Use the formula for

$$_nC_r$$

to solve. A four-person committee is to be elected from an organization's membership of 11 people. How many different committees are possible?

Use the formula for

$$_ { n } C _ { r }$$

to solve. A four-person committee is to be elected from an organization’s membership of 11 people. How many different committees are possible?

Thanh bought 11 pieces of fruit and spent $5.60. If apples cost$0.60 each and pears cost $0.35 each, how many of each kind of fruit did he buy?

Show that the atomic packing factor for BCC is 0.68.

In a race in which six automobiles are entered and there are no ties, in how many ways can the first three finishers come in?

A cylindrical specimen of stainless steel having a diameter of 12.8 mm (0.505 in.) and a gauge length of 50.800 mm (2.000 in.) is pulled in tension. Use the load-elongation characteristics shown in the following table to complete parts (a) through (f).

$$\begin{matrix}\text{Load} & \text{Length}\\\text{N} & \mathrm{lb_{f}} & \text{mm} & \text{in.}\\\text{0} & \text{0} & \text{50.800} & \text{2.000}\\\text{12,700} & \text{2,850} & \text{50.825} & \text{2.001}\\\text{25,400} & \text{5,710} & \text{50.851} & \text{2.002}\\\text{38,100} & \text{8,560} & \text{50.876} & \text{2.003}\\\text{50,800} & \text{11,400} & \text{50.902} & \text{2.004}\\\text{76,200} & \text{17,100} & \text{50.952} & \text{2.006}\\\text{89,100} & \text{20,000} & \text{51.003} & \text{2.008}\\\text{92,700} & \text{20,800} & \text{51.054} & \text{2.010}\\\text{102,500} & \text{23,000} & \text{51.181} & \text{2.015}\\\text{107,800} & \text{24,200} & \text{51.308} & \text{2.020}\\\text{119,400} & \text{26,800} & \text{51.562} & \text{2.030}\\\text{128,300} & \text{28,800} & \text{51.816} & \text{2.040}\\\text{149,700} & \text{33,650} & \text{52.832} & \text{2.080}\\\text{159,000} & \text{35,750} & \text{53.848} & \text{2.120}\\\text{160,400} & \text{36,000} & \text{54.356} & \text{2.140}\\\text{159,500} & \text{35,850} & \text{54.864} & \text{2.160}\\\text{151,500} & \text{34,050} & \text{55.880} & \text{2.200}\\\text{124,700} & \text{28,000} & \text{56.642} & \text{2.230}\\\end{matrix}$$

(a) Plot the data as engineering stress versus engineering strain. (b) Compute the modulus of elasticity. (c) Determine the yield strength at a strain offset of 0.002. (d) Determine the tensile strength of this alloy. (e) What is the approximate ductility, in percent elongation? (i) Compute the modulus of resilience.

Solve the equation. State any extraneous solutions.

$$\frac{3}{c} = \frac{2}{c + 2}$$

On September 11, 2002, the first anniversary of the terrorist attack on the World Trade Center, the New York State Lottery's daily number came up 9-1-1. An interesting coincidence or a cosmic sign? If every one of the 50 states has a three-digit lottery, what is the probability that at least one of them will come up 9-1-1 on September 11?

Find all rational, irrational, and complex zeros (and state their multiplicities). Use Descartes' Rule of Signs, the Upper and Lower Bounds Theorem, the Quadratic Formula, or other factoring techniques to help you whenever possible.

$$P ( x ) = x ^ { 4 } + 15 x ^ { 2 } + 54$$

Use the formula for

$$_ { n } P _ { r }$$

to solve. For a segment of a radio show, a disc jockey can play 7 songs. If there are 13 songs to select from, in how many ways can the program for this segment be arranged?

You want to find out how much time people in your town spend doing volunteer work. You call 100 homes in the community during the day. Of those surveyed, 85% are over the age of 60. How might this create bias in your survey results?

If $x ^ { 2 } + k x + 18$ is factorable, what are the possible values of k?

Which bones form the pectoral girdle?

Using the t tables, software, or a calculator estimate a) the critical value oft for a 90% confidence interval with df = 17. b) the critical value of t for a 98% confidence interval with df = 88.