The base of an aquarium with given volume V is made of slate and the sides are made of glass. If the slate costs three times as much (per unit area) as glass, use Lagrange multipliers to find the dimensions of the aquarium that minimize the cost of the materials. (Enter the dimensions as a comma-separated list.)

Evaluate the discriminant of each equation. tell how many solutions each equation has and whether the solutions are real or imaginary. x^2 - 4x - 5 = 0

Last week , donnell practiced the piano 3 hours longer than marcus . together, marcus and donnell practiced the piano 11 hours . for how many hours did each young man practiced the piano

Arecent study focused on the number of times men and women who live alone buy take-out dinner in a month. assume that the distributions follow the normal probability distribution and the population standard deviations are equal. the information is summarized below. statistic men women sample mean 24.85 21.33 sample standard deviation 5.54 4.93 sample size 34 36 at the 0.01 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month? state the decision rule for 0.01 significance level: h0: μmen= μwomen h1: μmen ≠ μwomen. (negative amounts should be indicated by a minus sign. round your answers to 3 decimal places.) compute the value of the test statistic. (round your answer to 3 decimal places.) what is your decision regarding the null hypothesis? what is the p-value? (round your answer to 3 decimal places.)