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What is the difference between transitive and substitution property of equality?
the transitive property is when x=y and y=z then x=z e.g 4+1 = 6-1 and 6-1 = 10/2 so 4+1 = 10/2 three terms involved and the substitution property is that if x=5 and x+1 =6 so 5+1 =6 that is you put the value of x into the equation and two terms are involved :)
What pattern involved in multiplying algebraic expression?
m(a + b) = ma + mb distributive property (a + b)(c + d) = a(c + d) + b(c + d) The use distributive prop. twice. (c + d)(x + y + z) = c(x + y + z) + d(x + y + z) Still use dist. prop. etc. These work for subtraction as well.
How do you find the number z such that 93 percent of all observations from a standard Normal distribution are greater than z?
The tables for Z-scores are given in the form of P = Prob(Z < z) for various value of P and z. Since Prob(Z > z) = 0.93 > 0.5, then by symmetry, z < 0. So suppose z = -a where a > 0 Now Prob(Z > -a) = 0.93 is the same as Prob(Z < a) = 0.93 [because the standard Normal is symmetric]. therefore, from the tables, a = 1.4758 (approx) and so z = -1.4758 (approx).
What is one-third of z?
z divided by 3
What is the absolute value of the difference of z and 8?
|z - 8| or whichever of (z - 8) and (8 - z) that is non-negative.
