Cascadia College Equivalency Guide. CEEB Code #2859. 18345 Campus Way NE Bothell, Washington 98011. Proof that 1 + 1 = 1? Date: 09/04/97 at 20:43:37 From: Ben Mayer Subject: 1 + 1 = 1? My programming teacher said that there was a proof that proved that 1 + 1 = 1. He also said in this proof that one of the steps was a little bit 'in the gray area.' I was wondering if you could shed any light on this subject. Thank you, Benjamin W. How to calculate 3/4 plus 1/9 Is 1/2 greater than 1/3? What is 4.56 as a fraction? How to calculate 3/7 divided by 4/5 Equivalent Fractions of 3/9 What is the factorial of 6? 1/2 divided by what equals 3/4? Reduce 5/25 What times 1/3 equals 1/2? 1/3 minus what equals 1/5? 4/9 Rounded to the Nearest Hundredth What is 1/4 of 1/2?
Here is the County’s Reorganization Plan for Cascadia (1 MB PDF) assembled document consisting of
Cascadia Behavioral Heath Financial Condition, memo from June 11
Our response to these documents.
1. The reorganization of Cascadia is tantamount to the reorganization of the county mental health system.
2. The goals and outcomes of the plan reflect the interests of county and state government. The outreach and contact the reorganization leaders had with those affected by the system’s change was not sufficient. According to the Surgeon General’s mental health report of 2002, 2.2% of the general population has a severe and persistent mental illness, and each of those persons has 4.5 persons who are closely attached to them – friends and family members. In Multnomah County this equals approximately 15,000 and 67,500 = 82,500. The largest County meeting in the past year about this issue drew less that 1/1000 of this number and the majority of persons at that meeting (at Benson High School) were employees of Cascadia or Multnomah County. The goals and outcomes selected may have been considerably different if those directly affected by the reorganization were brought to the discussion as equal stakeholders.
3. The plan as released is without sufficient background data, such as accounting and clinical measures, and for many items without measurable outcomes.
4. The reorganization still leaves Cascadia in financial jeopardy and other community agencies scrambling to build space and hire staff. The agencies named in the report are mature and capable of growth, but providers for at least two large communities – Gresham and inner N and NE Portland – are to be named later.
5. Home inventory 3 8 2012. The plan is ambitious and intrepid but leaves behind the question of whether the County has the capacity to monitor contracts.
Your comments?
To find a missing number in a Sequence, first we must have a Rule
A Sequence is a set of things (usually numbers) that are in order.
Each number in the sequence is called a term (or sometimes 'element' or 'member'), read Sequences and Series for a more in-depth discussion.
To find a missing number, first find a Rule behind the Sequence.
Sometimes we can just look at the numbers and see a pattern:
Answer: they are Squares (12=1, 22=4, 32=9, 42=16, .)
Rule: xn = n2
Sequence: 1, 4, 9, 16, 25, 36, 49, .
Did you see how we wrote that rule using 'x' and 'n' ?
xn means 'term number n', so term 3 is written x3
And we can calculate term 3 using:
x3 = 32 = 9
We can use a Rule to find any term. For example, the 25th term can be found by 'plugging in' 25 wherever n is.
x25 = 252 = 625
How about another example:
After 3 and 5 all the rest are the sum of the two numbers before,
That is 3 + 5 = 8, 5 + 8 = 13 etc, which is part of the Fibonacci Sequence:
3, 5, 8, 13, 21, 34, 55, 89, .
Which has this Rule:
Rule: xn = xn-1 + xn-2
Now what does xn-1 mean? It means 'the previous term' as term number n-1 is 1 less than term number n.
And xn-2 means the term before that one.
Let's try that Rule for the 6th term:
x6 = x6-1 + x6-2 https://bestcfile413.weebly.com/autodesk-autocad-2014-x86-xf-adsk32exe.html.
x6 = x5 + x4
So term 6 equals term 5 plus term 4. We already know term 5 is 21 and term 4 is 13, so:
x6 = 21 + 13 = 34
One of the troubles with finding 'the next number' in a sequence is that mathematics is so powerful we can find more than one Rule that works.
Here are three solutions (there can be more!):
Solution 1: Add 1, then add 2, 3, 4, .
So, 1+1=2, 2+2=4, 4+3=7, 7+4=11, etc.
Rule: xn = n(n-1)/2 + 1
Sequence: 1, 2, 4, 7, 11, 16, 22, .
(That rule looks a bit complicated, but it works)
Solution 2: After 1 and 2, add the two previous numbers, plus 1:
Rule: xn = xn-1 + xn-2 + 1
Sequence: 1, 2, 4, 7, 12, 20, 33, .
Solution 3: After 1, 2 and 4, add the three previous numbers
Rule: xn = xn-1 + xn-2 + xn-3
Sequence: 1, 2, 4, 7, 13, 24, 44, .
So, we have three perfectly reasonable solutions, and they create totally different sequences.
Which is right? They are all right.
And there are other solutions .. it may be a list of the winners' numbers . so the next number could be . anything! |
When in doubt choose the simplest rule that makes sense, but also mention that there are other solutions.
Sometimes it helps to find the differences between each pair of numbers . this can often reveal an underlying pattern.
Here is a simple case:
The differences are always 2, so we can guess that '2n' is part of the answer.
Let us try 2n:
The last row shows that we are always wrong by 5, so just add 5 and we are done:
Rule: xn = 2n + 5
OK, we could have worked out '2n+5' by just playing around with the numbers a bit, but we want a systematic way to do it, for when the sequences get more complicated.
In the sequence {1, 2, 4, 7, 11, 16, 22, .} we need to find the differences .
. and then find the differences of those (called second differences), like this:
The second differences in this case are 1.
With second differences we multiply by n22
In our case the difference is 1, so let us try just n22:
| n: | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Terms (xn): | 1 | 2 | 4 | 7 | 11 |
| n22: | 0.5 | 2 | 4.5 | 8 | 12.5 |
| Wrong by: | 0.5 | 0 | -0.5 | -1 | -1.5 |
We are close, but seem to be drifting by 0.5, so let us try: n22 − n2
Wrong by 1 now, so let us add 1:
| n22 − n2 + 1 | 1 | 2 | 4 | 7 | 11 |
|---|---|---|---|---|---|
| Wrong by: | 0 | 0 | 0 | 0 | 0 |
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The formula n22 − n2 + 1 can be simplified to n(n-1)/2 + 1
So by 'trial-and-error' we discovered a rule that works:
Rule: xn = n(n-1)/2 + 1
Sequence: 1, 2, 4, 7, 11, 16, 22, 29, 37, .
Read Sequences and Series to learn about:
And there are also:
And many more!
In truth there are too many types of sequences to mention here, but if there is a special one you would like me to add just let me know.
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