Suggest the following twenty-first-century amendment: By moving the term `` Republic '' to lower case, substituting the modern phrase, `` move ahead '' for the stodgy `` keep '', and by using the Postmaster's name on every envelope ( in caps, of course, with the `` in spite '' as faded as possible ), the slogan cannot fail.

By quickly setting up for the next play ( often within 5 – 10 seconds after the last play despite being afforded 45 seconds ) this hindered the other team's defense from substituting situational players, regrouping for tactics, and, some suggest, increased the defense's rate of fatigue ( This is attributed to the belief that the offense dictates when a play starts so they tend to be more mentally relaxed and prepared for the start of a play where the defense must remain on a higher level of alert before the play starts ).

By substituting these three verbs, even without clarifying morality ( ought, shall, should, must ) or the actor ( s ) who do or did something, becomes / remains / equals makes clear what time frame of relationship is asserted, and disallows assuming one stable past / present / future timeline-known as single scenario planning or blind linearity and considered a grave error in risk analysis.

By the turn of the century, American producers were experimenting with flavors such as almond extract and substituting Queen Anne cherries for marasca cherries.

By substituting,, and, one obtains respectively the euclidian, spherical, and hyperbolic cases of the law of sines described above.

By 1871 he had devised a method of using dry plates and substituting nitro-cellulose plastic for glass plates, thus initiating the age of convenience in photography.

By substituting the parameters by their rough estimates: m < sup > 2 </ sup >/ sec, ° C < sup >- 1 </ sup > and T < sub > 1 </ sub > ~ 1220 ° C ( for the atlantic and Indian oceans ) or ~ 1120 ° C ( for the eastern pacific ), we have:

By repeatedly substituting this expression for c < sub > n </ sub > back into right hand side, we get an iterative solution

By substituting interchangeable inserts, one mold may make several variations of the same part.

By substituting using the third equation above, we have:

By writing the inductive impedance as Z < sub > L </ sub > = jωL and capacitive impedance as Z < sub > C </ sub > = ( jωC )< sup >− 1 </ sup > and substituting we have

By substituting for y < sup > 2 </ sup > into the equation for triangle BHC and solving for x:

By substituting this, solve for y and h

By substituting the Hebrew word " eretz " into the passage makes it possible that " all the kingdoms of the land of Israel " were viewed from a high mountain such as Mount Tabor in Israel.

By substituting ( iii ) into ( i ) and applying ( iv ) it follows that

By the age of 11, Jehan was substituting at St. Germain-en-Laye.

By substituting x with x ∧ b, the modular law can be expressed as an equation that is required to hold unconditionally, as follows:

By early Islamic thinkers, nationalism had been viewed as an ungodly ideology, substituting " the nation " for God as an object of worship and reverence.

By substituting, we obtain

By substituting this function and its derivative into the differential equation, one can solve for A:

By substituting the expression for into Equation 1, it can be shown that

By substituting V < sub > 1 </ sub > to the first equation and solving in respect to V2, we get:

By substituting in the factorized version of,, parameterized over the hidden nodes as above, is simply the negative relative entropy between and plus other terms independent of if is defined as

By substituting for and for and by using the dummy variable as the variable of integration the general equation

By varying the formula, this curve may be moved forward or backward along the coordinates to produce any desired compression strength / density ratio.

By the continuous formula,

By using the formula

By doing this to the formula above, we find:

By using logarithmic identities to transform the formula, the multiplications can be expressed as a sum and the power as a multiplication.

By sorting formulas according to the number of atoms of each element present in the formula according to these rules, with differences in earlier elements or numbers being treated as more significant than differences in any later element or number — like sorting text strings into lexicographical order — it is possible to collate chemical formulas into what is known as Hill system order.

By degrees, however, Justinian came to understand that the formula at issue not only appeared orthodox, but might also serve as a conciliatory measure toward the Monophysites, and he made a vain attempt to do this in the religious conference with the followers of Severus of Antioch, in 533.

By the end of the 5th dynasty, the formula in all tombs becomes " An offering the king gives and Osiris ".

By most accounts, Coca-Cola was India's leading soft drink until 1977 when it left India after a new government ordered The Coca-Cola Company to turn over its secret formula for Coke and dilute its stake in its Indian unit as required by the Foreign Exchange Regulation Act ( FERA ).

By contrast, ext2 and other Berkeley FFS-like file systems of that time simply used a fixed formula for computing inode locations, hence limiting the number of files they may contain.

By the same formula we can find the geostationary-type orbit of an object in relation to Mars ( this type of orbit above is referred to as an areostationary orbit if it is above Mars ).

The canonical model is a model of L, as every L-MCS contains all theorems of L. By Zorn's lemma, each L-consistent set is contained in an L-MCS, in particular every formula unprovable in L has a counterexample in the canonical model.

By comparison, prediction in frequentist statistics often involves finding an optimum point estimate of the parameter ( s ) — e. g. by maximum likelihood or maximum a posteriori estimation ( MAP ) — and then plugging this estimate into the formula for the distribution of a data point.

By using this formula as distance, Euclidean space ( or even any inner product space ) becomes a metric space.

By the time of Diocletian, however, this two-stage process had largely disappeared, and the Praetor would either hear the whole case in person or appoint a delegate ( a iudex pedaneus ), taking steps for the enforcement of the decision ; the formula was replaced by an informal system of pleadings.

By convention, the formula is always true, regardless of the formula P ( x ); see vacuous truth.

By mid-century, Robert Wallace acquired the formula for nickel silver and established with Samuel Simpson, R. Wallace & Company the forerunner of Wallace Silversmiths.

By repeated applications of the half-angle formula

By Euler's formula the number of faces (' F '), vertices ( V ), and edges ( E ) of any convex polyhedron are related by the formula " F + V-E "

By Heron's formula, the area of the triangle is

By choosing a = 0, this formula gives both an integral and a series representation for a function that interpolates the harmonic numbers and extends a definition to the complex plane.

By inserting different prices into the formula, you will obtain a number of break even points, one for each possible price charged.