Answer:
Step-by-step explanation:
we have ΔLMN as our parent triangle, where M=90°. Another triangle ΔPQR is formed which was dilation of ΔLMN with a factor of one and half that is 1.5
We are also given that the center of dilation is M itself . Hence the point Q of the ΔPQR overlap with the M.
Now let us see the image attached with this. The Line LM and MN are extended further till Point P and R respectively.
If LN = x and MN = y
PM = 1.5x and MR = 1.5y
as the scale of dilation is 1.5
Now let us see the the ratio of the sides of the two triangles.
Hence the ratio of the sides is same. There for the triangles are similar to each other.
1.)
=(x-8i)(x+8i)
x^2+8ix-8ix-64i^2
x^2-64i^2
x^2-64(-1)
x^2+64
2.)
=(4x-7i)(4x+7i)
16x^2+28ix-28ix-49i^2
16x^2-49i^2
16x^2-49(-1)
16x^2+49
3.)
=(x+9i)(x+9i)
x^2+9ix+9ix+81i^2
x^2+18ix+81(-1)
x^2+18ix-81
4.)
=(x-2i)(x-2i)
x^2-2ix-2ix+4i^2
x^2-4ix+4(-1)
x^2-4ix-4
5.)
=[x+(3+5i)]^2
(x+5i+3)^2
(x+5i+3)(x+5i+3)
x^2+5ix+3x+5ix+25i^2+15i+3x+15i+9
x^2+6x+10ix+30i+25i^2+9
x^2+6x+10ix+30i+25(-1)+9
x^2+6x+10ix+30i-25+9
x^2+6x+10ix+30i-16
Hope this helps :)
Answer: -1.5
Step-by-step explanation:
When population standard deviation is known, then the formula to find the z-test statistic for population mean is given by :-
, where n= Sample size.
= Population mean
= Sample mean
= Population standard deviation.
As per given , we have 
(average infants contracted typhoid each month)
n= 4 (No. of months)
Then , the value of the appropriate test statistic will be :
Hence, the value of the test statistic = -1.5
