If Lawrence walked 4.0 kilometers at 3.0 kilometers per hour, how long was Lawrence walking? Answer:

A variable is a quantity that has a changing value; the value can vary from one example to the next. A continuous variable is a variable that has an infinite number of possible values. In other words, any value is possible for the variable.
A continuous variable is the opposite of a discrete variable, which can only take on a certain number of values.
Time it takes a computer to complete a task. You might think you can count it, but time is often rounded up to convenient intervals, like seconds or milliseconds. Time is actually a continuum: it could take 1.3 seconds or it could take 1.333333333333333… seconds.
A person’s weight. Someone could weigh 180 pounds, they could weigh 180.10 pounds or they could weigh 180.1110 pounds. The number of possibilities for weight are limitless.
Age. So, you’re 25 years-old. Are you sure? How about 25 years, 19 days and a millisecond or two? Like time, age can take on an infinite number of possibilities and so it’s a continuous variable.
Heights and weights are both examples of quantities that are continuous variables.
Next: Discrete vs continuous variables.
← What is a Discrete Variable in Statistics?

; Load up a color scheme which has a dark (black) background.
; measurements). Try to keep an aspect ratio of 1.333333 if at all possible.
; These numbers are NOT the true size of the window, but of the drawing area.

Man Climbs Ten Colorado 14ers in One Day – How is That Possible?
Here's to you, Josh Sanders. He just set the world record by climbing ten Colorado 14ers in one day. Not only is it a world record, it seems to be something of a miracle.
How did he pull this off? Well, he started at the stroke of midnight and then proceeded to hike continuously for the next 23 hours and 33 minutes. How far did he ultimately walk? Only 45 miles.
I'm wondering how this is possible. I'm certainly not disputing it happened. It simply seems impossible. Please consider the following.
According to Reference.com, the average human walking speed is 3.1 miles per hour. Per my math, Josh would have had to have maintained a constant speed of at least 1.9 miles per hour to complete his task. These are 14ers we're talking about. He wasn't walking some lovely trail along a creek, or power walking at the mall.
When I climb Mt. Garfield, I average about one-and-a-half hours. That's a two-mile walk ascending 2,000 feet. That's only 1.33333333 miles per hour. Let me assure you, I can only make this walk once a day. After that, it's off to Denny's and then nappy time. There's no way I'm doing that for 24 hours straight.
Did he ever get bummed during the ordeal? At one point he encountered a false summit, and it gave him a case of the blues. According to 9News.com, Josh said, "I was tired from 21 and a half hours just consistent movement through the mountains, up the passes, up the ridges, and really, there was a moment when I was traversing the saddle and thought I had gotten to the summit of Oxford, but once I got up - realized it was a false summit and I saw it looming seemingly a half mile in the distance that was probably the lowest point."
Getting burned by a false summit is really a drag. In any event, he made it and set the record with a handful of minutes to spare.

Convert 176 Minutes to Hours (min to h) with our conversion calculator and conversion tables. To convert 176 min to h use direct conversion formula below.
176 min = 2.9333333333333 h.
You also can convert 176 Minutes to other Time (popular) units.

Calculating the square footage of an area using imperial measurements.
6.4 * 4 = 25.6 sq. feet 25' 6 1/8"
Perfectly acceptable for most of your calculated needs but is it right?
In reality you should not be able to accurately multiply inches by feet on your regular calculator without converting the feet to inches. Now that should work right?
76" * 48" = 3648 sq. inches * 0.00694444 (converting sq. inch to sq. ft.) = 25.333 = 25' 4"
How about converting the foot and inch value to decimal format. Is that the way to go?
6.33333333 * 4.0 = 25.333 = 25' 4"
And this works too in fewer steps than converting to inches and back to feet.

As he reminded me with a wall post earlier, Jacob and I have been dating for 1.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333 months now, intense huh? I told him that I wasn’t counting our positive anniversaries so much as our negative ones. It’s funny how important our anniversaries were about 4-8 mo. Then we got engaged and there were more days to celebrate but the only one that “really” matters (at least monthly) is that day coming up in January 😀 And that one is less than 3 months away, yay!

- So that motor [Z-Axis] is a 7.5°, 48 step motor as I just listed. Since the motor is attached to a M4 rod, which has a 0.7 mm thread pitch, then in one revolution makes the Z-Axis travel up or down 0.7 mm. Since it took 48 steps to turn that rev, each step is 0.00145833333333333333333333333333 etc etc mm. To avoid rounding errors, you can use multiple of 3 of this number, which is a nice and pretty 0.04375 mm. That is a nice and handy number that effectively represents the layer heights that mathematically work the best for layer heights for this printer. + So that motor [Z-Axis] is a 7.5°, 48 step motor as I just listed. Since the motor is attached to a M4 rod, which has a 0.7 mm thread pitch, then in one revolution makes the Z-Axis travel up or down 0.7 mm. Since it took 48 steps to turn that rev, each step is 0.0145833333333333333333333333333 etc etc mm. To avoid rounding errors, you can use multiple of 3 of this number, which is a nice and pretty 0.04375 mm. That is a nice and handy number that effectively represents the layer heights that mathematically work the best for layer heights for this printer.

Re: How Fast can we count to a million?
Re: How Fast can we count to a million?
Re: How Fast can we count to a million?
Re: How Fast can we count to a million?
Re: How Fast can we count to a million?
Re: How Fast can we count to a million?
Since this thread now gets around 1 post a month, it will take us approximately 83333.3333333 years to count to a million from scratch.
I wonder who the lucky person will be who gets to post 4444.
Re: How Fast can we count to a million?

I know I should be happy that we are making progress. But it's not enough. Only doing 1% a month means it'll take 100 months and that's 8.33333 years. And that is far from my goal of 3 years.
Travel Budget is building but will be partial spent next month. But I am feeling good with our progress. Which is that we are making progress. I just want to be so much further ahead than we are.
There is a "Marvelous French Macarons" cooking class available this month. But it's $69.00 and I just don't know if I can justify the cost. It's also 9am on a Saturday... and I don't like getting out of bed before 11.
I've got decisions to make.

An inch (in) is a unit of length used in the English system of measurement.
One (1) inch is equal to 0.0833 feet.
One (1) inch is equal to 2.54 centimeters (cm).
One (1) inch is equal to 0.1262 links.
One (1) inch is equal to 0.0278 yards.
One (1) inch is equal to 0.0051 rods, poles, or perches.
One (1) inch is equal to 0.0013 chains.
One (1) inch is equal to 0.00013 furlongs.
One (1) inch is equal to 0.00002 miles.
One (1) inch is equal to 0.0254 meter (m).
One (1) inch is equal to 0.00003 kilometers (km).
For conversion examples, see the various Converting inches to... entries.

I’ve been trying to figure out how to enter in all information manually for my receipt. Such as I have an hourly rate but did not track the hours but agreed on the price.
The way its its set up I can only enter the price per item and the amount. Say someone paid me $175 for personal training. Such as 2 hours of work and gave them a little extra time for training but we both agree he will pay me $175 for me to stay for the remainder of his workout. The only way for me to charge the $25 is to enter a decimal value of the item by dividing 25 by my hourly rate so my number entered would have to be 2.333 hours in order for my total to display $175.
or if I discount an item or give someone a good deal by paying for credit hours that they can use in the future i would have to enter a new item for every single transaction and divide the remainder by my hourly rate every receipt.
You can create a service item for your hourly rate and create a different one for the excess time.
Click Sales on the left pane.
Click New and select Service.
Enter the Service item name and rate.
The next time you create a sales receipt, you can enter the quantity of each item.
Select Sales on the left pane.
You can also create a credit memo for your customer to use in the future. Check this article: Enter and apply a credit memo or delayed credit.
But it doesn’t enable me to enter a total number Calculate the amount of hours for me? Instead of me fill in the hours and it calculates the total.
The only way I can get the iOS app to enter information is by me putting a quantity of hours into the item portion. I want to be able to pick my hourly rate (65) as an item. I charged someone 200. Without using a calculator it’s going to be difficult to calculate for each specific total that I have . I attatched an image of the quantity of hours I’d need to enter for A 200 bill at 65 an hour so hopefully you can understand what I’m saying.
Thanks for getting back to us, TFarrz.
The ability to calculate the total number of hours is unavailable in the App. You'll need to enter it manually. I will share this feedback to our product development team, so they can consider this concern in their future updates.
Let me know if you have other questions. I'm always here to help.

Right now, Dr. Johnson is three times older than his son.
When Dr. Johnson was 37 years old, his son was 3 years old.
How old are Dr. Johnson and his son now?
Answer: Dr. Johnson is 51 and his son is 17 years old.
Assume that Dr. Johnson is X years old and his son is Y years old.
Then 3Y = X, and X – Y = 34.
Solving for X and Y, we get X = 51 and Y = 17.

Pond calculator - Buy pond equipment from Pondkeeper: fishing out the best deals on the net.
If your measurements are in feet and inches, converting it is easy.
1 foot = 0.3 metres, so just multiply your measurement in feet by 0.3 to get the value in metres. For example 2 feet = 2 × 0.3 = 0.6 metres.
Learn the easy way to calculate it.
The accompanying diagram shows a pond with a maximum length of 5 metres and a maximum width of 4 metres. The final measurement you will need is the maximum depth of your pond, the diagram to the right shows a maximum pond depth of 1 metre.

How tall are you? 5 feet and 8.333 inches (177.8 cm) or less or 5 feet and 8.34 inches (177.9 cm) or more?
177.8cm for males? It would be way too high if we count in females too.
I dont think thats accurate. For males its about 175-180cm, and 160-165cm for females. And dont forget 60% of people are asian and they are shorter than whites.
5'3... One day I'll be taller..... One day.

