Bosco

   Greg earns $850.00 per week plus 4% of net sales over $15,000.00.     

   Greg's sales were $19,950.00 and his returns were $875.00.     

   How much did Greg earn?     

   19,950 – 875 = 19,075 (net)     

   Earned   =  850 + (0.04)(19,075 – 15,000)     

                 =  850 + (0.04)(4075)     

                 =  850 + 163     

                 =  1013     

   _.     

   In a store window, there was a box of berries having a total weight of 200 kg.     

   The berries were 99% water, by weight.  After two days in the sun,     

   the water content of the berries was only 75%, by weight.     

   What was the total weight of the berries after two days, in kg?     

   You start with 200 kg of berries, and 99% of that is water.     

   They're 99% water, which means there's 1% of solid stuff.     

   And 1% of 200 kg means there are 2 kg of the solid stuff.     

   Some of the water evaporates in the sun, but the solid stuff doesn't.     

   So, after this evaporation, there remains the same 2 kg of solid stuff.     

   Since the new water content is 75%, now the solid stuff composes 25%.     

   So 2 kg (the solid stuff) is (100% – 75% water) = 25% of the total weight.     

   That means the new total weight is (2 kg / 0.25)  =  8 kg     

   _.     

   Find the discriminant of the quadratic 5x^2 - 2x + 8 - 2x^2 + 6x + 2.     

   When a quadratic equation is in the form ax² + bx + c = 0     

   the discriminant is given by b² – 4c.  So, combine terms:        5x² – 2x + 8 – 2x² + 6x + 2     

                                                                                                     3x² + 4x + 10     

                                      D  =  4² – (4)(3)(10)     

                                           =  16 – 120     

                                           =  – 104     

   Note that solutions to a quadratic with a negative discriminant are imaginary numbers.     

   _.     

   We have a piece of wire.  We pass $500$ volts through this wire and measure $25$ milliamps of current.     

   If I cut the wire in half and pass $175$ volts through it, how many milliamps of current will I measure?     

   V = IR     ==>>     R  =  V / I     

                                R  =  500 / 25 mA     

                                R  =  500 V / 0.025 A     

                                R  =  20,000 Ω     

                               (1/2) • 20,000 Ω  =  10,000 Ω     

   V = IR     ==>>     I  =  V / R     

                                I  =  175 V / 10,000 Ω     

                                I  =  0.0175 A     

                                I  =  17.5 mA     

   I don't like the expression "pass volts through a wire" but I won't quibble.     

   _.     

   Catherine rolls a standard $6$-sided die six times. If the product of her rolls is $300,$ then     

   how many different sequences of rolls could there have been? (The order of the rolls matters.)     

   The rolls could have consisted of     

   1  1  2  5  5  6  ==>> there could be ₆P₆ different sequences  =   720     

   1  1  3  4  5  5            ditto                                                         =   720     

   1  2  2  3  5  5            ditto                                                         =   720     

                                         total number of different sequences   =  2160     

   _.     

   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, each pile has two cards.     

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

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

   and that is when the stack cosists of both of the Two's.     

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

   _.     

                   20 cm           20 cm     

   a.   D  =  –––––––  =  –––––––  =  40 cm     

                   sin(30)         0.5000     

                            4.6 in                                           4.6 in     

   b.   12.4 in  =  –––––––    ==>>    arcsin(Θ)  =  –––––––  =  0.37097     

                          arcsin(Θ)                                      12.4 in     

                                                                             arcsin(Θ)  =  0.37097   

                                                                                        Θ   =  21.78^o      

   _.     

   Is the mean of these numbers 14.55?     

   6+9+10+10+10+12+15+15+17+17+18+18+18+18+19+19+19+20+21     

    291     

   ––––  =  15.32  (15.315789473684211 rounded to 2 significant digits)    

     19     

 _.     

   If Timmy has 4 apples and his friend Billy takes 3 how many apples does Billy have?     

   Billy has three apples, the three he took from Timmy.     

   Timmy has one apple, and his sister has a nice pear.     

   _.