For each function, find the percent increase or decrease that the function models. $y=16\left(\frac{1}{4}\right)^{x}$

Each dimension of a rectangular prism is tripled. How does the surface area of the new rectangular prism compare to the original surface area? A. The new surface area is 12 times as great. B. The new surface area is 9 times as great. C. The new surface area is 6 times as great. D. The new surface area is 3 times as great.

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.

Explain why the base b in $y=\log _{b} x$ cannot equal 1.

Write on equation of the direct variation that includes the given point. (2, 2)

The Clean Air Act prohibited the production of chlorofluorocarbons (CFCs) in the United States as of 1996. One widely used CFC, refrigerant R-12, has been replaced by R-134a in many applications because of their similar properties, including a low boiling point at atmospheric pressure, $T_{\mathrm{sat}}=243 \mathrm{K}$ and 246.9 K for R-12 and R-134a, respectively.

Compare the performance of these two refrigerants under the following conditions. The saturated refrigerant vapor at 310 K is condensed as it flows through a 30-mm diameter, 0.8-m-long tube whose wall temperature is maintained at 290 K. If vapor enters the tube at a flow rate of 0.010 kg/s, what is the rate of condensation and the flow rate of vapor leaving the tube?

The relevant properties of R-12 at $T_{\mathrm{sat}}=310 \mathrm{K}$ are $\rho_{v}=50.1 \mathrm{kg} / \mathrm{m}^{3}$, $h_{f g}=160 \mathrm{kJ} / \mathrm{kg}$, and $\mu_{v}=150 \times 10^{-7} \mathrm{N} \cdot \mathrm{s} / \mathrm{m}^{2}$ and those of liquid R-12 at $T_{f}=300 K$ are $\rho_{l}=1306 \mathrm{kg} / \mathrm{m}^{3}$, $c_{p, l}=978 \mathrm{J} / \mathrm{kg} \cdot \mathrm{K}, \mu_{l}=2.54 \times 10^{-4} \mathrm{N} \cdot \mathrm{s} / \mathrm{m}^{2}$, $k_{l}=0.072 \mathrm{W} / \mathrm{m} \cdot \mathrm{K}$.

The properties of the saturated R-134a vapor are $\rho_{v}=46.1, \mathrm{kg} / \mathrm{m}^{3}, h_{f g}=166 \mathrm{kJ} / \mathrm{kg}$, and $\mu_{v}=136 \times 10^{-7} \mathrm{N} \cdot \mathrm{s} / \mathrm{m}^{2}$.

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

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

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

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

.

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?

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. $7 x^{2}-x-12=0$

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

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