* If it is required to use a single number X as an estimate for the value of numbers, then the arithmetic mean does this best, in the sense of minimizing the sum of squares ( x < sub > i </ sub > − X )< sup > 2 </ sup > of the residuals.

When there are only two means to compare, the t-test and the ANOVA F-test are equivalent ; the relation between ANOVA and t is given by F = t < sup > 2 </ sup >.

The number of carbon atoms is used to define the size of the alkane ( e. g., C < sub > 2 </ sub >- alkane ).

The simplest possible alkane ( the parent molecule ) is methane, CH < sub > 4 </ sub >.

The reason why pHs of acids are less than 7 is that the concentration of hydronium ions is greater than 10 < sup >− 7 </ sup > moles per liter.

An Arrhenius acid is a substance that increases the concentration of the hydronium ion, H < sub > 3 </ sub > O < sup >+</ sup >, when dissolved in water.

BF < sub > 3 </ sub > is a Lewis acid because it accepts the electron pair from fluoride.

The species that gains the electron pair is the Lewis acid ; for example, the oxygen atom in H < sub > 3 </ sub > O < sup >+</ sup > gains a pair of electrons when one of the H — O bonds is broken and the electrons shared in the bond become localized on oxygen.

The Brønsted-Lowry definition is the most widely used definition ; unless otherwise specified acid-base reactions are assumed to involve the transfer of a proton ( H < sup >+</ sup >) from an acid to a base.

Reactions of acids are often generalized in the form HA H < sup >+</ sup > + A < sup >−</ sup >, where HA represents the acid and A < sup >−</ sup > is the conjugate base.

The acid dissociation constant K < sub > a </ sub > is generally used in the context of acid-base reactions.

The numerical value of K < sub > a </ sub > is equal to the concentration of the products divided by the concentration of the reactants, where the reactant is the acid ( HA ) and the products are the conjugate base and H < sup >+</ sup >.

Because the range of possible values for K < sub > a </ sub > spans many orders of magnitude, a more manageable constant, pK < sub > a </ sub > is more frequently used, where pK < sub > a </ sub >

After the indecisive < ref name =" British historian Townsend Miller "> British historian Townsend Miller: “ But, if the outcome of < nowiki > battle of </ nowiki > Toro, militarily, is debatable, there is no doubt whatsoever as to its enormous psychological and political effects ” in The battle of Toro, 1476, in History Today, volume 14, 1964, p. 270 </ ref > Battle of Toro in 1476 against King Ferdinand II of Aragon, the husband of Isabella I of Castile, he went to France to obtain the assistance of Louis XI, but finding himself deceived by the French monarch, he returned to Portugal in 1477 in very low spirits.

where is ƒ < nowiki >'</ nowiki > s Laplace transform.

Thus, for example, the English form is is an apparent cognate of German ist, Latin est and Russian < nowiki > jest '</ nowiki >, even though the Germanic, Italic, and Slavic language groups split at least three thousand years ago.

Quite a few of the names mean " five-six " in different languages, including both the robot Fisi ( fi-si ), the dead Lady Panc Ashash ( in Sanskrit " pañcha " is " five " and " ṣaṣ " is " six "), Limaono ( lima-ono, both in Hawaiian and / or Fijian ), Englok ( ng < sup > 5 </ sup >- luk < sup > 6 </ sup > < nowiki >- wikt: 六 # Cantonese | 六 < nowiki ></ nowiki >, in Cantonese ), Goroke ( go-roku < nowiki >- wikt: 六 # Japanese | 六 < nowiki ></ nowiki >, Japanese ) and Femtiosex (" fifty-six " in Swedish ) in " The Dead Lady of Clown Town " as well as the main character in " Think Blue, Count Two ", Veesey-koosey, which is an English transcription of the Finnish words " viisi " ( five ) and " kuusi " ( six ).

A number of non-Greek etymologies have been suggested for the name, The form Apaliunas (< sup > d </ sup >) is attested as a god of Wilusa in a treaty between Alaksandu of Wilusa and the Hittite great king Muwatalli II ca 1280 BCE.

* cyclic ( general formula, n > 2 ) wherein the carbon backbone is linked so as to form a loop.

While the complete title of the book is the Acts of the Apostles, really the book focuses on only two men: The Apostle Peter ( chs.

He is the 104th in a line which goes back more than 1400 years to St Augustine of Canterbury, the " Apostle to the English ", in the year 597.

This John is traditionally supposed to be John the Apostle, although recent scholarship has suggested other possibilities including a putative figure given the name John of Patmos.

He is also called the second Apostle of the Prussians ( Old Prussians ).

Paul the Apostle, an early Christian convert and missionary, wrote, " If Christ was not raised, then all our preaching is useless, and your trust in God is useless.

According to Paul the Apostle, marriage is a social obligation that has the potential of distracting from Christ.

