X=  2 1 2 1 3 2 2 1 4 3 2 1 where the rows represent breakfast, lunch, and dinner, and the  columns represent the number of exchanges for each of the four  food groups at each meal; Y= 5 0 7 0 10 1 0 15 2 10 12 8 where the rows represent the four food groups, and the columns  represent the amount of fat, carbohydrates, and protein per  exchange of each food group; and Z= 8 4 5 where the rows represent fat, carbohydrates, and protein, and  the column represents calories per exchange. (a)  Find the product matrix XY. What do the entries of this matrix represent? (b)  Find the product matrix YZ. What do the entries represent? (c)  Find the products 1XY2Z and X1YZ2 and verify that they  are equal. What do the entries represent

4 In the record books of Angorra, the following data was found: x - 2y = 6 Equation 1 -x + 4y = 6 .. Equation 2 Choose the most efficient approaches to solve the system given above. Add the equations. Multiply equation 1 by 2 and subtract the equations. Solve equation 1 for x and substitute the result in equation 2. Substitute -x + 4y for 6 in equation 1.

A researcher believed that the number of rental cars in service by a car rental company would have an impact on the total annual revenue for that car rental company. Five small car rental companies were surveyed, with the number of Cars in service recorded in units of 1000 (so if a car rental company had 54000 cars in service, a 54 would be recorded) and Annual Revenue measured in millions of dollars (so an Annual Revenue of $10,000,000 would be recorded as 10). The data follows: Cars (1,000s)       Annual Revenue ($ millions)11.5                   118 10.0                   135 9.0                     100 5.5                     37 3.3                     32 Part of the Excel-generated Simple Linear Regression output is provided below: ANOVA   df SS MS F Significance F Regression 1 7891.863897 7891.863897 22.91180151 0.017339231 Residual 3 1033.336103 344.4453677     Total 4 8925.2           Coefficients Standard Error t Stat P-value Intercept -19.12490108 23.1658578…

You are an analyst for a consumer products company. You run a survey of 1000 customers and find that 80% of customers use gel packs for laundry detergent (the rest use liquid or powder) and 40% of customers use gel packs for their dishwasher detergent (the rest use liquid or powder). You also learn that twice as many customers use laundry detergent than dishwasher detergent and that this relationship is independent of gel pack or other types of products (liquid or powder).

The following table provides data on three popular protein supplements. (Figures shown correspond to a single serving.)   Protein(g) Carbohydrates(g) Sodium(mg) Cost($) DesignerWhey (Next) 18 2 80 0.50 Muscle Milk(Cytosport) 32 16 240 1.60 Pure WheyProtein Stack(Champion) 24 3 100 0.60   You are thinking of combining Designer Whey and Muscle Milk to obtain a 7-day supply that provides exactly 448 grams of protein and 112 grams of carbohydrates. How many servings of each supplement should you combine in order to meet your requirements? Designer Whey ______ servingsMuscle Milk ______ servings What will it cost? $