All Answers 359400 Answers

   New York to Baltimore is 190 miles          190 mi / 175 ^mi/_hr  =  1.0857 hr     1 hr, 5 min, 9 sec     

   Baltimore to Tallahasse is 905 miles         905 mi / 250 ^mi/_hr  =  3.6200 hr     3 hr, 31 min, 12 sec     

   _.     

   weekly return 0n $200000 at 3% interest only     

     200,000 • 0.03     

   ––––––––––––––   =   115.38     

              52     

   Note:  Depending on compounding, the principal in a given week might be more than $200,000,

              thereby making the interest for that week more than in the above calculation.     

   _.     

Will and Grace are canoeing on a lake.  Will rows at $50$ meters per minute and Grace rows at $30$ meters per minute. Will starts rowing at $2$ p.m. from the west end of the lake, and Grace starts rowing from the east end of the lake at $2{:}45$ p.m. If they always row directly towards each other, and the lake is $2800$ meters across from the west side of the lake to the east side, at what time will the two meet?      

   D = Rate • Time       D_WILL     +  D_GRACE          =  2800 m     

                                   (50) (T)  +  (30) (T – 45)  =  2800      

                                       50T    +  30T  – 1350   =  2800 m     

                                                                    80T  =  4150     

                                                                        T  =  51.875 min     note that 0.875 • 60 = 43.75 call it 44     

                                      2:00 + (51 min 44 sec)  =  2:52 & 44 sec P.M.     

   _.     

   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?     

   15 m / 0.3048 ^m/_ft  =    49.2126 ft     

   60 m / 0.3048 ^m/_ft  =  196.8504 ft     

                        Area  =  (49.2126 ft)(196.8504 ft)     

                        Area  =  9687.52 sqft     

                        Paint  =  9687.52 sqft / 400 ^sqft/_gal     

                        Paint  =  24.22 gal     but you can't buy just 0.22 of a gallon     

                so,   Paint  =  25 gal     

   _.     

   what is 456 divided by450     

       456     

      ––––   =   1 ⁶/₄₅₀   =   1 ¹/₇₅     

       450     

   _.     

   In a row of five squares, each square is to be colored either red,     

   yellow, or blue, so that no two consecutive squares have the same     

   color. How many ways are there to color the five squares, if there     

   must be at least three yellow squares?     

   In order not to have two yellows next to each other,     

   the three yellows must occupy squares 1, 3, and 5.     

   That leaves squares 2 and 4 to fill, and two colors     

   to do it with. There are only four ways.     

   Blue Blue     Red Red     Blue Red     Red Blue     

   So, the answer is four ways.     

   _.     

   The distance from Capital City to Little Village is 5 miles.     

   The distance from Capital City to Mytown is 2 miles.     

   The distance from Mytown to Yourtown is 3 miles.     

   The distance from Little Village to Yourtown is 4 miles.     

   Find the distance from Capital City to Yourtown, in miles.     

   Little Village ----- 4 ----- Your Town ----- 1 ----- Capital City ----- 2 ----- My Town     

   _.     

   A geometric sequence has $400$ terms.     

   The first term is $500$ and the common ratio is $-\frac{1}{20}.$     

   How many terms of this sequence are greater than $1?$     

   1st                            =       + 500     

   2nd     –1/20  •  500  =      – 25     

   3rd      –1/20  •  – 25  =     + 1.25     

   4th      –1/20  •  1.25  =     – 0.0625     

   5th and beyond, everything will be so tiny that they're less than 1.     

   Looks like only 2 are greater than 1, namely the 500 and the 1.25.     

   The – 25 is disqualified because a negative number is less than 1.     

   _.     

   The diagram below consists of a small square, four equilateral triangles,     

   and a large square.  Find the area of the large square.     

   A trianagle base is 1 and there are 2¹/₂ bases going across the large square.     

   So, the length of the large square side is 2.5 units, and (2.5)² = 6.25 units²     

   _.     

   4.582575695 simplyfied     

   Well, it just so happens that it's the sqrt (21)     

   _.     

   what is 3 2/5 + 6 2/7?     

                                                      3 ²/₅  +  6 ²/₇     

                                                        17        44     

   change to improper fractons       –––  +  –––  =     

                                                         5          7     

                                                       119         220        339     

   convert to same denominator     ––––  +  ––––  =  ––––  =  9 ²⁴/₃₅          

                                                        35           35          35     

   _.     

     A store sold 8.5 pounds, 6.26 pounds, 9.2 pounds, and 4.54 pounds of apples each week during a month. 

     If the store started out the month with a inventory of 46.2 pounds of apples, how many were left at the end of the month     

     Started with                                                      46.2 lbs     

     Sold                 8.5  +  6.26  +  9.2  +  4.54  =  30.3 lbs     

     How many were left                                         15.0 lbs     

     _.     

   Our badminton team has finished 60% of its season.  So far, we have won 40%     

   of the games we played.  What percent of the remainder of our games must we     

   win in order to finish the season with the same number of wins as losses?     

   Say that the season is a 100 games.  You've won 40% of 60 games = 24 wins.     

   You need to win 26 more of the remaining 40 games to take you up to 50 wins.     

               X • 40  =  26     

               X         =  26 / 40     

               X         =  0.65  =  65%     

   _.     

   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?     

   Use Volts and Amps to find Ohms                      V = I • R    ==>>    R  =  V / I     

   Note that 25 mA is 0.025 A                                                               R  =  500 V / 0.025 A     

                                                                                                             R  =  20,000 Ω     

   Use Volts and Ohms to find Amps                       V = I • R    ==>>    I  =  V / R     

   Note that cutting the wire in half halves the R                                   I  =  175 V / 10,000 Ω     

                                                                                                              I  =  0.0175 A     

   Note that 1 A is 1,000 mA                                                                  I  =  17.5 mA     

   _.     

   A circle is inscribed in a rhombus with sides of length 4 cm.     

   If the two acute angles in the rhombus each measure $90^{\circ}$,     

   what is the length of the circle's radius? Express your answer in simplest radical form.     

   If the rhombus has two 90^o angles, the rhombus is the special case of a square.     

   The diameter of a circle inscribed in a square is the same as a side of the square.     

   So the diameter is 4 cm, and the radius is half the diameter, so the radius is 2 cm.     

   _.     

   convert 128 ounces to pounds     

   assuming avoirdupois              128 oz     

                                                    ––––––––  =  8 lb     

                                                      16 ^oz/_lb     

   _.     

   how do you find slope from 2 points?     

   Divide the line's vertical change by it horizontal change.     

   One way to rememberr the process is is "rise over run".     

   Example, given two points on the line:  (8,5) and (12,7)     

                    Δ y           7 – 5            2     

   Slope  =  ––––  =  ––––––––  =  –––  =  1 / 2     

                    Δ x         12 – 8            4     

   _.