A publishing company publishes a total of no more than 100 books every year. At least 20 of these are nonfiction, but the company always publishes at least as much fiction as nonfiction. Find a system of inequalities that describes the possible numbers of fiction and nonfiction books that the company can produce each year consistent with these policies. Graph the solution set.

A farmer has 300 acres of arable land on which she wants to plant cauliflower and cabbage. The farmer has $17,500 available for planting and$12,000 for fertilizer. Planting 1 acre of cauliflower costs $70, and planting 1 acre of cabbage costs$35. Fertilizer costs $25 for 1 acre of cauliflower and$55 for 1 acre of cabbage. (a) Find a system of inequalities that describes the number of acres of each crop that the farmer can plant with the available resources. Graph the feasible region. (b) Can the farmer plant 155 acres of cauliflower and 115 acres of cabbage? (c) Can the farmer plant 115 acres of cauliflower and 175 acres of cabbage?

A cat food manufacturer uses fish and beef by products. The fish contains 12 g of protein and 3 g of fat per ounce. The beef contains 6 g of protein and 9 g of fat per ounce. Each can of cat food must contain at least 60 g of protein and 45 g of fat. Find a system of inequalities that describes the possible number of ounces of fish and beef by products that can be used in each can to satisfy these minimum requirements. Graph the solution set.

A cyclotron with dee radius 53.0 cm is operated at an oscillator frequency of 12.0 MHz to accelerate protons. What magnitude B of magnetic field is required to achieve resonance?

Which of the following are subrings of $M(2, \mathbb{Z})?$

$$\left\{\left[\begin{array}{ll}{a} & {b} \\ {0} & {0}\end{array}\right]: a, b \in \mathbb{Z}\right\}$$

For the system

$$\begin{gather*} x' = \left(\begin{array}{cc}-1 & -5 \\ \,\,\,\,\, 1 & \,\,\,\,\, 3\end{array}\right) \ x. \end{gather*}$$

use the method of Laplace transforms to find the fundamental matrix ${e^{At}}$.

$$\begin{array}{l} \text{ Find the second derivative of the function.} \end{array}$$

$$f ( x ) = \left( x ^ { 3 } + x + 1 \right) ^ { 2 }$$

Use a Taylor series to approximate the following definite integrals. Retain as many terms a needed to ensure the error is less than $10^{-4}$. $\int _ { 0 } ^ { 0.35 } \tan ^ { - 1 } x d x$

Use the improved Euler’s method to obtain a four-decimal approximation to the indicated value. First use $h=0.1$ and then use $h=0.05$. $y^{\prime}=x y+\sqrt{y}, \quad y(0)=1 ; y(0.5)$

A farmer has 500 acres of arable land on which he wants to plant potatoes and corn. The farmer has $40,000 available for planting and$30,000 for fertilizer. Planting 1 acre of potatoes costs $90, and planting 1 acre of corn costs$50. Fertilizer costs $30 for 1 acre of potatoes and$80 for 1 acre of corn. Can the farmer plant 300 acres of potatoes and 180 acres of corn?

Discuss whether you think y would be a function of x: y = speed at which an object falls, x = weight of object

Find the equation of the line parallel to the line y = 2x + 1 and containing the point (3, 5). Express your answer in slope–intercept form and graph the line.

Factor each polynomial by grouping. Check your answer.

$$10 b ^ { 3 } - 16 b ^ { 2 } + 25 b - 40$$

The perimeter of a rectangle is 70, and its diagonal is 25. Find its length and width.