So a quasar at an absolute magnitude of − 25. 5 is 100 times brighter than our galaxy ( because ( 10 < sup > 0. 4 </ sup >)< sup >(− 20. 5 -(− 25. 5 ))</ sup >

So assume ƒ is differentiable at 0, as a function of two real variables from Ω to C. This is equivalent to the existence of two complex numbers and ( which are the partial derivatives of ƒ ) such that we have the linear approximation

So P < sub > n </ sub > agree with the Bernoulli polynomials on the interval ( 0, 1 ) and are periodic with period 1.

So even if the wheel has landed on red in ten consecutive spins the probability that the next spin will be black is still 48. 6 % ( assuming a fair European wheel with only one green zero: it would be exactly 50 % if there were no green zero and the wheel were fair, and 47. 4 % for a fair American wheel with one green " 0 " and one green " 00 ").

" So if you write something that knows 1. 0, what should you do if you encounter 2. 0 or 1. 1?

So a trash bag may be originally specified as 0. 35 mil thick, but stated as 8. 89 microns.

So any point P =( x, y ) on the parabola will be equidistant both to ( 0, f ) and ( x ,- f ).

So, the parabola can be written as ; and for a parabola such as f ( x )= x², the a coefficient is 1, so the focus F is ( 0, ¼ )

So we can conclude that the original proposition, ¬ p, must be true — " there is no smallest rational number greater than 0 ".

So, a diver with a 3 litre oxygen cylinder filled to 200 bar who leaves 25 % in reserve will be able to do a 450 minute = 7. 5 hour dive ( 3 L × 200 bar × 0. 75 / 1 ).

So, to completely react with 85. 0 g of ( 0. 532 mol ), 28. 7 g ( 1. 06 mol ) of aluminium are needed.

So for each angle one has to compute the intersection point ( s ) of the ray with the circular object and then sum the contributions for a certain number of angles between 0 and.

Indium antimonide, an example of a high mobility semiconductor, could have an electron mobility above 4 m < sup > 2 </ sup >· V < sup >− 1 </ sup >· s < sup >− 1 </ sup > at 300 K. So in a 0. 25 T field, for example the magnetoresistance increase would be 100 %.

So the item set 0 ( without lookaheads ) will look like this:

So, if n > 0 is an integer and there are integers 1 < a, b < n such that n = a × b, then n is composite.

So 0. 0123 would be written as 1. 23 * 10 < sup >- 2 </ sup >.

So the observer's position can be determined within ( theoretically ) 0. 2 miles, about 400 yards ( 370 m ).

So F can be replaced by F-G and G by the constant function 0, making the goal to prove that an everywhere differentiable function whose derivative is always zero must be constant:

So to take the example, if in market X company B ( with 10 % market share ) suddenly bought out the shares of company C ( with 10 % also ) then this new market concentration would make the index jump to 0. 162.

So, knowing log < sub > 10 </ sub >( 2 ) = 0. 301, the rest can be derived:

So, B1 is between A0 and A1 in size, with an area of 0. 707 m ( m ).

So for each list, we will have an matrix of zeroes and ones: is 1 if intervals and intersect, and 0 if they do not intersect.

So, if the Orioles are to improve, Brandt, Triandos and Walker will have to do it.

So obvious are these advantages that nearly 95 per cent of the population of New York State now has access to a system, and enthusiastic librarians foresee the day, not too distant, when all the libraries in the state will belong to a co-op.

So the Kirov will fly back to Russia, minus a Chicago engagement, a serious loss for dance fans -- and for the frustrated bookers, cancellation of one of the richest bookings in the country.

So it will be at the close of the age also known as the Last Day.

So, if a person has lived a good life, they will be rewarded in the afterlife.

So, according to Obadiah there will not remain even a remnant after Edom ’ s judgment ; This is in contrast to Amos 9: 12, where Amos refers to such a remnant, however, it is stated that their possession will be given to Israel.

So it is up to the software to decide in which direction these " weak " characters will be placed.

So if an electron passes through a double slit apparatus there are various probabilities for where on the detection screen that individual electron will hit.

So, in him, " all of them will rise again with their own bodies which they now bear ," but Christ " will change our lowly body to be like his glorious body ," into a " spiritual body "

So while there are many factors affecting the outcome of a trial, the cross-examination of a witness will often have an impact on an open minded unbiased jury searching for the certainty of facts upon which to base their decision.

James's tone delighted Elizabeth, who responded: " So trust I that you will not doubt but that your last letters are so acceptably taken as my thanks cannot be lacking for the same, but yield them to you in grateful sort ".

So there is no one source node for a key, and attempting to find where it is currently stored will result in it being cached more widely.

So the data in a newly started Freenet will be distributed somewhat randomly.

In 1702, Thomas Savery wrote in The Miner's Friend: " So that an engine which will raise as much water as two horses, working together at one time in such a work, can do, and for which there must be constantly kept ten or twelve horses for doing the same.

So if there are m factors, there will be 2 < sup > m </ sup > idempotents.

In this way he manifests " So the anarchist individualist tends to reproduce himself, to perpetuate his spirit in other individuals who will share his views and who will make it possible for a state of affairs to be established from which authoritarianism has been banished.

" So in this view, what human beings — you and I think of as our free will does not really exist.

So though workers may labor with greater skill or more productivity than others, these more skillful and more productive workers will thus produce more value through the production of greater quantities of the finished commodity: each unit still bearing the same value as all the others of the same class of commodity.

So, an aircraft traveling at Mach 1 at 20 ° C or 68 ° F, at sea level, will experience shock waves in much the same manner as when it is traveling at Mach 1 at 11, 000 m ( 36, 000 ft ) at-50 ° C or-58F, even though it is traveling at only 86 % of its speed at higher temperature like 20 ° C or 68 ° F.

So the logarithm cannot be defined for the whole complex plane, and even then it is multi-valued – any complex logarithm can be changed into an " equivalent " logarithm by adding any integer multiple of 2πi at will.