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20 Mountains All Skiers And Snowboarders Should Visit In Their Lifetime

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Aspen skiing

Ski bums and boarders follow the powder around the world to shred the slopes at the world's best ski resorts.

From ritzy Snowmass in Aspen, Colorado, to the steep terrain of Cerro Catedral in Argentina, here are 20 mountains that all skiers and boarders should visit in their lifetime.

Julie Zeveloff contributed to this story.

With a vertical drop of 4,105 ft. and 116 trails for expert, intermediate, and beginners skiers, Jackson Hole Mountain Resort has something for all skill levels. The Wyoming mountain was ranked the #1 overall resort by SKI Magazine in 2013.



Conquer the Andes Mountains at Valle Nevado, a ski resort just outside Santiago, Chile. After a day of skiing, don't forget to have a Pisco Sour on the outdoor deck.



Traverse over 8,000 acres of skiable terrain at Whistler Blackcomb in Canada's British Columbia region. The mountain has an epic 5,234 ft. vertical descent.



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Model Gets An Extreme Holiday Makeover In Photoshop Stunt

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girl photoshopped

In October, branded content producer and director Tim Piper made a time-lapse video showing how his model wife was photoshopped from her original appearance into a cover-ready figure with a thinner nose, longer neck, and flatter stomach.

The video quickly went viral, and sparked a social media discourse on how the media manipulates images to give the public a false sense of what natural bodies look like.

For its virtual holiday card this year, the ad agency Victors & Spoils decided to give Sally Gifford Piper a seasonally appropriate makeover of their own. While the agency's work was not quite as flattering as the makeover Tim Piper gave his wife, it will shock you nonetheless.

And here's the original video made by Tim Piper:

SEE ALSO: Amazing Gifs Show Just How Creative A Model's Photoshopper Can Get

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Three Reasons Why You Should Order Your Starbucks Drink 'Extra Hot'

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starbucks baristaA former Starbucks barista has revealed some tips and tricks for ordering a coffee at the perfect temperature. 

Alecia Li Morgan worked at Starbucks for five years, first as a barista and later as a store manager.

Throughout her time there, she had many customers who ordered their drinks "extra hot," she wrote in a thread on Quora.

"Back when I first started working at Starbucks, the acceptable range for beverage temperature was around 145-165 degrees," she wrote. "That's not really all that hot."

The perfect temperature for a coffee, she learned through extensive trial and error, is 180 degrees Fahrenheit. 

Morgan offered these tips and tricks for when and how to order a drink "extra hot:"

1. When it's cold outside. "When I worked at Starbucks in North Dakota, the temperatures would reach -30F plus wind chill, so drinks cooled down QUICKLY if taken outside/ordered in a drive thru," Morgan wrote. 

2. When you are ordering a milk-based drinks. Creamers, even when steamed, can cool down the temperature of a coffee. Tell the barista you want the milk steamed to 180 degrees, and it won't negatively affect the taste of the espresso or coffee.

3. When you don't plan to drink the coffee right away. If you want to enjoy your coffee at work but there's a convenient Starbucks location closer to home, ordering it extra hot will keep it warm during the commute.

SEE ALSO: Starbucks' $450 Gold Cards Sold Out In Seconds, But You Can Get Them On E-Bay For $5,000

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12 Baking Hacks That Will Seriously Improve Your Cookies

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christmas sugar cookies baking

It's the happiest time of the year — cookie-baking season.

Due to sheer amount of office holiday parties, family meals, and last-minute homemade gifts for friends, chances are you've spent at least one chilly night indoors whipping up batch after batch of cookies.

But just because two people make chocolate chip cookies doesn't mean both will taste equally delicious.

Be they gingerbread, sugar, or oatmeal, here are 12 kitchen hacks to up your cookie-baking game.

1. Use room temperature butter

butter and eggsYou can use cold butter if necessary, but the cookies won't be as chewy. Room temperature butter will mix better with dry ingredients, like sugar and flour, and will help hold the cookie shape as your cookie bakes. (Some recipes also call for half-melted or melted butter, but unless the recipe specifically asks for it, the safest bet is room temperature butter.)

The fastest way to get butter to room temperature is to cut it into pieces and let it sit on a plate for 30 minutes while you get the other ingredients ready.

2. Speaking of butter, it needs to be unsalted

The amount of salt in salted butter varies among brands, so there's no way of knowing how much salt it adds to the cookies. Better to use unsalted butter and add the exact amount of salt the recipe calls for to avoid salty, disgusting cookies.

3. Your eggs should be room temperature, too

Even though many Americans store their eggs in the fridge, you're actually supposed to use room temperature eggs when baking since the whites and yolks combine easier and more evenly into the batter (leading to a better, airier cookie texture).

Getting eggs to room temperature is really easy — just place an egg in a bowl of warm tap water for 10-15 minutes.

4. Spend time creaming your butter and sugar together

The process known as "creaming" is basically just blending ingredients together with a solid fat, like butter or shortening. Not to get too much into the science of baking, but the sugar crystals help aerate the butter by creating air bubbles as they cut into the fat.

