The time it takes for a planet to complete its orbit around a particular star is called the​ planet's sidereal year. The sidereal year of a planet is related to the distance the planet is from the star. The accompanying data show the distances of the planets from a particular star and their sidereal years. Complete parts​ (a) through​ (e).Planet             Distance from the Star, x (millions of miles)                            Sidereal Year, y1                           36                                                                                          0.242                           67                                                                                          0.643                            93                                                                                          1.004                           142                                                                                            1.865                           483                                                                                              11.86                           887                                                                                             29.37                          1785                                                                                              82.08                           2797                                                                                             163.09                            3675                                                                                               245.0I've attached a scatter diagram.(b) Determine the correlation between distance and sidereal year.The correlation between distance and sidereal year is __​(Round to three decimal places as​ needed.)

1. Point is reflected across the line . What are the coordinates of ? Show your work and explain.2. Suppose point is translated according to the rule . What are the coordinates of ? Explain.3. How many lines of symmetry does a regular heptagon have? Explain your answer.4. Suppose the point is reflected across the axis and then translated according to the rule . What are the coordinates of ? Show your work and explain.5. In the figure, . Solve for . Show your work.6. In the figure, . Solve for . Show your work.7. In the figure, . What is the perimeter of ? Show your work.8. What is the length of side in the triangle? Show your work.9. Find the length of in the triangle below. Show your work.10. Find the length of Show your work.11. Find the measure of . Show your work.12. Give the center, radius, and equation of the circle in the graph.13. Find the measure of . Show your work.14. What is the center and radius of the circle that has the equation ? Explain.15. What is the area of shown in the figure? Show your work.16. What is the area of a rhombus whose diagonals have lengths inches and inches? Show your work.17. What is the area of quadrilateral if and ? Show your work.18. What is the area of a circle whose diameter is inches? Use in your calculations. Show your work.19. What is the volume of a square pyramid whose length of one side of its base is cm and whose height is cm. Show your work.20. What is the exact volume of a cylinder whose diameter is meters and whose height is meters? Show your work.21. What is the exact volume of a sphere whose diameter is cm? Show your work.22. What is the exact volume of a cone whose base radius is feet and whose height is feet? Show your work.23. In his suitcase, Jack has shirts, pants, socks (pairs of socks), and shoes (pairs of shoes). How many unique ways can Jack get fully dressed? Show your work and explain.24. Suppose you throw two fair number cubes. What is the probability that the sum of the results of the throw is or ? Show your work and explain.25. Suppose you draw one card from a standard deck of cards. A standard deck of cards has 4 of each type of card, so the deck contains 4 kings and 4 queens. What is the probability that the card is a king or a queen? Explain.