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Unicum is a Hungarian herbal bitters, drunk as a digestif and apéritif. The liqueur is today produced by Zwack according to a secret formula of more than forty herbs, and the drink is aged in oak casks. During the Communist regime in Hungary, the Zwack family lived in exile in New York and Chicago, and Unicum in Hungary was produced using a different formula.
Left: A frosty bottle of Unicum.
After the fall of communism, Péter Zwack returned to Hungary and resumed the production of the original Unicum. Recently Zwack has also launched Unicum Next, a thinner-bodied drink with a more prominent citrus flavour.
Unicum is regarded as one of the national drinks of Hungary. The production facility offers tours which include a tasting session of the three different varieties (Unicum, Unicum Next, and Millenicum). Though Millenicum was a special edition, it can still be found at a few retailers. It is a little stronger than the standard, with a slightly sweeter aftertaste. Zwack Frissitők is a pineapple-based version of the drink. Unicum is available through select spirits distributors throughout the United States, as is Unicum Next, re-branded as "Zwack".

The area of a rectangle is represented by x^2+5x-14.
If the volume of a cube is 216 cubic meters, what is the length (in meters) of each side?
If the volume of a cube is 216 cubic meters, what is the length (in meters) of each side?
If the area of a room is 640 square feet, and its length is 40 feet, what is its width in feet?
Which expression represents the area of the base of the prism?
how many feet are in 34oo sq ft?
how many feet in 1 acre?
how many square feet are in 140 linear feet?
5 rows of wood 4' high, 6' wide and 8' long is how many cubic feet?
what is the area of 2 times 8?
how many acres is 218,300 sq ft?
Willa enclosed her patio with 40 m of fence. What are the length and width of her patio?
1 sq ft = how many meters?
Why is the area of the square larger than the area of the rectangle when perimeter is same?
1 Acre= 4840 sq. yards. Area of rectangular land is 242 feet by 360 feet, how many acres are there?
If the length is 8 feet, perimeter is 24 feet, what is the width and area?
if the area of a rectangle is 3x^2+9x, what is the length if the width is 3x?
how many different rectangles can I make from 36 square tiles?

Problem 1: Do you see a pattern in each table below? Use mental arithmetic to find each quotient, then mouse over the red text.
Explanation: The patterns in the tables above were created by multiplying the divisor and the dividend by the same power of 10. In each pattern, the quotient remains the same. Thus, multiplying both the divisor and dividend by the same power of 10 maintains the equality of the expression.
Problem 2: Continue each pattern below by multiplying the divisor and the dividend by 10 until the divisor is a whole number. Then find each quotient.
Let's compare Problems 1 and 2 above. In both problems, the quotients remain the same even though the divisors and dividends are multiplied by powers of 10. However, the divisors in Problem 1 are whole numbers; whereas the divisors in Problem 2 are decimals. Let's look at some examples of dividing by a decimal divisor.
Analysis: The divisor is 0.8. To make it a whole number, we will multiply both the dividend and the divisor by 10.
Multiply the divisor by a power of 10 to make it a whole number. Multiply the dividend by the same power of 10. Place the decimal point in the quotient. Divide the dividend by the whole-number divisor to find the quotient.
Answer: The quotient of 9.6 and 0.8 is 12.
Thus, the quotient of 9.6 and 0.8 and the quotient of 96 and 8 are both 12. Let's look at another example.
Analysis: The divisor is 0.35. To make it a whole number, we will multiply both the dividend and the divisor by 100.
Multiply the divisor by a power of 10 to make it a whole number. Multiply the dividend by the same power of 10. Place the decimal point in the quotient. Divide the dividend by the whole-number divisor to find the quotient.
Note that in Example 1, the quotient is a whole number (12), and in Example 2, the quotient is a decimal (39.8).
Analysis: The divisor is 0.009. To make it a whole number, we will multiply both the dividend and the divisor by 1,000.
Multiply the divisor by a power of 10 to make it a whole number. Multiply the dividend by the same power of 10. Place the decimal point in the quotient. Divide the dividend by the whole-number divisor to find the quotient.
Answer: The quotient of 5.4 and 0.009 is 600.
Analysis: The divisor is 3.06. To make it a whole number, we will multiply both the dividend and the divisor by 100. After dividing, we will round the quotient to the nearest tenth.
Multiply the divisor by a power of 10 to make it a whole number. Multiply the dividend by the same power of 10. Place the decimal point in the quotient. Divide the dividend by the whole-number divisor to find the quotient.
Answer: Rounded to the nearest tenth, the quotient of 201.4 and 3.06 is 65.8.
Analysis: The divisor is 5.3. To make it a whole number, we will multiply both the dividend and the divisor by 10. After dividing, we will round the quotient to the nearest cent (hundredth).
Multiply the divisor by a power of 10 to make it a whole number. Multiply the dividend by the same power of 10. Place the decimal point in the quotient. Divide the dividend by the whole-number divisor to find the quotient.
Answer: Rounded to the nearest cent, the quotient of $9 and 5.3 is $1.70.
Example 6: A retailer has 802.7 units of goods to sell. If one shipping box only holds 0.875 units, then how many customers can she ship her goods to? Round your quotient to the nearest whole number.
Answer: Rounded to the nearest whole number, the retailer can ship her goods to 917 customers.
Multiply the divisor by a power of 10 to make it a whole number.
Multiply the dividend by the same power of 10. Place the decimal point in the quotient.
Divide the dividend by the whole-number divisor to find the quotient.
5. If 5.2 pounds of nails cost $16.96, then how much would 1 pound cost? Round your answer to the nearest cent.


You have 7.0 balloons, and your friend has 5.0 balloons. How many more  balloons do you have than your friend? Answer:

Out of sixty students, there are 14 who are taking Economics and 29 who are taking Calculus. What is the probability that a randomly chosen student from this group is taking only the Calculus class ?
Out of sixty students, there are 14 who are taking Economics and 29 who are taking Calculus. What is the probability that a randomly chosen student from this group is taking only the Calculus class ?
Answer : 2 7/15 Explanation : Answer: B) 7/15 Explanation: Given total students in the class = 60Students who are taking Economics = 24 andStudents who are taking Calculus = 32Students who are taking both subjects = 60-(24 32) = 60 - 56 = 4Students who are taking calculus only = 32 - 4 = 28probability that a randomly chosen student from this group is taking only the Calculus class = 28/60 = 7/15.

The More You Have, The Less You See. What is it?
The More You Have, The Less You See. What is it?
Answer : 2 Darkness Explanation : Answer: B) Darkness Explanation: The More You Have the Darkness, The Less You See i.e, visible less.

Some children goto ice-cream shop. 9 flavours are available there. Each child takes a cone with two different flavours. No two children take same combination and they have taken all such possible combinations. How many children went to ice cream shop ?
Some children goto ice-cream shop. 9 flavours are available there. Each child takes a cone with two different flavours. No two children take same combination and they have taken all such possible combinations. How many children went to ice cream shop ?
Answer : 4 36 Explanation : Answer: D) 36 Explanation: Given there are 9 flavours of ice creams. Each child takes the combination of two flavours and no two children will have the same combination This can be done by ways i.e children. Number of children=C29 = 9 x 8 / 1x 2 = 36.

These are the best and most fun math riddles we can find. All of these tricky riddles are based on real math concepts and can be solved with purely math and logic.
Question: There are 6 sisters. Each sister has 1 brother. How many brothers are in the sisters' family?
Answer: 1 brother. If there was 6 brothers, each sister would have 6 brothers.

