This is what the steps look like when we complete the square
x^2 - 6x + 6 = 0
x^2 - 6x = -6
x^2 - 6x + 9 = -6+9
(x-3)^2 = 3
We add 9 to both sides so that we can factor x^2-6x+9 into (x-3)(x-3) = (x-3)^2
To get the 9, we cut the -6 (from -6x) in half to get -6/2 = -3. Then we square that to get (-3)^2 = 9
It might help to look at (a+b)^2 = a^2+2ab+b^2 and note the relationship between 2ab and b^2.
Hello from MrBillDoesMath!
Answer: 6 * p^(3/2) * q^4
Discussion:
We are evaluating
sqrt { 36 * p^3 q^8 }
where "sqrt" indicates the square root and the ^ (as in q^8) means "raised to the power of:
The square root of the product is the product of the square roots. (Say that 5 time out loud quickly!). So the above equation becomes
sqrt { 36 * p^3 q^8 } =
sqrt( 36) * sqrt( p^3) * sqrt (q^8)
The square root of 36 is 6 as 6* 6 = 36 so the equation equals
6 * p ^ (3/2) * q^ (8/2)
Note that the square root of a number, for example, r, is the same as raising the number to the (1/2) power. That's where the (1/2) terms came from above.
But 8/2 = 4 so the equation simplifies to
6 * p^(3/2) * q^4
Thank you,
MrB
The appropriate hypotheses for the engineer's hypothesis test on the proportion of households without power are the null hypothesis that the proportion is 19%, and the alternative hypothesis that the proportion is greater than 19%.
The appropriate hypotheses for the engineer's hypothesis test on the proportion of households without power after the tropical storm would be:
The engineer will collect data and perform the hypothesis test to determine if there is sufficient evidence to conclude that the estimate is too low.
#SPJ12
B.Drawing a graph
C.Reading a table
D.Drawing a diagram