Ismelda watches a soap bubble resting on a driveway. The bubble is in the shape of a hemisphere. When the bubble pops, the soap residue left behind is in the shape of a circle with the same diameter as the hemisphere. Ismelda measures the diameter of the bubble as 6 inches. What volume of air was in the hemisphere before the bubble popped? (Use 3.14 for π. Round the answer to the nearest tenth, if necessary. Recall that the formula for the volume of a sphere is V = 4/3 π R^3).

The rate of decay of a radioactive substance depends upon the amount present initially. the mass y (mg) of the radioactive substance cobalt-60 present in a sample at time t (years) is represented by the exponential equation y=50e −0.1315 t . answer the following questions in complete sentences. 1. how does the exponential equation above compare to the equation for simple interest that is compounded continuously? explain the similarities. 2. what is the initial amount of cobalt-60 in the sample? 2. how much cobalt-60 is left after 8.4 years? show your work. 3. what would be the y-intercept of the graph? what does it represent? 4. after how many years will the amount of cobalt-60 left be 6.25 mg? explain what happens to the cobalt-60 after 50 years? 5. discuss some “real-world” examples and uses of cobalt-60

Use the given information to determine the exact trigonometric value.

Which represents the number of times all outcomes less than a given outcome occur? cumulative frequency relative frequency frequency cumulative relative frequency