Shown again is the table indicating the marital status of the U.S. population in 2010. Numbers in the table are expressed in millions. Use the data in the table to solve Exercises 1-10. Express probabilities as simplified fractions and as decimals rounded to the nearest hundredth. Marital Status of the U.S. Population, Ages 15 or Older, 2010, in Millions

	Married	Never Married	Divorced	Widowed	Total
Male	65	40	10	3	118
Female	65	34	14	11	124
Total	130	74	24	14	242

If one person is randomly selected from the population described in the table, find the probability, expressed as a simplified fraction and as a decimal to the nearest hundredth, that the person among those who are divorced, find the probability of selecting a woman.

In a simplified model of the human eye, the aqueous and vitreous humors and the lens all have a refractive index of 1.40, and all the bending occurs at the cornea, whose vertex is 2.60 cm from the retina. What should be the radius of curvature of the cornea such that the image of an object 40.0 cm from the cornea’s vertex is focused on the retina?

What is the simplified form of $\left(2 x^{2}+4 x-3\right)(3 x+1)$? A. $6 x^{3}+10 x^{2}-5 x+3$ B. $6 x^{3}+14 x^{2}+5 x-3$ C. $6 x^{3}+14 x^{2}-5 x-3$ D. $6 x^{3}-10 x^{2}-5 x-3$

Shown again is the table indicating the marital status of the U.S. population in 2010. Numbers in the table are expressed in millions. Use the data in the table to solve Exercises 1-10. Express probabilities as simplified fractions and as decimals rounded to the nearest hundredth. Marital Status of the U.S. Population, Ages 15 or Older, 2010, in Millions

If one person is randomly selected from the population described in the table, find the probability, expressed as a simplified fraction and as a decimal to the nearest hundredth, that the person among those women, find the probability of selecting a married person.

Using the Expression Mat, the value -3 can be shown in several ways, two of which are shown at right. Note that in these examples, the diagram on the left side uses negative tiles in the"+" region, while the diagram on the right side uses positive tiles in the"-" region. a. Build two different representations for $-2x$ using an Expression Mat. b. Similarly, build $3x-(-4)$. How many different ways can you build $3x-(-4)$?

Hal earns n dollars per hour. Next month he will receive a 2 percent raise in pay per hour The expression n+0.02n is one way to represent Hal's pay per hour after the raise. Write an equivalent simplified expression that will represent his pay per hour after the raise.

When simplified, which expressions would be equal to -1? Check all that apply. A. $\csc \theta \sin (-\theta)$ B. $\cos \theta \sec (-\theta)$ C. $\sin ^{2} \theta+\cos ^{2} \theta$ D. $\cot (-\theta) \tan \theta$ E. $\sec ^{2}(-\theta)-\tan ^{2}(-\theta)$

Jill is studying a strange bacteria. When she first looks at the bacteria, there are 1000 cells in her sample. The next day, it has doubled (there are 2000 cells). Intrigued, she comes back the next day to find that there are 4000 cells! Create multiple representations (table, graph, rule) of the function whose inputs are the days that have passed after she first began to study the sample and whose outputs are the number of cells of bacteria.

Reflect about what you have learned from today's lesson as you answer the following question in your Learning Log. Title this entry "Representing Expressions on an Expression Mat" and include today's date. Using an Expression Mat, find two different ways to represent $x - 1 - (2x - 3)$. Sketch the two different representations and write a few sentences to describe the differences in the ways you built each representation.

A circle with its center at (2, 4) passes through point (-1, -1). What is the area of the circle in simplified radical form?

$$\begin{array}{ll}{\text{ A. } 34 \pi} & {\text{ B. } \pi \sqrt{34}} \\ {\text{ C. } 2 \pi \sqrt{34}} & {\text{ D. } 68 \pi}\end{array}$$

The formula for the kinetic energy of a moving object is $E=\frac{1}{2} m v^2$, where $E$ is the kinetic energy in joules, $m$ is the mass in kilograms, and $v$ is the velocity in meters per second.

Find the velocity of an object whose mass is $0.6$ kilogram and whose kinetic energy is $54$ joules. Write as a simplified radical expression.

Note: Assume that all the functions have power series representations.

Use

$$\begin{aligned} f(x)&=\sum_{n=0}^{\infty}\frac{f^{(n)(c)}}{n!}(x-c)^n\\ &=f(c)+f'(c)(x-c)+\frac{f"(c)}{2!}(x-c)^2+\frac{f"'(c)}{3!}(x-c)^3+\cdots \end{aligned}$$

to find the Taylor series of $f$ at the given value of $c$. Then find the radius of convergence of the series.

$$f(x)=\cos x, \hspace{6pt}c=-\frac{\pi}{6}$$

Shown again is the table indicating the marital status of the U.S. population in 2010. Numbers in the table are expressed in millions. Use the data in the table to solve Exercises 1-10. Express probabilities as simplified fractions and as decimals rounded to the nearest hundredth. Marital Status of the U.S. Population, Ages 15 or Older, 2010, in Millions

If one person is randomly selected from the population described in the table, find the probability, expressed as a simplified fraction and as a decimal to the nearest hundredth, that the person among those who are divorced, find the probability of selecting a man.

Use the Pythagorean Theorem and the square root property to solve this exercise. Express answers in simplified radical form. Then find a decimal approximation to the nearest tenth.

A supporting wire is to be attached to the top of a $70$ -foot antenna. If the wire must be anchored $70$ feet from the base of the antenna, what length of wire is required?