New Year With Continuation of Last Year's Class

Hi and happy new year everybody and I hope you all had a great holiday. Today we continued on what we left off on the last day of school before the holidays. We worked on some word problems that had to do with Venn- Diagrams. These are the questions:

1. Recently several DMCI students were surveyed about their favourite music groups.
The results were:

• 22 like Hole
• 25 like U2
• 39 like Third Eye Blind (TEB)
• 9 like U2 & Hole
• 17 like Hole & TEB
• 20 like U2 & TEB
• 6 like all three
• 4 like non of these three

a) How many students were surveyed?
b) How many students liked U2 only?
c) How many students like exactly 2 groups

2.Every year over 9 million tourists visit Turkey. Last year 9.8 million tourists vistited Turkey.

• 60% visited only Istanbul
• 20% visited Izmir
• Half of the tourists who visited Izmir also visited Istanbul
• 2% visited Istanbul, Izmir, and Antalya
• The number of tourists who visited only Antalya was half again as much as the number of the tourists who only visited Izmir
• Tourists who visited Antalya either saw only Antalya or Antalya, Istanbul, and Izmir
• The rest of the tourists visited other regions

How many tourists visited other regions?

Solutions
1.So first we fill in a three circle venn diagram because there are 3 different groups.
I'll explain the diagram, first we work our way from the middle and we know that there are 6 people who like all three groups. Now we pick one of the next 3 overlaps and find those. Lets use U2 & Hole as an example, we know from the clues that 9 people liked Hole & U2 so we subtract 6 from the 9 because the 6 represents 6 people that also like Hole & U2. So we have 3 in that section. Once those sections are complete we work on the outer sections. Like the overlaps we take the total number of people that like that group and subtract the number of people that like that group and other groups also.

a)This question asks us to find the number of students survey, so we just add all the numbers up and we get 50

b)This question asks us to find the number of students who only liked U2 and the answer is 2 according to the graph

c)This question asks us to find the number of students who like only 2 groups and the answer is 28. We get that by adding the numbers that are in the section of 1 overlap which are 3, 11, 14.

2.This quest is a doozy because we have to go back and forth with the clues.


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If the pictures are going too fast, feel free to pause or replay.

• The first picture shows inserting the info from the first clue and from the clue it tells us that 60% of the total tourists visited only Istanbul. We can put it on the venn diagram because the clue states that 60% visited only Istanbul.
• The second picture shows the third clue and with the second clue in mind we can find the Istanbul- Izmir overlap because the clue states that half of the number of tourists that visited Izmir also visited Istanbul. So half of 20% is 10% and that leaves us with 10% for Izmir.
• The third picture shows the addition of the middle section with the forth clue.
• The forth picture shows the sixth clue which states that the people who visited Antalya only visited Antalya or saw all three places and not 2 places. So we know that the Izmir-Antalya and Istanbul-Antalya sections have 0%'s. And now we can find how many people visited Izmir and it is 8% because before we had 10% and due to the forth cluwe are left with 8% and that 8% go into the Izmir section.
• The fifth picture shows the fifth clue and it states that the people that visited Antalya is equal to 1.5x the number of people who visited Izmir and 8 x 1.5= 12. So Antalya is 12%.
• The final picture shows the addition of the last clue which states that the remainder of the tourists visited other regions.

To answer the question we need to know the number of people who visited Turkey and the percentage of the tourists who visited the other regions. To find the number of people who didnt visit Istanbul, Izmir, and Antalya we take the total number of tourists multipied by the "other" percentage in decimal form.

After the explanation of those two questions we began with a new logic subject.
Mr. K told us to take out a new piece of loose leaf and draw the biggest circle you can draw on that paper and make a dot on the circumference. Then he asked us how many different flat areas there are in the circle and there are 1. He told us to make a second dot and connect the dots and asked us how many areas are there and there were 2. Then a 3rd dot and then connect that dot with every other dot and then do the same as before and there were 4 areas. Now look at the graph.
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So lets think of an equation to helps us find the number of areas if the number of points is 457.
As a class we discovered that the equation 2^(n-1) where n is the number points will work. So we tried the equation with 6 as the number of points and using the equation we predicted the number of areas will be 32. Now continue with the diagram with 6 dots and count the number of areas. Oh no there is only 31. That is situation called a counterexamples and that is when there is a theorem made and there is one example that doesn't fit the theorem. That just makes the theorem a theorem that is not true. Tomorrow will be the continuation about counterexamples.

Okay that was our first class back from the holidays and it was kind of tiring to go back to school after a 2 week break. Homework (homework*sigh*) is exercise #48 and it is about counterexamples.

The next scribe will be SAMUS!!!
Good Night :-)