Write and solve an equation to answer each problem. Katie, Elizabeth, and Siobhan volunteer at the hospital. In a week, Katie volunteers 3 hours more than Elizabeth does and Siobhan volunteers 1 hour less than Elizabeth. Over 3 weeks, the number of hours Katie volunteers is equal to the sum of Elizabeth's and Siobhan's volunteer hours in 3 weeks. Complete the table to find out how many hours each person volunteers each week.

$$\begin{matrix} \text{Volunteer} & \text{Volunteer Hours per week} & \text{Volunteer Hours over 3 weeks}\\ \text{Katie}\\ \text{Elizabeth}\\ \text{Siobhan}\\ \end{matrix}$$

An engine’s internal energy changes from 8093 J to $2.0920 \times 10^{4}$ J. If 6932 J are added as heat, how much work is done on or by the system?

Tell whether a parallelogram with the given vertices is a rectangle, rhombus, or square. Give all the names that apply. $(-3,1),(-1,3),(1,1)$, and $(-1,-1)$

Which amino acid will a tRNA molecule be carrying if its anticodon is the following?

a. GGG

b. GAC

c. AUA

d. CGA

The crystal line hydrate $\mathrm { Cd } \left( \mathrm { NO } _ { 3 } \right) _ { 2 } \cdot 4 \mathrm { H } _ { 2 } \mathrm { O } ( s )$ loses water when placed in a large, closed, dry vessel at room temperature: $\mathrm { Cd } \left( \mathrm { NO } _ { 3 } \right) _ { 2 } \cdot 4 \mathrm { H } _ { 2 } \mathrm { O } ( s ) \longrightarrow \mathrm { Cd } \left( \mathrm { NO } _ { 3 } \right) _ { 2 } ( s ) + 4 \mathrm { H } _ { 2 } \mathrm { O } ( g )$ This process is spontaneous and $\Delta H ^ { \circ }$ is positive at room temperature. If the hydrated compound is placed in a large, closed vessel that already contains a large amount of water vapor, does $\Delta S ^ { \circ }$ change for this reaction at room temperature?

Figure shows a rotating shaft carrying a steady downward load of $100\ \mathrm{lb}$ at $\mathrm{C}$. Specify a suitable material.

How would you respond to a stockout of your brand choice (or model) of dress shirt/blouse? What factors other than product category would affect your response?

Did van Helmont's experiment support or disprove Aristotle's hypothesis? Explain.

Identify the hypothesis and conclusion of each statement.

If $3 x-1=8$, then $x=3$.

Underline the hypothesis and circle the conclusion. If a polygon is a pentagon, then it has five sides.

A particle carrying charge $q _ { \mathrm { p } } = + 10 \mathrm { nC }$ is located at $y _ { p } = 0.030 \mathrm { m }$ on the y axis of an xy coordinate system. A nonconducting rod of length $\ell = 0.10 \mathrm { m }$ carrying charge $q _ { \mathrm { r } } = - 10 \mathrm { nC }$ lies on the x axis, extending from x = 0 to x = 0.10 m. Write an expression for the electrostatic potential for any position along the y axis.

Of the volunteers donating blood in a clinic, 80% have the Rhesus (Rh) factor present in their blood. What is the smallest number of volunteers who must be selected if we want to be at least 90% certain that we obtain at least five donors with the Rh factor?

During the course of a year, the number of volunteers available to run a food bank each month is modeled by $V(x)$, where

$$V(x)=2 x^2-32 x+150$$

between the months of January and August. Here $x$ is time in months, with $x=1$ representing January. From August to December, $V(x)$ is modeled by

$$V(x)=31 x-226.$$

Find the number of volunteers in each of the following months.

Sketch a graph of $y=V(x)$ for January through December. In what month are the fewest volunteers available?