Afacilities manager at a university reads in a research report that the mean amount of time spent in the shower by an adult is 5 minutes. he decides to collect data to see if the mean amount of time that college students spend in the shower is significantly different from 5 minutes. in a sample of 15 students, he found the average time was 4.61 minutes and the standard deviation was 0.75 minutes. using this sample information, conduct the appropriate hypothesis test at the 0.05 level of significance. assume normality. a) what are the appropriate null and alternative hypotheses? h0: μ = 5 versus ha: μ ≠ 5 h0: μ = 5 versus ha: μ < 5 h0: x = 5 versus ha: x ≠ 5 h0: μ = 5 versus ha: μ > 5 b) what is the test statistic? give your answer to four decimal places. c) what is the p-value for the test? give your answer to four decimal places. d) what is the appropriate conclusion? fail to reject the claim that the mean time is 5 minutes because the p-value is larger than 0.05. reject the claim that the mean time is 5 minutes because the p-value is larger than 0.05. fail to reject the claim that the mean time is 5 minutes because the p-value is smaller than 0.05. reject the claim that the mean time is 5 minutes because the p-value is smaller than 0.05.

The center of a circle represent by the equation (x+9)^2+(y-6)^2=10^2 (-9,6), (-6,9), (6,-9) ,(9,-6)

In δabc shown below, ∠bac is congruent to ∠bca: triangle abc, where angles a and c are congruent given: base ∠bac and ∠acb are congruent. prove: δabc is an isosceles triangle. when completed (fill in the blanks), the following paragraph proves that line segment ab is congruent to line segment bc making δabc an isosceles triangle. (4 points) construct a perpendicular bisector from point b to line segment ac . label the point of intersection between this perpendicular bisector and line segment ac as point d: m∠bda and m∠bdc is 90° by the definition of a perpendicular bisector. ∠bda is congruent to ∠bdc by the definition of congruent angles. line segment ad is congruent to line segment dc by by the definition of a perpendicular bisector. δbad is congruent to δbcd by the line segment ab is congruent to line segment bc because consequently, δabc is isosceles by definition of an isosceles triangle. 1. corresponding parts of congruent triangles are congruent (cpctc) 2. the definition of a perpendicular bisector 1. the definition of a perpendicular bisector 2. the definition of congruent angles 1. the definition of congruent angles 2. the definition of a perpendicular bisector 1. angle-side-angle (asa) postulate 2. corresponding parts of congruent triangles are congruent (cpctc)

What is the point slope form of a line with slope -5 that contains point (2,-1)