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Math 120 Finite Mathematics

 
  • Sample of what you should know before taking Math 120:
    1. Find the equation of the line (in both point-slope form and slope-intercept form) that goes through the points, (2, -1) and (-6, 3) .
      • Solution
        First, find slope of the line: (using the formula m equals start fraction y subscript 2 baseline minus y subscript 1 baseline over x subscript 2 baseline minus x subscript 1 baseline end fraction  )
        m equals start fraction 3 minus open parenthesis negative 1 close parentheses over negative 6 minus 2 end fraction equals start fraction 3 plus 1 over negative 8 end fraction equals start fraction 4 over negative 8 end fraction equals negative 1 half
        Now use either of the given points, say (2, -1) and the slope  m equals negative 1 half  to first find the equation of the line in point-slope form:  y minus open parenthesis negative 1 close parenthesis equals negative 1 half times open parenthesis x minus 2 close parenthesis
        Now, solve for  to get the slope-intercept form:  

        y plus 1 equals negative 1 half x plus 1  Therefore y equals negative 1 half x

    2. You invested $7000 in two accounts paying 6% and 8% annual interest. If the total interest earned for the year was $520, how much was invested at each rate?
      • Solution
        Let x be amount invested at 6% and let  be amount invested at 8%.
        Start set top row x plus y equals 7000 bottom row point 0 6 x plus point 0 8 y equals 520 end set 
        therefore, Start set top row x equals 7000 minus y bottom row point 0 6 x plus point 0 8 y equals 520 end set
        Substitute  7000 minus y  for  in the second equation:
        0 point 0 6 times open parenthesis 7000 minus y close parenthesis plus 0 point 0 8 y equals 520
        therefore 0 point 0 2 y equals 100 therefore y equals 5000
        x equals 7000 minus 5000 thus x equals 2000
        Thus, $2,000 invested at 6% and $5,000 invested at 8%.
    3. Graph: 3 x plus 4 y greater than or equal to 12
      • Solution
        Graph the line 3 x plus 4 y equals 12  and then pick a test point say (0, 0) and substitute into the original inequality 3 times open parenthesis 0 close parenthesis plus 4 times open parenthesis 0 close parenthesis greater than or equal to 12; becomes 0 greater than or equal to 12 which is an untrue statement, thus the opposite side of the line is shaded.
        Graph of solid line going down from left to right with slope negative 3 over 4 passing through the point 0 3 shaded above the line
    4. Solve 50 times e superscript 0 point 2 x baseline equals 2000   and round your answer to the nearest hundredth.
    5. Evaluate Summation from n equals 1 to 4 of open parenthesis n plus 1 close parenthesis factorial
  • Sample of what you will learn in Math 120:
    1. Given that Capital a equals 2 by 2 matrix with top row 1 1 bottom row 3 4 and Capital b equals 2 by 2 matrix with top row 5 1 bottom row 9 2 , find Capital a inverse minus capital b inverse
      • Solution
        Finding capital a inverse     and capital b inverse by row reduction techniques;
        Capital a inverse equals 2 by 2 matrix with top row 4 negative 1 bottom row negative 3 1  and  Capital b inverse equals 2 by 2 matrix with top row 2 negative 1 bottom row negative 9 5
        Capital a inverse minus capital b inverse Equals 2 by 2 matrix with top row 4 negative 1 bottom row negative 3 1 minus 2 by 2 matrix with top row 2 negative 1 bottom row negative 9 5 equals 2 by 2 matrix with top row 2 0 bottom row 6 negative 4
    2. Two fair coins were tossed, and it is known that at least one was a tail. Find the probability that both were tails.
      • Solution
        Let E be the event of at least one tail and let F be the event of two tails.
        Capital e equals start set h t comma t h comma t t end set and Capital f equals start set t t end set
        so, Probability of capital f given capital e equals start fraction probability of capital f intersection capital e over probability of capital e end fraction equals 1 third
    3. How many 5-digit zip codes are there that can be read upside down?
      • Solution
        There are five numbers that can be read upside down, namely zero, one, six, eight, and nine.  So there are 5 times 5 times 5 times 5 times 5 equals 5 superscript 5 baseline equals 3125  zip codes that can be read upside down.
    4. A small pizza parlor offers two different types of crusts: New York style and Chicago style; three different pie sizes: small, medium, and large; and ten different toppings.  How many possible four topping pizza pies can be ordered at this pizza parlor?
      • Solution
        The number of possible pizza pies is obtained by choosing a crust type, a size, and 4 toppings. 
        So, 2 choose 1 times 3 choose 1 times 10 choose 4 equals 2 times 3 times 210 equals 1260=1260 different four topping pizza pies can be ordered.
    5. Leslie is an athlete who believes that her playing career will last 7 years. To prepare for her future, she deposits $24,000 at the end of each year for 7 years in an account paying 6% compounded annually. How much will she have on deposit after 7 years?
      • Solution
        Her yearly payment form an ordinary annuity with periodic payments R equals 24000
        Since the interest is compounded annually, the interest per period is i equals start fraction 0 point 0 6 over 1 end fraction equals 0 point 0 6
        and the number of periods n equals 1 times open parenthesis 7 close parenthesis equals 7
        Using the formula for the future value of an annuity, the amount S that she will have on deposit after 7 years is:
        S equals r times open parenthesis start fraction open parenthesis 1 plus i close parenthesis superscript n baseline minus 1 over i end fraction close parenthesis Equals 24000 times open parenthesis start fraction open parenthesis 1 plus 0 point 0 6 close parenthesis superscript 7 baseline minus 1 over 0 point 0 6 end fraction close parenthesis