Basically, if you cream the butter and sugar correctly (about 10 minutes), you'll get evenly baked, fluffy cookies.

5. Reduce the flour to make even more tender cookies

Here's what most people do: Dip the measuring cup into a bag of flour, pack it in densely, and then swipe off the excess with a knife. These people are probably making rock-hard, dry cookies that their friends are politely nibbling and then throwing away.

Instead, take a spoon and fill up the measuring cup without packing in the flour, and then use a knife to swipe off the excess. This reduces your flour by a few tablespoons, which will make cookies even more chewy and tender.

6. Chill the dough before baking

chocolate chip cookies doughSome people think this is an unnecessary, time-consuming step, but those people are dead wrong.

Letting the dough chill in the refrigerator (from four hours to overnight) makes it easier to work with (less sticky), and really brings out the buttery flavor since the ingredients have had time really meld together.

7. Put coarse sea salt on top of chocolate chip cookies

Salty and sweet flavors always go really well together, but putting a sprinkling of sea salt on top of already delicious chocolate chip cookies will make the chocolate seem even richer, and help the buttery, sugary dough taste even better.

Try this once and you'll never go back.

8. Flour your cookie cutters before use

If you're making sugar cookies or gingerbread cookies and using cookie cutter shapes, make sure to dip the cutters into flour before use. This way, the dough will loosen easily from the cutter when you place it on the cookie sheet.

You should put flour on your hands and rolling pin for the same reason.

9. Invest in insulated cookie sheets

Insulated cookie sheets are worth investing in because they help cookies bake evenly and will not burn the bottoms. They're made with multiple layers of aluminum so that the air is insulated within the sheet, and not just whichever part of the oven is hottest.

10. Lower the oven temperature

If you're making a thicker cookie, dial the oven temperature back about 25 degrees. This will keep the exterior of the cookie from getting too crunchy before the inside finishes cooking.

Serious bakers should also invest in an oven thermometer to make sure the oven is the exact cookie-baking temperature.

11. Check on cookies 2-3 minutes before they should be done

sugar cookies baking in an ovenIf you like soft, slightly-underdone cookies (like most humans do) be ready to take your cookies out of the oven 2-3 minutes before the recipe says they should be done.

Cookies burn easily, and oftentimes don't appear "done" on top when they're actually perfect. Thick or moist cookies are done when you can press lightly and leave a small imprint, while thin or crispy ones are done when they're firm to the touch and have slightly golden edges.

12. Store an apple wedge with your cookies to keep them soft

The moist apple wedge will let your chewy cookies steal some of its moisture, keeping them soft and tender for longer.

Also, make sure to always put away cookies once they've completely cooled — otherwise, condensation will build up and the cookies will turn soggy.

SEE ALSO: 12 Sandwich Hacks That Will Completely Change Your Life

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The 8 Most Expensive Yacht Purchases Of All Time

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No billionaire is complete without a superyacht of his or her own. In fact, a November report from Wealth-X and the UBS Global Billionaire Census found that the average billionaire spends $22 million on yachts. 

The latest study from Wealth-X ranks the most expensive luxury asset acquisitions of all time, and it shouldn't come as too much of a surprise that eight of the top ten purchases were yachts. 

Wealth-X uses a proprietary valuation model to assess all asset holdings including privately and publicly held businesses and investible assets to develop their Net Worth Valuation. 

Here, in reverse order, are the 8 most expensive yacht purchases of all time. 

8. Dilbar, $263 million

dilbar yachtAlisher Usmanov, Russia's wealthiest man, bought this 360-foot superyacht for $263 million in 2012. Dilbar, named after the billionaire's mother, has accommodations for 20 guests and up to 47 crew members, in addition to a helicopter pad, swimming pool, and swanky formal dining room. 

7. Radiant, $286 million

Radiant yachtOriginally commissioned by Russian oligarch Boris Berezovsky, this 360-foot yacht was sold to Abdulla Al Futtaim, a billionaire car dealer from the United Arab Emirates. Radiant's amenities put a James Bond twist on the typical superyacht experience. It's equipped with sonic guns that would burst the eardrums of attackers, along with water cannons that could sink an approaching boat from 100 yards away. There's even a smaller speedboat designed specifically for a quick escape. 

5. (tie) Pelorus, $300 million

pelorusapMusic mogul David Geffen purchased Pelorus from Russian oligarch Roman Abramovich in May 2011. Since one helicopter pad just isn't enough, this superyacht has two, in addition to two swimming pools and a collection of smaller boats on the tender deck. One guest suite has a wall that lowers to transform into an ultra-private veranda.

5. (tie) Dubai, $300 million 

Dubai yachtThe Dubai, which currently belongs to Mohammed bin Rashid Al Maktoum, Sheikh of the emirate of Dubai, was the most expensive yacht in the wold when it was built by Blohm + Voss in 2006. At 524 feet, it's the third-largest private yacht in the world, and it boasts seven decks, a squash room, helicopter pad, and even a small submarine.

