Answer:
<u>Translations</u>
![f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}](https://tex.z-dn.net/?f=f%28x%2Ba%29%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Btranslated%7D%5C%3Aa%5C%3A%5Ctextsf%7Bunits%20left%7D)
![f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}](https://tex.z-dn.net/?f=f%28x-a%29%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Btranslated%7D%5C%3Aa%5C%3A%5Ctextsf%7Bunits%20right%7D)
![f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}](https://tex.z-dn.net/?f=f%28x%29%2Ba%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Btranslated%7D%5C%3Aa%5C%3A%5Ctextsf%7Bunits%20up%7D)
![f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}](https://tex.z-dn.net/?f=f%28x%29-a%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Btranslated%7D%5C%3Aa%5C%3A%5Ctextsf%7Bunits%20down%7D)
![y=-\:f\:(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}](https://tex.z-dn.net/?f=y%3D-%5C%3Af%5C%3A%28x%29%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Breflected%20in%20the%7D%20%5C%3A%20x%20%5Ctextsf%7B-axis%7D)
![y=f\:(-\:x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}](https://tex.z-dn.net/?f=y%3Df%5C%3A%28-%5C%3Ax%29%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Breflected%20in%20the%7D%20%5C%3A%20y%20%5Ctextsf%7B-axis%7D)
Parent function: ![f\:(x) = \ln(x)](https://tex.z-dn.net/?f=f%5C%3A%28x%29%20%3D%20%5Cln%28x%29)
Translated right 1 unit: ![f\:(x\:-1) = \ln(x - 1)](https://tex.z-dn.net/?f=f%5C%3A%28x%5C%3A-1%29%20%3D%20%5Cln%28x%20-%201%29)
Then translated down 9 units: ![f\:(x\: -1)-9 = \ln(x - 1) - 9](https://tex.z-dn.net/?f=f%5C%3A%28x%5C%3A%20-1%29-9%20%3D%20%5Cln%28x%20-%201%29%20-%209)
The reflected over the x-axis: ![-\:[f\:(x\:-1) - 9] = -\ln(x - 1) + 9](https://tex.z-dn.net/?f=-%5C%3A%5Bf%5C%3A%28x%5C%3A-1%29%20-%209%5D%20%3D%20-%5Cln%28x%20-%201%29%20%2B%209)
Therefore, ![g(x) = -\ln\:(x\:- 1) + 9](https://tex.z-dn.net/?f=g%28x%29%20%3D%20-%5Cln%5C%3A%28x%5C%3A-%201%29%20%2B%209)
⇒ g(30) = - ln(30 - 1) + 9
= -3.36729... + 9
= 5.6 (nearest tenth)
Answer:
A. 12.3%
Step-by-step explanation:
Model this as a binomial distribution
where X is the random variable, n is the number of trials, and p is the probability of success.
Therefore,
- X = lambs born male
- n = 60
- p = 0.5
(If the probability of lambs being male and female is equal, then the probability of males being born = 0.5)
![X \sim B(60,0.5)](https://tex.z-dn.net/?f=X%20%5Csim%20B%2860%2C0.5%29)
The probability that at least 35 lambs will be born male:
![\ \ \ \ \ \ \ P(X\geq 35)=1-P(X\leq 34)\\\\\implies P(X\geq 35)=1-0.8774695851...\\\\\implies P(X\geq 35)=0.1225304149\\\\\implies P(X\geq 35)=12.3 \%](https://tex.z-dn.net/?f=%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20P%28X%5Cgeq%2035%29%3D1-P%28X%5Cleq%2034%29%5C%5C%5C%5C%5Cimplies%20P%28X%5Cgeq%2035%29%3D1-0.8774695851...%5C%5C%5C%5C%5Cimplies%20P%28X%5Cgeq%2035%29%3D0.1225304149%5C%5C%5C%5C%5Cimplies%20P%28X%5Cgeq%2035%29%3D12.3%20%5C%25)
It’s sumerians for sure! i don’t know the rest sorry :(
Answer:
if it is multiple choice it's a bc I am on the same thing
They are equidistant from the origin. I.E., the mid-points are equidistant, or the same distance, to the center.