We are given eight rooks, five of which are red and three of which are blue. A) In how many ways can the eight rooks be placed on an 8 x 8 chessboard so that no two rooks can attack one another (differentcolor rooks cannot share the same row or column).B) In how many ways can the 8 rooks be placed on a 12 x 12 chessboard so that no two rooks can attack one another?

In two or more complete sentences, determine the appropriate model for the given data and explain how you made your decision. (1,-1), (2,0.5), (5,1.5), (8,2)

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

Astudent showed the steps below while solving the inequality |x-4|< 1 by graphing.