Bosco

if jennifer babysat on friday and made 52.50 in 6 hours. On sunday, she babysat for 4 hours and made $35. Was the amount she earned each day proportional to the hours that she worked?     

     (52.50 $) / 6 hr  =  8.75 $/hr     

     (35.00 $) / 4 hr  =  8.75 $/hr     

     Yes . . . . they're exactly proportional.     

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     32.5% as a fraction     

     32.5%  =  0.325  =  ³²⁵ / ₁₀₀₀ . . . . now reduce it     

     both 325 and 1000 are divisible by 25     

     32.5%  =  ¹³ / ₄₀     

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A cylinder has a height of 2 feet and a radius of 2 feet. What is its volume? Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth.     

          Volume of a cylinder is the area of the circular base, times the height.     

          V  =  π r² h     

          V  =  3.14 • (2 ft)² • 2 ft          

          V  =  (3.14) • (4) • (2) ft³     

          V  =  25.12 ft³     

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why is a negative times a negative a positive?     

A negative times a negative is a positive because it represents a double reversal of direction on the number line.  Multiplying by a negative number essentially flips the sign of the number being multiplied.  When you multiply two negatives, you are reversing the direction twice, which brings you back to the positive direction, according to Khan Academy.     

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how man plutos pheres will it take to fill earth     

Volume_Earth  =  1.083 x 10¹² cubic kilometers     

Volume_Pluto   =  6.97 x 10⁹ cubic kilometers     

I obtained these volumes from the internet.     

( 1.083 x 10¹² km³ ) / ( 6.97 x 10⁹ km³ )  =   0.1554 x 10³  =  1.554 x 10²     

In other words, it would take in the neighborhood of 155.4 Plutos to fill the Earth.     

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The length of a rectangle is 6 yds longer than its width. If the perimeter of the rectangle is 48 yd, find its area.     

        width   =  w     

        length  =  w + 6     

        perimeter  =  2w + 2l  =  2w + 2(w + 6)     

                   48  =  4w + 12     

                  4w  =  36     

                    w  =  9     

                      l  =  w + 6  =  9 + 6     

                      l  =  15     

              Area   =  length times width     

                    A  =  9 • 15     

                    A  =  135     

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