The graphs of $u\left(x\right)$ and $v\left(x\right)$ are shown in the following image.

Find the value of $u\left(u\left(9\right)\right)$.

Evaluate the composite function $a\left(b\left(y\right)\right)$ given the following:

$a\left(x\right)=x^2$

$b\left(x\right)=x^2-7$

A certain species of fish in a lake reproduces at a rate that doubles its population every $24~\text{hours}$. The initial population of the fish was $200$. If the population $t$ hours after the initial observation is represented by the function $p\left(t\right)=200\cdot{2^{\frac{t}{24}}}$, how long will it take for the fish population to reach $4000$?

Given that $\log_{c}a=0.45,\log_{c}b=0.65,$ find the value of $\log_{c}(a/b)$.

Determine the value of $z$ in the equation $3^z = 81$.

Determine the value of $z$ that satisfies $\ln5z+\ln(z+4)=0$.

Find the amplitude and period for the given trigonometric expression below.

$P\left(x\right)=5.7\sin\left(\frac19\left(x-7\right)\right)$

Is the following trigonometric equation an identity?

$\frac{\cos A}{1+\sin A}=\frac{1-\sin A}{\cos A}$

Evaluate the given expression:

$\cos\left(\cos^{-1}\left(-\frac12\right)\right)$