Bosco

The six faces of a three-inch wooden cube are each painted red. The cube is then cut into one-inch cubes along the lines shown in the diagram. How many of the one-inch cubes have red paint on at least one face?     

I count 26 of them.  The cube has been cut into 27 small cubes.     

Only the one-inch cube in the very center will have no paint on it.     

_.     

A toilet paper company sells rolls of toilet paper where the cardboard portion in the middle has a diameter of 1.8 inches and a height of 3.75 inches. How many square inches of cardboard would there be in a package of 24 rolls of toilet paper? Round your answer to the nearest roll.     

Area of one tube  =  circumference times length  =  1.8 • π • 3.75     

                                                                              =  1.8 • 3.1416 • 3.75     

                                                                              =  21.2058     

Area of 24 tubes  =  24 times Area of one tube    =  24 • 21.2058     

                                                                              =  508.9392  —>  rounds to 509     

_.     

Tony invests $3,000 dollars in an account earning 12% interest per year.     

How long will it take him to make $3,960 dollars in simple interest?     

3000 • 1.12ⁿ  =  3960     

3000 • 1.12^2.45  =  3960.09     

so it will take 2.45 years, aka 2 years, 5 months, & 12 days     

_.     

Find the measures of the exterior angles on following polygons.     

The sum of the exterior angles of any polygon is 360^o     

so, since the number of angles will be the same as the     

number of sides, then all you have to do is divide 360     

by the number of sides.     

• triangle                360 / 3    120     

• quadrilateral        360 / 4      90     

• pentagon             360 / 5      72     

• octagon               360 / 8      45     

• decagon              360 / 10    36     

• triacontagon        360 / 30    12     

• pentacontagon    360 / 50      7.2     

• hectogon             360 / 100    3.6     

_.     

Let X stand for the number of $2 books     

Let Z stand for the number of $3 books     

    X + Z  =  65      multiply both sides by 3  —>     3X + 3Z  =  195     

2X + 3Z  =  155                                           —>     2X + 3Z  =  155     

                                subtract                                    X          =    40     books @ $2     

    X + Z  =  65                                             —>        40 + Z  =  65     

                                                                                          Z  =  65 – 40     

                                                                                          Z  =  25     books @ $3     

check answer     

does   2•40 + 3•25  =  155  ?     

                  80 + 75  =  155  ?     

                        155  =  155  true     

_.     

Find all integers n such that when the clock strikes n o'clock, the acute angle between the hour and minute hands is 90 degrees.     

On a 12-hour clockface, at the top of the hour, the angle is 90^o at 3:00 and 9:00.  BTW, 90^o is not an acute angle.     

_.     

Write the phrase as an expression:     

The quotient of a number x and the sum of 3 and 7.     

I don't know if the phraseology implies a particular construction.     

If not, then there are two of them, namely:     

             x                             x     

         ––––––    which is    –––      is one of them.     

          3 + 7                         10     

          3 + 7                        10     

         ––––––    which is    –––      is the other one.     

             x                             x     

_.