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Sorry about mixing languages, but it makes finding jingles easier.
so x | y means y mod x = 0 , Thanks.
Draw the slanted square (rhombus), draw the diagonals so now you have a
picture of kite without the tail flying in the wind.
Notice the right triangles.
Assign values like x and x-2 and 10 and apply pythagoreans theorm
Then solve the quadratic equation using quadratic formula if it's hard.
Then the area is four right triangles, or two rectangles, if you pair up
the right triangles by sliding them all around.
Well a rhombus has all four sides the same length and is a special parallelogram,
so all sides are 10. Hope that helps you.
1.65 is the number looked up for 45.05%
Use 45.05%, not 44.95% in the table because you want to be on the
safe side, less than 5% break.
So 8 - 2*1.65 = 4.7 years.
So the guarantee should go for 4.7 years for under 5% of customers having breakdowns. But really remember, some will be replaced twice or more, so
the company loses out unless they say you only get one replacement, which is
a really bad idea. So if this was a real company, you would have to lower the
number even more, and offer a three year warranty, or do more math to
figure it out somehow. Good Luck to you, deepu4.
So anyway, you have to lookup .45 for the area in the table to get x/stdDEV,
this is because you should only be guaranteeing for a few years on the left side
of the bell curve until an area of 5% is reached of kaputs (brokens).
So lookup 45%, which is the area from mean to one side of interest.
Then multiply that value by 2 years to get the time prior to year 8.
So 8 - (2*number looked up) should be the guarantee, but the company will
really replace more because the some replacements are recursive (they happen two or more times within the warranty)
He's not really an idiot, but he shouldn't have called it a normal curve if it wasn't one. He/she should have said it only approximates a normal curve.
Anyway, at 4 stdDEVs before eight years, the motor was made, at time = zero.
At this point, (1 - 0.9999366) / 2 of the motors are already broken.
So tell your teacher that 0.00317% of the motors broke prior to being built!!!
As for the actual question at hand. At 8 years, half of the motors are kaput (broke),
but don't forget that if the manufacturer replaces a motor once, he still has to
replace the motor AGAIN, if it breaksdown a second time!!!! So this problem is
again really more complicated than the teacher is probably concerned with.
Okay, let's backup a little. I made a tiny mistake on the lookup table.
The reason requires you to visualize the normal curve on a time line.
And the time line goes from zero to infinite years, NOT NEGATIVE
INFINITY TO POSITIVE INFINITY years. So this first proves that this problem
is not totally valid in the first place. You can tell your professor that a small
percentage of the motors will breakdown before they were actually built!!!!!!
This is because the normal curve is symmetrical in both directions from the
8th year. So whoever made up the problem was an idiot!
Or it is just an approximation, in which case I will proceed, since the small
amount of the curve that goes in negative time is small enough to ignore, and
we should calculate that too, so we can tell the teacher about it.
The reason I didn't integrate the curve is because I read about trying to integrate a Gaussian curve, and it is really hard to do. There are various approximations.
Okay, I've got part of it. 1.96 is x/stdDev because you look it up in a table under the area of .475 because .475 is 2.5% less than 50% and therefore on both sides of the normal curve, you get 95% acceptable, twice as much as 47.5%.
So 1.96 is what the table says is x/stdDev so that only 5% will fail.
Next we have to learn what normal distribution is. I've used the bell shaped curve many years ago, but I'll do some reading and get back...
Let's first do an example comparing JohnsDeviation to Standard Deviation.
Two data points are given, 10 and 20.
JohnDeviation would be 5 because ((15-10) + (20-15))/2 = 5
StandardDeviation would be sqrt( ((15-10)^2+(15-20)^2) / 2 ) ,
which is also 5.
Now let's do another example.
One data point, the number 50. The deviation is zero for both ways I think.
Now another example.
Three data points: 20, 24, 28.
JohnDeviation is (4 + 4 + 0)/3 = 8/3, or 2.66666666
StandardDeviation is sqrt( (4^2 + 4^2 + 0^2)/3 ), or 3.265986324
Now let's do another example:
Five data points: 9, 19,19,19,19
JohnsDeviation = ((17 - 9)+(19-17)*4)/5, or 3.2
StandardDeviation is sqrt( (4*((19-17)^2) + (9-17)^2 )/5 ), or 4.
