Sketch a graph of the equation $y=\frac{\sqrt[3]{6 \pi^2 x}}{2 \pi}$, where $y$ is the radius of a sphere and $x$ is the volume of the sphere. Use the graph to estimate the volume of a sphere with a radius of $2 \mathrm{~cm}$. Use the graph to estimate the radius of a cube with a volume of $14 \mathrm{~cm}^3$.

The North Falls waterfalls in Silver Falls State Park in Oregon are 136 feet high. The equation $-16 t^2+136=0$ gives the number of seconds it takes for a drop of water at the top of the falls to reach the pool of water below. Solve the equation by using the Quadratic Formula. Round to the nearest hundredth of a second.

Let $f(x)=a x+b$ and $g(x)=c x+d$. Under which conditions will the composite functions $f(g(x))$ and $g(f(x))$ be equal?

Each side of a regular hexagon shown in 7 cm. Find the length of the diagonal $\overline{AE}$. Round your answer to the nearest tenth. (The measure of one interior angle of an n-gon is $\frac{(n - 2)180}{n}$.)

Suppose the graph of y = b$^x$ + k passes through the points (3, -3) and (5, 0). Determine whether the equation models exponential growth or decay.

Frets are small metal bars placed across the neck of a guitar so that the guitar can produce notes of a specific scale. To find the distance a fret should be placed from the bridge multiply the length of the string by $2^{-\frac{n}{12}}$, where $n$ is the number of notes higher than the string's root note. Where should a fret be placed to produce a high E note on the low E string ( 5 notes higher), if the length of the string is $64 \mathrm{~cm}$, rounded to the nearest hundredths place?

Which describes all the values of $\sin ^{-1} \frac{1}{2}$ ?

A $\frac{\pi}{6}+\pi n$ and $\frac{5 \pi}{6}+\pi n$, where $n$ is an integer

B $\frac{\pi}{6}+2 \pi n$ and $\frac{5 \pi}{6}+2 \pi n$, where $n$ is an integer

C $\frac{\pi}{3}+\pi n$ and $\frac{2 \pi}{3}+\pi n$, where $n$ is an integer

D $\frac{\pi}{3}+2 \pi n$ and $\frac{2 \pi}{3}+2 \pi n$, where $n$ is an integer

The volume of a can of dog food is 450 cubic inches. The height of the can is 5 inches greater than its radius. Write a polynomial in standard form, without $\pi$, that can be used to find the radius (Round the constant to the nearest integer.) Then find the approximate radius by using a graphing calculator.

Give an example of an event which has a probability of 0 . Explain why the probability is 0 .

An expression for the volume of the rectangular prism is V = 2x$^3$ + 7x$^2$ - 14x - 40. Find an expression for the missing dimension.

Venus is only slightly smaller than Earth; its radius is approximately 3757 miles. But it rotates much more slowly; it takes 243 Earth days for Venus to make one complete rotation. If an object is fixed on Venus's equator, how far does it travel in 1 hour due to Venus's rotation?

A student converted the exponential equation $4^{-2}=\frac{1}{16}$ to logarithmic form by writing $\log _4(-2)=\frac{1}{16}$. What is the error? Write the correct logarithmic equation.

Gravity on the planet Jupiter is almost three times stronger than on Earth. If an object is thrown into the air, with an initial velocity of 100 feet per second, from the surface of Jupiter, the height, $h$, of the object in feet after $t$ seconds can be approximated by the equation: $h=-42 t^2+100 t$. Find the time at which the object will first reach 50 feet. Round your answer to the tenths place.

A few different equations of the form y = b$^x$ are graphed. Describe in your own words how the shape of the graph depends on the value of b.