Two people working together can complete a job in 6 hours. If one of them
works twice as fast as the other how long would it take the faster person
to do the job working alone?

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 length of the normal and the angle it makes with the positive x-axis. (see pictured below)

Abag contains pieces of paper numbered from 5 to 9. a piece of paper is drawn at random. what is the theoretical probability of drawing a number less than 8?