________ variables are defined outside all functions and are accessible to any function within their scope.

The total area under the graph of a probability density function always equals ____.

Researchers have proposed that the amount a full-time student is educated (x) changes with respect to the student's age t according to the differential equation $\frac{d x}{d t}=1-k x$, where k is a constant measuring the rate that education depreciates due to forgetting or technological obsolescence. a. Solve the equation using the method of separation of variables. b.Solve the equation using an integrating factor. c. What does x approach over time?

Marie has a weekly budget of $24, which she likes to spend on magazines and pies. What is Marie’s opportunity cost of purchasing a pie?

What is a recursive sequence?

Assuming the relative rate of secondary to primary hydrogen atom abstraction to be the same in the chlorination of propane as it is in that of butane, calculate the relative amounts of propyl chloride and isopropyl chloride obtained in the free-radical chlorination of propane.

Find the general solution of the given Cauchy-Euler equation in x > 0: $x^{2} y^{\prime \prime}+4 x y^{\prime}+2 y=0$

Find the least squares regression line. (1, 0), (3, 3), (5, 6)

Carbon-carbon bond dissociation enthalpies have been measured for many alkanes. Without referring to the table, identify the alkane in each of the following pairs that has the lower carbon-carbon bond-dissociation enthalpy, and explain the reason for your choice. (a) Ethane or propane (b) Propane or 2-methylpropane (c) 2-Methylpropane or 2,2-dimethylpropane (d) Cyclobutane or cyclopentane

Convert the following temperatures to Celsius: (a) 0 K, (b) 250 K, (c) 273 K, and (d) 325 K.

identify and sketch the graph of the conic section. $x^{2}+4 y^{2}-16=0$

A metal wire 1.0 mm in diameter and 2.0 m long hangs vertically with a 6.0-kg object suspended from it. If the wire stretches 1.4 mm under the tension, what is the value of Young's modulus for the metal?

Use a software program or a graphing utility to solve the system of linear equations.

$$\begin{align*} 120.2x+62.4y-36.5z &= 258.64 \\ 56.8x-42.8y+27.3z &= -71.44 \\ 88.1x +72.5y -28.5z &= 225.88 \end{align*}$$

Find two $2 \times 2$ matrices A such that $A^{2}=O.$