Bosco

The base of a square pyramid has a side length of 50 centimeters the slant height is 32 centimeters. Find the surface area     

A_oneside  =  (50 cm / 2) • 32 cm  =  800 cm²     

A_allfoursides  =  4 •  800 cm²  =  3200 cm²     

A_base  =  50 cm • 50 cm        =  2500 cm²     

Area_total                                 =  5700 cm²     

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In one afternoon, 24 restaurant customers order steak, 18 order sandwiches, and 20 order salads.     

Based on these orders, what is the probability that the next customer will order a salad?      

              20                   20     

     –––––––––––   =   ––––   =   0.32258   =   32.26%     

      24 + 18 + 20           62     

 _.     

What is the length of the arc?     

The arc subtends a 60^o angle at the center,     

therefore the measure of the arc is also 60^o.     

A 60^o arc is 1 / 6 of the way around the circle.     

Given that the circumference of the circle is 1,     

the length of the arc is 1 / 6 unit.     

_.     

   In ΔJKL, the measure of ∠L=90°, JK = 99 feet, and KL = 58 feet. Find the measure of ∠J to the nearest degree.     

   Draw it.  From angle J, you have opposite (58) and hypotenuse (99)      

   sin(J)  =  58 / 99     

   sin(J)  =  0.585858 • • •     

          J  =  sin^–1(0.585858 • • •)     

          J  =  35.86^o  rounds  to 36^o     

_.     

The business helped a family buy a home for $204,000. The house is now worth $255,000. The family now owes only $180,000 on the home. The family has no other debts. What is the wealth of the family?     

The equity in the house adds 255,000 – 180,000 = 75,000 to their wealth.     

This neglects other probable assets that would increase their total wealth.     

_.     

What is the gcf of 49     

The greatest common factor of a single number is the number itself.     

Therefore, the GCF of 49 is 49     

_.     

The area of a shaded sector of the circle is 108pi square centimeters.     

Given an arc measure of 120, what is the length of the radius in centimeters?     

120^o is a third of 360^o so the area of the entire circle is 3 • 108π = 324π     

                                           A  = π r²     

                                     324π  =  π r²     

divide both sides by π        r²  = 324     

                                           r¹  =  sqrt(324)     

                                           r    =  18     

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