A key example is the Apostle Paul's Areopagus sermon that appears in.

They conclude that the Apostle Paul's statement sometimes called the " Magna Carta of Humanity " and recorded in applies to all Christian relationships, including Christian marriage: " There is neither Jew nor Greek, there is neither bond nor free, there is neither male nor female: for you are all one in Christ Jesus.

Both the Patriarchate of Addis Ababa and all Ethiopia, and the Patriarchate of Asmara and all Eritrea do acknowledge the supremacy of honor and dignity of the Pope and Patriarch of Alexandria on the basis that both Patriarchates were established by the Throne of Alexandria and that they have their roots in the Apostolic Church of Alexandria, and acknowledge that Saint Mark the Apostle is the founder of their Churches through the heritage and Apostolic evangelization of the Fathers of Alexandria.

* The leader of the Coptic Orthodox Church of Alexandria, is known as Pope of Alexandria and Patriarch of all Africa on the Holy See of St. Mark the Apostle.

* His full title is Pope and Lord Archbishop of the Great City of Alexandria and Patriarch of All Africa on the Holy Orthodox and Apostolic Throne of Saint Mark the Evangelist and Holy Apostle that is, in Egypt, Pentapolis, Libya, Nubia, Sudan, Ethiopia, Eritrea and all Africa.

This is because Alexandria was the Capital of the Province, and the preaching center and the place of martyrdom of Saint Mark the Evangelist and Apostle.

In his First Epistle to the Corinthians ( c 54-55 ), Paul the Apostle gives the earliest recorded description of Jesus ' Last Supper: " The Lord Jesus on the night when he was betrayed took bread, and when he had given thanks, he broke it, and said, ' This is my body which is for you.

Biblical scholars agree that it was composed by the Apostle Paul to explain that salvation is offered through the gospel of Jesus Christ.

In response to those who say that the Baptism in the Holy Spirit is not a separate experience from conversion, Pentecostals appeal to the question asked by the Apostle Paul to the Ephesian believers " Have ye received the Holy Ghost since ye believed?

' Along with Peter, the unnamed disciple is especially close to Jesus, and early-church tradition identified him as John the Apostle, one of Jesus ' Twelve Apostles.

* Thomas the Apostle is given a personality beyond a mere name, as " Doubting Thomas ".

Another criticism of image veneration is found in the non-canonical 2nd-century Acts of John ( generally considered a gnostic work ), in which the Apostle John discovers that one of his followers has had a portrait made of him, and is venerating it:

To be sure, when this is pointed out, a common response among certain churchmen is to fulminate about `` the little flock '' and `` the great crowd '' and to take solace from Paul's castigation of the `` wisdom of the wise '' in the opening chapter of First Corinthians.

Their conclusion is thus that Paul's writings on election should be interpreted in a similar corporate light.

* Ambrosiaster or the " pseudo-Ambrose " is a brief commentary on Paul's Epistles, which was long attributed to Ambrose.

Ambrosiaster is the name given to the writer of a commentary on St Paul's epistles, " brief in words but weighty in matter ," and valuable for the criticism of the Latin text of the New Testament.

Paul's own record of the meeting appears to be Galatians 2, however, due to the differences, some argue Gal 2 is a different meeting.

In Acts, attention is given to the religious persecution of the early Christians, as in the case of Stephen's martyrdom and the numerous examples are Paul's persecution for his preaching of Christianity.

Kropp was in Paul's class at school and is described as the clearest thinker of the group.

He is thus the last of Paul's close friends to die in battle.

He is the first of Paul's friends to die.

After this his name is not mentioned until after Paul's first imprisonment, when he was engaged in the organization of the church in Crete, where Paul had left him for this purpose.

A remnant of these earlier cardinals is retained by the Church of England, where the title of " cardinal " is still held by the two senior members of the College of Minor Canons of St Paul's Cathedral.

The city is home to the University of New Hampshire School of Law, New Hampshire's only law school ; St. Paul's School, a private preparatory school ; New Hampshire Technical Institute, a two-year community college ; and the Granite State Symphony Orchestra.

The application of the catenary to the construction of arches is attributed to Robert Hooke, whose " true mathematical and mechanical form " in the context of the rebuilding of St Paul's Cathedral alluded to a catenary.

Baron Harkonnen himself is poisoned with a gom jabbar by Paul's young sister Alia Atreides, his own granddaughter, and dies at the age of 83.

The Catholic Church sees as the main basis for this belief the words of Jesus himself at his Last Supper: the Synoptic Gospels (; ; ) and Saint Paul's recount that in that context Jesus said of what to all appearances were bread and wine: " This is my body … this is my blood.

Its authorship has traditionally been credited to Paul, but it is considered by some scholars to be Deutero-pauline, that is, written in Paul's name by a later author strongly influenced by Paul's thought.