Answer:
The 99% confidence interval for the true mean number of reproductions per hour for the bacteria is between 9.6 and 10.
Step-by-step explanation:
We have that to find our 
level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of 
.
So it is z with a pvalue of 
, so 
Now, find the margin of error M as such
In which 
is the standard deviation of the population and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 9.8 - 0.2 = 9.6 reproductions per hour.
The upper end of the interval is the sample mean added to M. So it is 9.8 + 0.2 = 10 reproductions per hour.
The 99% confidence interval for the true mean number of reproductions per hour for the bacteria is between 9.6 and 10.
Answer: t= 460.52 minutes
Step-by-step explanation:Q'=Q/100
Q'= rate in and out of water
Finding the differential equation
Let Q'(t)= The quantity of dye in the tank for t time
But rate in=0 Q/200 ×2=Q'
Q'/Q=-1/100
Dividing by Q gives
Ln/Q/ + c = -1/100 + c1
Integrating both sides gives
Ln/Q/ = -(1/100)t + c2
But c+c1=C2= A constant
Q=C2e(-t/100)
200e-(t/100)
t= ln200
t=460.52minutes
Answer: sqrt(61)
Step-by-step explanation:
For parts a) and c1), refer to the attached picture.
For part b), the distance formula is:
d = sqrt[(x2 - x1)^2 + (y2 - y1)^2]
Using x1 = -1, y1 = -4, x2 = -6, y2 = 2:
d = sqrt[(-6 + 1)^2 + (2 + 4)^2] = sqrt[25 + 36] = sqrt(61)
Part c2) Another way to find the length of AB without using the distance formula is by drawing the line and measuring it according to the scale.
Part d) This will only work as long as the graph paper is accurately made, and the scale computation is done correctly. However, this will only give approximations, and will not give an exact answer when radicals are involved.
