A scoop of ice cream in the shape of a whole sphere sits in a right cone. The radius of the ice cream scoop is 3.0 cm and the radius of the cone is 3.0 cm. What is the volume of the scoop of ice cream? Show all your work. How tall must the height of the cone be to fit all the ice cream without spilling if it melts? Show all your work.

The graph shows the function f(x) = (2.5)x was horizontally translated left by a value of h to get the function g(x) = (2.5)x–h.

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.

What are the solutions for the following system? -2x^2+y=-5 y=-3x^2+5