Since 2006, he has hosted the 11am – 3pm shift on 612 ABC Brisbane, with the show's first hour — known as The Conversation Hour — also broadcast on 702 ABC Sydney.

Since p ( x ) is irreducible, this means that p ( x ) = k ( x − a ), for some k ∈ F

Since the algorithm ensures that the remainders decrease steadily with every step, r < sub > k − 1 </ sub > is less than its predecessor r < sub > k − 2 </ sub >.

In the first step, the final nonzero remainder r < sub > N − 1 </ sub > is shown to divide both a and b. Since it is a common divisor, it must be less than or equal to the greatest common divisor g. In the second step, it is shown that any common divisor of a and b, including g, must divide r < sub > N − 1 </ sub >; therefore, g must be less than or equal to r < sub > N − 1 </ sub >.

Since r < sub > N − 1 </ sub > is a common divisor of a and b, r < sub > N − 1 </ sub > ≤ g.

Since the first part of the argument showed the reverse ( r < sub > N − 1 </ sub > ≤ g ), it follows that g = r < sub > N − 1 </ sub >.

Since bosons carry one unit of angular momentum, the fermion's spin direction will flip from + to − ( or vice versa ) during such an exchange ( in units of the reduced Planck's constant ).

Since 2 < sup >( q − 1 )</ sup > ≡ 1 ( mod q ), raising both sides of the congruence to the power x gives 2 < sup >( q − 1 ) x </ sup > ≡ 1, and since 2 < sup > p </ sup > ≡ 1 ( mod q ), raising both sides of the congruence to the power k gives 2 < sup > kp </ sup > ≡ 1.

Since p is prime q − 1 must be a multiple of p. Of course, if the number m = < sup >( q − 1 )</ sup >⁄< sub > p </ sub > is odd, then q will be even, since it is equal to mp + 1.

Since ω = − dΦ / dt and k = + dΦ / dx, the wave velocity is v = dx / dt = ω / k.

Since the r < sup > th </ sup > failure comes last, it remains to choose the k trials with successes out of the remaining k + r − 1 trials.

Since 2000, a small amateur experimental planting has been underway in the Lake Champlain valley of Vermont at the Vermont Experimental Cold-Hardy Cactus Garden where winter temperatures can reach − 37 ° C with variable snowcover.

Proof: Since p is a prime number the only possible values of gcd ( p < sup > k </ sup >, m ) are 1, p, p < sup > 2 </ sup >, ..., p < sup > k </ sup >, and the only way for gcd ( p < sup > k </ sup >, m ) to not equal 1 is for m to be a multiple of p. The multiples of p that are less than or equal to p < sup > k </ sup > are p, 2p, 3p, ..., p < sup > k − 1 </ sup > p = p < sup > k </ sup >, and there are p < sup > k − 1 </ sup > of them.

Since methane clathrates are stable at a higher temperature than liquefied natural gas ( LNG ) (− 20 vs − 162 ° C ), there is some interest in converting natural gas into clathrates rather than liquifying it when transporting it by seagoing vessels.

Since the fundamental theorem of arithmetic applied to a non-zero integer n that is neither 1 nor − 1 also asserts uniqueness of the representation for p < sub > i </ sub > prime and e < sub > i </ sub > positive, a primary decomposition of ( n ) is essentially unique.

Since the topology on R < nowiki ></ nowiki > X < nowiki ></ nowiki > is the ( X )- adic topology and R < nowiki ></ nowiki > X < nowiki ></ nowiki > is complete, we can in particular apply power series to other power series, provided that the arguments don't have constant coefficients ( so that they belong to the ideal ( X )): f ( 0 ), f ( X < sup > 2 </ sup >− X ) and f ( ( 1 − X )< sup >− 1 </ sup > − 1 ) are all well defined for any formal power series f ∈ R < nowiki ></ nowiki > X < nowiki ></ nowiki >.

Since 255 = 2 < sup > 8 </ sup >-1, it is a Mersenne number, and the fourth such number not to be a prime number.

Since June 1, the Eleventh Air Force has made 1, 454 sorties against Kiska, dropping 1, 255 tons ( 1, 138, 529 kg ) of bombs.

Since the number of lives is stored in the game as an 8 bit unsigned integer, the subtraction from zero will cause the integer to wrap around to the largest value representable with 8 bits, which is 255 in decimal.

The number of neutrons, N, is known as the neutron number of the atom ; thus, A = Z + N. Since protons and neutrons have approximately the same mass ( and the mass of the electrons is negligible for many purposes ), and the mass defect is usually very small compared to the mass, the atomic mass of an atom is roughly equal to A.

Since we are assuming circular motion, let r ( t ) = R · u < sub > r </ sub >, where R is a constant ( the radius of the circle ) and u < sub > r </ sub > is the unit vector pointing from the origin to the point mass.

Since the separation of variables in this case involves dividing by y, we must check if the constant function y = 0 is a solution of the original equation.

Since all probabilities p < sub > i </ sub > add up to one: p < sub > 1 </ sub > + p < sub > 2 </ sub > + ... + p < sub > k </ sub > = 1, the expected value can be viewed as the weighted average, with p < sub > i </ sub >’ s being the weights:

Since 1989-867 = 1122, we form a new pair of numbers

Since each region is triangular and each edge is shared by two regions, we have that 2e = 3f.

Since there are 24 hours in a day and 360 degrees in a circle, the sun moves across the sky at a rate of 15 degrees per hour ( 360 °/ 24 hours = 15 ° per hour ).

Since they derive from a strong acid but weak base, they are both at about pH = 5 ; as a consequence, the morphine salts are mixed with small amounts of NaOH to make them suitable for injection.

