It is believed that 25% of U. S. homes have a direct satellite television receiver. (Show your work on the back for both parts, since I have not left you enough space, but enter your answer here.) a. How large a sample is necessary to estimate the true population of homes which do with 95% confidence and within 3 percentage points?

b. How large a sample is necessary for a 95% confidence interval to be within 3 percentage points if nothing is known about the proportion?

Scale factor of 2 is used to enlarge a figure as shown below the area of is 18 in.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).

If t8 = 4 and t12 = −2, find the first three terms of the arithmetic sequence.