How you use the Pythagorean theorem in 3D.

What is the volume of the sphere shown below with a radius of 3?

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.

The brain volumes (cm cubed) of 50 brains vary from a low of 904 cm cubed to a high of 1488 cm cubed. use the range rule of thumb to estimate the standard deviation s and compare the result to the exact standard deviation of 175.5 cm cubed, assuming the estimate is accurate if it is within 15 cm cubed