The length of fence required to enclose a rectangular field is 3000 meters.What are the dimensions of the field if it is known that the difference between its length and width is 50 meters?

Claim: Fewer than 95% of adults have a cell phone. In a Marist poll of 1128 adults, 87% said that they have a cell phone. Find the value of the test statistic.

Roberta has $4.00 dimes and quarters. She has 5 more dimes than quarters. Write a system of equations you could use to find how many dimes and quarters she has.

How does electric force depend on the amount of charge and the distance between charges?

Random variables X and Y have joint PDF

$$f_{X, Y}(x, y)=\left\{\begin{array}{ll}{\operatorname{cxy}^{2}} & {0 \leq x \leq 1,0 \leq y \leq 1,} \\ {0} & {\mathrm { otherwise. }}\end{array}\right.$$

(a) Find the constant c. (b) Find P[X>Y] and $\mathrm{P}\left[Y<X^{2}\right]$. (c) Find $\mathrm{P}[\min (X, Y) \leq 1 / 2]$. (d) Find $\mathrm{P}[\max (X, Y) \leq 3 / 4]$.

Write each system as a matrix equation and solve using the inverse coefficient matrix. Use a graphing calculator or computer to perform the necessary calculations.

$$\begin{aligned} x_{1}+5 x_{2}+6 x_{3} &=76 \\ 2 x_{1}+3 x_{2}+8 x_{3} &=92 \\ 11 x_{1}+9 x_{2}+4 x_{3} &=181 \end{aligned}$$

A coin is tossed three times, and the number of heads that occur, X, is assigned to each outcome. List all possible outcomes and the corresponding value of X.

Use the van der Waals equation of state and mathematical software or a spreadsheet to plot the pressure of $1.5\ mol\ CO_{2} (g)$ against volume as it is compressed from $30\ \mathrm{dm}^{3}$ to $15\ \mathrm{dm}^{3}$ at (a) 273 K, (b) 373 K. (c) Redraw the graphs as plots of p against 1/V.

Review the major steps in blood clot formation.

This exercise concerns a particular orthogonal basis for $\mathbb{C}^{3}$. (a) Use the Gram-Schmidt Process to find an orthogonal basis for $\mathbb{C}^{3}$ containing $[1+i, i, 1]$. (b) Find a $3 \times 3$ unitary matrix having a multiple of $[1+i, i, 1]$ as its first row.

Answer for the sequence $\tau_0=5, \tau_2=5$. Is $\tau$ increasing?

List all of the ways to detect a magnetic field in a particular region. Explain how they work and how you can use them to determine the magnitude and the direction of the $\vec{B}$ field.

Find the mean and standard deviation of the population. List all samples (with replacement) of the given size from that population and find the mean of each. Find the mean and standard deviation of the sampling distribution of sample means and compare them with the mean and standard deviation of the population. The numbers of DVDs rented by each of four families in the past month are 8, 4, 16, and 2. Use a sample size of 3.

Write the word that is a synonym for, or means the same as, the vocabulary word on the right. a. waterfall b. gaudy c. cheapen d. pure e. tactful f. ruins g. provokes. chaste