Automobile exhaust gas capture has also been proposed to be economical but would require extensive design changes or retrofitting .< ref name = Musadi2011 > Since carbonic acid in seawater is in chemical equilibrium with atmospheric carbon dioxide, extraction of carbon from seawater has been studied.

Since the harmonic series, obtained when s = 1, diverges, Euler's formula ( which becomes ) implies that there are infinitely many primes.

Since the column vectors of A are the row vectors of the transpose of A ( denoted here by A < sup > T </ sup >), column rank of A equals row rank of A is equivalent to saying that the rank of a matrix is equal to the rank of its transpose, i. e. rk ( A ) = rk ( A < sup > T </ sup >).

Since 5 < sup > 2 </ sup > + 12 < sup > 2 </ sup > = 13 < sup > 2 </ sup >, ( 5, 12, 13 ) forms a Pythagorean triple.

Since τ refers to a vertical path, the optical depth for a slant path is τ ′ = m τ, where m is called the relative airmass, and for a plane-parallel

Since the E1 component of nuclear EMP depends on the prompt gamma ray output, which was only 0. 1 % of yield in Starfish Prime but can be 0. 5 % of yield in pure fission weapons of low yield, a 10 kiloton bomb can easily be 5 x 8 % = 40 % as powerful as the 1. 44 megaton Starfish Prime at producing EMP.

Since the surface area of a sphere of radius r is A = 4πr < sup > 2 </ sup >, then intensity I ( power per unit area ) of radiation at distance r is

Since 1 dB = 20 log < sub > 10 </ sub > 1. 122, we may say, in a voltage sense, that the 1dB compression point occurs when

Since ( 9 / 8 ) / ( 10 / 9 ) = ( 81 / 80 )— the syntonic comma — the fundamental characteristics of meantone systems are that all intervals are generated from fifths, and the syntonic comma is tempered to a unison.

Since the summer of 1997, when the 9-5 production began, 252, 236 saloons, and 231, 357 wagons were built.

Since appeals to morality, to humanity, and to sanity have had such small effect, perhaps our last recourse is the deterrent example.

Since the goal of our international planners is a World Government, this Atlantic Community would mark a giant step in that direction for, once American economic autonomy is absorbed, a larger grouping is a question of time.

Since our viewpoints in this respect coincided precisely, we present the fruits of our efforts herewith as a single social code for pool owners.

Since the 1950s, this type of fiction has to a large extent merged with science fictional tropes involving cross-time travel between alternate histories or psychic awareness of the existence of " our " universe by the people in another ; or ordinary voyaging uptime ( into the past ) or downtime ( into the future ) that results in history splitting into two or more time-lines.

Since tangents and inverse tangents are both continuous, our identification function is a homeomorphism between the real line and the unit circle without ∞.

Since our own Milky Way Galaxy has at least 200 billion stars, it must also contain tens or hundreds of billions of planets.

Since one cannot logically consider these subjects to be both " at the same moment " and " away in time ", an exclusive choice has to be made that defines these two separate domains, B and C. Our reality or domain B is created by the complex, but consistent transformation of A by our biological and mental makeup.

Since feelings do not cause our behavior, we can coexist with unpleasant feelings while still taking constructive action.

Since therefore all that the inspired authors or sacred writers affirm should be regarded as affirmed by the Holy Spirit, we must acknowledge that the books of Scripture firmly, faithfully, and without error teach that truth which God, for the sake of our salvation, wished to see confided to the Sacred Scriptures.

Since we've assumed that we can infallibly identify programs for computing squares, we can determine whether t, which depends on a and i, is such a program, and that for every a and i ; thus we have obtained a program that decides whether program a halts on input i. Note that our halting-decision algorithm never executes t, but only passes its description to the squaring-identification program, which by assumption always terminates ; since the construction of the description of t can also be done in a way that always terminates, the halting-decision cannot fail to halt either.

Since January 2012, four daytime soap operas – General Hospital, Days of our Lives, The Young and the Restless, and The Bold and the Beautiful – continue to air on the three major networks, down from 12 in 1990 – 91 and a high of 19 in 1969 – 70.

Since string theory is widely believed to be mathematically consistent, many hope that it fully describes our universe, making it a theory of everything.

Since our concepts of good and evil as instilled in us by God are only intended to facilitate ethical behaviour in our relations with other humans, we should have no expectation that our concepts are accurate beyond what is needed to fulfil this function, and therefore cannot presume that they are sufficient to determine whether what we call evil really is evil.

Since more massive stars use their fusion fuel more quickly than smaller ones, Vega's main sequence lifetime is roughly one billion years, a tenth of our Sun's.

Since Intranets are user-specific ( requiring database / network authentication prior to access ), you know exactly who you are interfacing with and can personalize your Intranet based on role ( job title, department ) or individual (" Congratulations Jane, on your 3rd year with our company!

Since mass media has enormous effects on our attitudes and behavior, notably in regards to aggression, it is an important contributor to the socialization process.

Since our planet rotates, it appears to a stationary observer on Earth that a gyroscope's axis is completing a full rotation once every 24 hours.

Since our present choices and acts, under determinism, are the necessary consequences of the past and the laws of nature, then we have no control over them and, hence, no free will.

Since neo-liberalism in the 1970 / 1980s and the emergence of the climate change crises, there has been abrupt evidence that the State is failing to effectively manage our environmental resources.

Since the meaning of the existential quantifier in formal notation is usually explained in terms of its equivalence to English expressions such as " there is " and " there exist ", and since these English expressions are not reliably ontologically committing, it comes to seem that we cannot be sure of our theory's ontological commitments even after it has been regimented into a canonical formulation.

Since our category C has a zero object, the empty biproduct exists and is isomorphic to the zero object.