Interesting, huh?
Okay, you've convinced me to restudy a little statistics.
I never liked the way they squared the differences from the mean in the standard deviation. I personally would have just taken the absolute value. Why not take absolute value and put to the power of 1.95, you know, it's just all man-made.
But I'll look into this...
krassi, It appears you've been learning a lot of new stuff lately.
That's terrific.
What does the "|" symbol mean in above work?
Thanks for the info, ryos, and Boy, this chemistry reading is really fascinating.
And difficult.
And this is fun to read... http://www.shu.ac.uk/schools/sci/chem/t … c/nmr1.htm
I found this, but wish it explained more.
http://www.wfu.edu/~ylwong/chem/nmr/h1/splitting.html
What is vicinal hydrogens?? Is it in close proximity to each other??
I really enjoyed MIF's pages on Pascal's triangle! My favorite part was the picture of the marbles in a tetrahedron. Wonderful implications, how the diagonal rows are possibly for each successive dimension that we cannot visualize in our 3-D world, at least that's what we can see with our eyes.
Diagonal rows:
1. all ones (0-D ?)
2. 1-D (counting numbers along a line)
3. 2-D triangle (like bowling pins)
4. 3-D triangle (like the marbles MIF has depicted)
5. 4-D triangle I am guessing, how could we prove this?????
On the web page krassi h. pointed out, their is a mistake in the diagram of pascal's triangle. The 186 in the bottom row should be a 286 I think.
Nice equations, irspow, but just one typo I think, the 2297.9 should be 2298.4 perhaps.
Here is a fun one.
To go from °F to °C or
to go from °C to °F, either way
you Add 40 first, then do the 9 5 thing and then subtract 40 when done.
So you always add first and subtract last, if you use the 40 method,
regardless if you are going from celsius to Farenheit or backwards.
Here's another one.
In this one you subtract before and after from °F to °C
and you add before and after for the °C to °F.
The number you add or subtract is 11 3/7.
The reason is because 11 3/7 °F equals -11 3/7 °C.
Pretty fun! huh?!
My Dad hates math, but he asked what is Kelvin.
So I got into a conversation about all three systems,
and how centigrade (celsius) has degrees the same
size as Kelvin except Kelvin starts way down 273.16 degrees
lower at the coldest possible temperature. And I told him
that Farenheit degrees are smaller than Celsius degrees and
gave him some examples.
He said there are formulas for the conversion, right?
And I said, yes, they involve the numbers 5, 9, and 32,
and told him I just figure it out each time I convert.
Then I got to thinking. You could use the numbers 5, 9
and 17 and 7/9ths just as well since 0°F is -17.7777°C.
And then I thought, why not go from any number at all
and just compute the difference from that point in both
systems. So another good one to figure the distance
from is -40°F, which is also -40°C.
Dual Polyhedra. I wondered what it would be called. I bet there aren't triple polyhedra! Maybe if you deal with unsymmetrical things like the continents on the Earth and draw a dot in middle of each and connect... I think that would just be a jumbled mess, I'm not sure. I suppose a 3-D computer program could do the process of finding the next shape and displaying it. Doesn't a golf ball have 236 indents? I thought that was a Trivial Pursuit question, but it was a long time ago, so I might have the # wrong.
Tree cat snooze, three quatre douze 3x4
See me sign, three three nine (sign language) 3x3
Shine, shine, hazy sun, nine nines eighty-one 9x9
Straight line, lengthy too, eight nines seventy-two 8x9
Meat boeuf croissant booze, huit neuf soixante-douze 8x9
Skate, skate, slippery floor, eight eight sixty-four 8x8
Fête wine croissant boire, sept nine soixante-troi 7x9
Wet feet, wake aunt niece, sept huit, cinquante-six 7x8
Seventh Heaven, storytime, seven sevens forty-nine. 7x7
Je drank tea deux cinq dix 2x5