking in which case she would not be breaking any laws - it is fine for her to not have her license, the stop sign is only for driver's and a one-way street does not apply to pedestrians. However, if she was driving a car, we could also come up with the fact that the policeman didn't see her when she broke the law but only saw her when she was actually obeying the rules.

3. The question mentions how the boxes are labeled APPLES, ORANGES and APPLES AND ORANGES. Therefore, we can lay this out as:

Box 1 --> APPLES

Box 2 --> ORANGES

Box 3 --> APPLES AND ORANGES

However, all the boxes have the incorrect labels.

Our task is to draw one fruit from only one box and determine the correct labels.

If all the labels are incorrect, we will end up with:

Box 1 --> ORANGES or APPLES AND ORANGES

Box 2 --> APPLES or APPLES AND ORANGES

Box 3 --> either APPLES or ORANGES

So, if we select a fruit from box 3 and it is an apple, then box 2 is a box with apples and oranges as we can eliminate the option of only apples. Therefore, Box 1 would contain just oranges as there no longer can be the option of apples and oranges. Consequently, it is possible to select one fruit from only one box and determine the correct labels.

4. Looking at this question, we can see that the gender of the "blind fiddler" is not specified. The question mentions that "I am the brother of the blind fiddler" so we know that "I" is a male. Futhermore, we can figure out that the blind fiddler is a female as he has no brothers which concludes us to the fact that the blind fiddler is his sister.

5. Both coins are quarters, meaning they have the same dimensions. Therefore, when it revolves once around it, it will only be halfway around the quarter. So, the coin would have to revolve twice to go back to its original position.

6. There are 3 kinds of apples: Apple a, b and c.

First pick --> Apple a

Second pick --> Apple b

Third pick --> Apple c

Fourth pick --> Apple a

Now we have two of the same kind of apple a. Therefore, we need to draw an apple at least 4 times t in order to get at least two of the same kind.

7. i) In order to be sure to pick a pair of the same colour socks, we must take 3 socks from the drawer since if only two socks were picked, there is a possibility that they are different colours. But, if we pick 3, then at least 2 of them will bound to be the same colour. ii) In order to pick a pair of different colour socks, we must also take 2 socks from the drawer since if only two socks were picked, there is a possibility that they are both the same colours but if we pick 3, then at least 2 of them will be different colours.

8. Reuben's birthday is on December 31st and he said "Two days ago I was 20 years old. Later next year I will be 23 years old" on January 1st. This means he was 20 years old on December 30th but turned 21 on December 31st last year. This year he will be turning 22 and so later next year, he will be 23 years old.

9. If the tide rises five feet, the boat would rise five feet as well. Therefore, the rope ladder hanging over the side of the boat would also rise five feet, leaving 10 rungs to be showing still.

10. i) No, it does not follow that one-fourth of all people are women chocolate eaters because if half of all people are chocolate eaters and half of all people are women, it does not necessary mean that one-fourth of all people are women chocolate eaters as there are many other possibilities of which half of the people are chocolate eaters.

Homework 4

Question 1- Ghita Youssefi

A table was made in order to break up the problem into three categories: Owners, Pets, and Pets Names.

Owners:

    Tosh --> (male)
    Bianca --> (female)
    Jaela ---> (female)
    Jun --> (male)
    Susan --> (female)

Pets Names:

   Cat --> Tosh
   Frog --> Bianca
   Turtle --> Susan 
   Parrot --> Jaela
   Snake --> Jun

In order to find who the turtle belonged to, I eliminated all the other owners and Susan was the only left.

Pets:

   Tosh --> Parrot 
   Bianca --> Snake 
   Jaela --> Turtle 
   Jun --> Cat  (provided)
   Susan --> Frog (provided)

We are told that the name by which they call the turtle is the name of the woman is Tosh, therefore, Tosh's owner is female and Bianca's pet is Susan. In consequence, Tosh has to be the Parrot and Jaela has to be the turtle. Finally, the only pet left is the snake and it is paired up with the last pet name which is Bianca.

The last step is finding out which pet belong's to Susan's mother. We know that Susan's pet is the turtle called Jaela. Also, the cat, Jun, belongs to Susan's (the frog) Mother (Bianca).

Problem 2 (Supreet) In this problem, we have five different basketball players. We are trying to find the center player who is left handed, and over 2m tall. Using Pólya’s method, our first step to understand the problem. The conditions we know are that two of the players are left handed and three right are handed. Bohao and Dylan use the same hand, white Tim and Chan use different hands. The condition about height we know is that two are over 2m tall and three are under 2m tall. Stewart and Chan are of the same height range, while Dylan and Tim are in different height ranges The second step in Pólya’s method is to plan a strategey. My strategey in this case is to use a chart, and use the process of elimation. The third step is to execute it. Firstly, we know that that theres 2/5 left handed, which mean Bohao and Dylan must be right-handed, as Tim and Chan are 2 different hands. If Bohao & Dylan were left handed, then there would be 3 left-handed, as either Tim and Chan would be left handed as well, which is a contradiction to the condition. Therefore, they are eliminated from being in centre position. Secondly, we also kown there are 2/5 over 2m tall. This is similar to the our reasoning above, as we know stewart and chan are the same height, when Dylan and Tim are different from each other, which means that stewart and chan must be under 2m. Dylan and Tim could be either or. The only one who hasn't been eliminated in both conditions it Tim. Our fourth step is to check and interpret our steps.Bohao, Dylan, Stewart, and Chan are elimanted as their conditions don't comply with the left-hand, and above 2m conditions of the centre player. Consequently, this leaves Tim. Tim is who we were looking for, he is left handed and over 2m. Therefore, Tim is centre player.

