If for a given vehicle it takes 20 hp to overcome aerodynamic drag while being driven at 55 mph, estimate the horsepower required at 65 mph.

Find the greatest common factor of the monomials. 5m, 20m³

Determine whether the distribution is a discrete probability distribution.

$$\begin{matrix} \text{x} & \text{P(x)}\\ \text{100} & \text{0.1}\\ \text{200} & \text{0.25}\\ \text{300} & \text{0.2}\\ \text{400} & \text{0.3}\\ \text{500} & \text{0.1}\\ \end{matrix}$$

Find a power series solution of the given differential equation. Determine the radius of convergence of the resulting series, and identify the series solution in terms of familiar elementary functions.

$$( x - 2 ) y ^ { \prime } + y = 0$$

Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(-b<z<b)=0.8664, find b.

Evaluate the expression when x = 7.1 and y = -2.5. 5.3 - (y - x)

Express in simplest form without negative or zero exponents.

$$\left( \frac { r ^ { - 1 } } { s ^ { - 1 } } \right) ^ { - 1 }$$

What is an equation of a circle with radius 16 and center (2, -5)?

$$\begin{array} { l } A.{ ( x - 2 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 16 } \\ B.{ ( x + 2 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 4 } \end{array} \quad \begin{array} { l } C.{ ( x + 2 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 256 } \\ D.{ ( x - 2 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 256 } \end{array}$$

Determine the singular points of the given differential equation. Classify each singular point as regular or irregular. $\left(x^{2}+x-6\right) y^{\prime \prime}+(x+3) y^{\prime}+(x-2) y=0$

A snack mix requires a total of 120 ounces of some corn cereal and some wheat cereal. Corn cereal comes in 12 ounce boxes. a. The last time you made this mix, you used 5 boxes of corn cereal and 4 boxes of wheat cereal. How many ounces are in a box of wheat cereal? b. Write an equation in standard form that models the possible combinations of boxes of wheat and corn cereal you can use. c. List all possible combinations of whole boxes of wheat and corn cereal you can use to make the snack mix.

How do you account for the early successes of the Germans from 1939 through 1941?

The radius $R_h$ and mass $M_h$ of a black hole are related by $R_h = 2 GM_h/c^2$, where c is the speed of light. Assume that the gravitational acceleration $a_g$ of an object at a distance $r_o = 1.001 R_h$ from the center of a black hole is given (it is, for large black holes). In terms of $M_h$, find $a_g$ at $r_o$.

Let

$$\Delta f = f ( 1 + h ) - f ( 1 ),$$

where

$$f ( x ) = x ^ { - 1 }.$$

Show directly that

$$E = \left| \Delta f - f ^ { \prime } ( 1 ) h \right|$$

is equal to

$$h ^ { 2 } / ( 1 + h ).$$

Then prove that

$$E \leq 2 h ^ { 2 }$$

if

$$- \frac { 1 } { 2 } \leq h \leq \frac { 1 } { 2 }.$$

Hint: In this case,

$$\frac { 1 } { 2 } \leq 1 + h \leq \frac { 3 } { 2 }.$$

Solve each system of inequalities by graphing.

$$\left. \begin{array} { l } { x + y \leq 2 } \\ { 4 x ^ { 2 } - y ^ { 2 } \geq 4 } \end{array} \right.$$