A's Shoes and B's Footwear both have outlets in city 1 and city 2. A's sells shoes for $90, sandals for $60, and boots for $120. B's prices are $40, $50, and $170 for shoes sandals, and boots, respectively. Half of all sales in city 1 stores are shoes,-are sandals, and-are boots. In city 2 the fractions are-shoes, sandals, and-boots. Complete parts (a) through (d) below (a) Write a 2x3 matrix called P representing prices for the two stores and three types of footwear. 4 4 (Type an integer or simplified fraction for each matrix element.) (b) Write a 3x 2 matrix called F representing the fraction of each type of footwear sold in each city (Type an integer or simplified fraction for each matrix element.) (c) Only one of the two products PF and FP is meaningful. Determine which one it is and calculate the product. Select the correct choice below and fill in the answer box to complete your choice (Type an integer or simplified fraction for each matrix element.) A. The product FPis meaningful B. The product PFis meaningful Describe what the entries represent. The (d) From the answer to part (c), what is the average price for a pair of footwear at an outlet of B's in city 1? a. give the average price per pair。 b. sold by each store, and the c. give the city

In δabc shown below, ∠bac is congruent to ∠bca: triangle abc, where angles a and c are congruent given: base ∠bac and ∠acb are congruent. prove: δabc is an isosceles triangle. when completed (fill in the blanks), the following paragraph proves that line segment ab is congruent to line segment bc making δabc an isosceles triangle. (4 points) construct a perpendicular bisector from point b to line segment ac . label the point of intersection between this perpendicular bisector and line segment ac as point d: m∠bda and m∠bdc is 90° by the definition of a perpendicular bisector. ∠bda is congruent to ∠bdc by the definition of congruent angles. line segment ad is congruent to line segment dc by by the definition of a perpendicular bisector. δbad is congruent to δbcd by the line segment ab is congruent to line segment bc because consequently, δabc is isosceles by definition of an isosceles triangle. 1. corresponding parts of congruent triangles are congruent (cpctc) 2. the definition of a perpendicular bisector 1. the definition of a perpendicular bisector 2. the definition of congruent angles 1. the definition of congruent angles 2. the definition of a perpendicular bisector 1. angle-side-angle (asa) postulate 2. corresponding parts of congruent triangles are congruent (cpctc)

Over the course of the school year, you keep track of how much snow falls on a given day and whether it was a snow day. your data indicates that of twenty-one days with less than three inches of snow, five were snow days, while of the eight days with more than three inches of snow, six were snow days. if all you know about a day is that it is snowing, what is the probability that it will be a snow day?

Jane’s favorite fruit punch consists of pear, pineapple, and plum juices in the ratio 5: 2: 3. how many cups of pear juice should she use to make 20 cups of punch?