An experiment was conducted to investigate the effect of extrusion pressure (P) and temperature at extrusion (T) on the strength y of a new type of plastic. Two plastic specimens were prepared for each of five combinations of five combinations of pressure and temperature. The specimens were then tested in a random order and the breaking strength for each specimen was recorded. The independent variables were coded (transformed) as follows to simplify the calculations: x1 = (P-200)/10, x2 = (T-400)/25. The n=10 data points are listed in the table:y X1 X25.2 -2 25 -2 20.3 -1 -1-0.1 -1 -1-1.2 0 -2-1.1 0 -22.2 1 -12 1 -16.2 2 26.1 2 2(a) Find the least-squares prediction equation of the form y=β0 + β1x1 + β2x2 + ε. Interpret the β estimates.(b) Find SSE, s2, and s. Interpret the value of s.(c) Does the model contribute information for the prediction of y? Test using α=0.05.(d) Find a 90% confidence interval for the mean strength of the plastic for x1=-2 and x2=2.

Acircle has a diameter will endpoints of (-2,8) and (6, 4). what is the center of the circle

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.

[15 points]find the least common multiple of the expressions: 1. 3x^2, 6x - 18 2. 5x, 5x(x +2) 3. x^2 - 9, x + 3 4. x^2 - 3x - 10, x + 2 explain if possible