Adiet is to include at least 140 milligrams of vitamin a and at least 145 milligrams of vitamin b. these requirements can be obtained from two types of food. type x contains 10 milligrams of vitamin a and 20 milligrams of vitamin b per pound. type y contains 30 milligrams of vitamin a and 15 milligrams of vitamin b per pound. if type x food costs $12 per pound and type y food costs $8 per pound how many pounds of each type of food should be purchased to satisfy the requirements at the minimum cost? round to the nearest hundredths.

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.)