The perimeter of a rectangular floor is 90 feet. Find the dimensions of the floor if the length is twice the width.

The cone of the volcano Parfcutin in Mexico had a height of 410 meters and a diameter of 424 meters. Approximate the volume of the cone. _

List four reasons that make a partnership a good business choice.

Explain why the law of sines cannot be used to solve a triangle if we are given the lengths of the three sides of the triangle.

Find the derivative of the function. $f ( x , y , z ) = \frac { x } { y } + \frac { y } { z } + \frac { z } { x }$ at point (5, -5, 5) in the direction the function increases most rapidly.

Evaluate the iterated integral. $\int_{0}^{1} \int_{0}^{x^{2}} \frac{x+1}{(y+1)^{2}} d y d x$

Prove that $\sum_{d | n} \sigma(d) \phi(n / d)=n \tau(n)$ and $\sum_{d | n} \tau(d) \phi(n / d)=\sigma(n)$.

Identifying definite integrals as limits of sums Consider the following limits of Riemann sums for a.function f on [ a, b]. Identify f and express the limit as a definite integral. $\lim _{\Delta \rightarrow 0} \sum_{k=1}^{n} x_{k}^{*}\left(\cos x_{k}^{*}\right) \Delta x_{k} \ \ \text { on }\ \ [1,2]$

Perform and document a simulation to find the chances of scoring 50% or higher on a 5 question multiple choice test. Each question has four choices, and you guess on each question.

You want to isolate a prokaryote that can live on discarded Styrofoam cups. Such an organism might live in a landfill where ground-up cups are discarded. How would you use metagenomics to identify such a bacterium?

Use a calculator to decide u whether each statement is true or false. It may be that a true statement will lead to results that differ in the last decimal place due to rounding error. $\sin 50^{\circ}=2 \sin 25^{\circ} \cos 25^{\circ}$

Use synthetic division to perform the division.

$$\frac { 4 x ^ { 4 } + 12 x ^ { 3 } - x ^ { 2 } - x + 12 } { x + 3 }$$

Explain the difference between the income effect and the substitution effect.

Use the given zero to find the remaining zeros of each function. $h(x)=3 x^{5}+2 x^{4}+15 x^{3}+10 x^{2}-528 x-352;$ zero: $-4 i$