Bosco

   All members of our painting team paint at the same rate.     

   If 20 members can paint a 2000 square foot wall in 40 minutes, then how long     

   would it take the 20 members to paint a 6000 square foot wall, in minutes?     

   20 mem   ==>>    paint 2000 ft² / 40 min  =  50 ft²/min     

   20 mem   ==>>    paint 6000 ft² /    x         =  50 ft²/min     

                                        6000 ft²                 =  50 ft²/min • x     

                                        6000 ft² / 50 ft²/min  =  x             

                                                                             x  =  120 min     

   Another way to do it is to consider the 6000 ft² wall as equivalent to three 2000 ft² walls     

   So, because one wall takes 40 minutes, three walls would take 3 • 40 min = 120 min     

   .     

   I have to paint one side of a wall.  The wall is 12 meters tall and 120 meters long.     

   Each gallon of paint covers 150 square feet. If a foot is approximately 0.3048 meters, then     

   what is the smallest whole number of gallons I can buy and have enough paint to cover the whole wall?     

   1 ft = 0.3048 m     ==>>     1 m = (1 / 0.3048) ft = 3.2808 ft     

   Height   =  (12 m)   • (3.2808 ft/m)  =    39.37 ft     

   Length  =  (120 m) • (3.2808 ft/m)  =  393.70 ft     ==>>     Area  =  (39.37 ft) • (393.70 ft)     

                                                                                                         =  15,499.97 ft²     

   Paint req'd     ==>>     (15,499.97 ft²) / (150 ft²/gallon)  =  103.33 gal     

   You can't buy just part of a gallon, so you will have to buy 104 gallons     

   _.     

   The following cards are split into three piles at random,     

   so that every pile contains the same number of cards.     

   What is the probability that every pile contains an Ace?     

   Ace of spades     

   Ace of hearts     

   Ace of diamonds     

   Ace of clubs     

   Two of spades     

   Two of hearts     

   Six cards divided evenly into three piles will create two cards per pile.     

   This makes 6C2 possible different piles, i.e., 15 possible combinations.     
 

   AS AH      AH AD      AD AC      AC 2S      2S 2H     

   AS AD      AH AC      AD 2S      AC 2H     

   AS AC      AH 2S      AD 2H     

   AS 2S      AH 2H     

   AS 2H     

   As illustrated above, every combination will have an Ace, except one.     

   The only pile that doesn't contain an Ace is the pile that has both 2's.     

   So the probability that a pile will contain an Ace is 14 / 15, i.e., 93.3%.     

   _.     

   how do you work out the rate of interest in the second year?     

   The interest rate is the same the second year as it was the first.     

   You have to add the first year's interest to the principal amount,     

   then figure the second year's interest using that new principal.     

   _.     

   a triangular prism has been created with two equilateral triangles and three congruent rectangles.     

   the height of the triangle is 3.5 inches. find the surface area of the triangular prism.     

   You could calculate the height of the rectangles by using     

   trigonometry and the fact that the triangles are equilateral.     

   But there’s no information given from which to deduce the     

   length of the rectangles, which is also needed to calculate     

   the area of the rectangles.     

   _.     

   how to find radius and height of cylinder given only a volume. The formula is V=1/3PIr^2h     

   No, it isn't.  The volume of a cone is         V = ¹/₃ • π • r² • h     

                      The volume of a cylinder is    V = π • r² • h     

   Either way, you can't do it.  You can't find two unknowns with only a single equation.     

   _.     

   When the same constant is added to the numbers 60, 120, and 160, a three-term geometric sequence arises.     

   What is the common ratio of the resulting sequence?     

      60 + x         120 + x     

   –––––––  =  –––––––     

    120 + x         160 + x     

   (120 + x) (120 + x)  =  (60 + x) (160 + x)     

   x² + 240x + 14400  =  x² + 220x + 9600     

          240x  – 220x  =  9600 – 14400     

                         20x  =  – 4800     

                             x  =  – 240     

      60 – 240          120 – 240     

   ––––––––––  =  ––––––––––     

    120 – 240          160 – 240     

       – 180                 – 120     

   ––––––––––  =  ––––––––––     =   1.5     

       – 120                   – 80     

   _.     

   A terminal zero is a $0$ that appears at the end of a number.     

   For example, the number $3,800$ has two terminal zeros.     
   How many terminal zeroes does $40 \cdot 6 \cdot 75 \cdot 12$ have?     

   I just did the multiplication, then counted the terminal zeros.     

   40 • 6 • 75 • 12  =  216,000     I count three of them.     

   _.     

   The product of a set of distinct positive integers is $630$.     

   If one of the numbers is 42, what are the other two numbers?     

    630 / 42  =  15     Therefore the other two numbers are  1 & 15    

                                                                                       or  3 & 5     

   _.