4. A, $323 million

Melnichenko boatThis elegant, Philippe Starck-designed superyacht belongs to Russian oligarch Andrey Melnichenko. Among its luxurious amenities are bath faucets worth $40,000, staircase banisters worth $60,000, and a bed that rotates with the touch of a button, allowing for perfect views of the sunrise and sunset. A has had its fair share of controversies, however, as the Melnichenkos are currently suing Dutch paint corporation Akzo Nobel, claiming the yacht's paint is not as reflective as they had requested. 

 3. Serene, $330 million

serene yachtRussian vodka distributor Yuri Scheffler owns this 440-foot yacht, which has turquoise neon lights that give it a nighttime glow. It has a combined 48,000 square feet of covered space on its seven decks, including indoor and outdoor pools, 12 staterooms, and an outdoor screening room. Scheffler purchased the Italian-designed yacht for $330 million in 2011. 

 2. Eclipse, $485 million

Roman Abramovich Yacht Eclipse Russian oligarch Roman Abramovich purchased the 536-foot-long Eclipse in 2010, when it still held the title for world's largest yacht. Eclipse has two helipads, a disco, cinema, hair salon, and restaurant, plus it's rumored to have a laser defense system against paparazzi trying to photograph high-profile guests. 

 1. Azzam, $627 million

Azzam from the airThe largest and most expensive yacht in the world is a staggering 590 feet long (longer than some commercial cruise ships) and owned by Sheikh Khalifa bin Zayed al-Nahyan, president of the United Arab Emirates. It took German shipbuilders Lürssen Yachts four years to build this behemoth of a ship, which is rumored to have up to 50 private suites. According to Wealth-X, the $627 million purchase was only about 3.5% of Sheikh Khalif's net worth of $17.9 billion. 

BONUS: The Other Two Most Expensive Purchases Of All Time

There have been two other luxury purchases in the range of these superyachts. They were: 

SEE ALSO: The Parking Lot At The American University Of Dubai Is Full Of Amazing Cars [PHOTOS]

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The Closest Thing To Candid Photos Of North Korea You'll Ever See

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After publishing hundreds of photos from six visits to North Korea, it was an offhand comment that got French photographer Eric Lafforgue banned.

Lafforgue had seen Spanish tourists wearing Kim Jung Il shirts and told a friend that they likely wouldn't wear them in Barcelona. The Spaniards heard it and told the guide. One month after returning from the trip, he recieved a letter with screen captures of his photos, saying they were not good for North Korea and that he could not return.

"They know that when I come, I take pictures. They prefer the tourism money, until it causes a problem for one of the people in charge," Lafforgue told Business Insider.

Lafforgue has always been well aware of this, but throughout the years, he's played "their game," as he calls it, to produce some incredible photography. 

“The North Korean regime controls everything that goes out of the country,” he said. “Even me, when they let me take a picture of kids smiling, its because it's good for the country. I take those pictures because there is a real part of the people that are happy and I want to document that ... North Koreans are brainwashed, but they live like everybody in the world.” 

Lafforgue shared a stunning selection of photos from his many trips to North Korea with us. Many of the photos are available in a calender Lafforgue produced with North Korea-watching website NK News.

This is Pyongyang airport, where Lafforgue flew into.



All tourists must go on a guided tour when they visit North Korea. According to Lafforgue, the guides show more to tourists than stated journalists, so he always declared himself a tourist.



Each time Lafforgue visited, the guides tried to take him on the same "classic" tour to the expected sites.



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The 20 Most Fun Colleges In America

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 20 most fun colleges in america

Higher education is certainly an opportunity to study and learn, but college can also be the most fun four years in someone's life. There's good reason for this — college is a time of seemingly endless parties, a constant supply of alcohol, and cherished sports teams to cheer on with fellow students.

In order to find the most fun colleges in the country, we looked at 10 categories from the Princeton Review's 2014 college rankings.

Click here to read our complete methodology.

Many of the schools that made our list share common traits. The typical "fun" school, based on our results, is a large public university with a strong Greek life and competitive athletics.

This is not to say that these colleges are all play and no work. Many of these schools were nationally ranked for their academics as well.

Penn State University was our number one most fun college, but only topped one of the Princeton Review's lists we used — Lots of Beer. The school was included in a whopping eight of the 10 categories we looked at, including high rankings in Students Pack the Stadiums, Everyone Plays Intramural Sports, Jock Schools, and Party Schools.

#20 University of Notre Dame

Notre Dame, Indiana

Due to its single-sex dorms and lack of Greek life, Notre Dame is often thought of as a gendered campus, with little interaction between male and female students.

However, everyone comes out to support the Fighting Irish, Notre Dame's storied sports teams.



#19 University of Missouri

Columbia, Missouri

Athletics are a big part of the Mizzou social scene, and students are strong supporters of their Tigers.

On campus, Greek life makes up much of the partying culture, but Columbia, Missouri is a great college town for those seeking an alternative. 



#18 University of Wisconsin — Madison

Madison, Wisconsin

There's a lot of alcohol at the University of Wisconsin — both beer and hard liquor — and students take advantage of a small, but active Greek scene, as well as other social opportunities in Madison, Wisconsin.

The school has historically participated in two massive annual parties — the State Street Halloween Party in October and Mifflin Street Block Party at the end of the academic year. 



