Answer:
Step-by-step explanation:
First we need to make sure that the leading coefficient is a 1. Ours is a 4, so we need to factor it out, leaving us with

To complete the square, take half the linear term, square it, then add it to both sides. But don't forget about that 4 hanging around out front, refusing to be ignored. Our linear term is 18. Half of 18 is 9, and 9 squared is 81. Add 81 into the parenthesis, but what we REALLY added in was 4*81 which is 324:

To solve this, we need to get the x terms all by themselves. So let's divide both sides by 4 to get

The process of completing the square created a perfect square binomial on the left. We will state this binomial now:

We isolate the x term by taking the square root of both sides:
x - 9 = ±9
From that we have 2 equations:
x - 9 = 9 and x - 9 = -9
Which means that x = 18 or x = 0
Hello from MrBillDoesMath!
Answer:
72
Discussion:
Total Surface area = area of pyramid base + 4 ( area of triangular face)
In our case this becomes
4*4 + 4( (1/2) (4)(7) ) =
= 16 + (2)(4)(7)
= 16 + 56
= 72
which is the first choice.
Note: the area of a triangular face was computed using (1/2) b h, which in our case is
(1/2) (4) (7)
Thank you,
MrB
Answer:
There is not sufficient evidence to support the claim that the technique performs differently than the traditional method.
Step-by-step explanation:
The null hypothesis is:

The alternate hypotesis is:

The test statistic is:

In which X is the sample mean,
is the value tested at the null hypothesis,
is the standard deviation and n is the size of the sample.
A researcher used the technique with 260 students and observed that they had a mean of 94 hours. Assume the standard deviation is known to be 6.
This means, respectively, that 
The test-statistic is:



The pvalue is:
2(P(Z < -2.69))
P(Z < -2.69) is the pvalue of Z when X = -2.69, which looking at the z-table, is 0.0036
2*(0.0036) = 0.0072
0.0072 < 0.01, which means that the null hypothesis is accepted, that is, there is not sufficient evidence to support the claim that the technique performs differently than the traditional method.