Bosco

One ordered pair (a,b) satisfies the two equations ab^4 = 384 and ab^5 = 4608. What is the value of a in this ordered pair?     

                                                        ab⁵  =  4608     (equation 1)     

                                                        ab⁴  =    384     (equation 2)     

Divide both sides of eq 1 by  

both sides of eq 2 respectively            b  =  12     

sub 12 into equation 2                a • 12⁴  =  384     

                                                  20736a  =  384     

                                                            a  =  384 / 20736     

                                                            a  =  1 / 54     

check answer     

sub values into eq 1                        ab⁵  =    4608     

                                      (1/54)(248832)  =?  4608     

                                                      4608  =    4608     

_.     

Find the coefficient of y^4 in the expansion of (2y - 7)^5.     

   32y⁵ – 560y⁴ + 3920y³ – 13720y² + 24010y – 16807     

             – 560     

_.     

Louise earned $529 dollars in a two-week period.  She had $85 deducted for health insurance, but got a $300 bonus.  Not considering any other deductions, how much did she receive?     

                    $529  –  $85  +  $300  =  $744     

_.     

A list of ten distinct, positive integers has a median of 5.5.  What is the smallest possible average of the ten positive integers?  Explain your ansswer in complete sentences.     

For the median to be 5.5, the list can have 5 and 6 in the middle.     

It could have 3 and 8 there, but then it wouldn't be the smallest.     

The list would look like this:                            5  6                             

You have to fill in the blanks with the smallest integers possible, and     

every integer has to be positive and every integer has to be different.     

This is the smallest possible:    1   2   3   4   5   6   7   8   9   10     

The average of that list is:    55 / 10  =  5.5     

_.     

Andre and elena are each saving money. Andre starts with $100 in his savings account and adds $5 per week. Elena starts with $10 in her savings account and adds $20 each week? After 4 weeks, who has more money in their savings account?     

End of Which Week     Andre's Balance     Elena's Balance     

end of 1st week                   105                             30     

end of 2nd week                  110                             50     

end of 3rd week                   115                             70     

end of 4th week                   120                             90     

The Andre account has more money than the Elena account.     

_.