Determine the sum of the products obtained in item 8 above, for all the States.

Determine the ratio that the amount being allotted is to the sum of the products for all the States.

I discern no limits to a faith vested in God and Christ, who is the sum of all wisdom and knowledge, and daring to trust Him even though called to stand alone before the world.

If one takes the middle number, 5, and multiplies it by 3 ( the base number of the magic square of three ), the result is 15, which is also the constant sum of all the rows, columns, and two main diagonals.

and the latter is the total sum of all the numbers in the square, by which all the other numbers are overshadowed and in which they may be said to be absorbed.

it is also their mathematical mean, since it is equal to half the sum of every opposing pair, all of which equal 10.

Anarcho-capitalists argue for a society based on the voluntary trade of private property and services ( in sum, all relationships not caused by threats or violence, including exchanges of money, consumer goods, land, and capital goods ) in order to minimize conflict while maximizing individual liberty and prosperity.

The Trust was funded by a gift of $ 10 million ( a then unprecedented sum: at the time, total government assistance to all four Scottish universities was about £ 50, 000 a year ) and its aim was to improve and extend the opportunities for scientific research in the Scottish universities and to enable the deserving and qualified youth of Scotland to attend a university.

As the title implies, any active device received the sum of all transmitted messages in universal space-time, in a single pulse, so that demultiplexing yielded information about the past, present, and future.

and mean that the sum or product is over all prime numbers:

Similarly, and mean that the sum or product is over all prime powers with strictly positive exponent ( so 1 is not counted ):

and mean that the sum or product is over all positive divisors of n, including 1 and n.

The notations can be combined: and mean that the sum or product is over all prime divisors of n.

and similarly and mean that the sum or product is over all prime powers dividing n.

In February 1705, Queen Anne, who had made Marlborough a Duke in 1702, granted him the Park of Woodstock and promised a sum of £ 240, 000 to build a suitable house as a gift from a grateful crown in recognition of his victory – a victory which British historian Sir Edward Shepherd Creasy considered one of the pivotal battles in history, writing – " Had it not been for Blenheim, all Europe might at this day suffer under the effect of French conquests resembling those of Alexander in extent and those of the Romans in durability.

The slope of the surface adjusts to make all three forces sum to zero.

To quote Anthony and Brackett: Moreover, because the element of water does not move, the sum of all three forces must be zero.

* Arithmetic mean – the sum of all measurements divided by the number of observations in the data set

The total contact force on the particular internal surface is then expressed as the sum ( surface integral ) of the contact forces on all differential surfaces:

Thus, the sum of all applied forces and torques ( with respect to the origin of the coordinate system ) in the body can be given by

In On War, Clausewitz sees all wars as the sum of decisions, actions, and reactions in an uncertain and dangerous context, and also as a socio-political phenomenon.

The censors had the general superintendence of all the public buildings and works ( opera publica ), and to meet the expenses connected with this part of their duties, the senate voted them a certain sum of money or certain revenues, to which they were restricted, but which they might at the same time employ according to their discretion.

The reflected light being the sum of the incoming light ( L < sub > i </ sub >) from all directions, multiplied by the surface reflection and incoming angle.

He theorized that all humans are born free of any knowledge and are the sum of their experiences.

Mr. Alexander H. Wheelan's Study Helps In Point And Figure Technique tells the readers: `` We assure you that the total number of people using this method of market analysis is a very small portion of the sum total of those operating in the securities and commodities markets ''.

where the first sum is over positive energy states and the second over those of negative energy.

The sum of the distances from any point P on the ellipse to those two foci is constant and equal to the major axis ( PF < sub > 1 </ sub > + PF < sub > 2 </ sub > = 2a ).

In many typical circuits, the single output signal actually contains multiple waveforms, namely those at the sum and difference of the two input frequencies and harmonic waveforms.

The output of the filter is formed as the weighted sum of those delayed signals, as is depicted in the accompanying signal flow diagram.

The Board cited several reasons for its action, including the fact that Hopkinson “ was not the only person consulted on those exhibitions of Fancy, and therefore cannot claim the sole merit of them and not entitled to the full sum charged .”

The entries in the third row are the sum of those in the first two.

Fermat's principle is the main principle of quantum electrodynamics where it states that any particle ( e. g. a photon or an electron ) propagates over all available ( unobstructed ) paths and the interference ( sum, or superposition ) of its wavefunction over all those paths ( at the point of observer or detector ) gives the correct probability of detection of this particle ( at this point ).

This involves solving a linear system such that the Taylor expansion of the sum of those points, around the center point, well approximates the Taylor expansion of the desired derivative.

Note that opportunity cost is not the sum of the available alternatives when those alternatives are, in turn, mutually exclusive to each other – it is the value of the next best use.

Most commonly, social capital, the sum of social bonds and relationships, has come to be recognized, along with many synonyms such as goodwill or brand value or social cohesion or social resilience and related concepts like celebrity or fame, as distinct from the talent that an individual ( such as an athlete has uniquely ) has developed that cannot be passed on to others regardless of effort, and those aspects that can be transferred or taught: instructional capital.

The fee for the academic year 2010-2011 is £ 29, 862 ( approximately US $ 48, 600 or € 35, 100 as of March 2011 ), although the sum is considerably lower for those pupils on bursaries and scholarships.

In the absence of heirs, Whittington left £ 7, 000 in his will to charity, in those days a large sum, with a modern-day equivalence of about £ 3m.

' Such a dictionary is what Egan offers, hoping in sum that his efforts work ' to improve, and not to degrade mankind ; to remove ignorance, and put the UNWARY on their guard ; to rouse the sleepy, and to keep them AWAKE ; to render those persons who are a little UP, more FLY: and to cause every one to be down to those tricks, manoeuvres and impositions practised in life, which daily cross the paths of both young and old.

In physical chemistry, the van der Waals force ( or van der Waals interaction ), named after Dutch scientist Johannes Diderik van der Waals, is the sum of the attractive or repulsive forces between molecules ( or between parts of the same molecule ) other than those due to covalent bonds, the hydrogen bonds, or the electrostatic interaction of ions with one another or with neutral molecules.

But those who wanted to see Johnson defeated badgered Jeffries unmercifully for months, and also offered him an unheard sum of money, reputed to be about $ 120, 000 and he finally acquiesced.

Annuities were valued as a lump sum necessary to produce the annual income over the original term at an assumed interest of 5 %, which favoured those with shorter terms still to run.

Therefore those of the first creation, in return for the honour, were each required to pay for the upkeep of thirty soldiers for three years amounting to £ 1095, in those days a very large sum.

Probability theory, as with quantum theory, would also require that the sum of the probabilities for all possible events, not just those satisfying the condition, be equal to unity ( i. e. to one hundred percent ).

Years of litigation did not end until 1824, at which point the State of New York and the federal government owed Tompkins $ 90, 000, a significant sum in those days.

Soon summer families built beautiful summer homes abounding with porches, turrets, and terraces and costing $ 30, 000 -$ 40, 000 ( an enormous sum in those days ).