What are people dying from?
Answer: well, people die from many things!
Are to many people dying now?
Why do people lie about dying when there really not?
Answer: It is unfortunate that people would do this but for some reasons they have of their own they do. Attention, lonliness, jealousy and possibly even control issues over the individual(s) the person have told.
What is the main cause of people dying in the us?
Answer: The main cause of people dying in the US as well as in the world is their heart stops circulating blood to the brain which deprives it of oxygen and thus all activity in the body ceases and the person dies. The causes of the heart ceasing to beat are to numerous to count. The ultimate cause of death is as stated.
Why do dying people see things that are not there?
Answer: they want to see all the important moments and memories in their lives.
Why are so many people in your family dying lately?
Answer: So many people are dying lately because many health problems arepresenting themselves. Health is not what it used to be.
Do people throw up when dying?
Answer: Some people will throw up when they are dying. This just depends onhow their body handles the process of passing away.
What do people experience before dying?
Answer: People experience denial, anger, bargaining, depression, then acceptance before dying. Death is change. Anyone making any kind of change will go through these stages. The time it takes is subjective. The more aware we become, the better we will be able to handle this process. Death can be a beautiful experience or a horrible one depending on our intention. The earlier we can learn to embrace change, the better prepared we will be for an eventual wihdrawal from the physical. At the last moment you can call out to someone you know who has preceded you and they will be there to aid you in the beginning of the assimilation process, the process of assessing the progress of this lifetime in addition to all the rest of them in preparation for the next time around. Most of us have a long way to go. The good news is that the learnig potential is speeding up so anyone at this present time can speed up their own evolution through study and practice.
What diseases were the people in the Crimean war dying from?
Answer: lots of things really!!
The rating of people dying from salmonella?
Answer: Statistics show about 1,000 per year.
Why do dying people call out the name of the living?
Does anyone experience the spirit of dying people?
Answer: some do but most do not.
Answer: Whether to keep a dying person on life support is a personal orfamily decision. If the person is suffering it might not be fair tokeep them on life support.
How many people are dying in the world daily?
Answer: a lot thats for sure.
What is the percentage of people dying from strokes?
10 percent of stroke victims require care in a nursing home or other long-term care facility.
15 percent die shortly after the stroke.
While subarachnoid hemorrhage (SAH) represents only about 7 percent of all strokes, it is the most deadly - with more than a 50 percent fatality rate. Of the survivors, approximately half will suffer permanent disability.
What is the percentage of people dying from strokes?
Answer: 10 percent of stroke victims recover almost completely.
10 percent of stroke victims require care in a nursing home or other long-term care facility.
15 percent die shortly after the stroke.
While subarachnoid hemorrhage (SAH) represents only about 7 percent of all strokes, it is the most deadly - with more than a 50 percent fatality rate. Of the survivors, approximately half will suffer permanent disability.
What is the percentage of people dying from Anorexia?
Answer: Roughly 10% of all anorexics will die directly as a result of the disorder, or directly from a Sid effect from the disorder.
How long does dying one live with cheyne strokes breathing?
Answer: Cheyne stoking, sadly, happens just before death. It can last minutes or hours; every person is different. By the time cheyne stoking is apparent, in my opinion, the person is no longer aware of their surroundings.
What percentage of cardiovascular disease and strokes are preventable?
Is it true dying people wait for loved ones to leave the room before dying?
Answer: No, they wait for their loved ones to arrive.
Actually it is extremely common for a dying person to wait until the loved one leaves the room. A loved one may hold vigil for days, step out of the room for just a moment, and that is when the dying person passes.
It is supposedly to protect the loved one from letting them see when they take their last breath.
Why do people have strokes?
Answer: Why do people have strokes?
Why do people get strokes?
Answer: People have a stroke when a blood clot forms in an artery. When theblood clot travels to your brain, that is when you have a stroke.
Why do people suffer strokes?
Answer: Stroke is a medical condition where part of the brain dies as aresult from a blood clot. The blod clot blocks the flow of blood tothe part, depriving that part of the brain with oxygen andnutrients. As such, paralysis of body parts which that part of thebrain controls, ensues.
Why are strokes important to people?
Answer: Strokes can lead to cognitive (brain) and physical damage, from mild to severe implications. In severe stroke, a person can be left without the capacity to think, feel, and move their body.
At what age do people commonly get strokes?
Answer: Stroke happens due to injury in head which causes some part or function of your brain inactive or half dead because cells get dead which may cause stammering or inability to move etc effecting some particular part of your body or you may experience seizures, it varies it can happen at any age.
What kills more people each year than heat strokes?
Answer: Breast cancer kills more women than heart disease.
What is the percentage of a spouse dying after another spouse dies?
Answer: to help prepare you for whats to come, and to encourage you to change the things that you can.
How do people try to get up when they are dying?

How many white dots should there be on the wings of the last ladybug?
Answer:Three. The difference between the number of black and white dots is always two. The last ladybug should have three white dots.

We start with six boxes. We divide these six boxes by three. This means: how many groups of three can we make with the six boxes that we have? Answer: 2.
We start with eighteen boxes. We divide these eighteen boxes by three. This means: how many groups of three can we make with the eighteen boxes that we have? Answer: 6.
We start with thirty-six boxes. We divide these thirty-six boxes by three. This means: how many groups of three can we make with the thirty-six boxes that we have? Answer: 12.

Question: You are trapped in a haunted house. There are three ways out. The first way you will fall in a pit. The next you will get attacked by lions that haven't eaten in a thousand years. In the third you will get shot at. Which way is safe?
Answer: The second one lions that haven't eaten in a thousand years would be dead.
Question: You are trapped in a haunted house with no electricity. There are four doors to get out of the house only one is safe. In one door a man will stab you, in another you will get electrocuted, in another one you will get shot at, in the final one it is filled with vicious dogs. Which door is safe?
Answer: The one where you get electrocuted, there is no electricity!
Question: Harry, the happy hippo, happily hopped from the hippo hospital. How many h's are in this sentence?
Answer: One: there is only one 'h' in 'this sentence'.
Question: Santa always leaves plans for his elves to determine the order in which the reindeer will pull his sleigh. This year, for the European leg of his journey, his elves are working to the following schedule, that will form a single line of nine reindeer: ReindeerComet behind Rudolph, Prancer and Cupid. Blitzen behind Cupid and in front of Donder, Vixen and Dancer. Cupid in front of Comet, Blitzen and Vixen. Donder behind Vixen, Dasher and Prancer. Rudolph behind Prancer and in front of Donder, Dancer and Dasher. Vixen in front of Dancer and Comet. Dancer behind Donder, Rudolph and Blitzen. Prancer in front of Cupid, Donder and Blitzen. Dasher behind Prancer and in front of Vixen, Dancer and Blitzen. Donder behind Comet and Cupid. Cupid in front of Rudolph and Dancer. Vixen behind Rudolph, Prancer and Dasher.
Answer: Orange, green, turquoise, scarlet.
Question: I have be checked over by experts lots of times. But the word is still spelled incorrectly. What is the word?
Question: We hurt without moving. We poison without touching. We bear the truth and the lies. We are not to be judged by our size. What are we?
Question: Every night I’m told what to do, and each morning I do what i’m told. But I still don’t escape your scold.
Question: I have keys but no locks. I have a space but no room. You can enter, but can’t go outside. What am I?
Question: I have four fingers and a thumb but I am not living. What am I?
Question: 1. A bat and a ball cast $1.10 cents in total. The bat costs one dollar more than the ball. How much does the ball cost? 2. If five machines made five gadgets in five minutes, how much time would it take for 100 machines to make 100 gadgets? 3. The was a lake, it was full with lily pads, each day the lily pads doubled in size, it took 48 days for the lily pads to cover all of the lake how long would it take for the lily pads to cover half of the lake?

Question: hows the yellow one?
Answer: (AP Reply) its the best on rusty metal!!

Hemavathi cut a cake into two halves and cuts one half into smaller pieces of equal size. Each of the small pieces is fifteen grams in weight. If she has nine pieces of the cake in all with her, how heavy was the original cake ?
Hemavathi cut a cake into two halves and cuts one half into smaller pieces of equal size. Each of the small pieces is fifteen grams in weight. If she has nine pieces of the cake in all with her, how heavy was the original cake ?
Answer : 1 240 gms Explanation : Answer: A) 240 gms Explanation: The nine pieces consist of 8 smaller equal pieces and one half cake piece.Weight of each small piece = 15 g.So, total weight of the cake = [2 x (15 x 8)]g = 240 g.

Which one has more carbs? 100g of rice or pasta? Answer: They are pretty much the same!!! Pasta has 131 calories and 25grams of carbs and rice has 130 calories and 28grams of carbs. How many of you got that one correct? Goes to show that you can keep on track with your diet without having to eat the same boring thing everyday.

The delta region of the eastern coast is frequently struck by cyclones.
Answer: The Bay of Bengal is the centre of various pressure changes and hence there is always a chance of development of cyclone.
Due to this, the delta region of the eastern coast is frequently struck by cyclones.

There is one big palace where 5 soldiers stay. Each soldier has 5 rooms. In each room there are 5 big tigers. Each big tiger has 5 little tigers. Each tiger has 4 legs. How many legs are there in the palace?
Answer: There are a total of 3010 legs in the palace.

How long would it take to fly anywhere on Earth using a SpaceX rocket?
How long would it take to fly anywhere on Earth using a SpaceX rocket?
Answer: less than an hour.
Before he gets us to Mars, Elon Musk wants to get us anywhere on Earth in under an hour.
At Friday’s International Astronautical Conference, the CEO of SpaceX revealed the company’s plans for its largest airborne vehicle yet, the BFR. While originally intended to facilitate SpaceX’s goal of putting humans on Mars by 2024, Musk announced that he also envisions using the rocket for high-speed Earth travel.
The world’s longest flight — from Doha, Qatar, to Auckland, New Zealand — currently takes 16.5 hours. However, with SpaceX’s BFR rocket, flight time would be just 45 minutes.

How many combinations are there in villain's range?
How many combinations are there in villain's range?
How many combinations are there in villain's range?
What percentage of the time does the villain have a set?
What is hero's equity assuming we're all-in?
Answer: Against AT, we have about 80% equity.
and 68 is 74. But, we have to slide it more towards 68.
Pokerstove it, you'll find our equity to be 71%.
What is hero's equity assuming we're all-in?
Pokerstove it, you'll find our equity to be 39%.
What is hero's equity assuming we're all-in?
Answer: Villain’s range divides into three categories.
What is hero's equity assuming we're all-in?
outs for 6% equity. Against 66, we are drawing dead.
equity, and 32 combinations where we have 80% equity.
Pokerstove it, you'll find our equity to be 60%.
pot is now $10. Villain goes all-in for $15, and you call.
pot is now $10. Villain goes all-in for $10, and you call.
Is a 1/2 pot bet profitable?
Is a pot bet profitable?
The bluff is not profitable.
Is a 2/3 pot bet profitable?
Is a 1/3 pot bet profitable?
The bluff is not profitable.

Write a program to provide a report of student grades. Each student is given four exams. The final grade of each student is determined by calculating the weighted average of all the exams. Your report should show the average of each student, the class average, and the maximum and minimum grades for the class.
-- make up the rest yourself.
Your output should be neat and readable with appropriate headings.