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ELON MUSK: The Incredible Life Of America's Greatest Innovator

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elon musk atlantic cover

Only 14 years after making his first millions, Elon Musk is one of the most influential businessmen alive today. He's involved with more industries than your average person has hobbies.

Rather than use the wealth he's attained for leisure, Musk has repeatedly shown that he would prefer to spend his money on turning his passion projects into companies that change the world.

This year alone, Elon Musk unveiled a concept for high-speed travel between Los Angeles and San Francisco, showed off a rocket the size of a ten-story building taking off and landing vertically, and bought a famous car from the James Bond films so he could personally convert it into a submarine.

SEE ALSO: The 20 Most Impressive People of the Year

Like Mark Zuckerberg, Elon Musk began programming at an early age. Unlike Facebook's founder, he taught himself — and sold the code for his first video game for $500 at age 12.



That isn't to say education wasn't important for Musk: He earned Bachelors degrees in both business and physics from the University of Pennsylvania before venturing into the world of startups.



His first big success came in 1999 when Compaq bought Zip2, an Internet company Musk founded with his brother, in a deal that earned him a cool $22 million.



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The 20 Most Impressive People Of 2013

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Most Impressive People of the Year

Before queuing up "Auld Lang Syne," let's reflect on 2013.

The Year of the Selfie brought us a government shutdown, a new pope, intelligence leaks of unparalleled proportions, and the Hyperloop. Physics' greatest mystery — the theory of how particles acquire mass— was resolved. Some "leaned in," others twerked.

We collectively named "Satoshi Nakamoto," the anonymous inventor of Bitcoin, Business Insider's Person of the Year.

From politics to sports, entertainment, finance, and more, people have done extraordinary things this year. These are the people who impressed us the most (listed in alphabetical order).

"Satoshi Nakamoto," Bitcoin inventor

Most Impressive Person of the Year

Satoshi Nakamoto is the pseudonym used by the anonymous inventor of Bitcoin, the electronic currency that seemingly came out of nowhere and has been taking over financial market headlines since.

Bitcoin is a form of digital currency that doesn't actually exist in the physical world, only as cryptic code in computers. Unlike the U.S. dollar, it's controlled privately, keeps no record of the identity of its owner, and can be transacted without the government's knowledge.

There have since been numerous attempts — comprehensively tracked by Hilary Sargent, AKA Chart Girl— to determine Nakamoto's identity, but nothing conclusive has yet emerged.

Click to get to know Satoshi Nakamoto, our Most Impressive Person of the Year »



Shinzo Abe, Prime Minister of Japan

Prime Minister Shinzo Abe pioneered a three-tier approach — nicknamed "Abenomics" — to get the Japanese economy humming again. The plan buoyed the Japanese stock market up more than 51% year to date.

Abe was elected in 2012 on the promise that he would pursue extremely aggressive stimulative policies, which included weakening the yen. The currency's plunge effectively makes the country's exports cheaper and stoked some moderate inflation.

It seems to be working. The Japanese stock market is at its highest level in almost six years and data shows the country is breaking out of its deflationary slump.

Click to see how Shinzo Abe radically transformed Japan's monetary policy »



Ben Bernanke, Chairman of the Federal Reserve

Federal Reserve chairman Ben Bernanke steered the U.S. out of the worst financial crisis and ensuing recession in the last 80 years.

The methods that Bernanke used to keep the economy going were untested — a highly accommodative monetary policy and near-zero interest-rate policy that's expected to outlast the man himself. His tenure as head of the U.S. central bank ends in January.

Bernanke made transparency and independence hallmarks of his leadership. He shocked market participants earlier this year with the decision not to taper despite pressure from more conservative economic thinkers.

Click for the 16 times when Ben Bernanke was a total badass »



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This Heartbreaking Rendition Of 'All You Need Is Love' Will Convince You To Stop Smoking Or Be Grateful That You Never Started

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A large audience assembled to see the São Paulo University Choir at the city's Museum of Art. When the curtain opened on stage, they clapped as usual, but their smiles soon turned into looks of concern, surprise, and even disgust.

It wasn't the choir they paid to see, but regardless of their initial reactions, they were all riveted: 

The twelve cancer patients worked with seven singers and the guitar lead as part of A.C. Camargo Cancer Center's latest partnership with agency JWT Brazil. The medley of The Beatles' "All You Need Is Love" and "She Loves You" sung through electronic voice boxes and prostheses served as both a celebration of the cancer patients' recoveries and a bold statement against smoking.

JWT Brazil produced the video this month for the cancer center's focus on throat cancer, which is largely caused by smoking. Last month, they tackled breast cancer by employing a female graffiti artist to paste mastectomy scars over street art of naked women, along with a message promoting cancer screenings.

A.C. Camargo's stunt was certainly risky, but regardless of the crowd's reception of the message, the choir of patients received an enthusiastic standing ovation.

This woman with red hair, like most in the audience, was initially confused and uncomfortable. She could barely look at the stage:

choir crowd 1

But after seeing the giddy patients smiling and proudly holding their anti-smoking signs, she couldn't help showing her support:

choir crowd 2

The A.C. Camargo Center is one of the largest oncological treatment, research, and teaching centers in Latin America and has an active public health program.

