An article investigates the effects of the levels of several vitamins in a cell culture on the yield (in g/l) of pyruvate, a useful organic acid. the data consists of two replicates of a 23 design. the factors are a: nicotinic acid, b: thiamine, and c: biotin. each factor was tested at two levels. the data can be found in the textbook or on the datasets page here (ex9-5-4). compute the estimates of the main effects and interactions, and the sum

4. bob solved the inequality problem below incorrectly. explain his error and redo the problem showing the correct answer. ? 2x + 5 < 17 ? 2x + 5-5 < 17-5 -2x/-2 < 12/-2 x < -6

Joe owns a fast-food restaurant and wants to know the average time it takes for customers to receive their orders. his restaurant serves about 500 customers a day. he timed 5 orders, and the order times he collected, given in minutes, are shown below. can the approximate order fulfillment time for all of the restaurant's customers be calculated from the given data? if so, calculate it. non-integer answers should be rounded to the nearest tenth. if no assumption can be made, type "0" in the box. the approximate order fulfillment time for all of the restaurant's customers is minutes.

Given: abcd is a square. prove: ac ? bd. we are given that abcd is a square. if we consider triangle aeb and triangle aed, we see that side is congruent to side ad because sides of a square are congruent. we know that side ae is congruent to side ae by using the . finally, we know that side de is congruent to side because the diagonals of a square bisect each other. therefore, triangle aeb is congruent to triangle aed by congruency. we see that angle aed and angle aeb are a linear pair, and congruent by cpctc. thus, the measure of these angles will be 90°, and diagonal ac is perpendicular to diagonal bd by the .