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Math 70S Integrated Intermediate Algebra

For more information about all math courses, please visit Math Courses.
  • Sample of what you should know before Math 70S:
    1. Given the formula for converting degrees Fahrenheit (F) to degrees Celsius (C), evaluate this formula when capital f equals negative 13 and capital c equals start fraction 5 over 9 end fraction open parenthesis capital f minus 32 close parenthesis
    2. On a map, 2 cm represents 15 miles. Ryan measures on the map and finds there are 11.5 cm between Springfield and Bloomton.  How many miles apart are the two cities?
    3. A $380 television is on sale for 25% off.  If the sales tax is 7.5%, what is the total price you would have to pay for the television?
    4. Solve: 3 open parenthesis x minus 2 close parenthesis equals 5 x plus 14
    5. Simplify: 24 minus 3 times negative 2 minus 2 squared plus start square root 25 minus 16 end square root
    6. Simplify: 2x open parenthesis 4 x squared minus 6 x plus 2 close parenthesis minus open parenthesis 2 x squared minus 8 x close parenthesis
  • Sample of what you will learn in Math 70S:
    1. Suppose two salt solutions are to be mixed to create a 25-liter salt solution with 5 gm of salt per liter. The solutions to be mixed contain 2 gm per liter and 10 gm per liter respectively.  How much of each solution should be used?
      • Solution
        Let x represent the volume in liters of the 2 gm per liter solution.
        Let y represent the volume in liters of the 10 gm per liter solution.
        Adding the volume in liters, we want x plus y equals 25
        Adding the mass in grams, we need 2 x plus 10 y equals 5 times 25
        This gives us the system of equations start set top row x plus y equals 25 bottom row 2 x plus 10 y equals 125 end set
        We can solve x plus y equals 25 for y to get y equals 25 minus x
        Substituting into the second equation, we get 2 x plus 10 open parenthesis 25 minus x close parenthesis equals 125
        2 x plus 250 minus 10 x equals 125
        negative 8 x equals negative 125
        x equals 125 over 8 equals 15 point 6 2 5
        So, y equals 25 minus start fraction 125 over 8 end fraction equals start fraction 75 over 8 end fraction equals 9 point 3 7 5
        We should use 15.625 liters of the 2 gm per liter solution and 9.375 liters of the 10 gm per liter solution.
    2. If you deposit $10,000 into an account that earns a fixed 8% annual interest rate, compounded quarterly, when will the account balance reach $25,000?
      • Solution
        Use the compound interest formula capital a equals capital p open parenthesis 1 plus start fraction r over n end fraction close parenthesis superscript n t baseline
        Here P = 10000, r = 0.08, n = 4, A = 25000, and we're solving for t.
        25000 equals 10000 open parenthesis 1 plus start fraction 0 point 0 8 over 4 end fraction close parenthesis superscript 4 t baseline
        2 point 5 equals 1 point 0 2 superscript 4 t baseline
        the natural log of 2 point 5 equals the natural log of 1 point 0 2 to the 4 t
        the natural log of 2 point 5 equals 4 t times the natural log of 1 point 0 2
        t equals start fraction the natural log of 2 point 5 over 4 times the natural log of 1 point 0 2 end fraction approximately equal to 11 point 5 6 7 8
        The account balance will reach $25,000 after 12 quarters (or 3 years).
    3. The following are root lengths (inches) of garlic cloves after soaking in water for one week. {2.23, 1.71, 1.45, 3.53, 2.57, 1.61, 1.64, 1.67, 1.79, 1.90, 3.04, 2.09, 1.42, 2.16, 1.52, 2.23, 2.26, 1.57, 2.33}.  Sketch a boxplot and identify outliers.  Describe the distribution of values in terms of center, shape and spread.
      • Solution
        First sort the data from smallest to largest:
        {1.42, 1.45, 1.52, 1.57, 1.61, 1.64, 1.67, 1.71, 1.79, 1.9, 2.09, 2.16, 2.23, 2.23, 2.26, 2.33, 2.57, 3.04, 3.53}
        The number of sample values is n = 19
        First quartile:  capital l equals start fraction 25 over 100 end fraction times 19 equals 4 point 7 5 so capital q sub 1 equals 1 point 6 1
        Second quartile: capital l equals start fraction 50 over 100 end fraction times 19 equals 9 point 5 so capital q sub 2 equals 1 point 9
        Third quartile: capital l equals start fraction 75 over 100 end fraction times 19 equals 14 point 2 5 so capital q sub 3 equals 2 point 2 6
        a vertical boxplot with a vertical scale ranging from approximately 1 to 4 a short horizontal line representing the minimum value 1 point 4 2 a vertical line from 1 point 4 2 to 1 point 6 1 a rectangle from 1 point 6 1 to 1 point 9 a rectangle from 1 point 9 to 2 point 2 6 a vertical line from 2 point 2 6 to 3 point 5 3 a short horizontal line maximum value 3 point 5 3
        I Q R equals capital q sub 3 minus capital q sub 1 equals 2 point 2 6 minus 1 point 6 1 equals 0 point 6 5
        1 point 5 times I Q R equals 1 point 5 times 0 point 6 5 equals 0 point 9 7 5
        capital q sub 1 minus 0 point 9 7 5 equals 1 point 6 1 minus 0 point 9 7 5 equals 0 point 6 3 5
        There are no sample values less than 0.635.
        capital q sub 3 plus 0 point 9 7 5 equals 2 point 2 6 plus 0 point 9 7 5 equals 3 point 2 3 5
        3.53 is more than 3.235, so 3.53 is an outlier.
        The center is 1.9.  The boxplot has a center of 1.9 and is skewed to the right.