SEE ALSO: Watch How These Cancer Patients Reacted To Getting Hilariously Awful Makeovers

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17 Name-Brand Products Worth Buying Instead Of Their Generic Versions

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Shoppers can save a lot of money buying generic brands. 

But some products are worth every penny. 

A recent Reddit thread asked which items are worth shelling out for. 

We selected some of our favorite responses. 

1. Shoes. 

"When I was a kid, my mom would always buy the Wal-Mart/KMart/Payless shoes that were no-name brand and my feet hurt all the time," writes IWannaBeAlone. "I'd also destroy them in the space of a month."

Everything changed when the author finally got a pair of Reeboks.

"I was amazed. My feet didn't hurt all the time! They lasted forever!" the happy shoe owner writes.

Miranda kerr reebok

2. Oreos. 

"No off-brand Oreos compare to the real thing," writes cmarmanoreos3. Q-tips. 

"It's the amount of cotton on the tip, which makes it softer," writes ABirdOfParadise. "Some off brands are just sticks with a thread on the end, I swear."q-tips4. SpaghettiO's. 

"Store brand versions are so terrible," writes angiehawkeyespaghetti o's5. Reese's Peanut Butter Cups. 

"The generic brands can never get the peanut butter-to-chocolate ratio right," writes bpxrainreeses peanut butter cups candy6. Crayola crayons. 

"Crayola is glorious," writes kelseykeefe. "Strong colors that are even and layer nicely for value—and don't break on a whim. Crayons7. Legos

"Someone who I blacked out from my memory got me Mega-Blocks once and I resented them until adulthood," writes McLarenF1God. "I never once played with them, nor do I recall when I last saw them."batman legos8. Leatherman. 

"When your generic tool breaks I will let you use my leathermen to fix it, is what I tell my friends," rottinguy writesleatherman tool 9. Heinz ketchup. 

"Nothing else will do," writes Lettuce617Heinz Ketchup 10. Toilet paper. 

"I don't care how much it costs, this is one area of your life where you should just never ever skimp," writes Sh--BeardThePiratetoilet paper roll11. Coca-Cola. 

"No 'cola' cannot even come close," writes Perstacoca-cola coke12. Nutella. 

"I don't know any off-brands of it... And even if they have off-brands, they won't be as good," writes eatfreely.  Nutella13. Contact solution. 

"I bought the generic brand once and I will never buy anything but Opti-Free from now on," writes sandykumquatuse your contacts14. Cheese. 

"I'm very unfussy and can usually always deal with the knock-off brand, even if it's noticeably worse, but cheap cheese is never ever worth it," writes apostrotastrophe.Paski Sir cheese15. Alcohol. 

"Both stronger drinks (rum, whiskey, vodka, etc.) and wine and beers," writes DemonicSquirrelmai tai liquor alcohol rum16. Eggo waffles.

"I'm willing to play the extra $1 for egos so I don't have to deal with those floppy disks from the generic brand," writes kaitepop96eggo_Waffles17. Ghiradelli chocolate chips. 

"Put some in your chocolate chip cookies and prepare to be amazed," writes StankCheesechocolate chip cookies baking

SEE ALSO: 20 Items Under $20 Everyone Should Own

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A Person Flying First Class Just Showed An Act Of Kindness That Wowed Passengers In Coach

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Yesterday, on Delta flight 928 from Denver to New York City, a passenger in first class was selfless.

According to Floored CEO Dave Eisenberg, who was also on the flight, the passenger gave up the top-notch seat. This person traded spots with another passenger in uniform, who was sitting in a middle seat in coach.

The tweet is being passed around as a source of inspiration just in time for the holidays.

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The World's Most Spectacularly Modern Places Of Worship

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Neue Synagogue Mainz

Church architecture often reflects the grandiosity of the higher power people gather to worship. In recent years, architects have sought out the most eye-catching designs possible.

But it's not just about having a steeple and pews. Some houses of worship mimick shapes in nature, like the Leaf Chapel in Hokuto, Japan. And the the Neue Synagogue in Mainz, Germany, is shaped like the Hebrew word Kedushah, meaning blessing.

Experts at the international building database Emporis.com rounded up a selection of the world's most spectacular churches based on modern architecture and design.

Catedral Metropolitana Nossa Senhora Aparecida is a Roman Catholic church in Brasilia, Brazil. Designed by famed architect Oscar Niemeyer, it consists of 16 concrete pillars.



Cathédrale de la Résurrection, a Roman Catholic cathedral in Évry, France, is unique for its rotund main sanctuary. Designed by Mario Botta Architetto, it is finished with brick and topped with 24 linden trees, meant to symbolize life.



The Chapel of the Holy Cross is a Roman Catholic church built into the buttes of Sedona, Arizona. Designed by Anshen + Allen, it's nicknamed "Beverly Hills of the Rocks."



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Math Says You Should Buy A Mega Millions Ticket Right Now

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man with a pile of money

Earlier this year, we considered the math behind deciding when to buy a Powerball ticket.