TNR 2000 Telonics Noise Reduction Kit | Telonics Inc.
Removes steady-state tones such as "whines" and "whistles"
Without reducing the level of the desired telemetry pulses.
Not to be confused with old-fashioned "noise-blanking" circuits, the TNR2000 employs the most advanced Digital Signal Processing circuitry and programming available today. The DSP algorithms employed were specifically developed for dramatically improving the quality of wildlife telemetry signals under the worst possible conditions of man-made interference; static from older engines in cars, trucks, and planes, from nearby radiating sites such as high voltage power lines, generator facilities, and radio towers, and also from atmospheric interference.
The more experience you have had listening to the hiss and roar of telemetry receivers while straining to pick a weak signal out of the noise, the more dramatic will be the effect of switching on the TNR2000! From a medical standpoint, the reduction in background noise levels experienced by the ear of the user will reduce operator fatigue, maintain hearing acuity (and thus operator effectiveness), by prolonging attention spans, and can potentially reduce hearing loss due to cumulative noise exposure.
Designed primarily for use in vehicles and fixed sites, the TNR2000 is a small, rugged, rectangular metal-cased unit measuring 1.1H x 2.75W x 5.5L inches (2.8H x 7W x 14L centimeters), and weighing 12 ounces (0.37 kg). It plugs into the audio output of your receiver and your headphones or speaker then plug into it's output jack. It may be powered from any 12-14 volt DC source and comes complete with a built-in power cord which is terminated in a standard "cigar-lighter" plug. For portable operation, it may be powered from any 12-14 volt battery pack which is capable of providing the required operating current in the range 35-200 milliamperes (dependent upon speaker/earphone volume desired). With the exception of an ON/OFF switch, operation is completely automatic, there are no operator controls or adjustments.
Under the worst possible conditions of interference, the TNR2000 will substantially improve the low-signal performance of virtually any telemetry receiver to which the user listens by means of a speaker or headphones.
If your receiver has a weak audio output, the TNR2000 provides a very powerful output circuit designed to drive large speakers as well as all types of monaural headphones, headsets and intercom systems.
The following sounds files are actual recordings of the devices in use. The sound files have not been synthetically produced or altered in anyway. Both sounds are the same telemetry signal. One is using the Noise Reduction Unit, and the other is not.

advanced-mp3-converter.exe is a binary executable program for Windows. The download size as indicated by the server is 3.45MB (3620563 bytes). The host server on www.mp3do.com has returned application/x-msdownload as the content type of the download which was updated on 02/22/2012 and was last checked by Webeaver.com crawlers on 11/19/2018. You may use one or more of the following keywords [advanced mp3 converter exe] to search for other files related to the one you are about to download.

Hi, I need a banner or two for my website - I could do it, but don't have the time. How much would it cos...I could do it, but don't have the time. How much would it cost - my website is - [se connecter pour voir l'URL] - one spring looking with my logo and a key phrase or two - My site is a gift and personalized product site. I could supply images of products.
Good day Shant. I have wholesale site [se connecter pour voir l'URL] selling my product WAFF and i need help to direct traffic (wholesale stores, like gift shops, toy shops, stationery shops) to come to my website and place orders through [se connecter pour voir l'URL] . Faire is offering new customers 200$ money credit and 60 days terms on a first PO. Can you help me with that.

From calming to stimulating, vibrating pillows are becoming a popular way to provide tactile input.
For those who don’t have the time or money to spend with a masseuse or the thousands of dollars for a massage chair, a good alternative is a massage cushion. Massage provides health benefits of stress relief and increases circulation. It is often used as therapy to treat pain from arthritis, fibromyalgia and other medical conditions, or just everyday tension.
Many people wrongly expect that most of their body aches and pains are the result of sore bones and joints, and while this may be confirmed in a number of cases, it's the muscles that are most often causing the ache. The automatic massage pillow can assist to reduce or bump off the discomfort caused by strained, overworked muscles. Relief from muscle stiffness all through the body, including extreme back and collar inflexibility and pain, can be a direct benefit of the massage pillow. Our Massage Pillow with it's random,quiet, pulsating massage has no continuing pattern. Therefore it becomes a soothing rhythmic massage which can be relieving to anyone in just a few minutes. It helps in relieving the aches and pains brought on by arthritis, bursitis, muscle soreness, stress and tension.
At Home>place it behind your shoulders or neck and lean back on it; works instantly to relax tight shoulders and neck muscles with a gentle pulsating action ..or sit down, kick off your shoes and place your feet on the Massage Pillow; then enjoy a tingling massage that will perk up your tired feet, you'll feel like dancing!
When You Travel>place the Automatic Massage Pillow behind the small of your back while you drive, or while you travel by plane, train or bus. There's nothing to plug in, no cords to get tangled in. Just lean back and enjoy!
At The Office>use the Massage Pillow to massage tired, aching muscles in your back, shoulders, legs or feet; when you're done, just tuck your pillow away in a desk drawer until next time.
Seniors greatly benefit from the therapeutic healing and relaxation powers of these massage pillows. They are a most comfortable way to target certain areas of the body that need to be soothed and comforted. You can put these pillows on sore tired muscles; neck, shoulders, feet, legs, or your back. Relaxation will come, muscle aches and soreness will fade! Although targeted to the specific area which is in contact with the pillow, its calming and relaxing effects will certainly impact the entire sensory system as each part relaxes. After all, who doesn't enjoy a good vibration massage?"


2.0 birds were sitting on the fence. 4.0 more birds came to join them. How many birds are sitting on the fence? Answer:

2.0 What is meant by an “imprest system”?
3.0 Why is it necessary for businesses to maintain a sale ledger?
4.0 What types of transaction are recorded in the journal?
7.0 What is the difference between the cash book and the petty cash book?

There are five frogs sitting on a log over a stream. Four of the frogs decided to jump into the stream. How many frogs are left sitting on the log?
Answer: Five! Deciding to do something is not necessarily actually doing it.
Moral of the story? Don’t analyse a task to death or procrastinate; just do it!

2.0 courses in Religious Studies at the 2100 level or above.
2.0 courses in Religious Studies at the 2200 level or above.
Note: Students wishing to retain the option of upgrading to one of the other Catholic Studies modules should use 2200 level courses.

2.0 courses: Political Science 2230E, Political Science 2246E.
1.0 course: Political Science 3339E.
1.0 additional course in Political Science at the 2200 level or above.
Note: Students registered in a Minor in Public Administration may not register in a Major in Political Science.

Right now, Dr. Johnson is three times older than his son.
When Dr. Johnson was 37 years old, his son was 3 years old.
How old are Dr. Johnson and his son now?
Answer: Dr. Johnson is 51 and his son is 17 years old.
Assume that Dr. Johnson is X years old and his son is Y years old.
Then 3Y = X, and X – Y = 34.
Solving for X and Y, we get X = 51 and Y = 17.

Question: There are several books on a bookshelf. If one book is the 4th from the left and 6th from the right, how many books are on the shelf?
Answer: 9. Try sketching the problem out to see it.
Haha. There could also be seventeen in that case.

2.0 You lack court experience and your strokes need developing. You are familiar with the basic positions for singles and doubles.
6.0 to 7.0 You have had intensive training for national tournament competition at the junior and collegiate levels and have obtained a sectional and/or national ranking.

1.1. Good morning, Eddi. 1.2. How do you spell it?
1.3. Good Bye, Eric. 2.1.Is this your family?
2.2. Now I'm your friend,too 2.3. What's his sister's name?
3.1. Look! He is red! 3.2. Where's Masid?
6.2. Drive a car 7.1. You've got a happy face!
8.1. Are there any bananas? 8.2. Is there any chichen?
9.3. What's the weather like?

Annex Floor Matting, Blue 2.5m x 4.0m.
Annex Floor Matting, Blue 2.5m x 6.0m.
Annex Floor Matting, Green 2.5m x 6.0m.
Annex Floor Matting, Grey 2.5m x 4.0m.
Annex Floor Matting, Grey 2.5m x 6.0m.

Universal Bathroom Sink Drain Stopper is free HD wallpaper. This wallpaper was upload at May 27, 2018 upload by admin in bathroom ideas.
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2.0 new poster: Is Amy Jackson a humanoid? Are Chitti Amy’s character romantically involved?
2.0 new poster: Is Amy Jackson a humanoid? Are Chitti Amy’s character romantically involved?
2.0 new poster: Is Amy Jackson a humanoid? Are Chitti, Amy’s character romantically involved?

Each passing year bears witness to the development of ever more powerful computers, increasingly fast and cheap storage media, and even higher bandwidth data connections. This makes it easy to believe that we can now – at least in principle - solve any problem we are faced with so long as we only have enough data.
Yet this is not the case. Although large databases allow us to retrieve many different single pieces of information and to compute simple aggregations, general patterns and regularities often go undetected. Furthermore, it is exactly these patterns, regularities and trends that are often most valuable.
To avoid the danger of "drowning in information, but starving for knowledge" the branch of research known as data analysis has emerged, and a considerable number of methods and software tools have been developed. However, it is not these tools alone but the intelligent application of human intuition in combination with computational power, of sound background knowledge with computer-aided modeling, and of critical reflection with convenient automatic model construction, that results in successful intelligent data analysis projects. Guide to Intelligent Data Analysis provides a hands-on instructional approach to many basic data analysis techniques, and explains how these are used to solve data analysis problems.
This practical and systematic textbook/reference for graduate and advanced undergraduate students is also essential reading for all professionals who face data analysis problems. Moreover, it is a book to be used following one's exploration of it.
Dr. Michael R. Berthold is Nycomed-Professor of Bioinformatics and Information Mining at the University of Konstanz, Germany. Dr. Christian Borgelt is Principal Researcher at the Intelligent Data Analysis and Graphical Models Research Unit of the European Centre for Soft Computing, Spain. Dr. Frank Höppner is Professor of Information Systems at Ostfalia University of Applied Sciences, Germany. Dr. Frank Klawonn is a Professor in the Department of Computer Science and Head of the Data Analysis and Pattern Recognition Laboratory at Ostfalia University of Applied Sciences, Germany. He is also Head of the Bioinformatics and Statistics group at the Helmholtz Centre for Infection Research, Braunschweig, Germany.
forces instead of independently pursuing our individual projects.
about the processes, algorithms, and theories to successfully tackle these problems.
There are many people to be thanked, and we will not attempt to list them all.
our thanks for an intense last minute round of proof reading.
1.1 Motivation . . . . . . . . . . . . . . . . .
1.1.1 Data and Knowledge . . . . . . . .
1.1.2 Tycho Brahe and Johannes Kepler .
1.1.3 Intelligent Data Analysis . . . . .
1.2 The Data Analysis Process . . . . . . . . .
1.3 Methods, Tasks, and Tools . . . . . . . . .
1.4 How to Read This Book . . . . . . . . . .
Practical Data Analysis: An Example . . . .
2.1 The Setup . . . . . . . . . . . . . . . .
2.3 Explanation Finding . . . . . . . . . . .
2.4 Predicting the Future . . . . . . . . . . .
2.5 Concluding Remarks . . . . . . . . . . .
Project Understanding . . . . . . .
3.2 Assess the Situation . . . . . .
3.3 Determine Analysis Goals . . .
3.4 Further Reading . . . . . . . .
Data Understanding . . . . . . . . . . . . . . . .
4.1 Attribute Understanding . . . . . . . . . . . .
4.2 Data Quality . . . . . . . . . . . . . . . . . .
4.3 Data Visualization . . . . . . . . . . . . . . .
4.3.1 Methods for One and Two Attributes .
4.4 Correlation Analysis . . . . . . . . . . . . . .
4.5 Outlier Detection . . . . . . . . . . . . . . . . . . .
4.5.1 Outlier Detection for Single Attributes . . .
4.6 Missing Values . . . . . . . . . . . . . . . . . . . .
4.7 A Checklist for Data Understanding . . . . . . . . .
4.8 Data Understanding in Practice . . . . . . . . . . .
4.8.1 Data Understanding in KNIME . . . . . . .
4.8.2 Data Understanding in R . . . . . . . . . .
Principles of Modeling . . . . . . . . . . . . . . . . . . . . . . . . .
5.1 Model Classes . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Fitting Criteria and Score Functions . . . . . . . . . . . . . . . .
5.2.1 Error Functions for Classification Problems . . . . . . . .
5.2.2 Measures of Interestingness . . . . . . . . . . . . . . . .
5.3 Algorithms for Model Fitting . . . . . . . . . . . . . . . . . . .
5.3.1 Closed Form Solutions . . . . . . . . . . . . . . . . . .
5.3.2 Gradient Method . . . . . . . . . . . . . . . . . . . . . .
5.3.3 Combinatorial Optimization . . . . . . . . . . . . . . . .
5.4 Types of Errors . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.1 Experimental Error . . . . . . . . . . . . . . . . . . . .
5.4.2 Sample Error . . . . . . . . . . . . . . . . . . . . . . . .
5.4.3 Model Error . . . . . . . . . . . . . . . . . . . . . . . .
5.4.4 Algorithmic Error . . . . . . . . . . . . . . . . . . . . .
5.4.5 Machine Learning Bias and Variance . . . . . . . . . . .
5.4.6 Learning Without Bias? . . . . . . . . . . . . . . . . . .
5.5 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.1 Training and Test Data . . . . . . . . . . . . . . . . . . .
5.5.2 Cross-Validation . . . . . . . . . . . . . . . . . . . . . .
5.5.3 Bootstrapping . . . . . . . . . . . . . . . . . . . . . . .
5.5.4 Measures for Model Complexity . . . . . . . . . . . . .
5.6 Model Errors and Validation in Practice . . . . . . . . . . . . . .
5.6.1 Errors and Validation in KNIME . . . . . . . . . . . . .
5.6.2 Validation in R . . . . . . . . . . . . . . . . . . . . . . .
5.7 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . .
Data Preparation . . . . . . . . . . .
6.1 Select Data . . . . . . . . . . . .
6.1.1 Feature Selection . . . .
6.1.3 Record Selection . . . . .
6.2 Clean Data . . . . . . . . . . . .
6.2.1 Improve Data Quality . .
6.2.2 Missing Values . . . . . . .
6.3 Construct Data . . . . . . . . . . .
6.3.1 Provide Operability . . . .
6.3.2 Assure Impartiality . . . .
6.3.3 Maximize Efficiency . . . .
6.4 Complex Data Types . . . . . . . .
6.5 Data Integration . . . . . . . . . .
6.5.1 Vertical Data Integration . .
6.6 Data Preparation in Practice . . . .
6.6.2 Data Preparation in R . . .
Finding Patterns . . . . . . . . . . . . . . . . . . .
7.1 Hierarchical Clustering . . . . . . . . . . . . .
7.1.1 Overview . . . . . . . . . . . . . . . . .
7.1.2 Construction . . . . . . . . . . . . . . .
7.1.3 Variations and Issues . . . . . . . . . . .
7.2 Notion of (Dis-)Similarity . . . . . . . . . . . .
7.3 Prototype- and Model-Based Clustering . . . . .
7.3.1 Overview . . . . . . . . . . . . . . . . .
7.3.2 Construction . . . . . . . . . . . . . . .
7.3.3 Variations and Issues . . . . . . . . . . .
7.4 Density-Based Clustering . . . . . . . . . . . .
7.4.1 Overview . . . . . . . . . . . . . . . . .
7.4.2 Construction . . . . . . . . . . . . . . .
7.4.3 Variations and Issues . . . . . . . . . . .
7.5 Self-organizing Maps . . . . . . . . . . . . . .
7.5.1 Overview . . . . . . . . . . . . . . . . .
7.5.2 Construction . . . . . . . . . . . . . . .
7.6.1 Overview . . . . . . . . . . . . . . . . .
7.6.2 Construction . . . . . . . . . . . . . . .
7.6.3 Variations and Issues . . . . . . . . . . .
7.7 Deviation Analysis . . . . . . . . . . . . . . . .
7.7.1 Overview . . . . . . . . . . . . . . . . .
7.7.2 Construction . . . . . . . . . . . . . . .
7.7.3 Variations and Issues . . . . . . . . . . .
7.8 Finding Patterns in Practice . . . . . . . . . . .
7.8.1 Finding Patterns with KNIME . . . . . .
7.8.2 Finding Patterns in R . . . . . . . . . .
7.9 Further Reading . . . . . . . . . . . . . . . . .
Finding Explanations . . . . . . . . . . . . . . . . . . . . . . .
8.1 Decision Trees . . . . . . . . . . . . . . . . . . . . . . . .
8.1.1 Overview . . . . . . . . . . . . . . . . . . . . . . .
8.1.2 Construction . . . . . . . . . . . . . . . . . . . . .
8.1.3 Variations and Issues . . . . . . . . . . . . . . . . .
8.2 Bayes Classifiers . . . . . . . . . . . . . . . . . . . . . . .
8.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . .
8.2.2 Construction . . . . . . . . . . . . . . . . . . . . .
8.2.3 Variations and Issues . . . . . . . . . . . . . . . . .
8.3 Regression . . . . . . . . . . . . . . . . . . . . . . . . . .
8.3.1 Overview . . . . . . . . . . . . . . . . . . . . . . .
8.3.2 Construction . . . . . . . . . . . . . . . . . . . . .
8.3.3 Variations and Issues . . . . . . . . . . . . . . . . .
8.3.4 Two Class Problems . . . . . . . . . . . . . . . . .
8.4 Rule learning . . . . . . . . . . . . . . . . . . . . . . . . .
8.4.1 Propositional Rules . . . . . . . . . . . . . . . . .
8.4.2 Inductive Logic Programming or First-Order Rules .
8.5 Finding Explanations in Practice . . . . . . . . . . . . . .
8.5.1 Finding Explanations with KNIME . . . . . . . . .
8.5.2 Using Explanations with R . . . . . . . . . . . . .
8.6 Further Reading . . . . . . . . . . . . . . . . . . . . . . .
Finding Predictors . . . . . . . . . . . . . .
9.1 Nearest-Neighbor Predictors . . . . . . .
9.1.1 Overview . . . . . . . . . . . . .
9.1.2 Construction . . . . . . . . . . .
9.1.3 Variations and Issues . . . . . . .
9.2 Artifical Neural Networks . . . . . . . .
9.2.1 Overview . . . . . . . . . . . . .
9.2.2 Construction . . . . . . . . . . .
9.2.3 Variations and Issues . . . . . . .
9.3 Support Vector Machines . . . . . . . .
9.3.1 Overview . . . . . . . . . . . . .
9.3.2 Construction . . . . . . . . . . .
9.3.3 Variations and Issues . . . . . . .
9.4 Ensemble Methods . . . . . . . . . . . .
9.4.1 Overview . . . . . . . . . . . . .
9.4.2 Construction . . . . . . . . . . .
9.4.3 Further Reading . . . . . . . . .
9.5 Finding Predictors in Practice . . . . . .
9.5.2 Using Predictors in R . . . . . .
10 Evaluation and Deployment . .
10.1 Evaluation . . . . . . . . .
References . . . . . . . . .
Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.1 Terms and Notation . . . . . . . . . . . . . . . . . . . . .
A.2 Descriptive Statistics . . . . . . . . . . . . . . . . . . . . .
A.2.1 Tabular Representations . . . . . . . . . . . . . . .
A.2.2 Graphical Representations . . . . . . . . . . . . . .
A.2.5 Principal Component Analysis . . . . . . . . . . .
A.3 Probability Theory . . . . . . . . . . . . . . . . . . . . . .
A.3.1 Probability . . . . . . . . . . . . . . . . . . . . . .
A.3.2 Basic Methods and Theorems . . . . . . . . . . . .
A.3.3 Random Variables . . . . . . . . . . . . . . . . . .
A.3.4 Characteristic Measures of Random Variables . . .
A.3.5 Some Special Distributions . . . . . . . . . . . . .
A.4 Inferential Statistics . . . . . . . . . . . . . . . . . . . . .
