Joe is considering two jobs. One pays 50k/yr and one pays 60k/yr. What’s the difference between them?
PS lol:
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I finished the class with an A. Ended with a 90.55.
Nearly had a heart attack when the website froze on me for my final exam. Luckily I was allowed/able to refresh it with no consequences.
There’s a difference of 10k.
Do you want me to answer this one too?
I assume so. I will do it in a bit.
Confused with “Count of integers from A to C”. Is it asking how many integers are between A and C?
Count starting at A and ending on C
The English word difference means ways things are dissimilar or unlike. It’s ways stuff isn’t the same. Like two cars could be the same color but have different top speeds.
The standard English concept of things being different can be calculated, mathematically, using subtraction (and absolute value – differences in English are usually done as non-negative numbers), when it’s a numerical difference in a single dimension.
Does that make sense?
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I think so.
Difference is how some things are different, unlike, or dissimilar. Two cars could be similar by their color but different by how fast they go.
You said:
That makes sense. 10 and 5 are different by 5.
Difference between A and C? B
Distance between A and C? B
Count of integers from A to C? B+1? I think this is related to what we’ve been talking about. And the integers from 2 to 5. Are 2, 3, 4, and 5.
From C to A? B + 1
From 0 to C? C + 1
From 0 to A? A + 1
Start at A, subtract B, how much do you have left? C
You have rocks numbered with every integer from 0 to A and you have one of each rock. How many rocks do you have? You would have A + 1 rocks. Since it starts from 0, if A was 1, Then you would have 1 + 1 rocks. If you A was 2. You would rocks 0, 1, and 2.
You subtract B rocks and remove the highest numbered rocks. How many rocks do you have now? Well you had A + 1 rocks. You removed B rocks. So you have (A+1) - B rocks left.
What are the highest and lowest numbered rocks you have now? Highest - A -B. Should I call this C? If so C. Lowest numbered rock would be 0.
What are the highest and lowest numbered rocks that you subtracted? I’m a bit confused what this is asking. The highest and lowest numbered rocks that I subtracted? Like, removed? I only removed B rocks. Oh I see. I removed rocks. The highest rock I removed was A. The lowest rock I removed? It would be A - B + 1.
What common mathematical concept, related to number lines, are these rocks equivalent to? Integers?
I have to go to work but I can mark my answers on the diagram when I come back. Figured I’d still post it now.
Why do you have a question mark after B+1? Are you unsure how to count? Or do you know the answer for counting from 1 to 13 or 25 to 27 but you’re unsure if the formula holds for all counting?
Can you simplify that to use fewer variables?
The rocks are the integer points on the number line.
For integers:
Count and distance are apart by 1.
After subtracting, if you think in terms of number line points or rocks, highest remaining number and lowest removed number are apart by 1 (C and C+1).
When you start counting from 1, the adjustment of 1 is hidden because starting at 1 cancels it out. Counting from A to B is B-A+1 integers. When A is 1, you get B-1+1 which just simplifies to B which is how people are used to doing counting.
Clear? Can you now answer why there is a +1 in the permutations formula?
Earlier for permutations you were trying to figure out what the lowest factor should be when multiplying e.g. 20*19*18 etc and wanting e.g. 7 factors. Do you see which question from the diagram worksheet this is equivalent to?
I was initially unsure. I think I could’ve made it clearer that I was sure afterwards. It wasn’t because of counting. It was because the answer looked similar to what we’re talking about that made unsure for a second.
Is this rock problem separate from the number line problem? If not, I think C + 1 could work.
If it is separate: you have A+1 rocks and you removed B rocks. Idk how to simplify it more.
Ah ok. Thats what I was kinda thinking. Mmm. Does 0 being counted have anything to do with this? 0 to A is A + 1 rocks. 1 to A is just A rocks.
6- 4 = 2
We removed 6, the remaining number is 2, the lowest removed number is 3. 2 is remaining, 3 is the lowest removed ok.
1 to 5. 5 numbers. 1 2 3 4 5.
So is counting from 1 kind of like doing +1 to the number line, shifting it right?
Oh. I see. B-A + 1. If A is 1m then B-1+1. Which is just B.
I think so. Something just came up. I will respond to these hopefully in a couple hours or so.
Mmm. It’s because we start counting up to k factors starting from 1 not 0. You make the adjustment with +1.
Mmm. I’m a bit unsure if I’m actually understanding versus just repeating stuff.
I think so. So to find the the 7th factor it would’ve been something like 20-7+1 = 14. “What are the highest and lowest numbered rocks that you subtracted?” We would of had 21 rocks. We took away 7 rocks. We took away 20, 19, 18, 17, 16, 15, 14. The lowest numbered rock we would have subtracted in this case is 14.
I tried to mark the stuff on the diagram and got a bit confused:
Those three I could mark. I didn’t know how to mark the count of integers. And for the rock questions is it possible to mark on the diagram as is or would I need to mark points on the number line and stuff.
That doesn’t sound to me like you understand it. One issue is, in the formula, we’re counting down.
you can add marks on the diagram.
i don’t care if it’s messy but i think you should be able to take each of the things and understand a way to draw it out.
yes. so do you now understand why the formula has a +1?