Bosco

What is the median of the data set {4, 16, 0, 8, 3, 11, 7, 25, 20}?      

Arrange them in order:     0  3  4  7  8  11  16  20  25     

The median is the middle value in a dataset that has been arranged in order from smallest to largest.     

If the dataset has an odd number of values, the median is the single middle number.     

If the dataset has an even number of values, the median is the average (mean) of the two middle numbers.     

Since our problem has nine values, the median is the middle one:     8          

_.     

the sale proce of the home was 375,000 at 5.5% commission     

So what are we looking for?     

If it's the agent's commission, then proceed as follows:     

                                                  C  =  ($375,000)(5.5%)     

                                                  C  =  ($375,000)(0.055)     

                                                  C  =   $20,625     

.     

Brian has earned 65%, 80% and 60% on his three pre-final exams. These exams are not weighed equally: the lowest counts for only 25% of his overall grade, while the other two count for 30% each. If the final exam is the remainder of the overall grade and there are no opportunities for extra credit, what is the highest grade Brian can earn in the class? Express your answer to the nearest whole percent.      

                                        65% x 30%  =  19.5     

                                        80% x 30%  =  24.0     

                                        60% x 25%  =  15.0     

If Brian makes 100%     

on the fourth test  —>   100% x 15%  =  15.0     

                                                               –––––     

                                                                 73.5 is the highest grade he can make in the class.     

              rounded to the whole number is 74     

.     

A bag contains red, blue and green marbles. 2/3 of the marbles are not red and 3/4 of the marbles are not blue. What fraction of the marbles are not green? Express your fraction in lowest terms.     

Given that 2/3 of the marbles are not red, then 1/3 of the marbles are red.     

Given that 3/4 of the marbles are not blue, then 1/4 of the marbles are blue.     

1/3  =  4/12 are red         

1/4  =  3/12 are blue        

total    7/12 are either red or blue, so if they're red or blue they're not green     

_.     

The number a is 5 times as large as b.     

The sum of a and b is 18.     

What is the value of the product ab? Express your answer as a common fraction.      

                    a + b  =  18     

                          a  =  5b     

                    5b + b  =  18     

                          6b  =  18     

                            b  =  3     

                    a + 3  =  18     

                          a  =  15     

                    ab  =  (15)(3)     

                    ab  =  45     

_.     

A furniture store had a sale with 30%  off all items. If the sale price for a chair was $42 , what was the original price, in dollars?     

     Sale Price  =  Original Price minus Discount     

                                     SP  =  OP –  30%     

                                     SP  =  0.70 OP     

                                     SP / 0.70  =  OP     

                                   $42 / 0.70  =  OP     ——>     OP  = $60     

_.     

Which of the following sets of numbers could not represent the three sides of a triangle?     

\{8,14,20\}     

\{4,6,7\}     

\{6,8,10\}     

\{4,14,19\}      

     4, 14, 19  does not comply with the Triangle Inequality Theorem.     

_.     

     Determine the missing side length.     

     ?²  =  15² – 9²     

     ?²  =  225 – 81     

     ?²  =  144     

     ?    =  12     

_.     

     Determine the missing side length.     

     x²  =  14² – 9²      per Pythagoras Theorem     

     x²  =  196 – 81     

     x²  =  115     

     x    =  sqrt(115)     

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