A população brasileira sabe, pelo menos intuitivamente, que a probabilidade de acertar as seis dezenas da mega sena não é zero, mas é quase. Mesmo assim, milhões de pessoas são atraídas por essa loteria, especialmente quando o prêmio se acumula em valores altos. Até junho de 2009, cada aposta de seis dezenas, pertencentes ao conjunto {01, 02, 03, ..., 59, 60}, custava R$ 1,50.

Disponível em: www.caixa.gov.br. Acesso em: 7 jul. 2009.

Considere que uma pessoa decida apostar exatamente R$ 126,00 e que esteja mais interessada em acertar apenas cinco das seis dezenas da mega sena, justamente pela dificuldade desta última. Nesse caso, é melhor que essa pessoa faça 84 apostas de seis dezenas diferentes, que não tenham cinco números em comum, do que uma única aposta com nove dezenas, porque a probabilidade de acertar a quina no segundo caso em relação ao primeiro é, aproximadamente:

Carlos comprou papelão para construir duas caixas, a fim de guardar os seus brinquedos especiais. Sabendo que as caixas possuem o mesmo volume, determine o valor de x.

(ENEM 2018 2ª APLICAÇÃO) O parlamento britânico aprovou uma lei, em 1835, cujo objetivo era regular o tráfego crescente nas principais vias no interior da Inglaterra, uma espécie de “código rodoviário”. A lei de 1835 estabeleceu a velocidade máxima de 4 milhas por hora para veículos autopropulsionados. As regras foram revistas pelo parlamento em 1896, quando foi aumentada a velocidade máxima para 10 milhas. Em 1903, novamente elevou-se o limite de velocidade para 20 milhas por hora. Em 1930, aboliu-se o limite de velocidade para carros e motos.

ELIAS, N. Tecnização e civilização. In: ELIAS, N. Escritos e ensaios. Rio de Janeiro: Zahar, 2006 (adaptado).

O processo descrito alude à necessidade de atualização da legislação conforme

(AFA) TEXTO:THE RELATIONSHIP BETWEEN FRIENDS AND TYPES OF FRIENDSHIP

Everyone has at least one best friend, some maybe even more. There are also those people who are just friends and also arch-enemies. People may think that just because they are your friends it means that they are your best friend. The thing is, even though they are your friend, the relationship between a best friend and a friend is different. Either way regardless of archenemies, friends or best friends, there are not many ways to compare any of these different types of friends, but you can easily contrast them from one another.

Arch-enemies often know more about each other than two friends. In a comparison of personal relationships, ¹friendship is considered to be closer than association, although a wide range of degrees of intimacy exists in friendships, arch-enemies, and associations. Friendship and association can be thought of as spanning across the same continuum. ²The study of friendship is included in the fields of sociology, social psychology, anthropology, philosophy, and zoology. Even animals have familiars! Various academic theories of friendship have been proposed, among which are social exchange theory, equity theory, relational dialectics, and attachment styles. ³In Russia, one typically bestows very few people the status of “friend”.

These friendships, however, make up in intensity what they lack in number. Friends are entitled to call each other by their first names alone, and to use diminutives. A customary example of polite behavior is addressing "acquaintances" by full first name plus their patronymic. These could include relationships which elsewhere would be qualified as real friendships, such as workplace relationships of long standing, or neighbors with whom one shares an occasional meal or a social drink with.

Also in the Middle East and Central Asia, male friendships, while less restricted than in Russia, tend to be reserved and respectable in nature. They may use nicknames and diminutive forms of their first names. In countries like India, it is believed in some parts that friendship is a form of respect, not born out of fear or superiority. Friends are people who are equal in most standards, but still respect each other regardless of their attributes or shortcomings. Most of the countries previously mentioned (Russia, Asia, and even the Middle East) and even our own nation are suffering a decline in genuine friendships.

According to a study documented in the June 2006 issue of the Journal American Sociological Review, Americans are thought to be suffering a loss in the quality and quantity of close friendships since at least 1985. The study’s results state that twenty-five percent of ⁴Americans have no close confidants, and the average total number of confidants per citizen has dropped from four to two. According to the study, ⁵Americans' dependence on family as a safety net went up from fifty-seven percent to eighty percent; Americans dependence on a partner or spouse went up from five percent to nine percent.

Recent studies have found a link between fewer friendships, especially in quality, and psychological and physiological regression. In the sequence of the emotional development of the individual, friendships come after parental bonding and before the pair bonding engaged in at the approach of maturity. In the intervening period between the end of early childhood and the onset of full adulthood, friendships are often the most important relationships in the emotional life of the adolescent, and are often more intense than relationships experienced later in life.

⁶Unfortunately, making friends seems to trouble many of people. Having no friends can be emotionally damaging for all ages, from young children to full grown adults. A study performed by researchers from Purdue University found that post-secondary-education friendships, college and university last longer than the friendships before it. Children with Asperger syndrome and autism usually have some difficulty forming friendships. ⁷Socially crippling conditions like these are just one way that the social world is so difficult to thrive in. ⁸This does not mean that they are not able to form friendships, however. With time, moderation and proper instruction, they are able to form friendships after realizing their own strengths and weaknesses.

⁹There is a number of theories that attempt to explain the link, including that; Good friends encourage their friends to lead more healthy lifestyles; ¹⁰Good friends encourage their friends to seek help and access services, when needed; ¹¹Good friends enhance their friend’s ¹²coping skills in dealing with illness and other health problems; and/or Good friends actually affect physiological pathways that are protective of health. Regardless of what we think, we can clearly see that there are some ways that friends, best friends and archenemies are the same, but in the end they are clearly more different. ¹³Nonetheless we all have every single type in our lives.

(Adapted from: http://www.ukessays.com/essays/philosophy/therelationship- between-friends-and-types-of-friendship-philosophyessay. php)

“Nonetheless we all have every single type in our lives” (reference 13). The option that contains a synonym for the underlined expression is :

Muitas sínteses orgânicas podem ser realizadas como uma sequência de reações químicas. Considere a sequência de reações químicas representadas a seguir, como a monocloração de alcanos (1ª etapa) e a reação de haletos orgânicos com compostos aromáticos (2ª etapa). 

Para obtenção de um haleto orgânico, na primeira etapa é feita uma reação de halogenação (“substituição de hidrogênios de compostos orgânicos por átomos de haletos como o cloro, denominada de reação de cloração”).

Em seguida, na segunda etapa, é feito um processo conhecido por reação de alquilação Friedel-Crafts (“reação de haletos orgânicos com compostos aromáticos ou, simplesmente, a ligação de grupos alquil à estrutura de compostos orgânicos como anéis aromáticos”).

A análise das informações permite concluir que os compostos A e B podem ser identificados como, respectivamente,