A.4.1 Random Samples . . . . . . . . . . . . . . . . . .
A.4.2 Parameter Estimation . . . . . . . . . . . . . . . .
A.4.3 Hypothesis Testing . . . . . . . . . . . . . . . . . .
The R Project . . . . . . . . . .
B.1 Installation and Overview .
B.4 Libraries/Packages . . . . .
B.5 R Workspace . . . . . . . .
B.6 Finding Help . . . . . . . .
B.7 Further Reading . . . . . .
KNIME . . . . . . . . . . . .
C.2 Building Workflows . . .
C.3 Example Flow . . . . . .
C.4 R Integration . . . . . . .
and provide a brief catalog of methods and tools to tackle them.
principle—basically any problem we are faced with if only we have enough data.
order to invite even more customers to buy them together).
analysis problems if relevant data is available.
consequence, their domain of application and thus their utility is necessarily limited.
are thus highly useful (at least if they are relevant to us).
such statements qualify, in our use of the term, as knowledge.
• describes general patterns, structures, laws, principles, etc.
the properties of new cases are the main reasons for this superiority.
neither of the two areas can afford to neglect the other criteria.
motions of the celestial bodies over several years.
with the sun at a focal point.
during equal intervals of time.
T12 /T22 = a13 /a23 , and therefore generally T ∼ a 2 .
knowledge and thus became one of the most famous “data miners” in history.
moment, we can compute its future course by drawing on Kepler’s laws.
How did Johannes Kepler find the simple astronomical laws that bear his name?
thus revolutionizing astronomy? We know fairly little about his searches and efforts.
tenacious work, and a significant amount of good luck finally led him to success.
or method to discover physical or astronomical laws.
tools, could have reached his goal a little earlier.
from collecting and analyzing data about the population and the state in general.
process. The conclusions drawn in inferential statistics are only valid if these assumptions are satisfied.
decide which and how many people should be assigned to a certain diet.
how many people we will have for each diet in our data.
independencies are required in order to ensure that the test decisions are valid.
based on a rigorous model as in inferential statistics.
The typical situation we assume in this book is that we already have the data.
it is often difficult to make specific assumptions about the data generating process.
such questions or to solve our problems.
[1, 5] (and is used today almost synonymously with the KDD process).
become more familiar with the area of intelligent data analysis.
us to find solutions to certain problems or provide answers to questions that arise.
discovered from the data to gain insights into this unfamiliar area.
experimental design of data acquisition is beyond the scope of this book.
widely used process model for intelligent data analysis today.
project, such that a deliberate decision on conducting the full project can be made.
suffices to solve the problem, it may be necessary to revise the project’s objective.
many techniques an unnecessarily hard time.
different techniques. Background knowledge may provide hints on useful transformations that simplify the representation of the solution.
steps is not predetermined but influenced by the process and findings itself.
the found and optimized model may be deployed.
that these assumption still hold to prevent decision-making on outdated information.
the project domain in particular, and the software suites.
phases and providing first instructions to get along with the software suites.
expensive, difficult, or cumbersome to determine it.
our mailing? Will the technical quality be acceptable?
of interest is numerical in nature.
money will the customer spend for vacation next year? How much will the machine’s temperature change within the next cycle?
group may be considered as abnormal or outliers.
Typical questions: Do my customers divide into different groups? How many operating points does the machine have, and what do they look like?
Find any correlations or associations to better understand or describe the interdependencies of all the attributes. The focus is on relationships between all attributes rather than focusing on a single target variable or the cases (full record).
do the various qualities influence each other?
that behaves differently with respect to some target attribute.
Typical questions: Under which circumstances does the system behave differently? Which properties do those customers share who do not follow the crowd?
association analysis may help to identify relationships among attributes or records.
analysis can help to focus on exceptional situations that deviate from regularity.
want to get a full picture and do not concentrate on a single target attribute yet.
association analysis, or deviation analysis.
care about the how and why but are just interested in the best-possible prediction.
We may apply methods from, for instance, classification or regression.
are of great help as they reduce data formatting efforts and ease method linking.
commercial product from SPSS, now IBM.
A commercial data mining solution from SAS.
developed by the University of Waikato, New Zealand.
human data analyst by sophisticated graphical user interfaces, graphical configuration and reporting, while others are better suited for batch processing and automatization.
and its ability to integrate other well-known toolkits.
the chapters about intelligent data analysis.
supports the composition of complex workflows in a graphical user interface.2 Appendices B and C provide a brief introduction into both systems.
8. Kurgan, L.A., Musilek, P.: A survey of knowledge discovery and data mining process models.
workflows discussed in this book are available for download at the book’s website.
methods. They will be discussed in depth in subsequent chapters.
Disclaimer The data and the application scenario used in this chapter are fictional.
setups would have been entirely out of the scope of this book, since in order to understand the actual issue, a bit of domain knowledge is often helpful if not required.
strange, to say the least. Have fun.
the data you need—an assumption which is, unfortunately, frequently not true.
when these customers signed up for frequent shopper cards.
• Products: A list of products with their categories and prices.
customer card ID used during checkout.
a lot of this data has been merged—however, still without a clear picture in mind.
marketing of the southern and northern markets decided to launch a similar program.
• help design a marketing campaign to attract core customers to increase their purchases.
experience on the job and some more applied knowledge about the different techniques, whereas Laura has some training in statistics, data processing, and data analysis process planning.
his database to compute the total price of the shopping baskets for each customer.
Stan then applies a well-known clustering algorithm which results in five prototypical examples, as shown in Table 2.1.
the results are similarly uninteresting.
also roughly match her expectations: the majority of the customers are employees, while the second and third groups are students and freelancers, respectively.
she decides to filter the data to only include people between the ages of 18 and 100.
range. Figure 2.1 shows the result of this analysis.
aged, and the number of shoppers continuously declines toward higher age groups.
age 48 using finer setting for the bins. Figure 2.2 shows the result of this analysis.
observation with colleagues and the administrator of the shopping card database.
“missing” in order to be able to distinguish them in future analyses.
three attributes to make sure they all three contribute equally to the clustering result.
for the number of clusters to be found, she gets the result shown in Table 2.2.
the ones which seem to be under-represented.
product dependencies in order to better plan campaigns.
He quickly infers that this representation must mean that foie gras is bought whenever champagne and truffle oil are bought together and similarly for the other rule.
these rules (champagne, truffle oil) to increase the sales of the left side (foie gras).
in sales. He proudly sends the results of his analysis to Laura.
there is essentially no influence on the overall revenue.
whereas the apple/tomato-rule is a known aspect.
appropriate campaigns should be launched, once she has the results of her analysis.
this will affect our future revenue.
lack of performance and fires Stan.
existing purchases and those who are actually enticed to purchase additional items.
but only how well it performs.
be enticed by the coupon to buy products for the underperforming segment also.
predictor to detect such dependencies if they exist.
and also technically by means of feature selection methods.
for the next quarter. She keeps monitoring the performance of these coupon campaigns over future quarters and updates her model sporadically.
prominent and most often used examples in the following chapters.
later in more depth as well.
care to keep the project on the right track.
We have already sketched the data analysis process (CRISP-DM in Sect. 1.2).
(20% : 80%), the importance to success is just the opposite (80% : 20%) .
explorative tools such as mind maps or cognitive maps to sketch beliefs, experiences, and known factors and how they influence each other.
understanding and adjustment of expectations.
direct connection from size of household to frequency of product in shopping basket.
software that uses the final model to automatize decisions.
slots for meetings should be arranged.
a model from this data later anyway. Unfortunately, this is only half of the truth.
prevent us from carrying out an expensive project having almost no prospect of success, we have to carefully track all assumptions and verify them as soon as possible.
the sample in the database must be representative for the whole population.
the cognitive map) should be represented by attributes in the database.
unambiguous thanks to the available documentation.
change their current strategy or product portfolio at all.
Every assumption inherently represents a risk (there might be other risks though).
invalid, including options such as the acquisition of additional data sources.
achieve this analogy, the discussions about the project domain are of great help.
company wants to increase the sales of some high-end product by direct mailing.
to be useless in the end.

