Math

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1)If a (theres a square)b is defined as the average of a and b, what is the value of 2 (theres a square) 4 (theres a square) 9?

a) 3
b)5
c) 6
d)7.5
e) 18



2)If A=(r+s)F, what is the average of r and s when A=8 and F=2?


3) For the three numbers a,j,k, (a<j<k),the arithmetic mean is median and k is three times as large as j,What is the value of a/j?

  • Math -

    using a • instead of a square,

    If a•b means (a+b)/2, whats is 2•4•9?

    2•4 = 3
    3•9 = 6
    so (2•4)•9 = 6

    how about 2•(4•9)?
    That is 2•(13/2) = 17/4

    so, since • is not associative, asking what 2•4•9 is has no answer.

    after all,

    (a•b)•c = ((a+b)/2 + c)/2 = a/4 + b/4 + c/2

    a•(b•c) = (a+(b+c)/2)/2 = a/2 + b/4 + c/4

    -----------------
    8 = (r+s)2
    4 = (r+s)
    avg(r,s) = (r+s)/2 = 2
    -----------
    mean = (a+j+k)/3
    median = j, so

    (a+j+k)/3 = j
    a+j+k = 3j
    but, k=3j, so
    a+4j = 3j
    a = -j
    a/j = -1

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