Thus, knowing the students ' level on a developmental sequence provides information on the kind and level of knowledge they can assimilate, which, in turn, can be used as a frame for organizing the subject matter to be taught at different school grades.

Thus, measurement of the tension in the string identifies the inertial frame: it is the one where the tension in the string provides exactly the centripetal force demanded by the motion as it is observed in that frame, and not a different value.

Thus IPv4 provides an addressing capability of 2 < sup > 32 </ sup > or approximately 4. 3 billion addresses.

Thus Irenaeus provides the earliest witness to the assertion of the four canonical Gospels, possibly in reaction to Marcion's edited version of the Gospel of Luke, which Marcion asserted was the one and only true gospel.

Thus, union density provides a rough picture of union membership only ; it does not account for the circumstance that in some countries, also many persons under education, many unemployed persons, many retired persons and / or many persons who had to leave work due to occupational injuries may also be union members.

Thus, two of the three color channels for each sensor must be interpolated and a so-called N-megapixel camera that produces an N-megapixel image provides only one-third of the information that an image of the same size could get from a scanner.

Thus, Electronic Support provides a source of information required for decisions involving Electronic Protection ( EP ), Electronic Attack ( EA ), avoidance, targeting, and other tactical employment of forces.

Thus a virtual connection, also known as a virtual circuit or byte stream is provided to the end-user by a transport layer protocol, although intermediate network nodes only provides a connectionless network layer service.

Thus STR analysis provides an excellent identification tool.

Thus, opportunity costs are not restricted to monetary or financial costs: the real cost of output forgone, lost time, pleasure or any other benefit that provides utility should also be considered opportunity costs.

Thus fiscal federalism provides the tools for " application of the federal approach to governance which lies in its ability to balance the contrasting forces of centralization and decentralization " ( Sharma, 2005b: 177 ).

) Thus, the group of conformal transformations in spaces of dimension greater than 2 are much more restricted than the planar case, where the Riemann mapping theorem provides a large group of conformal transformations.

Thus they help create a denser dike surface, which in case of storm surges provides less area for the waves to impact.

Thus it provides an intense, detailed exploration of its subject, providing to some degree both the concentrated focus of the short story and the broad scope of the novel.

Thus in most " natural " settings, if a complex number provides a solution to a problem, so does its conjugate, such as is the case for complex solutions of the quadratic formula with real coefficients.

Thus the neutral theory provides a rationale for the molecular clock, although the discovery of a molecular clock predates neutral theory.

Thus, it provides the basis of an alternative route to analytical results compared with working directly with probability density functions or cumulative distribution functions.

Thus, the trust center maintains both the network key and provides point-to-point security.

Since any vector v is a linear combination ∑ v < sup > j </ sup > e < sub > j </ sub > of its components, df is uniquely determined by df < sub > p </ sub >( e < sub > j </ sub >) for each j and each p ∈ U, which are just the partial derivatives of f on U. Thus df provides a way of encoding the partial derivatives of f. It can be decoded by noticing that the coordinates x < sup > 1 </ sup >, x < sup > 2 </ sup >,... x < sup > n </ sup > are themselves functions on U, and so define differential 1-forms dx < sup > 1 </ sup >, dx < sup > 2 </ sup >, ..., dx < sup > n </ sup >.

Thus, Bluestein's algorithm provides an O ( N log N ) way to compute prime-size DFTs, albeit several times slower than the Cooley – Tukey algorithm for composite sizes.

Thus, a regulation that allows member states to privatise roads would not have direct effect and could not be enforced in the courts, because it provides that states may privatise roads, not must privatise roads.

Thus the connection ∇ defines a way of moving elements of the fibers along a curve, and this provides linear isomorphisms between the fibers at points along the curve:

In such cases, the family relationship between two distant family members A and C can often be demonstrated by finding an additional family member B that shares significant similarity with both A and C. Thus, B provides a connecting link between A and C. Another approach is to examine distant alignments for highly conserved matches.

Thus, the Treaty of Waitangi voided the Declaration for all practical purposes ; the Treaty rather than the Declaration provides the legal foundation of claims for the redress of historical wrongs.

Thus, Elizabeth was as at ease among the upper classes as she was among the fishing folk of the area also enjoyed good health, which she maintained throughout her life.

Thus in the upper block there are 2 < sup > n </ sup > − 3 codes available to the decoder that won't trigger an increase in code width.

Thus, because of the O ( n log n ) upper bound on heapsort's running time and constant upper bound on its auxiliary storage, embedded systems with real-time constraints or systems concerned with security often use heapsort.

Thus the learned and upper class religious churches who preach the theodicy of fortune, ultimately support capitalism and corporation, while the churches who adopted the theodicy of misfortune, instead preached equality and fairness.

Thus an individual item might be described as being " in the upper quartile ".

Thus, Romania was created as a personal union, albeit a Romania that did not include Transylvania, where the upper class and the aristocracy remained mainly Hungarian, although Romanian nationalism inevitably ran up against Hungarian nationalism at the end of the 19th century.

Thus ducks belong to both the upper world and the world below.

Thus, with the exception of Liguria and the upper valley of the Po River, all Italy south of the Alps is brought within the Roman sphere.

Thus, a program will achieve greater performance if it uses memory while it is cached in the upper levels of the memory hierarchy and avoids bringing other data into the upper levels of the hierarchy that will displace data that will be used shortly in the future.

Thus the role of the matchmaker has become institutionalized, as a bureaucrat, and every citizen in Singapore has access to some subset of the matchmaking services that were once reserved for royalty or upper classes.

Thus, the maximum margin of error represents an upper bound to the uncertainty ; one is at least 95 % certain that the " true " percentage is within the maximum margin of error of a reported percentage for any reported percentage.

Thus u is an upper bound for S. To see that it is a least upper bound, notice that the limit of ( u < sub > n </ sub > − l < sub > n </ sub >) is 0, and so l =

Thus, one symptom is pain in the right upper quadrant.

Thus, despite the involvement of mestiços in the nationalist struggle beginning in 1961 and their very important role in the upper echelons of the government and party, significant segments of the African population tended to resent them.

Thus the lower stage motors are designed for use at atmospheric pressure, while the upper stages can use motors suited to near vacuum conditions.

Thus, by convention, one frequently writes and in terms of the period ratio and take to lie in the upper half-plane.

Thus, the design made provisions for future expansion that would have allowed the seating capacity to grow to nearly 40, 000 by adding an upper deck above the existing mezzanine should a major-league team decide to relocate to Buffalo.

Thus, in the case of a firearm that has multiple receivers ( such as the AR-15, which has an upper and lower receiver ), the legally controlled part is the one that is serialized ( the lower, in the AR-15's case ).

Thus, the positive gravitational anomalies associated with these impact basins indicate that some form of positive density anomaly must exist within the crust or upper mantle that is currently supported by the lithosphere.

Thus the diskette could save three ' upper ' sounds and three ' lower ' sounds.

Thus, when a person with an upper-body weight of W < sub > torso </ sub > lifts a load with a weight of W < sub > load </ sub >, the load and upper torso create a combined clockwise rotational moment that can be calculated as