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PDF Editor FAQ

How many even numbers are there with three digits such that if 5 is one of the digits, then 7 is next digit?

There are exactly 900 3 -digit numbers. Half of these are even and half are odd.So, we have 450 3-digit even numbers. From these even numbers, we should subtract out the count of 3-digit even numbers that have 5 as a digit but where 5 is not immediately followed by 7.In a 3 -digit number the digit 5, if it appears, can do so at the unit's place, the ten's place or the hundred's place. We'll consider these case by case5 in the unit's place: No even number possible with this arrangement.5 in the ten's place: All such 3-digit even numbers violate the rule that 5 should be followed by 7, hence the count of all such numbers should be subtracted from the count of 3-digit even numbers. To calculate the count of such numbers, we note that the hundred's place can be filled in 9 ways, the ten's place can be filled in 1 way and the unit's place can be filled in 5 ways. So, we have 45 such numbers (9x1x5)5 in the hundred's place: All 3-digit even numbers which have 5 in the hundred's place, and do not have 7 in the ten's place have to be counted. So, we have 1 way to fill the hundred's place, 9 ways to fill the ten's place and 5 ways to fill the unit's place. So, the count of such numbers is 45 (1x9x5). However, due to principle of inclusion and exclusion, we will have to add back the count of numbers that have 5 in both the ten’s place and the hundred’s place. There are 5 such numbers, viz., 550, 552, 554, 556, 558Therefore the count of numbers that satisfy the given criteria = 450 - 45 - 45 + 5 = 365

What are some of the most mind-blowing facts?

(This will blow your mind) Few of the ringtones in the old Nokia phones were actually coded in morse. One such code is like this (… __ …),which when decoded gives SMS. And there is also another which translates to “connecting people”. You can just search for the audio files to check.Burj Khalifa ,which currently holds the record of the tallest building in the world with a height of 828 metres will lose its title to Jeddah Tower in 2020 whose height being approximately 1km. Its initial proposed height was 1 mile ,but due to unsupportive geographical conditions it is limited to 1km.[Bonus fact- Burj Khalifa was built by Samsung]India is one of the most stable economic countries in the world. This was proved when India sustained the two great recessions in the world despite being a developing country.Some obvious facts about the universe…The Milky way galaxy is a huge city of stars,so big that even at the speed of the light ( which is the fastest),it would take 100,000 years to travel across it.The Milky Way moves through space at a velocity of about 552 kilometres per second (343 miles per second) with respect to the Cosmic Microwave Background radiation.The Milky Way’s central core contains a supermassive black hole. It is commonly referred to as Sagittarius A*. It contains the mass of about 4.3 million Suns.Proxima Centuari is the nearest star to the Earth which is just 4 light years away.Curiosity is not the only rover sent to the Mars for exploration. In total 13 rovers or artificial objects were sent to Mars. Although many are defunct now after serving their purpose and only these three are operational currently (Spirit[MER A],Opportunity [MER B] , Curiosity).The money spent on Mars Orbiter Mission (a.k.a Mangalyaan) ,a probe sent to Mars by the Indian Space Research Organization is lesser than the money spent on the movie Gravity (former 74 million dollars and latter 100 million dollars).Asteroids are the leftover pieces in the solar system and they actually were to form a planet, but it was Jupiter’s huge gravitational pull that stopped them.Some asteroids have moons of their own!Some bizarre facts…The total weight of all the ants on earth is about the same as the weight of all the humans on earth.There is enough fuel in a full tank of a jumbo jet to drive an average car four times around the world.A human will create enough saliva to fill two average size swimming pools during his/her lifetime.It was Hitler who actually started the Anti-Tobacco movement in Germany.Some facts about the Tech Giants…Google has been acquiring, on average, more than one company per week since 2010.Samsung’s revenue is 3 times bigger than Apple’s revenue.Microsoft holds over 10,000 patents and files around 3,000 every year, ranking as one of the top five patent owners in the U.S.How much energy does a single Google Search take up? Google says it’s about 1KJ (Kilo Joules). In green terms, it’s approximately equal to .2g of CO2 emitted per search.˜Macintosh’ is in fact a variety of apple. It also was the first commercially successful personal computer that resembles the ones we use today. It was the first ones to have a graphical user interfaces (GUI) and mouse instead of command line interfaces.The first version of Microsoft Excel was not made for Microsoft DOS but forApple Machintosh.(IBM made the first smartphone)Before Apple revolutionized the mobile landscape with the iPhone, IBM proved it was way beyond the curve when it released the Simon Personal Communicator in 1994. Yes, the massive handset lacked web browser support, but it featured email access and the ability to send faxes.(IBM’s early tech innovations formed today’s PC industry).Floppy disks and hard disk drives might seem archaic for modern times, but the technologies have laid the groundwork for multimedia storage. We tip our hat to IBM for creating both, along with the magnetic stripe, RAM, relational databases, UPC bar codes, and the world’s first disk storage system: RAMAC.Amazon's warehouses have more square footage than 700 Madison Square Gardens and could hold more water than 10,000 Olympic Pools.Edit: Sun rises in the East, and sets in the west. You know what, this is a misconception. This only happens during equinoxes, two times a year. And during the rest of the year it rises somewhere in the horizon.Edit: For those who want to know such facts,download an application called "curiosity" from the google play store.

