. Suppose that ABCD is a rhombus and that the bisector of angle BDC meets side BC
at F. Prove that angle DFC is three times the size of angle FDC.

Twenty-five percent of the customers entering a grocery store between 5 p. m. and 7 p. m. use an express checkout. consider five randomly selected customers, and let x denote the number among the five who use the express checkout.

You coordinate volunteers for litter cleanup in local parks. your spreadsheet lists drivers and the number of seat belts in each driver’s car. the spreadsheet calculates the number of drivers (d) and the total number of seat belts (s). you want to know the maximum number of volunteers, besides drivers, that can be transported to the park in a single trip given that each person must have a seat belt of their own.

Arandom sample of n = 25 observations is taken from a n(µ, σ ) population. a 95% confidence interval for µ was calculated to be (42.16, 57.84). the researcher feels that this interval is too wide. you want to reduce the interval to a width at most 12 units. a) for a confidence level of 95%, calculate the smallest sample size needed. b) for a sample size fixed at n = 25, calculate the largest confidence level 100(1 − α)% needed.