Write in the blank whether the sentence is simple or compound. _____ Valery ran her fingers through her long, straight hair.

Solve the inequality. Graph the solution.

$$10 k<75 \text { and } 4-k \leq 0$$

Circle the infinitive or infinitive phrase in each sentence. It was difficult to identify the type of bacteria under the microscope.

Use a dictionary to define innovate.

Identify the isoclines for the given differential equation. $\frac{d y}{d x}=\frac{x-y}{x+y}$

Draw one line under each main clause and two lines under each subordinate clause. Write C in the blank if the sentence is complex and CC if it is compound-complex. _____ As long as Rick is going to the store, could he buy some nachos for me?

Use the Laplace transform to solve the given differential equation subject to the indicated initial conditions. Where appropriate, write f in terms of unit step functions. $y^{(4)}-y=0, \quad y(0)=1, y^{\prime}(0)=0, y^{\prime \prime}(0)=-1, y^{\prime \prime \prime}(0)=0$

Find the slope of the line tangent to the graph of $f(x)=\frac{x}{x+6}$ at the point (3, 1/3) and at (-2, -1/2).

a. Does the function f(x)=x sin (1/x) have a removable discontinuity at x=0? Explain. b. Does the function g(x)=sin(1/x) have a removable discontinuity at x=0? Explain.

Write LV in the blank if the verb is a linking verb and AV if the verb is an action verb. _____ Scholars recognize Alsace as Barthldi's birthplace.

Find and simplify the derivative of the following functions. $g(t)=\frac{t^{3}+3 t^{2}+t}{t^{3}}$

Use the Product Rule to find f'(1) given that $f(x)=x^{4}(1+\sqrt{x})$.

Complete the following steps for each function. a. Use the continuity checklist to show that f is not continuous at the given value of a. b. Determine whether f is continuous from the left or the right at a. c. State the interval(s) of continuity.

$$f(x)=\left\{\begin{array}{ll}{2 x} & {\text { if } x<1} \\ {x^{2}+3 x} & {\text { if } x \geq 1}\end{array} ; a=1\right.$$

A community consists of 100 married couples. If 50 members of the community die, what is the expected number of marriages that remain intact? Assume that the set of people who die is equally likely to be any of the

$$\left(\begin{array}{c}{200} \\ {50}\end{array}\right)$$

groups of size 50. Hint: For i = 1, . . . , 100 let

$$X_{i}=\left\{\begin{array}{ll}{1} & {\text { if neither member of couple } i \text { dies }} \\ {0} & {\text { otherwise }}\end{array}\right.$$