Use the formula for

$$_nC_r$$

, to solve. There are 14 standbys who hope to get seats on a flight, but only 6 seats are available on the plane. How many different ways can the 6 people be selected?

Fill in the blanks using the named events. 30% of all lawyers who lost clients (L) were antitrust lawyers (A), whereas 10% of all antitrust lawyers lost clients. P(___ | )=; P(___ | )=

Find the volume of the solid bounded on the front and back by the planes

$$x = \pm \pi / 3,$$

on the sides by the cylinders

$$y = \pm \sec x,$$

above by the cylinder

$$z = 1 + y ^ { 2 },$$

and below by the xy-plane.

Solve each exponential equation. Express answers to the nearest hundredth of a unit. a)

$$A=250\left(1.05\right)^{10}$$

b)

$$P=9000\left(\frac{1}{2}\right)^8$$

c)

$$500=N_0\left(1.25\right)^{1.25}$$

d)

$$625=P\left(0.71\right)^9$$

Summarize Earth's crust, mantle, and core on the basis of relative position, density, and composition.

During the 109th Congress (2005-2006), the U.S. Senate had a total of 99 Democrats and Republicans. There were 11 more Republicans than Democrats. How many Democrats and Republicans were there in the Senate?

Use the formula for

$$_nC_r$$

to solve. The U.S. Senate of the 109th Congress consisted of 55 Republicans , 44 Democrats, and 1 Ind ependent. How many committees can be formed if each committee must have 4 Republicans and 3 Democrats?

37. In how many ways can a committee of four men and five women be formed from a group of seven men and seven women?
38. How many different committees can be formed from 5 professors and 15 students if each committee is made up of 2 professors and 10 students?

Which of the following are second-order linear homogeneous recurrence relations with constant coefficients? a.

$$a _ { k } = 2 a _ { k - 1 } - 5 a _ { k - 2 }$$

, b.

$$b _ { k } = k b _ { k - 1 } + b _ { k - 2 }$$

, c.

Find the cube root.

$$\sqrt [ 3 ] { - 1000 }$$

Divide.

$$\frac { 2 x ^ { 4 } - x ^ { 3 } y + x ^ { 2 } y ^ { 2 } + 4 x y ^ { 3 } - 4 y ^ { 4 } } { 2 x ^ { 2 } + x y - 2 y ^ { 2 } }$$

What are the x-intercepts of the graph of A(x)? What is the significance of each x-intercept in terms of the calendar problem?

What will happen to American exporters to China if the trend continues and imports from China continue to grow? In which direction will the demand curve move?

Identify the most important types of interparticle forces present in the solids of each of the following substances. $\mathrm { CaCl } _ { 2 }$