Now, the Mega Millions jackpot has reached a ludicrously high $636 million, and so we decided to repeat the analysis for this lottery— ahead of tonight's drawing is at 11 PM EST.

The most basic thing to consider in any game of chance, whether you are looking at a lottery, a roulette wheel, or a deck of cards in a blackjack game, is your expected winnings from the game. This is basically a measure of how much you will win on average by playing the game a large number of times.

The expected winnings for a game can be found if we know the probabilities of the different outcomes in the game, and the earnings (or losses) associated with each outcome. We multiply the probabilities by the earnings or losses, and then add these up.

The expected value will tell us what will happen on average if we play a game a large number of times. If the expected value is positive, then on average we are winning money, and so if we play the game long enough, we should end up in the black. If the expected value is negative, then on average we are losing money, and so we should not be playing this game.

We can find the expected value for playing Mega Millions with the current ridiculous jackpot. In Mega Millions, you pick five different numbers between 1 and 75, and one number between 1 and 15. If all six match, you win the jackpot. If you match some of the first five numbers and/or the last number, you win a smaller prize.

The Mega Millions website helpfully includes the odds of winning either the jackpot, or of winning various smaller prizes. Since the cost of a Mega Millions ticket is $1.00, we can subtract this from each of the prizes to get our actual take home winnings for each of these outcomes, and so find the expected value of a Mega Millions ticket:

mega millions expected 3

The first column shows each outcome — how many of the five numbers from 1 to 75 we got right, and whether or not we got the last number from 1 to 15. The second column shows the prize and the third the prize less our investment of a dollar per ticket. In the fourth column, we have the odds of getting each outcome, as per the Mega Millions website. In the fifth column, we convert those odds into a probability between zero and one by taking the reciprocal of the odds. Finally, we multiply together our winnings less investment by the probability, and sum these up, giving us the expected value.

Notice that by far our most likely outcome is that we get none of the numbers right. There is about a 93% chance that we just wind up losing our dollar. Despite this, since the jackpot is so enormously high right now, our average winnings are a nice positive $1.63, indicating that we should consider buying a ticket.

Another notable property of Mega Millions is that the lower prizes do not help us too much. Without that jackpot, the expected value is a very unhappy —$0.82. So, Mega Millions really is all about the jackpot.

One factor to consider is that, as with most lotteries, there are two options for the prize: the advertised prize of $636 million is based on a thirty year annuity, receiving the prize in smaller annual chunks for thirty years. The other option is to take cash up front, but at a huge discount. Today's up front cash prize is $341 million — a big drop, but nothing to sneeze at. We can find the expected winnings for taking the cash up front:

mega millions expected up front

The expected value of a Mega Millions ticket here is lower — just $0.49 as opposed to the $1.63 taking the annuity — but it is still positive, and this is still a viable option.

There are other confounding factors — you also have to consider the effect of taxes, and how that plays with both options. Even though this lottery has a positive expected value, it has an extremely high variance and standard deviation, owing to the fact that there is one very, very unlikely outcome where you do incredibly well, and the overwhelming majority of the time, you just lose a buck.

The most interesting confounding factor is the possibility of multiple winners. How many people are playing will affect the odds of a split and the size of the resulting jackpot (whether it is broken in to two parts, or three, or four, or however many winners there are). We can, however, estimate the expected value of a ticket based on how many tickets have been sold, and thus on the odds of a split, and the consequent value of the jackpot:

ticket split

The horizontal axis shows the number tickets sold, in millions, and the vertical axis shows the expected value in dollars of a ticket, based on the likelihood of a split, and the size of a split jackpot. The blue curve shows the outcome for taking the annuity prize, and the red line shows the outcome for taking the cash prize.

Here, we can see that the expected value of a ticket stays positive (meaning you should consider buying a ticket) as long as fewer than 730 or so million tickets have been sold. The cash prize fares far worse — you run into expected losses with only 265 million tickets sold. 

So, as long as there are fewer than 730 million tickets sold, a fairly likely situation right now, the expected value of a ticket should be positive, and so you should consider buying a Mega Millions ticket today.

Bear in mind that there are many caveats to this analysis. Taxes will likely hurt your expected winnings pretty severely — the Feds will take about 40%, and your home state will claim anywhere from 0% to around 13%.

A lot of people have been buying tickets, and as discussed above, this will greatly increase the odds of a tie, and the reduced payout that goes with it.

The value of the annuity opposed to the cash payout can also be a complicated question — it is certainly possible that one could take $341 million and, through prudent investment, end up with a better 30 year return than the total advertised value of the $636 million annuity.

Given the questionable returns and extreme variance of the lottery, while the expected value of a Mega Millions ticket might be positive, the more cautious investor may want to consider instead adding that dollar to his IRA for a much smaller, although safer, return. Of course, that is a far less fun option than going out and writing your six favorite numbers on a ticket.

SEE ALSO: A New Online Dating Algorithm Will Match You With Someone You Might Actually Have A Chance With

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Michael Jordan's Extravagant Estate Fails To Sell At Auction

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michael jordan house1

Michael Jordan failed to sell his extravagant Chicago home at auction on Monday, according to CNN. The auction was scheduled for last month but was postponed after potential bidders wanted more time. 

