Answer:
<em>The size of the sample 'n' = 2401</em>
Step-by-step explanation:
<u><em>Step:1</em></u>
Given that the margin of error = 2 % = 0.02
The margin of error is determined by
![M.E = \frac{Z_{0.05} \sqrt{p(1-p)} }{\sqrt{n} }](https://tex.z-dn.net/?f=M.E%20%3D%20%5Cfrac%7BZ_%7B0.05%7D%20%5Csqrt%7Bp%281-p%29%7D%20%7D%7B%5Csqrt%7Bn%7D%20%7D)
we know that the proportion
![\sqrt{p(1-p)} < \frac{1}{2}](https://tex.z-dn.net/?f=%5Csqrt%7Bp%281-p%29%7D%20%3C%20%5Cfrac%7B1%7D%7B2%7D)
<u><em>Step:2</em></u>
<em>The margin of error is determined by </em>
<em> </em>
<em></em>
![\sqrt{n} = \frac{1.96}{2 X 0.02}](https://tex.z-dn.net/?f=%5Csqrt%7Bn%7D%20%3D%20%20%5Cfrac%7B1.96%7D%7B2%20X%200.02%7D)
√n = 49
Squaring on both sides, we get
n = 49 × 49
n = 2401
<u>Final answer:-</u>
<em>The size of the sample 'n' = 2401 </em>
Given that the debt has been represented by the function:
f(x)=-6x^2+8x+50
To get the number of years, x that it would take for the company to be debt free we proceed as follows:
we solve the equation for f(x)=0
hence:
0=-6x^2+8x+50
solving for x using the quadratic formula we get:
x=[-b+/-sqrt(b^2-4ac)]/2a
x=[-8+/-sqrt(8^2-4*(-6)*50)]/(-6*2)
x=[-8+/-√1264]/(-12)
x=27.552
x~28
Read more on Brainly.com - brainly.com/question/10301284#readmore
Answer:
Liliana can raise 35 zombie soldiers
Step-by-step explanation:
Hello, I can help you with this
to solve this kind of question you can use a rule of three , that is a proportion
Step 1
define
Liliana used 4 dark power crystals to raise 14 zombie soldiers.
4 power crystals⇔
then, How many(x) zombie soldiers can Liliana raise with 10 power crystals?
10 power crystals=x zombie soldiers
Step 2
do the relation and solve for x , the proportion is
![\frac{4\ power\ crystals}{14\ zombie\ soldiers}=\frac{10\ power\ crystals}{x} \\\\solve for x\\\{x*4\ power\ crystals}={14\ zombie\ soldiers*10\ power\ crystals}\\x=\frac{14\ zombie\ soldiers*10\ power\ crystals}{4\ power\ crystals}\\ x=35\ zombie\ soldiers\\](https://tex.z-dn.net/?f=%5Cfrac%7B4%5C%20%20power%5C%20crystals%7D%7B14%5C%20zombie%5C%20soldiers%7D%3D%5Cfrac%7B10%5C%20%20power%5C%20crystals%7D%7Bx%7D%20%5C%5C%5C%5Csolve%20for%20x%5C%5C%5C%7Bx%2A4%5C%20%20power%5C%20crystals%7D%3D%7B14%5C%20zombie%5C%20soldiers%2A10%5C%20%20power%5C%20crystals%7D%5C%5Cx%3D%5Cfrac%7B14%5C%20zombie%5C%20soldiers%2A10%5C%20%20power%5C%20crystals%7D%7B4%5C%20%20power%5C%20crystals%7D%5C%5C%20x%3D35%5C%20zombie%5C%20soldiers%5C%5C)
Liliana can raise 35 zombie soldiers
Have a great day.
Answer:
![\frac{dy}{dx}=-\frac{3}{2(1-x)}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D-%5Cfrac%7B3%7D%7B2%281-x%29%7D)
Step-by-step explanation:
We are given that a function
![y=ln(1-x)^{\frac{3}{2}}](https://tex.z-dn.net/?f=y%3Dln%281-x%29%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D)
We have to find the derivative of the function
![y=\frac{3}{2}ln(1-x)](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B3%7D%7B2%7Dln%281-x%29)
By using ![lna^b=blna](https://tex.z-dn.net/?f=lna%5Eb%3Dblna)
Differentiate w.r.t x
![\frac{dy}{dx}=\frac{3}{2}\times \frac{1}{1-x}\times (-1)](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D%5Cfrac%7B3%7D%7B2%7D%5Ctimes%20%5Cfrac%7B1%7D%7B1-x%7D%5Ctimes%20%28-1%29)
By using formula
![\frac{d(lnx)}{dx}=\frac{1}{x}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%28lnx%29%7D%7Bdx%7D%3D%5Cfrac%7B1%7D%7Bx%7D)
![\frac{dy}{dx}=-\frac{3}{2(1-x)}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D-%5Cfrac%7B3%7D%7B2%281-x%29%7D)
Hence,the derivative of function
![\frac{dy}{dx}=-\frac{3}{2(1-x)}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D-%5Cfrac%7B3%7D%7B2%281-x%29%7D)
Answer:
-15g+11.1+4k
Step-by-step explanation:
5g - 10g)+4K+(-10g+11.1)
-15g+11.1+4k
add like terms together