Eighty-two resident-owned manufactured housing parks serve over 4,000 New Hampshire families. Despite their popularity, one important question remains: do they outperform investor-owned manufactured housing parks from a social and economic standpoint? A research team from UNH set out to answer this question through a comprehensive study that engaged subjects from resident-owned parks and investor-owned parks and officials from seven New Hampshire towns. The research findings suggest that resident-owned manufactured housing parks indeed provide a more affordable housing option for low-income families, as well as an enhanced sense of ownership and an opportunity to build equity. Implications for Extension are discussed.
Between 1984 and 2006, the New Hampshire Community Loan Fund, referred to as "The Loan Fund," has helped residents from 82 manufactured (mobile) home parks to purchase the land on which their homes are situated. Each of these cooperatively owned parks, known as "Resident-owned Communities" (ROC's), formed a self-governing corporation to manage their park. Through this model of resident ownership, residents have gained financial and managerial control of their park and their lives.
While a number of studies examine the social and economic benefits of home ownership (Haurin, Deitz, & Weinburg 2003), few studies examine the social and economic benefits of cooperative home ownership. In fact, the concept of cooperative (resident) ownership of manufactured home communities is relatively new, with the first ROC having been established in New Hampshire in 1984. Yet ROC's have already had a significant impact on the state's affordable housing sector. Today, over 4,000 New Hampshire families reside in ROC's--more than in any other state.
Additionally, the team was charged with providing The Loan Fund with recommendations that would help them to strengthen the resident ownership model in New Hampshire. Provided that there is strong evidence supporting the advantages outlined above, the hope is that the resulting recommendations will also highlight opportunities for Extension Services to provide educational outreach to help build the capacity of existing and potential ROC's and thereby help promulgate the resident ownership model nationally.
Home ownership is the main source of equity for most Americans. However, due to rapidly escalating housing costs relative to personal income, an increasing number of Americans cannot afford to purchase a home (Apgar, 2005).
Of those who were able to purchase a home in the United States between 1980 and 2000, 29% opted to purchase a manufactured home (Genz, 2001). The vast majority of these manufactured homes are located in IOC's, where residents rent their plot from a landlord. Only a small fraction of manufactured homes are located in ROC's.
A number of factors explain why ROC's have not proliferated nationwide. Foremost, few lenders are willing to provide financing with interest rates comparable to conventional mortgage loans for the purchase of manufactured homes located in parks. Most lenders only provide access to personal property loans or variable-rate loans for the purchase of manufactured homes. Interest rates for these loans are typically several percentage points higher than conventional home loans (Bradley, 2003). And, without access to mortgage-competitive financing, prospective homeowners may not see advantages to buying a home in an ROC.
In New Hampshire, however, mortgage-rate financing is increasingly becoming available for the purchase of manufactured homes in ROC's.
Another factor limiting the expansion of ROC's is the lack of technical, financial, and managerial support to the ROC Boards responsible for managing and maintaining their respective parks. New Hampshire is one of the few states where support is readily available to ROC Boards. Without this support, it is unlikely that residents of New Hampshire's 82 ROC's would have been able to purchase their parks in the first place.
To determine if resident-owned parks pose certain advantages over investor-owned parks, a study was designed to compare ROC's with IOC's on a range of social and economic variables. Overall, seven New Hampshire towns with at least one ROC and one IOC were selected for the study to encompass a wide geographic distribution and a broad range of demographic characteristics (Figure 1). Within each of these towns, one to two ROC's and an equivalent number of IOC's were selected for comparison. The parks within each town were selected to be comparable in terms of location, size, and demographics of the park residents. The final sample consisted of eight ROC's and 12 IOC's (Ward, French, & Giraud, 2005).
The primary sources of data for the study were a mailed questionnaire, secondary data from town tax cards and the Multiple Listing Service (MLS), and interviews with ROC Board Members and Town Officials.
Using elements from Don Dillman's Total Design Method for conducting surveys (1978), a self-administered survey was mailed to residents of both ROC's and IOC's to query them about basic demographic information, household economic factors, as well as their perceptions about living in their park. All of the residents in the sampled parks were mailed surveys, with the exception of one town, where only 50% of the homes were sampled due to the town's large size and the possibility that a full sample could skew the results. Of the 1,187 surveys sent out, 698 were returned for an overall response rate of 59%. Overall, the response rates were very similar between the two groups, with 356 surveys completed by residents of ROC's and 342 completed by residents of IOC's (Ward, French, & Giraud, 2005).
Town Tax Cards were accessed in order to analyze and compare information on assessed value of homes. Likewise, data from the state's Multiple Listing Service (MLS) were used to compare lot rent fees and the number of days on the market for homes sold in ROC's and IOC's.
In addition, one to two town officials were interviewed in each of the seven sample towns to determine their perceptions of ROC's and IOC's. The 12 town officials who were interviewed fell into one of three categories; safety officer, elected representative, or administration professional (e.g., planner, assessor, etc.).
Although there were a number of economic variables examined in the study, only four are addressed in the following section, as they relate to the four advantages that were proposed above. These variables are access to mortgage-competitive financing, stabilization of housing costs, opportunity to build equity, and sense of ownership and control.
Data on home loans were collected from the surveys to determine whether ROC residents have better access to financing than IOC's. One theme that appeared in numerous surveys was the stated lack of availability of low interest loans for the purchase of manufactured homes.
As Figure 2 below illustrates, homeowners from ROC's obtained more loans to help finance their home purchases than those from IOC's between 1995 and 2005. Moreover, the number of loans to ROC's increased dramatically over the past few years as new lenders made mortgage financing available to homeowners. In contrast, residents of IOC have had fewer loans and were often forced to purchase their homes outright in order to avoid the high interest rates available through personal property loans or variable-rate loans.
Adapted from Ward, S., French, C., & Giraud, K. (2005). The effect of cooperative ownership on appreciation of manufactured housing. Cooperative Housing Journal. 2005/2006 Annual Issue, p. 22.
The second hypothesis is that ROC's provide more stable housing costs than IOC's. This was tested by comparing monthly lot fees paid by homeowners in ROC's and IOC's. The monthly lot fees paid by homeowners in ROC's are used to pay off their share of the mortgage for the land, as well as for maintenance and improvements. In contrast, monthly lot fees paid by homeowners in IOC's go to the landlord for land rent, much of which is converted to profit.
As Table 1 above illustrates, the average lot fee for ROC's ($265.93) is nearly $12.00 per month less than the lot fees for IOC's ($277.62). Taking into consideration that lots in ROC's tend to be larger than lots in IOC's, this appears to be a significant factor. In effect, homeowners in ROC's pay less in lot fees in spite of the fact that, on average, their homes reside on more land. Additionally, the monthly lot fees for ROC's tend to drop after the ROC has been in operation for 11 or more years, after which average monthly lot fee for ROC's drops to about $242. In contrast, monthly lot fees tend to go up over time in IOC's (Ward, French, & Giraud, 2005).
Albeit there are certainly other costs associated with living in a manufactured housing park aside from monthly lot fees. However, because lot fees are somewhat less on average for ROC's than IOC', and because these fees tend to go down over time, this suggests that there is more stability with regard to housing costs in ROC's. It is in ROC residents' own interest to keep costs down, as each owns a collective share of the park.
The third hypothesis, that ROC's provide residents more opportunities to build equity than IOC's, was tested by comparing homes' assessed value, as well as the sale price of homes sold recently in both IOC's and ROC's. The assessed values of individual homes were pulled directly from tax cards, while data on recent sales of homes in the study-sample parks were derived from the local Multiple Listing Service (MLS).
As Table 2 shows, homes in ROC's sold for $4566 more, on average, than homes in IOC's between 1999 and 2005. Part of this price differential might be attributed to the fact that the homes tend to be slightly larger. However, just looking at sales from 2004 to 2005, the price differential increases to $7234. Paul Bradley, with The Loan Fund, believes that this is due to the fact that potential homeowners, lending institutions, and other supporting organizations are finally realizing the financial advantages that ROC's pose to homeowners by virtue of the fact that each owns a share of their park.
Adapted from S. Ward, S., French, C., & Giraud K. (2005). The effect of cooperative ownership on appreciation of manufactured housing. Cooperative Housing Journal. 2005/2006 Annual Issue, p. 22.
The fact that homes in ROC's spend, on average, 23 fewer days on the market than homes in IOC's suggests that they may be more desirable to potential homeowners. And, the more demand that there is for a particular housing sector, the more likely it is that it will increase in value. This provides existing and future homeowners in ROC's with enhanced opportunity to build equity, something which lending institutions in New Hampshire are beginning to recognize in their lending habits.
The data collected via mail survey and interviews were coded and analyzed using NVIVO 2.0, a qualitative analysis software package. The results of the analysis suggest that ROC's pose a number of social and economic advantages to park residents as compared to IOC's. Foremost of these benefits is the increased sense of ownership and control over their homes and their communities that is perceived by ROC residents.
I am a part owner of this whole community. I have a say in everything that goes on here whether I'm on the board or not . . . that is something that you don't normally have in a mobile home park . . . I own this.
That same individual suggested that this sense of ownership was not present when an investor owned the park just a few years prior.
I've heard more from outside people how much nicer the park looks since we've taken over . . . a lot of the changes are gradual changes . . . [p]eople that don't come in here often are the ones that notice the difference.
This sentiment was echoed by the town officials who were interviewed, most of whom stated that ROC's were better maintained.
Last, it is important to note that many of the ROC Board members interviewed in the study have become involved with informal leadership roles as a direct result of their experience on the board. Such roles include coordinating volunteer beautification projects, organizing social events, and heading up a recreation committee. Others have taken on formal leadership roles, including serving on the Parent Teacher Association, Planning Board, Town Council, emergency services coordinator. One Board member became so well known for her success at advocating for her ROC with the state legislature that she was subsequently elected as President of the Manufactured Home Owner Tenants Association of New Hampshire (MOTA).
Based on the analysis of data acquired via personal interviews, tax records, and the Multiple Listings Service, we conclude that resident ownership provides a range of economic and social benefits. Foremost, resident-owned communities provide homeowners with greater access to mortgage financing, whereas homeowners in investor-owned communities are often limited to securing personal property loans or variable-rate loans at a significantly higher interest rate.
A second benefit that resident ownership provides to homeowners is the stability in monthly lot fees compared to monthly lot fees paid by homeowners in investor-owned communities. Not only are the fees lower on average in resident-owned communities, but they also appear to decrease over time. Fees in investor-owned communities generally go up over time.
Resident ownership also appears to have positive implications on home values. On average, manufactured homes in resident-owned communities are valued 10% higher than homes in investor-owned communities and perhaps even more so over the last couple of years, as new lenders have made mortgage loans available to ROC's.
Finally, ROC's pose a number of social advantages, such as residents' increased sense of ownership and control over their homes and their communities that is manifest in how they take care of their homes and yards.
These findings suggest that resident ownership could be an important sectoral strategy to help low and middle-income families attain social and economic well-being. That is not to say that resident ownership goes without its challenges, such as negative stereotypes that many have of the manufactured housing sector, and the financial and organizational challenges that self-management poses. However, if New Hampshire is any indication, then perhaps the resident ownership model could help manufactured homeowners around the country achieve social and economic well-being.
The resident ownership model poses a number of advantages to homeowners. In spite of this, the model has not taken off across the country because most states provide little in the way of technical, financial, and managerial support to help manufactured homeowners form ROC's and manage them once they are established. The fact is, there is a host of financial, managerial, legal, and infrastructural challenges involved with starting and managing ROC's. Overcoming many of these challenges requires material resources. Perhaps equally important, overcoming these challenges requires a high level of technical and organizational skills that are not likely to be maintained by the residents of manufactured home communities without some external support.
Given that Cooperative Extension specializes in providing individuals, organizations, and communities with educational outreach, perhaps there is an opportunity for Extension to provide ongoing training to ROC Board members (or potential Board members) to build their capacity to address complex issues pertaining to ROC management and thereby increase their likelihood of achieving success through the resident-ownership model.
Organizational management (e.g., running meetings, board decision-making, sharing responsibilities).
Financial management (e.g., billing, business contracts, accounting).
Maintenance of infrastructure (e.g., contracting, sewer/water maintenance, landscaping).
Conflict resolution (e.g., interpersonal relations, addressing park violations, resolving disputes with park neighbors and municipalities).
Cooperative Extension already provides training in the above-mentioned areas. Thus, developing training specific to ROC Boards might simply be a matter of tailoring existing curriculum to address issues that ROC's face. Through the provision of training, Cooperative Extension could help advance the ROC model nationally.
With the exception of one or two states, including Minnesota, Cooperative Extension services have not yet worked extensively with ROC's. Perhaps the concept of resident ownership is so new that Extension has not had time to focus its energies on this important affordable housing sector. Or perhaps collaborative partnerships have not yet been established with organizations, agencies, and institutions whose expertise is needed to ensure the success of ROC's.
But one thing is certain; if housing costs continue to rise faster than incomes, the housing crisis will only worsen. The resident ownership model provides Extension with an opportunity to get involved at the ground floor in helping low to moderate-income communities to build wealth through home ownership.
Apgar, W., Calder, A., Collins, M., & Duda, M. (2002). An examination of manufactured housing as a community- and asset-building strategy. Report to the Ford Foundation by the Neighborhood Reinvestment Corporation. Cambridge, Massachusetts: Joint Center for Housing Studies, Harvard University.
Bradley, P. (2002). No longer a secret: The manufactured housing sector can create long-term value for homeowners. Rural Voices. 8(2), 16-20.
Dillman, D. (1978). Mail and telephone surveys: The total design method. New York: John Wiley and Sons.
Ward, S., French, C., & Giraud K. (2005). The effect of cooperative ownership on appreciation of manufactured housing. Cooperative Housing Journal. 2005/06 Combined Issue, 16-24.
US Census Bureau (2005). Housing vacancy survey. Washington, D.C.

