Type the correct answer in the box. Use numerals instead of words. Jack and his friends are going hiking next week. There are four trails they can hike: Grayson Pass, Giant’s Ridge, Three Summits, and Elderberry. To make a decision, they use a spinner divided into four colors. They spin it 60 times to check the fairness of their model and record the results in this table.

ColorTimes Result Occurs
green
6
blue
24
yellow
9
red
21

The relative frequency of the spinner landing on green is
.

The relative frequency of the spinner landing on blue is
.

The relative frequency of the spinner landing on yellow is
.

The relative frequency of the spinner landing on red is

What are the coordinates of the point that is 1/3 of the way from a to b? a (2,-3) b (2,6)

The boiling point of water at an elevation of 0 feet is 212 degrees fahrenheit (°f). for every 1,000 feet of increase in elevation, the boiling point of water decreases by about 2°f. which of the following represents this relationship if b is the boiling point of water at an elevation of e thousand feet? a) e = 2b - 212 b) b = 2e - 212 c) e = -2b + 212 d) b = -2e + 212

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).