State the conclusion based on the results of the test. the standard deviationstandard deviation inin the pressure required to open a certain valve is known to be sigma equals 1.3 psi.σ=1.3 psi. due to changes in the manufacturing process, the quality-control manager feels that the pressurepressure variabilityvariability has changedchanged. the null hypothesis was rejected. choose the correct answer below. a. there is not sufficient evidence that the mean of the pressure required to open a certain valve has not changed. b. there is sufficient evidence that the mean of the pressure required to open a certain valve has changed. c. the mean of the pressure has not changed. d. the mean of the pressure has changed. e. there is sufficient evidence that the mean of the pressure required to open a certain valve has not changed. f. there is not sufficient evidence that the mean of the pressure required to open a certain valve has changed.

noncoplanar points are points that do not lie on the same line.

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.

answer: the proof is mentioned below.

step-by-step explanation:

since, given:   lines bc = ef

prove:   lines ac > ef

          statements                                           reason

1. bc=ef                                           1. given

2. ac= ab+bc                                 2. because b is the point between the  

                                                            line segment ac

3.   ac > bc                                       3. because if a line segment is equal to

                                                          the sum of two line segments then it is

                                                          always greater then each of these

                                                          individual line segments

4. ac > ef                                         4. by equality property.