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99 points at a zoo, the leopard pen has a ring-shaped sidewalk around it. the outer edge of the sidewalk is a circle with a radius of 12 m. the inner edge of the sidewalk is a circle with a radius of 8 m. (1 point for showing all of your work) a. write and simplify an expression for the exact area of the sidewalk. (1 point for the answer) b. find the approximate area of the sidewalk. use 3.14 to approximate π. (1 point for the answer)

Triangle inequality theorem state if each set of three numbers can be the lengths of the sides of a triangle. 1. 9, 8, 22. 2. 5,10,12. 3. 7,10,22. 4. 4,11,12. 5. 11,9,10. 6. 10,4,19. 7. 3,12,10. 8. 4,3,2. 9. 6,5,13. 10. 7,12,20. me .

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