1. pia printed two maps of a walking trail. the length of the trail on the first map is 8 cm. the length of the trail on the second map is 6 cm. all work must be shown to earn credit! (a) 1 cm on the first map represents 2 km on the actual trail. what is the scale factor from the map to the actual trail? what is the length of the actual trail? (b) a landmark on the first map is a triangle with side lengths of 3 mm, 4 mm, and 5 mm. what is the scale factor from the first map to the second map? what are the side lengths of the landmark on the second map? show your work. 15 points

Assume that 1400 births are randomly selected and 1378 of the births are girls. use subjective judgment to describe the number of girls as significantly high, significantly low, or neither significantly low nor significantly high. choose the correct answer below. a. the number of girls is neither significantly low nor significantly high. b. the number of girls is significantly high. c. the number of girls is significantly low. d. it is impossible to make a judgment with the given information.

Which equation is true? i. 56 ÷ 4·7 = 82 ÷ (11 + 5) ii. (24 ÷ 8 + 2)3 = (42 + 9)2 neither i nor ii ii only i and ii i only

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).