Posted by **Grace** on Sunday, August 5, 2012 at 8:59pm.

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 -
**Steve**, Monday, August 6, 2012 at 4:48am
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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