Graph several functions that satisfy the following differential equations. Then find and graph the particular function that satisfies the given initial condition. f'(x)=2x-5; f(0)=4

State if the possible arrangements represent permutations or combinations, then state the number of possible arrangements. A student chooses at random 4 books from a reading list of 11 books.

Determine the system of differential equations corresponding to each compartment model and analyze the stability of the equilibrium (0, 0). a = 0.2, b = 0.1, c = 0, d = 0

Review the chart that you kept in your Reader's Notebook.Then summarize the new insights that you gained into the character of Martin Luther King, Jr., from reading this selection.

The population of a species of elk on Reading Island in Canada has been monitored for some years. When the population was $6(00$, the relative birth rate was $35 \%$ and the relative death rate was $15 \%$. As the population grew to $800 .$ the corresponding figures were $30 \%$ and $20 \%$. The island is isolated so there is no hunting or migration.
Find the equilibrium size of the population. Today there are $900$ elk on Reading Island. How do you expect the population to change in the future?

Find the general solutions of the differential equations. $2 \frac{d^{2} y}{d t^{2}}+5 \frac{d y}{d t}+2 y=0$

Find the general solution of the system of differential equations.

$$\begin{align*} y_1'&=2y_1\\ y_2'&=3y_1+2y_2+3y_3\\ y_3'&=-3y_1-y_3 \end{align*}$$

The flow lines (or streamlines) of a vector field are the paths followed by a particle whose velocity field is the given vector field. Thus the vectors in a vector field are tangent to the flow lines. If parametric equations of a flow line are $x = x(t), y = y(t)$ explain why these functions satisfy the differential equations $dx/dt = x$ and $dy/dt = -y$. Then solve the differential equations to find an equation of the flow line that passes through the point (1, 1).

Shown in the following table are the reading scores of a second-grade class given individualized instruction and the reading scores of a second-grade class given traditional instruction in the same school:

Find the mean and standard deviation for the traditional instruction scores.

In lab you find that a 1-kg rock suspended above water weighs $10 \mathrm{~N}$. When the rock is suspended beneath the surface of the water, the scale reads $8 \mathrm{~N}$. a. What is the buoyant force on the rock? b. If the container of water weighs $10 \mathrm{~N}$ on the weighing scale, what is the scale reading when the rock is suspended beneath the surface of the water? c. What is the scale reading when the rock is released and rests at the bottom of the container?

History of corporate acquisitions. Refer to the Academy of Management Journal (August 2008) investigation of the performance and timing of corporate acquisitions, Exercise $2.12$ (p. 50). Recall that the investigation discovered that in a random sample of 2,778 firms, 748 announced one or more acquisitions during the year 2000 . Does the sample provide sufficient evidence to indicate that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than $30 \%$ ? Use $\alpha=.05$ to make your decision.

Find the mean and standard deviation for each of the sample data sets. The grade-level reading scores from a reading test given to a random sample of 12 students in an urban high school graduating class are:

$$\begin{matrix} \text{9} & \text{11} & \text{11} & \text{15}\\ \text{10} & \text{12} & \text{12} & \text{13}\\ \text{8} & \text{7} & \text{13} & \text{12}\\ \end{matrix}$$

Draw the directional field for the following differential equations. What can you say about the behavior of the solution? Are there equilibria? What stability do these equilibria have? y’ = y - x

For each of the following differential equations in Problem, apply the method of Frobenius to obtain the solution. $x^{2} y^{\prime \prime}+\left(x^{2}-x\right) y^{\prime}+2 y=0$