A bag contains 3 red marbles and 4 blue marbles a marble is taken randomly from the bag and replaced
another marble is taken from the bag
work out the probability that the two marble taken from the bag are the same colour
give your answer as a fraction

1. writing an equation for an exponential function by 2. a piece of paper that is 0.6 millimeter thick is folded. write an equation for the thickness t of the paper in millimeters as a function of the number n of folds. the equation is t(n)= 3. enter an equation for the function that includes the points. (-2, 2/5) and (-1,2)

After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. you notice the rainbow is the shape of a parabola. the equation for this parabola is y = -x2 + 36. graph of a parabola opening down at the vertex 0 comma 36 crossing the x–axis at negative 6 comma 0 and 6 comma 0. in the distance, an airplane is taking off. as it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow. analyze the two functions. answer the following reflection questions in complete sentences. what is the domain and range of the rainbow? explain what the domain and range represent. do all of the values make sense in this situation? why or why not? what are the x- and y-intercepts of the rainbow? explain what each intercept represents. is the linear function you created with your table positive or negative? explain. what are the solutions or solution to the system of equations created? explain what it or they represent. create your own piecewise function with at least two functions. explain, using complete sentences, the steps for graphing the function. graph the function by hand or using a graphing software of your choice (remember to submit the graph).

I'm at a bookstore with $\$35$ in my pocket and a $20\%$-off coupon. what is the cost of the most expensive book i can buy with my money and the coupon? (assume that there are books of every possible price in the bookstore. it's a large bookstore! )