Answer:
The answer is below
Step-by-step explanation:
The horizontal asymptote of a function f(x) is gotten by finding the limit as x ⇒ ∞ or x ⇒ -∞. If the limit gives you a finite value, then your asymptote is at that point.
![\lim_{x \to \infty} f(x)=A\\\\or\\\\ \lim_{x \to -\infty} f(x)=A\\\\where\ A\ is\ a\ finite\ value.\\\\Given\ that \ f(x) =25000(1+0.025)^x\\\\ \lim_{x \to \infty} f(x)= \lim_{x \to \infty} [25000(1+0.025)^x]= \lim_{x \to \infty} [25000(1.025)^x]\\=25000 \lim_{x \to \infty} [(1.025)^x]=25000(\infty)=\infty\\\\ \lim_{x \to -\infty} f(x)= \lim_{x \to -\infty} [25000(1+0.025)^x]= \lim_{x \to -\infty} [25000(1.025)^x]\\=25000 \lim_{x \to -\infty} [(1.025)^x]=25000(0)=0\\\\](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20f%28x%29%3DA%5C%5C%5C%5Cor%5C%5C%5C%5C%20%5Clim_%7Bx%20%5Cto%20-%5Cinfty%7D%20f%28x%29%3DA%5C%5C%5C%5Cwhere%5C%20A%5C%20is%5C%20a%5C%20finite%5C%20value.%5C%5C%5C%5CGiven%5C%20that%20%5C%20f%28x%29%20%3D25000%281%2B0.025%29%5Ex%5C%5C%5C%5C%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20f%28x%29%3D%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%5B25000%281%2B0.025%29%5Ex%5D%3D%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%5B25000%281.025%29%5Ex%5D%5C%5C%3D25000%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%5B%281.025%29%5Ex%5D%3D25000%28%5Cinfty%29%3D%5Cinfty%5C%5C%5C%5C%20%5Clim_%7Bx%20%5Cto%20-%5Cinfty%7D%20f%28x%29%3D%20%5Clim_%7Bx%20%5Cto%20-%5Cinfty%7D%20%5B25000%281%2B0.025%29%5Ex%5D%3D%20%5Clim_%7Bx%20%5Cto%20-%5Cinfty%7D%20%5B25000%281.025%29%5Ex%5D%5C%5C%3D25000%20%5Clim_%7Bx%20%5Cto%20-%5Cinfty%7D%20%5B%281.025%29%5Ex%5D%3D25000%280%29%3D0%5C%5C%5C%5C)
![Since\ \lim_{x \to -\infty} f(x)=0\ is\ a\ finite\ value,hence:\\\\Hence\ the\ horizontal\ asymtotes\ is\ at\ y=0](https://tex.z-dn.net/?f=Since%5C%20%20%5Clim_%7Bx%20%5Cto%20-%5Cinfty%7D%20f%28x%29%3D0%5C%20is%5C%20a%5C%20finite%5C%20value%2Chence%3A%5C%5C%5C%5CHence%5C%20the%5C%20horizontal%5C%20asymtotes%5C%20is%5C%20at%5C%20y%3D0)
Answer:
14) 21.136505024965 m
15) 43.076759215619 km
Step-by-step explanation:
14)
let h be the height of the lighthouse:
tan(41.3) = 18.7/h
Then
h = 18.7÷tan(41.5)
= 21.136505024965 m
………………………………………
15)
90-71.4 =18.6
Let s be the distance that the plane flew
towards the south:
tan(90 - 71.4) = s/128
Then
tan(18.6) = s/128
Then
s = tan(18.6)×128
= 43.076759215619 km
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Answer:
Given:
Sample size, n = 120
P = 48% = 0.48
p' =
= 0.4
Significance level = 0.10
Null and alternative hypotheses are:
H0 : P = 0.48
H1 : P ≠ 0.48
For the test statistics:
Z = -1.754
P-value: This is a two tailed test.
For Z = -1.754 the P-value = 0.7943
Critical value: a = 0.10, 2 tailed test, Z critical = +1.645, -1.645
Decision Rule: We reject H0, if pvalue is less than significance level. We also reject H0 is Z observed is greater than Z critical.
Decision: Since pvalue, 0.7943 is greater than significance level, 0.10 we fail to reject null hypothesis, H0.
Conclusion:
There is not enough sufficient evidence to conclude that percentage of people who believe there is life on other planets differs from 48%