Suppose we want to choose 2 colors, without replacement, from the 3 colors red, blue, and green. (a) How many ways can this be done, if the order of the choices is relevant? X (b) How many ways can this be done, if the order of the choices is not relevant? ​

Rectangle abcd is translated to get rectangle a’b’c’d’. rectangle abcd moves units along the x-axis to get rectangle a’b’c’d’. rectangle abcd moves units along the y-axis to get rectangle a’b’c’d’. the algebraic rule that describes this translation is t(x, y), where x = and y = .

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

How is the equation of this circle written in standard form? x2 + y2 - 6x + 14y = 142 a) (x - 3)2 + (y + 7)2 = 200 b) (x+ 3)2 + (y - 7)2 = 200 (x - 6)2 + (y + 14)2 = 142 d) (x+6)2 + (y- 14)2 = 142