SHOW ALL WORK PLEASE DO NOT USE LINKS A bag is filled with 4 red marbles, 3 blue marbles, 3 yellow marbles, and

2 green marbles. You randomly choose one marble from the bag. (a) Find

the number of ways the event can occur. (b) Find the favorable outcomes

of the event.

1. Choosing red 2. Choosing green

3. Choosing yellow 4. Choosing not blue

5. In order to figure out who will go first in a game, your friend asks you to

pick a number between 1 and 25.

a. What are the possible outcomes?

b. What are the favorable outcomes of choosing an even number?

c. What are the favorable outcomes of choosing a number less than 20?

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).