Why is Japan's Shinkansen so expensive?

To operate a Shinkansen line in Japan (in my case, the Tokaido Shinkansen), you have to pay for the following:Trains. it can cost you 4 billion yen per train set (16 cars). These trains usually have 20 to 25 years of life.Rail. it cost you 6,500 yen per meter. you need 2 per railway track and you have 2 railway tracks. The Tokaido Shinkansen is 552 kilometers long and has to be replaced about every 10 years.Electricity. To run a train from Tokyo to Shin-Osaka (the Tokaido Shinkansen), you have to pay 300,000 yen for electricity. There are about 320 trains per day in Tokaido Shinkansen. That’s 35 billion a year.Maintenance cost. JR Central overhauls their Shinkansen trains every 4 years. In these 4 years, they also perform some basic checks and maintenance on their train. A train will be checked for over 500 times in this 4 year. And the cost of these maintenances is about 200 million yen per train set. And they have 127 train sets in service. That means 25.4 billion per yearDevelopment cost. They keep improving their facilities and technology for safety. This cost is huge, around 450 billion this year.Salary. The average annual salary of their employees is around 7.25 million yen. JR Central has 18,000 employees and we can count 1/3 of them are specified for operating the Shinkansen, that’s 43 billion per year.Debt from the JNR. Before JR Central is founded, the JNR (Japan National Railway) has a debt over a trillion yen, JR Central has to pay for the debt every year with a huge amount of 255 billion yen.Let’s sum it up:Train = 4 billion × 127 sets ÷ 25 years = 20.32 billionsRail = 6,500 × 1000 meters × 552 km × 2 per track × 2 ÷ 10 years = 1.44 billionsElectricity = 300k × 320 × 365 days = 35.04 billionsMaintenance = 2 million × 127 sets = 25.4 billionsDevelopment = 450 billionsSalary = 43.5 billionsDebt = 255 billionsTo run a Shinkansen a year, it will cost you about 830.7 billion yen per year, or 2.27 billion yen per day. So they must make at least 2.27 billion yen every day.So how well JR Central can do? A 16-car train set can carry 1,323 passengers. For flights, over 58% of seats are sold can make a profit. This is hard to predict for a Shinkansen because they don’t always make the whole journey right? You may get off at Nagoya but somebody may start their journey at Nagoya. Let’s assume 45% are sold here.Including children / green car, we assume 13,500 yen be the ticket price, we have 1,323 × 45% seats are filled with passengers each trip and there are around 320 trains per day and we got: 13,500 × 595 tickets × 320 trains = 2,570,400,000 or 2.57 billion.It’s the ticket expensive? I do think so but actually not that bad. Don’t think JR Central can make a lot of profit because they have a lot of local lines losing money. Almost 90% of the revenue comes from Tokaido Shinkansen. Image what would happen If they lose it…Disclaimer: All value I got is from the Internet and this comparison is nothing official. You should assume there are errors and this calculation is not precise. I am just a railway transportation fan, not an accountant, not good at math at all. Just an estimation for this question, don’t use it as your report or something like that. I take no responsibility for this calculation.

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