A real-estate company appraised the market value of 36 homes in Lyttelton and found that the sample mean and standard deviation were $150,000 and $17,000 respectively. The real-estate company also appraised the market value of 45 homes in Aranui and found that the sample mean and standard deviation were $100,000 and $12,000 respectively. Calculate the 90% confidence interval estimate for the population difference in market value between the Lyttelton and Aranui areas .

Solution :

                    Sample size       Sample mean             Sample S.D.

Sample 1                                    

Sample 2                                  

   = 60

Therefore, significance level, α = 0.1

Critical value, t* = 1.6706

So, the margin of error,

                                          = 559.9896

Lower limit,

Upper limit,  

Therefore 90% C.I. is (44402.0104, 55597.9896)   or

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.