The city transit authority plans to hire 12 new bus drivers. from a group of 100 qualified applicants, of whom 65 are men and 35 are women, 12 names are to be selected by lot. suppose that mary and john lewis are among the 100 qualified applicants.

1. what is the probability that both mary's and john's names will be selected? (round your answer to four decimal places.)

2. if it is stipulated that an equal number of men and women are to be selected (6 men from the group of 65 men and 6 women from the group of 35 women), what is the probability that mary's name will be selected? (round your answer to four decimal places.)

3. what is the probability that mary's and john's names will be selected? (round your answer to four decimal places.)

Browning labs is testing a new growth inhibitor for a certain type of bacteria. the bacteria naturally grows exponentially each hour at a rate of 6.2%. the researchers know that the inhibitor will make the growth rate of the bacteria less than or equal to its natural growth rate. the sample currently contains 100 bacteria. the container holding the sample can hold only 300 bacteria, after which the sample will no longer grow. however, the researchers are increasing the size of the container at a constant rate allowing the container to hold 100 more bacteria each hour. they would like to determine the possible number of bacteria in the container over time. create a system of inequalities to model the situation above, and use it to determine how many of the solutions are viable.

Find the cosine function that is represented in the graph.

The avenues in a particular city run north to south and are numbered consecutively with 1st avenue at the western border of the city. the streets in the city run east to west and are numbered consecutively with 1st street at the southern border of the city. for a festival, the city is not allowing cars to park in a rectangular region bordered by 5th avenue to the west. 9th avenue to the east, 4th street to the south, and 6th street to the north. if x is the avenue number and yis the street number, which of the following systems describes the region in which cars are not allowed to park? 5th ave 9th ave