Prove: the segment joining the midpoints of the diagonals of a trapezoid is parallel to the bases. slopes are equal; therefore, segments are parallel

Let f(x) = 5/x and g(x)=2x2+5x. what two numbers are not in the domain of f o g

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.)

Abarge can safely haul no more than 400 tons across the river. the barge has an empty weight of 24 tons. the average weight of the railroad cars is 4 tons each.bhow many railroad cars can the barge haul?