A geometric progression has non zero first term 'a' ansd connon ratio 'r' where 0<r>1, given that the sum of the first 8 terms of the progression is equal to half the sum to infinty, find the value of 'r' correct to 3 decimal places.​

Asocial networking site currently has 400,000 active members, and that figure is predicted to increase by 32% each year. the following expression represents the number of active members on the site after t years.

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).

If two angles of a triangle have equal measures and the third angle measures 90°, what are the angle measures of the triangle? a. 60°, 60°, 60° b. 45°, 90°, 90° c. 30°, 30°, 90° d. 45°, 45°, 90°