Using the z-distribution, as we have the standard deviation for the population, it is found that the smallest sample size required to obtain the desired margin of error is of 77.
<h3>What is a z-distribution confidence interval?</h3>
The confidence interval is:
![\overline{x} \pm z\frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%20%5Cpm%20z%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
In which:
is the sample mean.
is the standard deviation for the population.
The margin of error is given by:
![M = z\frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
In this problem, we have that the parameters are given as follows:
.
Hence, solving for n, we find the sample size.
![M = z\frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
![3 = 1.645\frac{16}{\sqrt{n}}](https://tex.z-dn.net/?f=3%20%3D%201.645%5Cfrac%7B16%7D%7B%5Csqrt%7Bn%7D%7D)
![3\sqrt{n} = 1.645 \times 16](https://tex.z-dn.net/?f=3%5Csqrt%7Bn%7D%20%3D%201.645%20%5Ctimes%2016)
![\sqrt{n} = \frac{1.645 \times 16}{3}](https://tex.z-dn.net/?f=%5Csqrt%7Bn%7D%20%3D%20%5Cfrac%7B1.645%20%5Ctimes%2016%7D%7B3%7D)
![(\sqrt{n})^2 = \left(\frac{1.645 \times 16}{3}\right)^2](https://tex.z-dn.net/?f=%28%5Csqrt%7Bn%7D%29%5E2%20%3D%20%5Cleft%28%5Cfrac%7B1.645%20%5Ctimes%2016%7D%7B3%7D%5Cright%29%5E2)
![n = 76.97](https://tex.z-dn.net/?f=n%20%3D%2076.97)
Rounding up, the smallest sample size required to obtain the desired margin of error is of 77.
More can be learned about the z-distribution at brainly.com/question/25890103
Answer:
For y(-7) =6.4
The largest interval is between
![-\infty \to -5](https://tex.z-dn.net/?f=-%5Cinfty%20%5Cto%20-5)
For y(-2.5) = -0.5.
The largest interval is between
![-5 \to 5](https://tex.z-dn.net/?f=-5%20%5Cto%205)
For y(0) = 0
The largest interval is between
![-5 \to 5](https://tex.z-dn.net/?f=-5%20%5Cto%205)
For y(4.5) = -2.1.
The largest interval is between
![-5 \to 5](https://tex.z-dn.net/?f=-5%20%5Cto%205)
For y(14)= 1.7.
The largest interval is between
Step-by-step explanation:
From m the question we are told that
The first order differential equation is ![\frac{y' - t}{ t^2 -25} = \frac{e^t}{t-9}](https://tex.z-dn.net/?f=%5Cfrac%7By%27%20-%20%20t%7D%7B%20t%5E2%20-25%7D%20%3D%20%20%5Cfrac%7Be%5Et%7D%7Bt-9%7D)
Now the first step is to obtain the domain of the differential equation
Now to do that let consider the denominators
Now generally
side calculation
=>
![t^2 - 25 = 0](https://tex.z-dn.net/?f=t%5E2%20-%2025%20%3D%20%200)
![t = \pm 5](https://tex.z-dn.net/?f=t%20%3D%20%5Cpm%205)
Also
![t -9 = 0](https://tex.z-dn.net/?f=t%20-9%20%3D%200)
=>
This means that this first order differential equation is discontinuous at
![t = -5 , \ \ t = 5 \ \ t = 9](https://tex.z-dn.net/?f=t%20%3D%20%20-5%20%2C%20%20%5C%20%20%20%5C%20%20t%20%3D%20%205%20%5C%20%5C%20%20t%20%3D%20%209)
![This \ is \ illustrated \ below \ \\ ------------------\\\. \ \ \ | \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ | \ \ \ \ \ \ \ \ \ \ \ \ \ |\\. \ -5 \ \ \ \ \ \ \ \ \ \ \ \ 5 \ \ \ \ \ \ \ \ \ \ \ \ \ 9](https://tex.z-dn.net/?f=This%20%20%5C%20%20is%20%5C%20%20illustrated%20%5C%20%20below%20%20%20%20%5C%20%20%5C%5C%20%20%20%20%20%20------------------%5C%5C%5C.%20%5C%20%5C%20%5C%20%20%7C%20%5C%20%5C%20%5C%20%20%20%5C%20%5C%20%5C%20%20%20%5C%20%5C%20%5C%20%5C%20%20%5C%20%5C%20%5C%20%5C%20%5C%20%7C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%7C%5C%5C.%20%5C%20%20-5%20%5C%20%5C%20%5C%20%5C%20%5C%20%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%205%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%20%209)
So
For y(-7) =6.4
The largest interval is between
![-\infty \to -5](https://tex.z-dn.net/?f=-%5Cinfty%20%5Cto%20-5)
For y(-2.5) = -0.5.
The largest interval is between
![-5 \to 5](https://tex.z-dn.net/?f=-5%20%5Cto%205)
For y(0) = 0
The largest interval is between
![-5 \to 5](https://tex.z-dn.net/?f=-5%20%5Cto%205)
For y(4.5) = -2.1.
The largest interval is between
![-5 \to 5](https://tex.z-dn.net/?f=-5%20%5Cto%205)
For y(14)= 1.7.
The largest interval is between
Answer:
Answer is 106
Step-by-step explanation:
Let two numbers be x and y.
x * y =13832
Let x=76
so, 76*y=13832
y=13832/76
y=182.
difference is 182-76=106
68% if you take 31 and divide it by 45 you’ll get .68 which you then turn into a percentage
Another way of presenting this question is to ask: what is the volume of the prism. Sometimes, you can get tripped up on the terminology and fail to discover what it is the question is really asking. To find the volume of this concave prism, we can divide it into two boxes: top box and bottom box. Imagine slicing a knife through the line where the two "steps" intersect. From there, we can apply the basic formula for a rectangular prism and add up the volumes.
Top Box:
A = height x length x width
A = 10 x 40 x 20
(the height is 10 because it is equal to the tallest height minus the shorter height)
A = 8000 in. cubed
Bottom Box:
A = height x length x width
A = 20 x 60 x 20
A = 24000 in. cubed
Total Volume = 24000 in. cubed + 8000 in. cubed = 32000 in. cubed
Hoped this helped!