To participate in the auction, bidders had to put up a bond worth $250,000.

The 56,00o square-foot-compound went on the market in February 2012 for $29 million and failed to sell even after dropping the asking price to $21 million in January of 2013.

Michael Jordan's spokesperson told CNN:

"We are disappointed that the high bid in today's auction of Michael Jordan's residence in Highland Park did not meet the reserve price...we will be evaluating options for the property in the new year."

The home is located in Highland Park,  just north of Chicago and features a full-sized NBA regulation indoor basketball court, 9 bedrooms, 15 baths,- and a putting green.

Click here to tour the estate >

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Inside Florida's Beautiful And Strange Mermaid Theme Park [PHOTOS]

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weeki wachee mermaids

An hour’s drive from Tampa, Florida, there's a spring so deep that no one has ever found the bottom.

And in that spring, beautiful women with intricate fishtails swim through the 74-degree water that bubbles up out of the ground.

Welcome to Weeki Wachee Springs, where "mermaids" are real and perform three shows every day.

Click here to jump right to the mermaid photos >>

The park was opened in 1946 by a former Navy officer named Newton Perry who had previously trained SEALS to swim underwater. After happening upon the spring, he built a theater with 18 seats six feet below the surface. In those days, if the female performers heard a car passing by on highway U.S. 19, they'd run to their pedestals in their swimsuits and wave to the passers-by to come see their show.

In 1959, the park was purchased by the American Broadcasting Co. and a new, larger theatre was built with 500 seats 16 feet below the surface. Celebrities like Elvis Presley and Esther Williams began to flock to the shows, which by then featured as many as 35 mermaids. 

But with the opening of larger parks like Disney World, people began to lose interest in the vintage-y mermaid park. In 2003, Weeki Wachee was threatened with permanent closure, but a campaign by the current and former mermaids saved it. Today, it's an official Florida State Park.

British photographer Annie Collinge first stumbled upon the park online, and the more she read about it, the more she realized she needed to visit the park herself to believe it.

"I was actually having a look at a website about the Coney Island Mermaid Parade and there was an interview with a guy that makes Mermaid tails," she explained in her artist's statement. "They asked him what first inspired him to start making them and he said that he had grown up next to the Weeki Wachee Springs.  I had a look on Google and instantly knew I had to go there."

What she discovered was a group of women who not only love their jobs, but who are exceptional swimmers and athletes as well.

"The thing that you don't realise about their job is, its very physically demanding," Collinge says. "They all have advanced Scuba qualifications and are very strong swimmers.  To get into the theatre you have to swim without air down a tunnel with their tails on, and that is definitely not for the faint-hearted."

Collinge’s exhibition, “Annie Collinge: The Underwater Mermaid Theater,” is currently on display now through January 5 at the Ogden Museum of Southern Art. You can follow the photographer on Facebook and Instagram, as well as on her website.

Welcome to Weeki Wachee Springs, the vintage mermaid park that was first opened back in 1946 by a former Navy officer named Newton Perry.

Source: Weeki Wachee Springs



Newt trained the girls to swim with air hoses that were peppered throughout the landscape so they didn't need to use a visible breathing apparatus or carry an air tank on their backs.

Source: Weeki Wachee Springs



The women perform 16 to 20 feet below the surface where the current runs a strong five miles an hour. Even staying in one place takes an immense effort.

Source: Weeki Wachee Springs



See the rest of the story at Business Insider
    






The Most Blinding Christmas Decorations On Instagram

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The countdown to Christmas is on. Whether you celebrate the day or not, you can still spend the month of December enjoying the festive holiday light displays.

We scoured Instagram to find some of the coolest Christmas lights on houses across the country. California seems to really go all out.

This home on Balboa Island near Newport Beach, Calif., is practically blinding.

34th Street in Baltimore, Md., is known as "Christmas Street." We can see why.

This Burbank, Calif. home features a merry-go-round and some recognizable film characters.

This Dallas, Tex. house has more Santas than we care to count.

You don't see too many penguins in Tucson, Ariz., but here's a festive one.

And here are some videos of elaborate holiday light decorations around the country.

These homes in Dyker Heights in Brooklyn, N.Y., put on quite a light show.

Deacon Dave's house in Livermore, Calif., has become a tourist attraction.

SEE ALSO:  25 Awesome Gifts Under $25 For Your Office Secret Santa Pool

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This British Academy Trains Butlers For Wealthy Families Around The World [PHOTOS]

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butler training

From Batman's Alfred Pennyworth to Downton Abbey's Carson, the British Butler is a character that has been immortalized in pop culture countless times

Though the British model of home service has been around for centuries, it continues to rise in popularity in affluent households all over the world.

Sara Vestin Rahmani founded the British Butler Academy to meet the growing demand. 

"Anyone trained in the British method has the potential to become very good," Vestin Rahmani said to Business Insider. "In Britain we have this old-school hierarchy and military tradition that's really important, especially because the royal family is very prominent. Other markets and other countries are fascinated by that." 

