On a mountain bike trip along the Gemini Bridges Trail in Moab, Utah, Safiya stopped on the canyon floor to get a good view of the twin sandstone bridges. Safiya is standing about 60 meters from the base of the canyon cliff and the natural arch bridges are about 100 meters up canyon wall. If her line of sight is 5 meters above the ground, what angle is she looking up to the top of the cliff?

Atextile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. the company wishes to test the hypothesis upper h subscript 0 baseline colon mu equals 12 against upper h subscript 1 baseline colon mu less-than 12 using a random sample of n equals 4 specimens. calculate the p-value if the observed statistic is x overbar equals 11.8. round your final answer to five decimal places (e. g. 98.76543).

Parabolas y=−2x^2 and y=2x^2 +k intersect at points a and b that are in the third and the fourth quadrants respectively. find k if length of the segment ab is 5.

Vanessa earns a base salary of $400.00 every week with an additional5% commission on everything she sells. vanessa sold $1650.00 worth of items last week.