Identify the type I error and the type II error that correspond to the given hypothesis. The proportion of car crashes occurring less than a mile from home is 0.23.

Suppose you roll a number cube. Find each theoretical probability. P(8)

Solve each equation. Round to the nearest ten-thousandth. $5^{x}+3=12$

Liquid nitrogen is stored in a thin-walled spherical vessel of diameter $D_{i}=1 \mathrm{m}$. The vessel is positioned concentrically within a larger, thin-walled spherical container of diameter $D_{o}=1.10 \mathrm{m}$, and the intervening cavity is filled with atmospheric helium. Under normal operating conditions, the inner and outer surface temperatures are $T_{i}=77 \mathrm{K}$ and $T_{o}=283 \mathrm{K}$. If the latent heat of vaporization of nitrogen is $2 \times 10^{5} \mathrm{J} / \mathrm{kg}$, what is the mass rate $\dot{m}(\mathrm{kg} / \mathrm{s})$ at which gaseous nitrogen is vented from the system?

Consider the general linear model

$$Y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \cdots + \beta _ { k } x _ { k } + \varepsilon$$

, where

$$E ( \varepsilon ) = 0 \text { and } V ( \varepsilon ) = \sigma ^ { 2 }$$

. Notice

$$\hat { \beta } _ { i } = \mathbf { a } ^ { \prime } \boldsymbol { \beta }$$

, where the vector a is defined by

$$a _ { j } = \left\{ \begin{array} { l l } { 1 , } & { \text { if } j = i } \\ { 0 , } & { \text { if } j \neq i } \end{array} \right.$$

. Use this to verify that

$$E \left( \hat { \beta } _ { i } \right) = \beta _ { i } \text { and } V \left( \hat { \beta } _ { i } \right) = c _ { i i } \sigma ^ { 2 }$$

, where

$$c _ { i i }$$

is the element in row i and column i of

$$\left( \mathbf { X } ^ { \prime } \mathbf { X } \right) ^ { - 1 }$$

.

The leg opposite the $60^{\circ}$ angle of a 30-60-90 triangle has a length of $7 \sqrt{3}$. What is the length of the hypotenuse?

Part A Assestinents: Complete the following statements: 1. The pelvic girdle consists OL TWO 9 The head of the femur articulates with the ee ss cethe hip bone.

Solve each equation using the Quadratic Formula. Find the exact solutions. Then approximate any radical solutions. Round to the nearest hundredth. $7 x^{2}-x-12=0$

List all of the properties of a rectangle. Begin with the properties of a parallelogram.

Solve each equation or inequality. Use interval notation to express solution sets of inequalities and graph these solution sets on a number line.

$$\sqrt { x - 3 } + 5 = x$$

Use the table, which shows the age groups of students in a college sociology class.

$$\begin{matrix} \text{Age} & \text{Number of students}\\ \text{18–19} & \text{11}\\ \text{20–21} & \text{18}\\ \text{22–30} & \text{2}\\ \text{31– 40} & \text{1}\\ \end{matrix}$$

A student from the class is randomly chosen for a project. Find the probability that the student is the given age. 18 or 19 years old

Graph the function and its parent function. Then describe the transformation. f(x) = x - 6

Choose two positive numbers. Find their geometric mean.

Your friend’s portfolio manager has suggested two energy stocks: Exxon Mobil (XOM) and British Petroleum (BP). XOM shares cost $80, yield 2% in dividends, and have a risk index of 2.5. BP shares cost$50, yield 7% in dividends, and have a risk index of 4.5. Your friend has up to $40,000 to invest, and would like to earn at least$1,400 in dividends. How many shares (to the nearest tenth of a unit) of each stock should she purchase to meet your requirements and minimize the total risk index for your portfolio? What is the minimum total risk index?