Vestin Rahmani and her team of 25 butler instructors aim to recreate that model in homes across the United Kingdom and the world. Courses are taught in central London year-round, catering to private, wealthy individuals who want to have their staff trained in the British tradition. They'll also travel to other countries, including the United States, to troubleshoot with staffs of five-star hotels, restaurants, and even superyachts. 

"We teach British butlering, but we're a modern trade, so we'll bring it into China, the Middle East, and America," Vestin Rahmani said.

Butler trainees go through a rigorous training program that includes 20 different modules: etiquette, silver service, valet, wardrobe management, and pet care, just to name a few. They also learn to behave with tact towards their employers, many of whom draw significant media attention in countries all over the world.

"People who hire butlers — often the media are interested in them, so discretion and paparazzi security are very important," she said. 

Though the British tradition is globally known, Vestin Rahmani says that being British isn't the only thing that makes a good butler. 

"The most important thing is that they need to have service at heart. They've got to love to serve people — as long as you work as a butler you're basically giving up your life for the sake of the contract," she said. 

Reuters photographer Olivia Harris traveled to the Norfolk countryside last July to take a closer look at what goes on during a special intensive session of the British Butler Academy that runs in the summer. 

Anyone can apply for the intensive 14-day summer course, though only about 1 in 4 applicants will be accepted to the program. It costs about 3,000 pounds for two weeks in Norfolk, where trainees live in residence and practice their skills in situations that mimic real life. 

"If they're lucky or do really well we can find them a job," Vestin Rahmani said. 

Here, head butler trainer George Telford leads trainees in carrying punch and canapes during the intensive summer course. 

butler training

 Telford discusses the proper way to carry a cake stand with trainees. 

"Each time we have meals, everything must be set up to perfection," Vestin Rahmani said.

butler training

Telford knew he wanted to be a butler when he was just 11 years old, according to Vestin Rahmani.

"He's worked his way up from nothing and has built a great career as a butler," she said. "He represents us really well, also this industry that we're very proud of."

Butler training

Posture is very important for a butler's image. 

Butler training

Trainee Dwayne Cross learns how to use a feather duster. 

Butler training

Trainee Ben Mandeng serves a glass of champagne to Vestin Rahmani. 

Butler training

SEE ALSO: Check Into The New York Palace's Lavish 'Jewel' Suite For $25,000 A Night [PHOTOS]

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The Most Interesting Cars Of 2013

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2014 Chevrolet Corvette yellow

Google has released its 2013 Zeitgeist, its annual breakdown of what people searched for online this year.

That included data for searches in the U.S. for new car models in two forms: most searched, and trending.

The first measures sheer volume of searches. Trending measures the increase in search volume from the previous period (2012).

Both categories provide insight into the cars Americans most want to know about — in other words, the most interesting cars on the road.

There are few surprises here. Most of the models here have big fan bases (like the Camaro and Corvette) or are perennial best-sellers (like the F-150, Civic, and Accord).

These were the new cars people searched for most in 2013:

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And the top trending new models:

Here are the top trending car companies in 2013. It's surprising no General Motors brands are on the list — the automaker has had an excellent year, which it topped off with an official end to the government bailout and the announcement that Mary Barra will become the industry's first CEO next month.

SEE ALSO: Big Chunks Of The US Couldn't Care Less About Tesla

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A Fascinating New Poll Shows That Americans Are Losing Faith In God

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jesus christ painting Ary Scheffer

A new Harris Poll released today reveals that only 74% of Americans believe in God, an 8% decline since 2009.

Before today, U.S. adults had remained fairly consistent in their religious beliefs — 82% of U.S. respondents previously reported that they believed there was a God since 2005.

In another decline, only 54% of Americans are now "absolutely certain" in God's existence, a 12% decrease over the last decade.

Not all of us feel this way. The groups most likely to be certain of God's existence are Black Americans (70%), Republicans (65%), Baby Boomers (60%), Southerners (61%), and Midwesterners (58%), as well as anyone with a high school education or less (60%).

A few other notable takeaways from the poll:

  • Almost a quarter of Americans (24%) believe in reincarnation

  • Only 1% of U.S. adults believe God is a woman, and more women than men are likely to believe that God is male (43% women, 34% men)

  • 23% of Americans say they are "not at all" religious, a figure that has nearly doubled since 2007, when it was 12%

  • 42% of Americans believe in ghosts, only slightly less than the 58% who believe in Hell and the Devil

The poll was conducted this past November, with 2,250 adults responding. The questions were administered by a computer, which the researchers explained led to more "accurate" data:

Other research has shown that when replying to a question administered impersonally by a computer, people are less likely to say they believe in God, or attend Church services when they really don't. It is generally believed that surveys conducted by live interviewers tend to exaggerate the numbers of people who report the socially desirable, or less embarrassing, behavior, and that the replies given to an online survey such as this, are more honest and therefore more accurate.

Check out some more data from the Harris Poll below.

 Harris Poll religion data

Harris Poll religion data

See the rest of the charts at Harris Interactive.

SEE ALSO: The World's Most Spectacularly Modern Places Of Worship

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