Commercial real estate prices and rental rates suffered substantial declines in 2008 and 2009.† these declines were particularly severe in asia; annual lease rates in tokyo, hong kong, and singapore declined by 40% or more. even with such large declines, annual lease rates in asia were still higher than those in many cities in europe. annual lease rates for a sample of 30 commercial properties in an asian city showed a mean of $1,114 per square meter with a standard deviation of $230. annual lease rates for a sample of 40 commercial properties in a european city showed a mean lease rate of $985 per square meter with a standard deviation of $195.

a. on the basis of the sample results, can we conclude that the mean annual lease rate is higher in hong kong than in paris? develop appropriate null and alternative hypotheses.
b. use ? = .01. what is your conclusion?
c. are rental rates higher in hong kong than in paris?

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).