The data sets below show the price that a homeowner paid, per term, for natural gas during each of the first ten months of 2011 and 2012. Use the data for 1–4.

2011: $1.59, $1.72, $1.71, $1.86, $2.32, $2.54, $2.45, $2.80, $2.38, $2.25

2012: $1.57, $1.61, $1.96, $1.71, $1.98, $2.17, $2.51, $2.44, $2.52, $2.10

1. Find the mean, median, range, and interquartile range for 2011

2. Find the mean, median, range, and interquartile range for 2012.

3. Find the standard deviation for each year. Round to the nearest hundredth.

4. Use your statistics to compare the overall trend in prices for

the two years.

5. To earn an exemption from the final exam, Aaron needs his mean test score to be 92 or greater. If Aaron scored 90, 96, 87, and 90 on the first four tests and he has one test still to take, what is the lowest he can score and still earn an exemption?

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Suppose a man is heterozygous for heterochromia, an autosomal dominant disorder which causes two different‑colored eyes in an individual, produced 25‑offspring with his normal‑eyed wife. of their children, 15 were heterochromatic and 10 were‑normal. calculate the chi‑square value for this observation.

For this option, you will work individually. the pythagorean theorem can be used in many real-world scenarios. part 1 write your own real-world scenario where the pythagorean theorem can be applied to find a missing piece. you may choose to write a problem that is two- or three-dimensional in nature. be sure that you will be able to draw a diagram of your scenario. write out your problem and submit it for part 1. be sure to end your scenario with a question. part 2 draw a diagram of the scenario you created in part 1. you may draw by hand and scan and upload your drawing or create a computer-generated drawing for submission. be sure to label all parts and dimensions of the drawing. part 3 solve the question that you posed in part 1. show all of your steps in answering the question. for this option, you will need to submit all three parts for full credit—your real-world problem and question, the diagram that you created, and your work solving the problem, showing all steps. * note that your instructor is looking for your own original idea. while it is acceptable to use the internet for research and inspiration, academic integrity policies apply.

Simplify. −4x^2 (5x^4−3x^2+x−2) −20x^6−12x^4+8x^3−8x^2 −20x^6+12x^4−4x^3+8x^2 −20x^8+12x^4−4x^2+8x −20x^6+12x^4+4x^3−8x^2