Bosco

   Find the length of an arc that subtends a central angle of 45° in a circle of radius 30 m.     

   (Round your answer to two decimal places.)     

   All the way around the circle is 60 • π = 60 • 3.1416 = 188.496     

   All the way around the circle is 360^o, thus 45^o is 1/8 of the way     

   The length of the arc is 1/8 • 188.496 which rounds to 23.56 m     

   _.     

   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, has two cards per pile.     

   There can be 6C2 different piles, i.e., 15 different combinations.     

   There's only one way that a pile won't contain at least one Ace,     

   and that's when it's the stack consisting of both of the Two's.     

   So, 14 will and 1 won't, thus the probability is 14 / 15, i.e., 93.33%.     

   _.     

   Find the last two digits of $16*{37}$.     
   (Compute the remainder when $16*{37}$ is divided by 100.)     

   a.  16 x 37 = 592     ==>>     last two digits are 92     

   b.  No need for computation.     

        Just by looking at it               592 / 100 = 5 R 92          

   _.     

   Laverne starts counting out loud by 5's.  She starts with 2.     

   As Laverne counts, Shirley sums the numbers Laverne says.     

   When the sum finally exceeds 20, Shirley runs screaming from the room.     

   What number does Laverne say that sends Shirley screaming and running?     

   Laverne   Shirley     

         2             2     

         7             9     

       12           21     

   _.     

   If the equation y = 2x squared minus 3x minus 5 is shown on a grid, between     

   which two integers will the graph cross the x-axis (List both crossing areas)     

   y  =  2x² – 3x – 5     The curve crosses the x-axis when y = 0     

                                    2x² – 3x – 5  =  0     

                                    (2x – 5)(x + 1)  =  0          ==>>   (2x – 5)  =  0     

                                                                                          2x         =  5     

                                                                                                   x  =  2.5     

                                                                                          (x + 1)  =  0     

                                                                                                   x  =  – 1     

   The curve crosses the x-axis at (2.5, 0) and (–1, 0)     

   _.     

   what is the vertex of p=8x^2-112x+570     

   take the first derivitive     

   and set it equal to zero          16x – 112  =  0     

                                                           16x  =  112     

                                                               x  =  7        this is the x-coordinate of the vertex     

   plug the x value into the     

   original equation                     p  =  8x^2 – 112x + 570     

                                                  p  =  (8)(49) – (112)(7) + 570     

                                                  p  =  392 – 784 + 570     

                                                  p  =  178                 this is the p-coordinate of the vertex     

   so, the vertex is at (7, 178)     I verified this answer by plotting the curve on Desmos.     

   _.     

   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?     

     x + 60            x + 120     

   ––––––––  =  ––––––––     

     x + 120          x + 160     

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

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

           220x + 9600  =         240x + 14400     

                      – 20x  =  4800     

                             x  =  – 240     

    – 240 + 60           – 240 + 120     

   –––––––––––  =  –––––––––––     

    – 240 + 120         – 240 + 160     

    – 180         – 120          3     

   ––––––  =  ––––––  =  –––     

    – 120         – 80            2     

   _.     

   A salesperson's salary consists only of commissions, and she receives a 6 percent commission on all her sales.     

   As an extra incentive, this month her actual sales will be increased by 20 percent, and she will receive a commission     

   on the adjusted amount. Which of these represents the salesperson's salary this month as a function of her actual sales?

   unadjusted sales  =    S     

   adjusted sales      =    1.20 S     

   pct of adj sales     =    0.06 x 1.20 S  =  0.072 S     

   _.     

   a faucet drains a tank in 8 hours and an other one fills it in 6 hours ,

   in how many hours will the tank fill up if it is empty and both faucets are turned on the same time ?     

   Rate _{TO FILL}     = ¹/₆ tank per hour     

   Rate _{TO EMPTY} = ¹/₈ tank per hour     

   Net  =  ( ¹/₆ – ¹/₈ ) tank per hour     need common denominator     

           =  ( ⁴/₂₄ – ³/₂₄ ) tank per hour     

           =  ¹/₂₄ tank per hour     

   At ¹/₂₄ tank per hour, it will take 24 hours to fill the tank.     

   _.     

   The simple interest rate on a 90-day, 8% loan can be restated as     

   0.08 x ⁹⁰/₃₆₅     (doing the arithmetic, it rounds to 0.02)     

   _.