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   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     

   _.     

The answer is 5/12.

The answer is 16.

The answer is (1 + sqrt(5))/2.

The answer is 13/16.

The answer is 7/8.

The answer is 16.

The answer is 18.

The answer is 1/2.

   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.     

   _.     

   If a triangle has an area of 6 feet square and the base of the triangle is 6 feet, what are the      

   lengths of the other sides of the triangle, and what is that triangle’s perimeter approximately?     

   The second easiest solution is if the triangle is isoceles     A  =  (¹/₂) b h     

                                                                                                6  =  (¹/₂) • 6 • h     

                                                                                                6  =  3h  ==>>  h = 2       

   Pythagoras Theorem  c² = a² + b²     ==>>     Side²  =  3² + 2²     draw it and you'll see     

                                                                            Side²  =  9 + 4  =  13     

                                                                            Side¹  =  sqrt(13)     

   So the sides of the triangle if it is isoceles are 6, sqrt(13), and sqrt(13)     

   The first easiest way is if the triangle is a right triangle and its two legs are 6 and 2.     

   If the triangle is neither isoceles nor a right triangle, then there isn't enough information     

   given to determine what its other two sides are.     

   _.     

   I have to paint one side of a wall.  The wall is $15$ meters tall and $60$ meters long.     

   Each gallon of paint covers $400$ 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     

   H _wall = (15)(3.2808) ft =   49.212 ft     

   L _wall  = (60)(3.2808) ft = 196.848 ft     ==>>     Area _wall = (49.212 ft)(196.848 ft)     

                                                                                           = 9687.284 sqft     

   Paint req'd     ==>>     (9687.284 sqft) / (400 sqft/gallon)  =  24.218 gal     

   You can't buy just part of gallon, so you need to buy 25 gallons.     

  _.      

   What is the measure (in degrees) of the smallest [b]interior[/b] angle of a triangle     

   in which the exterior angle measures have the ratio 4:2:8?     

   The exterior angles of any polygon always sum to 360^o.     

   So the exterior angles are (⁴/₁₄)(360), (²/₁₄)(360), and (⁸/₁₄)(360).     

   The largest exterior angle would have the smallest interior angle.     

   Therefore, the smallest interior angle is 180 – (⁸/₁₄)(360) degrees.     

   Doing the arithmetic gives us that the smallest angle is – 25.71^o.     

   A triangle can't have a negative angle, so this triangle cannot exist.     

   _.     

Let WXYZ be a square.  Let P be a point inside the square, so that triangle PWX is right isosceles.  Compute \angle PYZ.     

Since PWX is right isoceles, P has to be the center of the square, thus angle PYZ = 45^o.      

_.     

   what is negative 4 over 5 but you have to divide 4 with the 5     

   Odd way to state it,     

   caught my attention.                        – 4                 4     

                                                           ––––   or   – ––––     

                                                              5                  5     

                                                           either way, equals  – 0.8     

   _.