Two fair dice are thrown together once. find the probability that the sum of the outcome is
at least 10
at most 10
at most 5
less than 3
a total of 7

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.

In the given figure ar(adf) =ar(cda) and ar(cdf) = ar(cdf). show that abdc and cdfe are trapeziums.

What is the length of ac in the given triangle?