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course Mth 151
Consider the statement “If that group of six-year-olds doesn’t have adult supervision, they won’t act in an orderly manner.” Under which of the following circumstances would everyone have to agree that the statement is false?The group does have supervision and they don’t act in an orderly manner.
List the different orders in which the letters a, b, & c could be arranged (examples are “acb” and “cba”). Explain how you know that your list contains every possible order.
“abc”, “acb”, “bca”, “bac”, “cab”, “cba”
I know I have all the possible orders because I did it in order by first choosing a to be the letter then you put the second and three letter. You only have three letters and each can only have two different ways.
One collection consists of the letters a, c, d and f. Another collection consists of letters a, b, d and g.
1. List the letters common to both collections: a and d
2. List the letters which appear in at least one of the collections: b, c, f and g
3. List the letters in the first half of the alphabet which do not appear in either of the collections: e
Self-Critique:
I made the mistake of not even going through the whole alphabet. I just put what letter hadn’t been listed up to the g.
Give the next element in each of the following patterns and explain how you obtained each.
2, 3, 5, 8, 12.….: the next # would be 17. I got it because the first number 2 you add 1 and get three. You take 3 and add 2 to it and you get 5. You take the five and add 3 to it and you get 8. Then you take 8 and add 4 to it you get 12. Last you take the 12 and add 5 to it because it is the 5th number and you get 17.
3, 6, 12, 24.…….: the next # would be 48. I got this because if you take 3 and times it by 2 you get 6. You take 6 and times it by 2 you get 12. You take the 12 and times it by 2 you get 24. So you take 24 and times it by 2 and get 48.
1, 3, 4, 7, 11, 18.……: the next # would be 29. I got this because you take the first two #’s 1 and 3 and add them you get 4. Then you take the #3 and 4 and add them and get 7. Then you take the #4 and 7 and add them you 11. Then you take the #7 and 11 and add them and you get 18. To get the 29 you take the #11 and 18 and add them.
Self-Critique:
I like my idea’s better for the first two patterns, but see where you got that. The first I added instead of subtracting and on the second one I times instead of divided. I got the third one right though. Yea me!!!
The #18 can be “broken down” into the product 9 x 2, which can be broken down into the product 3 x 3 x 2, which cannot be broken down any further. Alternatively 18 can be broken down into 6 x 3, which can be broken down into 2 x 3 x 3.
Show how the #’s 28 & 34 can be broken down until they can’t be broken down any further.
Show that there are at least two different ways to break down 28, but that when the break down is complete both way s end up giving the same #.
Okay, the two different ways you can break down 28 is this: 2 x14; 14 is broken down to 2 x 7. So it gives you 2 x 2 x 7. The other way is 4 x 7; 4 can be broken down to 2 x 2. So it gives you 7 x 2 x 2. As for the number 34 it is broken down by 2 x 17. And that is the only way.
Self-Critique:
Yea I did it right!!!!
Give the average of the numbers in the following lists: 3, 4, 6, 6, 7, 7, 9. By how much does each number differ from the average?
First you will take the numbers and add them together, you will get 42. Then you take the 42 and divide it 7 which is the total of numbers. It will give you 6.
3 - 3 way
4 - 2 way
6 - zero
7 - 1 more
9 - 3 more
Self-Critique:
I am not sure but I think I got it.
Which of the following list of numbers is more spread out, 7, 8, 10, 10, 11, 13 or 894, 897, 902, 908, 910, 912? On what basis did you justify your answer.
The list that is more spread out is the one with 894. It is more spead out because if you take 912 and minus the 894 and it gives you 13. With the other list you minus 13 from 7 and you get 6.
Self-Critique:
Yea me again. I got it right again!!!
12 is 9 more than 3 and also 4 times 3. We therefore say that 12 differs from 3 by 9, and that the ratio of 12 to 3 is 4. What is the ratio of 36 to 4 and by how much does 36 differ from 4? If 288 is in the same ratio to a certain number as 36 is to 4, what is that number?
The ratio of 36 to 4 is 9 and by how much does 36 differ from 4 is 32. The number that belongs to the ratio of 288 to ? = 9 is 32.
I got this by 36/4 = 9 and then 36 - 4 = 32. And 36 is 32 more than 4 and 4 x 9 is 36.
Self-Critique:
Got it right again. I hope I explained it right.
A triangle has sides 3, 4, & 5. Another triangle has the identical shape of the first but is larger. It shorter sides are 12 and 16. What is the length of its longest side?
I believe it would be 18. The first is 3, 4 and 5 one number right after each other. So if you have sides of 12 and 16 the next number would be 2 more giving you 18.
Self-Critique:
I am kind of mad at myself, because as I was going back to look at the answer the way you did it came to my head I just didn’t write it down. I do understand how you got the answer thought.
@& You are doing a lot of very good thinking. I'm looking forward to seeing more of your work in this course.
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