This is laura_genial. Female, bisexual, stormy eyes, 5'8", 45 kg. What do you want in your mouth? Thrust into me as you pull my hair… oooh yeah, just like that.
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Editing and reviewing a text after it has been translated is an essential step in achieving the optimum quality in any job.
A good editor will thoroughly review each term in the text to ensure that there is no error or inconsistency, as well as to improve the text as much as possible. In addition,the work must be checked to ensure that it is well organized and can be understood and read without any problems.
Review entails other types of corrections such as printing, punctuation or grammatical errors; inappropriate page breaks; missing or misplaced accents; verification of the specialized terms used, and sentence structure.
In short, review and check as many times as necessary the entire work to ensure that it is delivered to the client with the highest possible level of quality.
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Editing and reviewing a text after it has been translated is an essential step in achieving the optimum quality in any job.

Their work is truly something to be admired; though its true form would not culminate until future releases. Daitro - Laisser Vivre Les Squelettes. I only enjoy this band in small doses.

Question: There are 20 birds in a tree. A man comes and shoots one of the birds. How many birds are left?
Answer: None, because all the birds flew away after hearing the gun shot.

Building an office, even a small one, is not always synonymous to affordable expenses. The common thinking is that if you want to build your own office, you have to allocate lot money for its construction. However, this does not mean that you cannot have a decent work space if you have limited budget.
You can build your own office without having to sacrifice all of your savings. There are many ways that you can do to make your project much cheaper and more reasonably priced.
The first step towards building a frugal office is to have a solid plan. You should know what type of office you want to build so you can budget your money well, preventing you from spending in excess. This phase should be taken seriously as it will serve as your project’s guide and reference once it starts. In this phase, it is recommended that you consult with a design expert or contractor in order to know what type of office space would complement your needs and budget.
After knowing what type of office you would want to pursue, your next big step is to create a budget plan. Your budget is crucial throughout the office construction, which is why you should go for an accurate and realistic budget. You should know how much money you are willing to spend for the materials, supplies, and services that will be used.
However, if you really want to save on costs, you might want to consider outsourcing services like human resources-related services. There are many respected HR support UK companies out there that can handle your HR needs such as employee handbook, training and development, payroll, and so on. By working with an HR support UK company, you don’t need to directly hire people for HR services. This will help you cut down on the expenses.
You should know that you only get what you pay for, so keep your expectations grounded. If you have limited budget, do not expect a grandiose and world-class office space. As it is, don’t be picky and be realistic. It is important to be practical if you want to build an affordable work space, this means resorting to cheaper furniture items like desks and chairs. However, you should still go for quality. Do not settle for materials that are immensely cheap but have very poor quality. You would want to go somewhere in the middle.
In relation to looking for affordable materials and office furniture, you would want to go online to look for such items. There are many companies throughout UK that offer affordable but good quality materials and supplies to office builders. You may want to check these companies online. Go to classifieds sites where these companies post their ads. You may also want to go for pre-owned items online, just make sure that what you will get is still in good working condition. However, you should be wary of the items you buy online since there are people who target unsuspecting online shoppers.
Buying affordable office construction materials and supplies is not enough if you want to have a frugal construction. If you want to save more, hire a construction company that is known for providing quality services at a more affordable price. Avoid companies that work with bigger and more established business as they are likely to charge more. Instead, go for a local construction business with good track record and charges less.
Office construction does not always need to be expensive. If you know how to find your way to a cheaper construction, it can be done for sure.

Are you looking for that Hollywood Smile? Well we can give you that smile. Our top range cosmetic dental procedures will help get rid of cracks, discolored teeth, and other issues that have been affecting your self-esteem and confidence. There are many cosmetic dentistry options available to improve the appearance of your teeth today. Our friendly staff of Professional dentists and healthcare personnel are on ground to give you the perfect sparkling smile through these options.
Discoloration from poor dental hygiene.
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One of the most effective options for smile enhancements are Porcelain Veneers. They are often the ideal option for concealing an assortment of cosmetic imperfections. Veneers are thin shells of porcelain that are custom-made to improve the teeth’s appearance. It could be for one tooth or for a series of teeth, or it could be for a complete smile makeover.
Improving your smile with porcelain veneers is a relatively simple process that yields great results. The size, color and overall appearance of each veneer is built to match the specifications of your tooth, which ensures you get results that look and feel very natural.
Reshaping or recontouring is an instant cosmetic dental treatment that is used on cracked or chipped teeth to shapen and give the teeth a much more appealing look. In some instances, reshaping is done as an alternative to braces and is used to alter the shape and length as well as the positioning of the teeth with little to no discomfort.
Copyright © 2019 by oraldesignspecialists. All rights reserved.

I commented just some minutes ago on this question, and every post in math.SE returned a [Math Processing Error]. Not only for me, but for every other user.
How can I be sure that this won't happen again? (Mostly because if I hadn't been online, you'd have to ask a mod to delete the comment, or something of the sort, which'd have been quite a problem.
I have figured out both the problem with the \limits macro and with the failure to process the rest of the mathematics that it caused. It is basically as I outlined in my comment on @Zev's answer. The TeX input jax had an internal failure (it tried to use a null pointer), and that was trapped by MathJax as it was supposed to be. But it also meant that the internal form for that equation was not available, and when the HTML-CSS (or SVG or NativeMML) output jax went to typeset that internal form, it wasn't there, so there was another null pointer problem.
Each output jax makes an initial pass through all the math in order to determine the surrounding font size (this is done before any math is actually typeset in order to improve IE performance). It was on that pass that the output jax failed. That was also trapped by MathJax, but it meant that the output jax only had determined the sizes for some of the math on the page, and when it went to typeset the rest of the math, that size data was unavailable, which caused the "[Math Processing Error]" messages for those expressions.
The earlier expressions were actually typeset, but because MathJax displays the mathematics in blocks of 50 expressions (again for performance reasons), the earlier math was not displayed, leaving only the previews in place, not the typeset math.
The upshot is that there were a bunch of places where the output jax had to check that the input had actually been processed where it wasn't doing so. I have fixed this in all three output jax, but it will not appear on the CDN until the next release. We are expecting to make a v2.0a release in the near future to take care of a bunch of bug fixes of this sort.
Thanks for your patience, and for reporting the issue.
The problem was that the second \limits command was misplaced.
MathJax v2.1 should resolve this issue. Since math.SE is now using the beta version of MathJax v2.1, so you should see the correct rendering these characters now (both the empty sets and the setminus issues should be fixed). Please let me know if that is not the case.
Note that if you keep your browser open continually, you may need to empty the cache and reload the page (or perhaps even restart the browser) to get the new copy of MathJax. (MathJax's About box should tell you which version you are getting; make sure all the files in the list show v2.1).
See MathJax 2.1 beta for more details on the changes in MathJax v2.1.