A serving of banana contains 0.7 grams of protein, 0.2 grams of fat, and 13.5 grams of carbohydrates. A serving of mandarin oranges contains 0.5 grams of protein, 0.3 grams of fat,
and 8.5 grams of carbohydrates. A serving of grapes contains 0.3 grams of protein, 0.2 grams of
fat, and 8 grams of carbohydrates. How many servings of each are needed to supply exactly 3.2
grams of protein, 1.5 grams of fat, and 60.5 grams of carbohydrates?

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.)