Bosco

What is the average speed (in feet/second) of a baseball that is thrown 88 feet in 4 seconds?     

(Write your answer to the nearest hundredth, or second decimal place.)     

Velocity  =  Distance / Time     

              =  88 ft / 4 sec     

              =  22 ^ft/_sec     

_.     

The area of one lateral face of a right pyramid with an equilateral triangular base is 75 square meters. If the slant height is 25 meters, what is the length of the side of its base, in meters?     

The slanted face is a triangle.  A_triangle  =  (1/2)(base)(height)     

                                                          75  =  (1/2)(base)(25)     

                                                   75 / 25  =  (1/2)base     

                                                            3  =  (1/2)base     

                                                      base  =  6     

_.     

 Two containers designed to hold water are side by side, both in the shape of a cylinder.     

 Container A has a diameter of 30 feet and a height of 18 feet.     

 Container B has a diameter of 26 feet and a height of 19 feet.     

 Container A is full of water and the water is pumped into Container B until Conainter B is completely full.     
 After the pumping is complete, what is the volume of the empty space inside Container A, to the nearest tenth of a cubic foot?      

V_CylB  =  π r² h     

V_CylB  =  (3.1416)(13²)(19)     

V_CylB  =  10,087.6776     

V_CylB  =  10,087.7 ft³    ——>>  Full container B was pumped out of container A.     

                                                   The amount that container B holds is how much     

                                                    empty space is left in container A.     

_.     

  A bouquet of lilies and tulips has 20 flowers. Lilies cost $3 each and tulips cost $2 each.     

  The bouquet costs $48. How many lilies x and tulips y are in the bouquet?      

  3L + 2T  =  48                      ——>   3L + 2T  =  48     

    L +   T  =  20   multiply x2  ——>   2L + 2T  =  40     

                             subtract     ——>             L  =   8 Lilies     

    L  +  T  =  20     

            T  =  20 – 8                ——>             T  =  12 Tulips     

_.     

Andrei has a glass tank. First, he wants to put in some marbles, each of which has a volume of 0.04 liters. Then, he wants to fill the tank with water until it's completely full. If he uses 50 marbles, he will have to add 33 liters of water.     

To find the total volume of the tank     

            add the volume of marbles     (50)(0.04 liter)  =    2 liters     

            plus the volume of water                                     33 liters     

                                                           total volume     =  35 liters     

_.     

The local library have a children section with picture books and chapter books the ratio is 2:3. If there is a total of 500 books in the children's section how many chapter books are there in the section     

The ratio is 2 picture books to 3 chapter books.     

This is 2 parts to 3 parts, so the total is 5 parts.     

Since there are 5 parts, each part is 500 / 5 so     

each part is 100 books.  That makes the ratio     

in the values of 200:300.  300 chapter books     

_.     

  The lateral area of a right cylinder which has a base diameter of 12 cm and a height of 8 cm     

  A_Lateral  =  circumference x height     

                =  π d h     

                =  (3.14)(12 cm)(8 cm)     

                =  301.44 cm²     —–>>  Call it 301 cm² to match the choice.    

_.     

An alloy is a mixture of metals. Suppose that a certain alloy is made by mixing 300 grams of an alloy that contains 72% copper with 20 grams of pure copper. How many grams of copper are in the resulting mixture? What percentage of the resulting mixture is copper?     

Which Ingredient   Amount Cu   Amount Not Cu     

    Alloy 1                     216                     84      

    Pure Cu                     20     

    New Alloy                 236                    84     

Amt cu in resulting alloy  =  236     

Pctg cu in resulting alloy  =  (236) / (236+84)  =  0.7375  =  74%     

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