Problem 4 Yuri Tomura

Firstly, I made a table that looked like this and filled out the known information given in the question:

Then, I used Petra's column to fill up the blanks by trial and error. I started of with Petra playing against Fernanda on the third day:

Now we have Petra yet left to play with Janet and Li on the second and fifth day. However, we can see that Janet is already playing Carla on the second day which means Petra cannot play Janet on the second day, hence, Petra played Li on the second day and Janet on the fifth:

Next we can see that Janet only has either the first day or fourth day left to play against Sandra or Fernanda. It is obvious that Sandra is already playing on the fourth day against Petra so we can conclude that Janet will be playing Sandra on the first day and Fernanda on the fourth:

Now looking at Fernanda's column, we can see that she still needs to play on the first, second and fifth day against Carla, Sandra and Li. However, it is clear that Fernanda cannot play Carla or Li on the second day as they are playing on that day already. This leaves us with Fernanda playing against Sandra on the second day:

Finally, since Carla is already playing Petra on the first day from the table above, it results as Fernanda playing against Li on the first day, thus leaving Fernanda to play Carla on the fifth day. Therefore, the answer is Carla:

Problem 5 (Jon)

Conditions:

(a) No one of the noisemakers were quiet for 3 consecutive days
(b) No pair of the noisemakers made noise on more than 1 day

Possible combinations of noisemakers include:

Salesman & Dog
Salesman & Construction
Construction & Dog

The provided information in the problem is:

Monday - salesman
Sunday - dog
Monday - salesman & construction
Tuesday -
Wednesday - salesman & dog
Thursday -
Friday -
Saturday - construction
Sunday - dog

Therefore, dog barking must wake Homer on Saturady since no noisemaker can be quiet for 3 consecutive days and the previous day was Wednesday. This completes the combinations leaving on single noisemakers to disturb Homer. Between Wednesday and Sunday the salesman must occur on Friday since he can't occur on Saturady due to the contruction and the dog, therefore he must occur Friday in order to obey condition (a). Construction must once again occur on Thursday since the previous day for construction was Monday.

Determined Days:

Saturday - salesman
Sunday - dog
Monday - salesman & construction
Tuesday -
Wednesday - salesman & dog
Thursday - CONSTRUCTION
Friday - SALESMAN
Saturday - construction & DOG
Sunday - dog

The only remaining day whereby no violoations of the conditions occur and where Homer is able to sleep in is Tuesday.

Problem 4(Daisy)

Fristly I said Clara played Petra on the first day.Jannet played Sandra and Li played Fernanda. This was because each of them was to play each ther once during the competion. On the second day Jannet will play clara as we are told in the ouestion and so Petra will play Li since we are told on the fourth day Sandra will play Petra that means they can't play now since they are too meet each other just once in the competition. On the second day Sandra will paly Li. On the third day We are told that Li played Jannet, So since Clara has already played Petra and Jannet so she is eligible to play only Sandra ,Li and Fernanda and so since Sandra is still to play Petra , Clara can only play Sandra and Petra will play Fernanda.On the fourth day Petra plays Sandra and Since Li has already played Jannet she cannot play her again so Jannet will play Fernanda and Li will play Clara. On the Fourth day Since Petra has played Clara,Li,Fernanda Sandra the only person she can now play on the fifth day is Jannet. Since Sandra has played Jannet,Fernanda,Clara and Petra the only person she can now play is Li. Eventually Clara and Fernanda are left so they are going to play against each other . So on the fifth day Clara is going to play Fernanda

Basic Skills Project

What I understand - Yuri

Basic Functions
Properties of functions
Equations
Graphs of functions
Polynomial long division
Intersections of functions
Distances and lines
Construction of graphs
Trigonometry and the Pythagorean theorem
Areas and volumes
Mathematical writing

What I don't - Yuri

Inequalities
Composition of funcitons
Operations on graphs of functions

JON - Understand

Basic functions
Properties of functions
Equations
Inequalities
Composite functions
Graphs of functions
Readings graphs of functions
Distances & lines
Operations on graphs of functions
Construction of graphs
Areas & volumes
Math writing
Pythagorean theorem

JON - Don't Understand

Domain of radicals (especially writing interval notation, at least for WeBWork)
polynomial long division
Intersection of functions
Limited understanding if trig

polynomials

What I understand- Supreet:-

Basic Funtions
Property of functions
Equations
Inequalties
Composite Functions
Trigonometry and the Pythagorean theorem
Areas and volumes
polynomial long division

What I don't Understand:-

Reading Graph of Functions
Distances of Lines
Mathematical writing
Intersection of functions
Graph of Functions
Construction of graphs

What I Understand-Ghita Youssefi

Properties of functions Equations Inequalities Composition of functions Distances and lines Trigonometry and the Pythagorean theorem Areas and volumes Mathematical writing

What I Don't Understand- Ghita Youssefi:

Properties of functions Composition of functions Polynomial long division Graphs of functions Intersections of functions Reading graphs of functions Operations on graphs of functions Construction of graphs

SOME of us understand: Properties of functions Composition of functions Polynomial long division

NONE of us understand: polynomial long division Intersection of functions Operations on graphs of functions

Daisy Gobina I understand most of the topics on the basic skills test but i think i have forgotten how to go about some things e.g i dont really remember Trigonometry and i think i really do bad at it. I also dont know volumes and areas of figures execpt those i think am ok with the others realatively. That is i understand what is happening

Group 3 Basic Skills Project: Absolute Value Functions

[ http://wiki.ubc.ca/Course:MATH110/003/Groups/Group_03/Basic_Skills_Project]