Stan the stochastic southpaw has a pitching algorithm that never changes. in the first pitch of each plate appearance, he throws a fastball 70% of the time (and therefore, an off-speed pitch 30% of the time). the following pitch selection is determined *only* by the type of pitch immediately preceding it. if the previous pitch was off-speed, he will throw a fastball 80% of the time and an off-speed pitch 20% of the time. if the previous pitch was a fastball, however, he will throw either a fastball or off-speed pitch with 50% probability. in your excitement to see stan pitch, you spilled your soda in the concourse and missed the first two pitches of his first plate appearance of the game. you are able to see that his third pitch is an off-speed pitch. given this information, what is the probability that the first pitch was an off-speed pitch?

saving = more money

step-by-step explanation:

if you have 100 bucks, and you want to buy a candy bar, even if you have one at home, if you choose not to buy it, you save.

~courtney

step-by-step explanation:

to find if any function is an inverse of the other, put the first equation in as x in the next one. then simplify and solve. if at the end you get the statement y = x, then it is an inverse. if you get anything else, it is not.

step-by-step explanation: the declaration of the rights of man and of the citizen (french: déclaration des droits de l'homme et du citoyen de 1789), set by france's national constituent assembly in 1789, is a human civil rights document from the french revolution.[1]

the declaration was drafted by the abbé sieyès and the marquis de lafayette, in consultation with thomas jefferson.[2] influenced by the doctrine of "natural right", the rights of man are held to be universal: valid at all times and in every place, pertaining to human nature itself. it became the basis for a nation of free individuals protected equally by the law. it is included in the beginning of the constitutions of both the fourth french republic (1946) and fifth republic (1958) and is still current. inspired by the enlightenment philosophers, the declaration was a core statement of the values of the french revolution and had a major impact on the development of freedom and democracy in europe and worldwide.[3]

the 1789 declaration, together with the 1215 magna carta, the 1689 english bill of rights (1689), the 1776 united states declaration of independence, and the 1789 united states bill of rights, inspired in large part the 1948 united nations universal declaration of human rights

step-by-step explanation: