1.4: The Protestant Reformation and Metrical Psalms
In this chapter you will
- explore the musical impact of the Protestant Reformation
- learn about the Bible and music in early colonial North America
- discover what meter is and how it allows the same words to be sung to different melodies
- create your own adaptation of a biblical text to a standard meter that can then be sung to a familiar tune
Do you know the first book printed in colonial North America ? It was a collection of psalms known as the Bay Psalm Book . This tells us something about the centrality of the Psalms in the Protestant worship that these European colonists engaged in. The book was a collection of metrical psalms, meaning that the biblical psalms were translated not merely from the original Hebrew into English but into English verses that followed a regular meter. Meter in this context means a regular pattern of numbers of syllables and rhythms. Meter is not just a number of syllables; it also has to do with where the emphasis falls in words. That is why even though the tune “Yankee Doodle” has the same number of syllables in each line as the melody you know as “Amazing Grace,” you cannot sing the words of one of them to the other melody and have it sound right and natural. The melody traditionally used for “Amazing Grace” is in what is known as common meter, so called because it was and is so widely used. It consists of groups of four lines that alternate between eight and six syllables. You may see this abbreviated in metrical psalm collections as CM (for common meter) or <IP_ADDRESS>, indicating the actual meter.
The slogan sola scriptura means “scripture alone.” This became a key slogan of the Protestant Reformation, emphasizing the Bible as ultimate (even if in practice never the only ) authority.
The fact that the Bay Psalm Book was the first book to be printed in the American colonies tells us something. So too does the fact that a printing press was set up at such an early point. These facts together highlight some important things one can learn about the Protestant Reformation at the intersection of the Bible and music. You definitely will want to explore these things further if you are interested in this topic, and just as there are many copies of and exhibits about the Bay Psalm Book online, there are many introductions to the Protestant Reformation . In this context, we can sum up a few major points. One is an emphasis on individual Christians reading the Bible. English translations of the Bible are so numerous and widespread, and the act of reading it so common, that it can be hard to imagine a world without those things. The printing press was a major innovation around the time of the Protestant Reformation that made it possible and dovetailed into its emphases. Just as individual Christians should, according to Protestants, take responsibility for reading and interpreting the Bible, so too worship became more participatory, with all believers having the same access to God in prayer without a need for other human mediators and everyone joining together in song. Put these emphases together, and the composition of singable songs derived from Scripture is a natural direction to take things. In the seventeenth century, the English Puritan minister Thomas Ford called the singing of psalms a “Christian duty.” [1]
The Bay Psalm Book is in the public domain (not surprising given its age), and so it can be read online in a variety of places , including Google Books . You will undoubtedly find aspects of such an old book difficult to read, but at least take a peek inside .
In order to adapt the psalms to a regular meter, it is inevitably necessary to paraphrase them at least somewhat. Some settings diverge more significantly from the source material than others. That’s the thing about translation and paraphrase: the one blurs into the other. No translation is without interpretation, and every genuine paraphrase remains connected to the meaning of the original. They represent a spectrum rather than two distinct and separate categories. Two settings by the famous hymnwriter Isaac Watts provide an example of how the same psalm might be rendered into metered English in two significantly different ways. Here are two renderings of Psalm 100 , which he calls a “plain translation” and a “paraphrase,” respectively.
Two Renderings of Psalm 100 in Metrical Form by Isaac Watts
Psalm 100. A Plain Translation
Ye nations round the earth, rejoice
Before the Lord, your sovereign King;
Serve him with cheerful heart and voice,
With all your tongues his glory sing.The Lord is God; ’tis he alone
Doth life, and breath, and being give;
We are his work, and not our own,
The sheep that on his pastures live.Enter his gates with songs of joy,
With praises to his courts repair;
And make it your divine employ
To pay your thanks and honors there.The Lord is good, the Lord is kind,
Great is his grace, his mercy sure;
And the whole race of man shall find
His truth from age to age endure.
Psalm 100. A Paraphrase
Sing to the Lord with joyful voice,
Let every land his name adore;
The British isles shall send the noise
Across the ocean to the shore.Nations, attend before his throne
With solemn fear, with sacred joy;
Know that the Lord is God alone;
He can create and he destroy.His sovereign power, without our aid,
Made us of clay and formed us men;
And when, like wand’ring sheep, we strayed,
He brought us to his fold again.We are his people, we his care,
Our souls and all our mortal frame:
What lasting honors shall we rear,
Almighty Maker, to thy name?We’ll crowd thy gates with thankful songs,
High as the heav’ns our voices raise;
And earth with her ten thousand tongues
Shall fill thy courts with sounding praise.Wide as the world is thy command,
Vast as eternity thy love!
Firm as a rock thy truth must stand,
When rolling years shall cease to move.
Another famous setting of Psalm 100 has become known as “Old Hundredth” because it is one of the very early metrical settings of Psalm 100 (written by Louis Bourgeois in Geneva for use in Reformer John Calvin’s church), and its melody continues to be used to this day. There are many recordings of the psalm, including instrumental ones that you can sing along with . Here is a recording by the Harvard University Choir, conducted by Edward Elwyn. [2] The choir is accompanied by organ, which is how you will often hear it performed as well as sung in churches.
You will also find that some of these melodies have been arranged by famous composers (in this case, Ralph Vaughan Williams is an example) and that others may appear woven into other musical works. That’s not something we’ll explore here, but you may wish to if you haven’t had enough of this music or want to see how it has been influential beyond the boundaries of religious communities. In at least one famous instance, a melody originally composed for use with metrical psalms has become more closely associated with other words: many know the tune “Old Hundreth” as the music to which they sing words known as the “Doxology.” [3]
Some Reformed/Presbyterian churches practice exclusive psalmody, meaning they consider Psalms to be the only biblically authorized words for Christians to sing in worship.
Next you should try to participate in the singing and then the creation of metrical psalms yourself. Begin by singing along with some metrical psalms where the words and music are provided. Eventually, try adapting words from the Bible to a melody that you like, but start by finding a metrical psalm that already exists with words you like and then see if you can find a melody that suits it. Below I suggest some pairings of what may be familiar melodies with metrical psalms, but my musical tastes may not be yours, so look for ones that make sense for you. You can often find an instrumental karaoke track on YouTube to sing along with! Here are some suggestions:
Psalm 2 to the melody of “America the Beautiful”
Psalm 42 to the tune of the Gilligan’s Island theme
Psalm 113 to the melody of “House of the Rising Sun”
There are lots of different melodies that you already know that have a regular meter and thus to which it will be straightforward to sing any number of metrical psalms. There are free metrical psalm lyrics online , many being in the public domain, such as the Scottish Metrical Psalter of 1650 . Metrical psalms also continue to be created, and there are recently published compilations that can be purchased. What happens when you sing an arrangement of a psalm to a tune you already know? What is the experience like? How does doing this influence your perception of the words and the music? Compare several different metrical arrangements of the same psalm. How do they convey the meaning of the original psalm in different ways? How much do they differ, and how much remains the same despite those differences?
For the record, the first printed book that we know for certain was published in the Americas was printed in Mexico . There is also very interesting early music from that era reflecting the Catholic tradition of the Spanish colonizers that draws on the Bible and more specifically the Psalms, with Hernando Franco’s “Circumdederunt Me” as one of the very first. Here is a performance by the Coro Melos Gloriae, conducted by Juan Manuel Lara Cárdena. [4]
For Further Reading
Anderson, Fred R. Singing God’s Psalms . Grand Rapids: Eerdmans, 2016.
Bertoglio, Chiara. Reforming Music: Music and the Religious Reformations of the Sixteenth Century . Berlin: De Gruyter, 2017.
Duguid, Timothy. “Early Modern Scottish Metrical Psalmody: Origins and Practice.” Yale Journal of Music Religion 7, no. 1 (2021): 1–23.
Marín, Javier. “Hernando Franco’s Circumdederunt me: The First Piece for the Dead in Early Colonial America.” Sacred Music 135, no. 2 (2008): 58–64.
Stowe, David Ware. How Sweet the Sound: Music in the Spiritual Lives of Americans . Cambridge, MA: Harvard University Press, 2004.
Tierno, Alanna Ropchock. “The Lutheran Identity of Josquin’s Missa Pange Lingua: Renaissance of a Renaissance Mass.” Early Music History 36 (2017): 193–249.
- Thomas Ford, Singing of Psalmes the duty of Christians under the New Testament, or a vindication of that Gospel ordinance in V. sermons upon Ephesians 5. 19 (London: W. B., 1659). ↵
- The recording is shared by Memorial Church Harvard on their YouTube channel. ↵
- For those familiar with it or interested, the origins of the words for the Doxology can be traced to the hymnwriting career of Thomas Ken. ↵
- Shared by Enrique Guerrero on his Early Latin American Music YouTube channel. ↵


1.17: Putting It Together- Science of Geology
Summary
In this section, you learned the following:
- The extensive definition of geology
- The various fields within geology and what they study
- How scientists use the scientific method to answer questions
Synthesis
While we have not thoroughly answered our questions from the beginning of the outcome, we should be able to understand the connection these questions have to geology. We now know that geology is more than rocks—it deals with the resources we use in our everyday life, and it explains why some areas are more tectonically active than others. As we move through the course, keep these questions in mind.
So let’s get started on this course and see why geology rocks .
Contributors and Attributions
CC licensed content, Original
- Authored by : Kimberly Schulte. Provided by : Columbia Basin College. Located at : https://www.columbiabasin.edu/ . License : CC BY: Attribution


10.3: References
- Math in Society: A survey of mathematics for the liberal arts major by David Lippman, Chapter on Logic
- LibreTexts Mathematics for Elementary School Teachers: Problem Solving Strategies
- Math in Society: A survey of mathematics for the liberal arts major by David Lippman, Chapter on Problem Solving
- Varsity Tutors’ webpage on Really Big and Really Small Numbers
- Math in Society: A survey of mathematics for the liberal arts major by David Lippman, Chapter on Finance
- Dr. Fisher Burns’ webpage on Continuous Compounding
- Lumenlearning Macroeconomics: Federal Budgets and National Debt
- Math in Society: A survey of mathematics for the liberal arts major by David Lippman, Chapter on Probability
- Field Epidemiology Manual: Odds , by Alain Moren, Marta Valenciano, & Arnold Bosman
- Math in Society: A survey of mathematics for the liberal arts major by David Lippman, Chapter on Statistics
- Math in Society: A survey of mathematics for the liberal arts major by David Lippman, Chapter on Describing Data
- CK-12: The z-Score and the Central Limit Theorem
- Math in Society: A survey of mathematics for the liberal arts major by David Lippman, Chapter on Growth Models
- Lumenlearning Algebra and Trigonometry: Logarithmic Functions
- Opentextbc Introductory Chemistry Chapter on The pH Scale by Jessie A. Key
- Wikibooks’ Webpage on Projective Geometry
- Simple English Wikipedia’s pages on the Golden Ratio/ Fibonacci number
- Math in Society: A survey of mathematics for the liberal arts major by David Lippman, Chapter on Fractals
- Math in Society: A survey of mathematics for the liberal arts major by David Lippman, Chapter on Apportionment
- Math in Society: A survey of mathematics for the liberal arts major by David Lippman, Chapter on Voting Theory
- Math in Society: A survey of mathematics for the liberal arts major by David Lippman, Chapter on Weighted Voting
- simple.Wikipedia.org/wiki/Four_color_theorem
- simple.Wikipedia.org/wiki/Seven_Bridges_of_K%C3%B6nigsberg
Contributors and Attributions
-
Saburo Matsumoto
CC-BY-4.0


7.3: Howard Gardner’s Theory of Multiple Intelligences
-
- Last updated
- Save as PDF
Another champion of the idea of specific types of intelligences rather than one overall intelligence is the psychologist Howard Gardner (1983, 1999). Gardner argued that it would be evolutionarily functional for different people to have different talents and skills, and proposed that there are nine intelligences that can be differentiated from each other.
Gardner contends that these are also forms of intelligence. A high IQ does not always ensure success in life or necessarily indicate that a person has common sense, good interpersonal skills, or other abilities important for success. Gardner investigated intelligences by focusing on children who were talented in one or more areas. He identified these 9 intelligences based on other criteria including a set developmental history and psychometric findings.26
Howard Gardner (1983, 1998, 1999) suggests that there are not one, but nine domains of intelligence. The first three are skills that are measured by IQ tests:
| Intelligence | Description |
|---|---|
| Linguistic | The ability to speak and write well |
| Logical- mathematical | The ability to use logic and mathematical skills to solve problems |
| Spatial | The ability to think and reason about objects in three dimensions |
| Musical | The ability to perform and enjoy music |
| Kinesthetic (body) | The ability to move the body in sports, dance, or other physical activities |
| Interpersonal | The ability to understand and interact effectively with others |
| Intrapersonal | The ability to have insight into the self |
| Naturalistic |
The ability to recognize, identify, and understand animals, plants, and other living things |
| Existential | The ability to understand and have concern from life’s larger questions, the meaning of life, and other spiritual matters |
The concept of multiple intelligences has been influential in the field of education, and teachers have used these ideas to try to teach differently for individual students. For instance, to teach math problems to students who have particularly good kinesthetic intelligence, a teacher might encourage the students to move their bodies or hands according to the numbers. On the other hand, some have argued that these “intelligences” sometimes seem more like “abilities” or “talents” rather than real intelligence. There is no clear conclusion about how many intelligences there are. Are a sense of humor, artistic skills, dramatic skills, and so forth also separate intelligences?28
Contributors and Attributions
26. Lifespan Development: A Psychological Perspective by Martha Lally and Suzanne Valentine-French is licensed under CC BY-NC-SA 3.0
28. Lifespan Development: A Psychological Perspective by Martha Lally and Suzanne Valentine-French is licensed under CC BY-NC-SA 3.0


14.11: California’s Demographics and Spatial Patterns
The spatial distribution of a population and development are closely related to each other, especially in the context of sustainability. The challenges related to the spatial spread of a population include rapid urbanization and population concentration, rural population, urban management and poverty housing, displaced persons and refugees. Migration is a basic element in the spatial distribution of a population, and it may remain a key driver in the coming decades, especially as an element of urbanization in developing countries.
Languages
As of 2023, over 78% of California residents age 5 and older spoke English at home as a primary language. Many California residents also speak another language, such as Spanish (61%), Chinese, which includes Cantonese and Mandarin (48%), and many others (Tagalog, Vietnamese, Korean, Armenian, and Persian).
Comparatively, according to the 2007 American Community Survey, 42.6 percent of California's population older than five spoke a language other than English at home, with 73 percent of those also speaking English well or very well, while 9.8 did not speak English at all.
California had the highest concentration of Vietnamese or Chinese speakers in the United States, second highest concentration of Korean or Spanish speakers in the United States, and third highest concentration of Tagalog speakers in the United States. California was historically one of the most linguistically diverse areas in the world and is home to more than 70 indigenous languages derived from 64 root languages in 6 language families. A survey conducted between 2007 and 2009 identified 23 different indigenous languages of Mexico that are spoken among California farmworkers.
Over 200 languages are known to be spoken and read in California, with Spanish used as the state's "alternative" language. California has more than 100 indigenous languages, making California one of the most linguistically diverse areas in the world. All of California's indigenous languages are endangered, although there are now efforts toward language revitalization.
The official language of California has been English since the passage of Proposition 63 in 1986. However, many state, city, and local government agencies continue to print official public documents in numerous languages. For example, the California Department of Motor Vehicles offers the written exam for the standard C Class driver's license in 31 languages along with English, and the audio exam in 11 languages. The politics of language is a major political issue in the state, especially regarding language policy controlling the teaching and official use of immigrant languages.
As a result of the state's increasing diversity and migration from other areas across the country and around the globe, linguists began noticing a noteworthy set of emerging characteristics of spoken English in California since the late 20th century. This dialect, known as California English, has a vowel shift and several other phonological processes that are different from the dialects used in other regions of the country.
LGBTQA+ Communities
California is seen as one of the most liberal states in the U.S. regarding lesbian, gay, bisexual, transgender (LGBT) rights, which have received nationwide recognition since the 1970s. Same-sex sexual activity has been legal in the state since 1976.  Transgender people are also permitted to change their legal gender on official documents without any medical interventions, and mental health providers are prohibited from engaging in conversion therapy on minors.
California became the first state in the U.S. to legalize domestic partnerships between same-sex couples in 1999. Same-sex marriage was legalized in 2008 for five months until voters approved a ban in November of the same year. After the U.S. Supreme Court refused to recognize the legal standing of same-sex marriage opponents on June 26, 2013, the ban was no longer enforceable, allowing same-sex marriages to recommence starting on June 28. Same-sex adoption has also been legal statewide since 2003, permitting stepchild adoption and joint adoption between same-sex couples.
In 2014, California became the first state in the U.S. to officially ban the use of gay panic and transgender panic defenses in murder trials. Public schools are also teaching about the history of the LGBTQ+ community, and transgender students can choose the appropriate restroom or sports team that match their gender identity. Most support for LGBTQ+ rights can be seen in the largest cities, such as Los Angeles, San Diego, and San Francisco, as well as many cities on the Pacific coast. A 2017 survey from the Public Religion Research Institute showed that 66% of Californians supported same-sex marriage. Since November 2022, 10% of the individuals within the California Legislature are LGBTQ+ members immediately after the elections - a record first for the United States. Modern diversity includes persons who are lesbian, gay, bisexual, and transgendered (“LGBT”). Del Martin and Phyllis Lyon met in 1949 in San Francisco.
Case Study - Indigenous Peoples of California & LGBTQ+
Prior to European settlement and colonization in the 18th century, many Native American groups in California recognized a "third gender" role in their societies. These individuals, who were often referred to as "two-spirit," were not strictly male or female. They might take on the roles and responsibilities of both genders, and they were often respected and valued members of their communities.
Some of the terms used to refer to third gender individuals in California include:
- Tüdayapi (Northern Paiute)
- 'Aqi (Chumash)
- Wergern (Yurok)
- Í-wa-musp (Yuki)
- Brumaiwi (Astugewi)
- Musp-íwap náip (Yuki)
- T'winiːq (Klamath and Modoc)
- Tonoo'tcim (Kings River Yokuts)
This acceptance of third gender individuals is a testament to the cultural diversity and openness of Native American societies in California. It is a reminder that there is no one right way to be a man or a woman, and that gender is a spectrum.
Religion
California is a diverse state with a wide range of religious beliefs. The largest Christian denominations in California are the Catholic Church, the Church of Jesus Christ of Latter-day Saints, and the Southern Baptist Convention. California also has a large Jewish population, as well as significant populations of Hindus, Buddhists, and Muslims.
The Catholic Church is the largest religious denomination in California, with over 10 million adherents. Most California Catholics are of Mexican, Central American, Irish, German, Italian, Vietnamese, Filipino, or Korean ancestry. The Catholic Church in California is organized into 12 archdioceses and 47 dioceses.
The Church of Jesus Christ of Latter-day Saints is the second-largest religious denomination in California, with over 500,000 adherents. The Latter-day Saints have played an important role in the settlement of California, and they have a significant presence in the state's history. The church's headquarters are in Salt Lake City, Utah, but it has a large presence in California, with over 1,400 congregations statewide.
The Southern Baptist Convention is the third-largest religious denomination in California, with over 400,000 adherents. The Southern Baptist Convention is a Protestant denomination that was founded in 1845. It is the largest Protestant denomination in the United States.
There is also a large Jewish population in the state, with over 1 million adherents. Most California Jews are of Ashkenazi Jewish ancestry, but there is also a significant Sephardic Jewish population. The Jewish community in California is concentrated in the Los Angeles area, but there are also significant Jewish communities in San Francisco, San Diego, and other parts of the state.
California has a growing Hindu population, with over 750,000 adherents. Most California Hindus are of Indian ancestry, but there is also a significant Sri Lankan Hindu population. The Hindu community in California is concentrated in the Los Angeles area, but there are also significant Hindu communities in the San Francisco Bay Area and other parts of the state.
California also has a growing Buddhist population, with over 600,000 adherents. Most California Buddhists are of Asian ancestry, but there is also a growing non-Asian Buddhist population. The Buddhist community in California is concentrated in the Los Angeles area, but there are also significant Buddhist communities in the San Francisco Bay Area and other parts of the state.
In addition to the major religious groups mentioned above, California is also home to several smaller religious groups, including Muslims, Sikhs, Jains, and Baha'is. The state also has a growing number of people who identify as non-religious or atheist.
A Pew Research Center survey revealed that California is less religious than the rest of the United States. The survey found that 62% of Californians say they are "absolutely certain" of the belief "in God or a universal spirit," while in the nation 71% say so. The survey also found that 48% of Californians say religion is "very important," while the figure for the U.S. in general is 56%.
California is a diverse state with a wide range of religious beliefs. The state's religious landscape is constantly changing, as new immigrants bring their faiths to California. The state's religious diversity is one of its many strengths, and it contributes to the state's rich cultural heritage.
Socioeconomic Factors
California's income distribution is quite broad compared to the country’s as a whole. Its proportions of residents with no income and of residents with income over $100,000 are both higher than the national average. This broad distribution combined with high housing and living costs give California an abnormally high poverty rate. The Census Bureau's Supplemental Poverty Measure, calculated by comparing household income to a locally adjusted poverty threshold, reports that 20.7% of California's population has income insufficient for their basic needs, as compared to 12.9% for the U.S. This calculation of income includes the benefits of California welfare programs such as food stamps and earned income tax credits — without these, the state's poverty rate would be 28%.
Increasing income inequality has had many effects on Californians' lives, including on life expectancy, which can be taken as a proxy for health or even general welfare. A study conducted by Clarke et al. related life expectancy to socioeconomic status (SES, an index including income and other related factors), finding that Californians in the top 20% by SES live on average six years longer than those in the bottom 20% (81 years, compared to 75). This disparity becomes even more pronounced when intersected with race: White males in the top 20% live 14 years longer than African American males in the bottom 20% (for females, the difference is 10 years).
The complexity of the state's low-income trends were visible when, in response to growing Chinese and Spanish-speaking populations, the city of Oakland implemented the nation's first policy of recruiting bilingual applicants for public-facing city jobs in 2001. This increased the employment of Hispanic and Chinese bilinguals throughout the public workforce, but also lowered (monolingual) Black employment.


12.1: Introduction
-
- Last updated
- Save as PDF
Learning outcomes
- Identify the important characteristics of an online course outline.
- Use sound principles to articulate an online course for transfer credit.
- Minimize transfer difficulties for students who take online courses.
As the quote from Dr. Adelman illustrates, students are mobile. They move between post-secondary institutions, carrying their accumulated credits with them in the expectation that the learning they have acquired will be acknowledged by the next institution they attend, that they will receive appropriate transfer credit for relevant courses they have taken and be able to apply that credit to fulfill program requirements. Formal transfer systems have been a feature of the higher education landscape for at least 50 years in North America, and are rapidly developing in Europe (though the European Credit Transfer System) and elsewhere. Online learning has had a significant impact on mobility and transfer: students can and do access high quality courses from all over the world, and deserve to be awarded transfer credit for their learning, where it fits with their educational program.
In any post-secondary environment where transfer of credits is permitted and encouraged, transfer credit is based on course equivalency. Within a provincial, state or national transfer system, course-to-course transfer credit is often established as soon as a new course is developed, in advance of any student enrolling. The process begins when the sending institution submits a course to the receiving institution, with a request that the receiving institution assess the course for equivalence to one of its own courses. Once that assessment has taken place, and transfer credit awarded, a course is said to be “articulated.” For example, a college course on the Sociology of the Family, Soci 220, may be assessed as equivalent to a university course called The Modern Family with the number Soc 235. Or, there may be no direct equivalent at the university, and the transfer credit awarded might be for “three credits in second year sociology”. The transfer credit is listed in the institution’s database, and students know in advance what credit they will receive after transfer for the sociology course they have taken.
In some jurisdictions higher level articulation agreements are often negotiated, such as 2+2 agreements (associate degree to degree, diploma to degree) or agreements about the general education curriculum. Such agreements can be local or statewide but the principle at the heart of the transaction remains the same: transfer is awarded when an assessment of the curriculum, program or courses at the sending institution reveals an appropriate match with that at the receiving institution. The other common way in which transfer credit is assigned is on the basis of a student request: the student presents a transcript, and an analysis is conducted of the equivalence of the courses he or she has taken to those in the institution to which he or she is transferring. Such case-by-case assessments may remain one-off, but may also result in formal or recorded articulation agreements.
Articulation, then, is a process of jointing two or more elements, to allow them to function as a coherent whole (as the femur is articulated with the tibia to form the main structure of the leg) and through this process students can move from institution to institution while maintaining a sound educational program and working towards their chosen credential. Articulation agreements, whether course-to-course or higher level, have traditionally been negotiated locally, either between a university and its nearest feeder institutions, or within a state or provincial transfer system in which institutions are familiar to each other, and relationships and infrastructure are developed to support the transfer environment. They have also predominantly been concerned with the assessment of courses offered in the traditional and familiar face-to-face classroom environment.
Increasingly, however, institutions are being asked to assess the equivalence of courses taught in online formats. Herein lies a central dilemma for a transfer environment—transfer systems are organized locally, but online education is developed and delivered globally.
Faculty who assess online courses may be faced with several challenges: the time available for the task, the level of information available about the course and the institution delivering it, their own understanding of the norms of an online environment, their own commitment to online learning, and their institution’s policy regarding the acceptability of online courses or regarding the accreditation status of the sending institution.
Even within an integrated post-secondary environment characterized by open and transparent articulation relationship, faculty frequently raise the question of whether mode of delivery can affect, or should affect, the articulation of a course. For example, in British Columbia, faculty members from each institution in the BC Transfer System meet every year in discipline-based groups, known as Articulation Committees. These committees operate under the aegis of the British Columbia Council on Admissions and Transfer (BCCAT). Meeting minutes collected by BCCAT reveal that the articulation of online courses is often debated (BCCAT 2005). Issues and concerns are varied:
- Many groups are enthusiastic about converting their curriculum to online delivery formats, and see this mode of delivery as attractive to potential students
- Concerns are raised about quality control, and about assessment methods used in online courses and how student evaluation is safeguarded and authenticated
- Some faculty worry about the use of online delivery for students who need intrinsic motivation, structure and an encouraging classroom atmosphere, especially academically fragile students in developmental programs
- Faculty query how lab, field work, practica, and other non-classroom experiences can best be organized in online courses.
Where such discussions become problematic is where, in the absence of reliable information and processes for assessing equivalence, faculty and administrators with concerns about online learning deny transfer credit to students who have successfully completed online courses.
In some cases, the accreditation of the institution delivering the online courses is cited as the reason for denying transfer credit. In this scenario, the courses are often not assessed. Rather, credit is denied on the basis of where the course was taken, regardless of its quality or content. Carnevale (2002) outlines the “rude surprise” awaiting students who try to transfer such courses.
Concerns will always exist about the quality of some deliverers of courses and programs, including online courses. However, for legitimate institutions and their students, it is vital that evaluators can rely on excellent information about the online courses and can call on sound principles and processes to evaluate them for transfer credit. In this transaction, both deliverer and evaluators have parts to play. The ultimate beneficiaries of a sound articulation process, however, are the students, who can be assured that their learning will be appropriately recognized. All articulation should, after all, support the fundamental principles of equity on which an articulation environment is built: that students should not have to repeat content which they have already mastered, nor be denied credit because of technicalities. Nor should they be credited with learning they have not acquired, especially if that learning is fundamental to their advancement to further study, or a required element of their program (Finlay 2005, p. 7).
Many jurisdictions and organizations publish “best practice” statements for online education. For a good example see the Commission on Institutions of Higher Education (CIHE, no date) Best Practices for Electronically Offered Degree and Certificate Programs. Others provide sets of guidelines exhorting their members to be fair and reasonable. However, most of these documents provide little guidance as to what “fair and reasonable” actually looks like in practice. Few resources exist that will assist practitioners at sending institutions to ensure the successful articulation of their online courses, and give the assessors at receiving institutions the tools they need to make confident decisions. This chapter aims to fill that gap.


8.7: Reading- Implementing Positioning Strategy
Putting Positioning into Practice
The positioning strategy, embodied in a strong positioning statement, is a touchstone for marketing and brand-building activities as marketers work to align everything they do in support of this core idea. In simple terms this means aligning the positioning strategy with the marketing mix.
Positioning statements provide a relatively easy way to check whether some aspect of the marketing mix is on target or off target: if a particular marketing message or activity reinforces the positioning statement, it’s probably consistent with your goals for reaching a target segment. If a marketing activity doesn’t reinforce the positioning statement, it will probably create some confusion among customers about what your product, service, or brand stands for.
What does this mean in practice?
As you consider what you’re doing in each area of the marketing mix, think about what your positioning statement is communicating to customers. Then ask yourself how each part of the marketing mix is helping you deliver on the expectations you are setting with those customers.
- Product: Is your product, service, or brand capable of delivering everything your positioning statement claims? Are any competitors doing it better than you? How should you adjust your offering to ensure that it lives up to the promises?
- Price: When it comes to pricing, how are you positioning your offering relative to competitors? If pricing is part of your positioning strategy, is your offering well aligned with the price you’re asking customers to pay? What pricing strategies should you consider in order to compete more effectively? (More on this in the Pricing module.)
- Place (Distribution): Are any distribution-related themes like convenience or availability part of your positioning strategy or competitive advantage? If so, what are you doing to ensure that you can live up to what you promise? How are you communicating your new positioning approach to distribution and channel partners, and how does it impact them? (More on this in the Place module)
- Promotion: How are you translating your positioning strategy into messaging and actual communications with your target audiences? What behavioral shift are you trying to create as you launch your new positioning? Where and how do you need to alter existing materials to make them consistent with the new positioning (e.g., Web site, print, ads, social media, marketing content, sponsorships, events, etc.)? What types of campaigns will you use to introduce the new positioning? Which communication tools will be most effective at reaching target audiences, and what are you doing to coordinate marketing messages and activities across different channels? (Much much more to come in this area in the Promotion: Integrated Marketing Communications module.)
Persistence Pays
Implementing a new positioning or repositioning strategy is not a simple task. It takes time and effort to bring all the pieces together, to update the old and create the new. Implementing a positioning strategy resembles turning a ship: At first the maneuver is slow and deliberate. But once you’ve turned and charted the new direction, momentum picks up.
 Depending on your goals and implementation activities, what you measure can vary, but may include one or more of the following:
- Sales/revenue
- Number of new/returning customers
- Average spending per transaction
- Brand/product awareness or perceptions
- Favorability toward product/service/brand
- New leads or inquiries from inside and outside your target segments
- Web site traffic
- Social media “buzz”
- Media attention
- Customer satisfaction
- Return on investment for marketing campaigns and other activities
Above all, don’t forget to check in with customers directly to monitor how they are responding to the new positioning efforts. In all likelihood, there are things that will work and things that won’t work as you introduce the new direction. Having a direct line to customers for constructive feedback and recommendations can help you identify potential improvements and adjust course early to strengthen your impact and results.
Before leaving the topic of implementing positioning, another application of positioning strategy deserves attention. For large, complex organizations that have many products and serve many different markets and customer types, effective positioning is crucial. It’s the only way to ensure that the organization can deliver a coherent message and unique value to each target segment.
What does this look like in practice? Let’s examine how the electronic security company Tyco Integrated Security (TycoIS) uses positioning.
Tyco Integrated Security is a B2B company that sells electronic security products, installation, and services in the U.S. and Canada. They recently merged with Johnson Controls. TycoIS produces a variety of security-related products and services that can be used across many different industries and sizes of companies. When you think about the security-related needs of different kinds of businesses, you realize that their needs vary widely.  Large companies have extremely complex needs around physical, financial, personnel, supply chain, and information security. Needs also differ by industry. For instance, companies in the food business are concerned about food safety, handling, protection, and complying with regulations and inspections in order to stay in business. Most other industries have similarly specialized needs.
Company-Level Positioning
TycoIS must communicate at several different levels in order to convince people that it’s the right partner for their business. Operating at the highest level, company-to-company, the following statement explains TycoIS’s company-level positioning:
We help companies protect their employees, customers, facilities, and operations from internal and external threats, and allow business to work smarter through enhanced security management and information management solutions. [1]
This positioning statement from the company’s Web site fits our positioning formula quite nicely, except for one thing: the defined target segment is “companies.” Is it possible to market anything effectively to all companies everywhere? No. This target is too broad. But it is a great starting point for businesspeople looking for security systems; it encourages them to delve deeper.
Two-Tiered Segmentation
To divide up “all companies” into manageable chunks for marketing purposes, TycoIS uses two different segmentation schema at the same time: segmentation by 1) organization size and 2) industry. Figure 1, below, illustrates how Tyco mixes these schema together:
Given the separate messaging for each business size, it’s clear that TycoIS has developed positioning around three unique market segments: small businesses, medium-sized businesses, and large enterprises.
The “Small Business” positioning uses a tone of personal reassurance: “We’re right here with you.” And, going a level deeper, “We offer affordable products and services to help you, as a small business owner, protect your investment.”
The “Medium Business” positioning mentions “industry-leading” solutions—a term that resonates with these organizations, which are striving to grow and become leaders. The “Enterprise” positioning emphasizes TycoIS expertise working at the global, national, and regional level. It also offers to “help enhance” security and business intelligence, rather than “provide” them. This subtle wording is wise: large, enterprise organizations tend to have a lot of legacy infrastructure and processes already in place, as well as in-house security expertise. With this positioning, TycoIS suggests that it will be an expert, helpful partner to complement and strengthen the security large companies already have.
Industry-Specific Positioning
Within each business-size segment, TycoIS has identified the common types of industries it works with. For each of these industries, TycoIS has unique positioning to convey that 1) we speak your language, 2) we understand your needs, and 3) we have a great combination of solutions just for you.
Figure 2, above, illustrates how TycoIS positions its offering for medium-sized businesses in the restaurant and entertainment industry. For this target segment, the company clarifies the category of security solutions it offers: physical security, theft protection, food inventory and protection for restaurants, nightclubs, and other entertainment venues. The messaging highlights TycoIS’s competitive advantage of offering industry-specific security specialists and business insights—on top of all the systems and gadgets it provides.
This detailed, industry-specific positioning flows across each of the company-size segments, and it effectively communicates the following: “Regardless of your company size or industry, TycoIS has relevant experience and familiarity with your security challenges and needs.” On the company’s Web site, it is easy to browse the matrix of company types and industries to find the area that matches your business. Then, as you dig deeper, TycoIS’s attention to target-segment positioning ensures that you will find information that speaks to your unique needs.
It’s mind-boggling to imagine all the positioning-strategy and messaging work that has gone into this type of marketing effort. In all, TycoIS actively targets 35+ different business segments! Not every organization needs this kind of detailed targeting and positioning schema. But many organizations, ones smaller and larger than TycoIS, find that this highly targeted use of positioning strategy is an effective way to do business and support their ongoing focus on customer needs.
- www.tycois.com/ ↵
Contributors and Attributions
- Implementing Positioning Strategy. Authored by : Lumen Learning. License : CC BY: Attribution
- Screenshot of Tyco Solutions by Industry. Provided by : TycoIS. Located at : www.tycois.com/. License : All Rights Reserved . License Terms : Fair Use
- Screenshot of Tyco Restaurants and Entertainment. Provided by : TycoIS. Located at : www.tycois.com/. License : All Rights Reserved . License Terms : Fair Use


12.4E: Rotation of Axes (Exercises)
For the following exercises, determine which of the conic sections is represented.
33. \(16 x^{2}+24 x y+9 y^{2}+24 x-60 y-60=0\)
34. \(4 x^{2}+14 x y+5 y^{2}+18 x-6 y+30=0\)
35. \(4 x^{2}+x y+2 y^{2}+8 x-26 y+9=0\)
For the following exercises, determine the angle \(\theta\) that will eliminate the \(x y\) term, and write the corresponding equation without the \(x y\) term.
36. \(x^{2}+4 x y-2 y^{2}-6=0\)
37. \(x^{2}-x y+y^{2}-6=0\)
For the following exercises, graph the equation relative to the \(x^{\prime} y^{\prime}\) system in which the equation has no \(x^{\prime} y^{\prime}\) term.
38. \(9 x^{2}-24 x y+16 y^{2}-80 x-60 y+100=0\)
39. \(x^{2}-x y+y^{2}-2=0\)
40. \(6 x^{2}+24 x y-y^{2}-12 x+26 y+11=0\)


8.3.7: The Statement of Cash Flows
Why is the Statement of Cash Flows an Important Source of Information?
Net profit or loss is one measure of a company’s financial performance. However, creditors and investors are also keenly interested in how much cash a business generates and how it is used. The statement of cash flows , a summary of the money flowing into and out of a firm, is the financial statement used to assess the sources and uses of cash during a certain period, typically one year. All publicly traded firms must include a statement of cash flows in their financial reports to shareholders. The statement of cash flows tracks the firm’s cash receipts and cash payments. It gives financial managers and analysts a way to identify cash flow problems and assess the firm’s financial viability.
Using income statement and balance sheet data, the statement of cash flows divides the firm’s cash flows into three groups:
- Cash flow from operating activities: Those related to the production of the firm’s goods or services
- Cash flow from investment activities: Those related to the purchase and sale of fixed assets
- Cash flow from financing activities: Those related to debt and equity financing
Delicious Desserts’ statement of cash flows for 2018 is presented in the table below. It shows that the company’s cash and marketable securities have increased over the last year. And during the year the company generated enough cash flow to increase inventory and fixed assets and to reduce accounts payable, accruals, notes payable, and long-term debt.
| Statement of Cash Flows for Delicious Desserts, Inc. for 2018 | ||
|---|---|---|
| Cash Flow from Operating Activities | ||
| Net profit after taxes | $27,175 | |
| Depreciation | 1,500 | |
| Decrease in accounts receivable | 3,140 | |
| Increase in inventory | (4,500) | |
| Decrease in accounts payable | (2,065) | |
| Decrease in accruals | (1,035) | |
| Cash provided by operating activities | $24,215 | |
| Cash Flow from Investment Activities | ||
| Increase in gross fixed assets | ($ 5,000) | |
| Cash used in investment activities | ($5,000) | |
| Cash Flow from Financing Activities | ||
| Decrease in notes payable | ($ 3,000) | |
| Decrease in long-term debt | (1,000) | |
| Cash used by financing activities | ($4,000) | |
| Net increase in cash and marketable securities | $15,215 |
CONCEPT CHECK
- What is the purpose of the statement of cash flows?
- Why has cash flow become such an important measure of a firm’s financial condition?
- What situations can you cite from the chapter that support your answer?


10.10: Equal Pay Act of 1963
- Discuss the Equal Pay Act of 1963
In the early 1900s, women comprised less than a quarter of the workforce. However, when men joined the military to fight in World War II, women were recruited to take their place and by 1945, 37% of the civilian workforce was female. Since women had traditionally earned less for doing similar work, unions and male workers feared that this growing source of cheap labor would lower their wages. In order to avoid future wage cuts, unions started to advocate for equal pay.
In 1942, the National War Labor Board also endorsed the idea of equal pay for equal work, issuing a “General Order supporting equal pay for men and women for work that was of ‘comparable quality and quantity.’” [1] Over two decades later, the Equal Pay Act of 1963 (EPA) was enacted as an amendment to the Fair Labor Standards Act of 1938. [2]
For perspective on the intervening years, see the Equal Pay Act write-up on the National Park Service’s website.
To quote from the U.S. Equal Employment Opportunity Commission site: “The Equal Pay Act requires that men and women be given equal pay for equal work in the same establishment. The jobs need not be identical, but they must be substantially equal. It is job content, not job titles, that determines whether jobs are substantially equal.”
Specifically, the EPA requires that employers cannot compensation men and women differently when they “perform jobs that require substantially an equal level of skill, effort and responsibility and when those jobs are performed under similar working conditions within the same establishment.” Permitted pay differentials include those based on seniority, merit, quantity or quality of production, or other non-gender based factors. These factors are referred to as “affirmative defenses”; the employer has the burden of proving that their stated rationale applies. Finally, pay differentials can only be corrected with an increase; no employee’s pay may be reduced.
EPA Violations
In EPA cases, the burden of proof is on the plaintiff. In Gordon v. U.S., the court held that “To state a claim of an EPA violation, an employee must show the employer: [3]
- Paid employees of opposite sexes different wages;
- For substantially equal work;
- In jobs that require substantially equal skill, effort, and responsibility; and
- That are performed under similar working conditions.
Once those elements have been established, “the burden shifts to the employer to prove the pay disparity is justified under one of four affirmative defenses: (1) a seniority system; (2) a merit system; (3) a pay system based on quantity or quality of output; or (4) any factor other than sex.”
-
"
Equal Pay Act of 1963
." National Park Service. April 01, 2016. Accessed August 22, 2019. ↵
-
Fugiero, Melissa. "Equal Pay Act of 1963."
Encyclopedia Britannica. Accessed August 22, 2019. ↵
-
Chrisbens, F. Christopher. "
Equal Pay Act Claim Requires Show of Pay Disparity "Based on Sex
" as Part of Prima Facie Case, Court Holds." Jackson Lewis, Pay Equity Advisor Blog. September 19, 2018. Accessed August 22, 2019. ↵
Contributors and Attributions
- Untitled. Authored by : rawpixel. Located at : www.pexels.com/photo/woman-holding-disposable-cup-1426941/. License : CC0: No Rights Reserved


21.2D: Plant Viruses
- Give examples of plant viruses and explain why they can be costly to the economy
Plant Viruses
Plant viruses, like other viruses, contain a core of either DNA or RNA. As plant viruses have a cell wall to protect their cells, their viruses do not use receptor-mediated endocytosis to enter host cells as is seen with animal viruses. For many plant viruses to be transferred from plant to plant, damage to some of the plants’ cells must occur to allow the virus to enter a new host. This damage is often caused by weather, insects, animals, fire, or human activities such as farming or landscaping. Additionally, plant offspring may inherit viral diseases from parent plants.
Plant viruses can be transmitted by a variety of vectors: through contact with an infected plant’s sap, by living organisms such as insects and nematodes, and through pollen. When plant viruses are transferred between different plants, this is known as horizontal transmission; when they are inherited from a parent, this is called vertical transmission.
Symptoms of viral diseases vary according to the virus and its host. One common symptom is hyperplasia: the abnormal proliferation of cells that causes the appearance of plant tumors known as galls. Other viruses induce hypoplasia, or decreased cell growth, in the leaves of plants, causing thin, yellow areas to appear. Still other viruses affect the plant by directly killing plant cells; a process known as cell necrosis. Other symptoms of plant viruses include malformed leaves, black streaks on the stems of the plants, altered growth of stems, leaves, or fruits, and ring spots, which are circular or linear areas of discoloration found in a leaf.
Plant viruses can seriously disrupt crop growth and development, significantly affecting our food supply. They are responsible for poor crop quality and quantity globally, and can bring about huge economic losses annually. Other viruses may damage plants used in landscaping. Some viruses that infect agricultural food plants include the name of the plant they infect, such as tomato spotted wilt virus, bean common mosaic virus, and cucumber mosaic virus. In plants used for landscaping, two of the most common viruses are peony ring spot and rose mosaic virus. There are far too many plant viruses to discuss each in detail, but symptoms of bean common mosaic virus result in lowered bean production and stunted, unproductive plants. In the ornamental rose, the rose mosaic disease causes wavy yellow lines and colored splotches on the leaves of the plant.
Contributions and Attributions
- OpenStax College, Biology. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44597/latest...ol11448/latest . License : CC BY: Attribution
- virion. Provided by : Wiktionary. Located at : http://en.wiktionary.org/wiki/virion . License : CC BY-SA: Attribution-ShareAlike
- retrovirus. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/retrovirus . License : CC BY-SA: Attribution-ShareAlike
- glycoprotein. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/glycoprotein . License : CC BY-SA: Attribution-ShareAlike
- OpenStax College, Virus Infections and Hosts. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44597/latest...e_21_02_01.png . License : CC BY: Attribution
- lysogenic cycle. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/lysogenic_cycle . License : CC BY-SA: Attribution-ShareAlike
- OpenStax College, Biology. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44597/latest...ol11448/latest . License : CC BY: Attribution
- OpenStax College, Biology. October 23, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44597/latest...ol11448/latest . License : CC BY: Attribution
- bacteriophage. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/bacteriophage . License : CC BY-SA: Attribution-ShareAlike
- lytic cycle. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/lytic_cycle . License : CC BY-SA: Attribution-ShareAlike
- OpenStax College, Virus Infections and Hosts. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44597/latest...e_21_02_01.png . License : CC BY: Attribution
- OpenStax College, Virus Infections and Hosts. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44597/latest...e_21_02_03.png . License : CC BY: Attribution
- OpenStax College, Virus Infections and Hosts. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44597/latest...e_21_02_02.jpg . License : CC BY: Attribution
- OpenStax College, Biology. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44597/latest...ol11448/latest . License : CC BY: Attribution
- receptor-mediated endocytosis. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/recepto...%20endocytosis . License : CC BY-SA: Attribution-ShareAlike
- OpenStax College, Virus Infections and Hosts. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44597/latest...e_21_02_01.png . License : CC BY: Attribution
- OpenStax College, Virus Infections and Hosts. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44597/latest...e_21_02_03.png . License : CC BY: Attribution
- OpenStax College, Virus Infections and Hosts. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44597/latest...e_21_02_02.jpg . License : CC BY: Attribution
- OpenStax College, Virus Infections and Hosts. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44597/latest...21_02_04ab.jpg . License : CC BY: Attribution
- OpenStax College, Biology. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44597/latest...ol11448/latest . License : CC BY: Attribution
- horizontal transmission. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/horizon...20transmission . License : CC BY-SA: Attribution-ShareAlike
- vertical transmission. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/vertical%20transmission . License : CC BY-SA: Attribution-ShareAlike
- OpenStax College, Virus Infections and Hosts. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44597/latest...e_21_02_01.png . License : CC BY: Attribution
- OpenStax College, Virus Infections and Hosts. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44597/latest...e_21_02_03.png . License : CC BY: Attribution
- OpenStax College, Virus Infections and Hosts. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44597/latest...e_21_02_02.jpg . License : CC BY: Attribution
- OpenStax College, Virus Infections and Hosts. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44597/latest...21_02_04ab.jpg . License : CC BY: Attribution
- Table Rock Galls. Provided by : Wikimedia. Located at : commons.wikimedia.org/wiki/Fi...Rock_Galls.jpg . License : CC BY-SA: Attribution-ShareAlike
Key Points
- Plants have cell walls which protect them from viruses entering their cells, so some type of damage must occur in order for them to become infected.
- When viruses are passed between plants, it is called horizontal transmission; when they are passed from the parent plant to the offspring, it is called vertical transmission.
- Symptoms of plant virus infection include malformed leaves, black streaks on the stems, discoloration of the leaves and fruits, and ring spots.
- Plant viruses can cause major disruptions to crop growth, which in turn can have a major impact on the economy.
Key Terms
- horizontal transmission : the transmission of an infectious agent, such as bacterial, fungal, or viral infection, between members of the same species that are not in a parent-child relationship
- vertical transmission : the transmission of an infection or other disease from the female of the species to the offspring


7: Cellular Respiration
Like a generating plant, plants and animals also must take in energy from the environment and convert it into a form that their cells can use. Energy enters an organism’s body in one form and is converted into another form that can fuel the organism’s life functions. In the process of photosynthesis, plants and other photosynthetic producers take in energy in the form of light (solar energy) and convert it into chemical energy, glucose, which stores this energy in its chemical bonds. Then, a series of metabolic pathways, collectively called cellular respiration, extracts the energy from the bonds in glucose and converts it into a form that all living things can use—both producers, such as plants, and consumers, such as animals.
-
- 7.0: Prelude to Cellular Respiration
- Energy enters an organism’s body in one form and is converted into another form that can fuel the organism’s life functions. A series of metabolic pathways, collectively called cellular respiration, extracts the energy from the bonds in glucose and converts it into a form that all living things can use—both producers, such as plants, and consumers, such as animals.
-
- 7.1: Energy in Living Systems
- Energy production within a cell involves many coordinated chemical pathways. Most of these pathways are combinations of oxidation and reduction reactions. Oxidation and reduction occur in tandem. An oxidation reaction strips an electron from an atom in a compound, and the addition of this electron to another compound is a reduction reaction. Because oxidation and reduction usually occur together, these pairs of reactions are called oxidation reduction reactions, or redox reactions.
-
- 7.2: Glycolysis
- Glycolysis is the first step in the breakdown of glucose to extract energy for cellular metabolism. Nearly all living organisms carry out glycolysis as part of their metabolism. The process does not use oxygen and is therefore anaerobic. Glycolysis takes place in the cytoplasm of both prokaryotic and eukaryotic cells.
-
- 7.3: Oxidation of Pyruvate and the Citric Acid Cycle
- If oxygen is available, aerobic respiration will go forward. In eukaryotic cells, the pyruvate molecules produced at the end of glycolysis are transported into mitochondria, which are the sites of cellular respiration. There, pyruvate will be transformed into an acetyl group that will be picked up and activated by a carrier compound called coenzyme A (CoA). The resulting compound is called acetyl CoA. CoA is made from vitamin B5, pantothenic acid.
-
- 7.4: Oxidative Phosphorylation
- You have just read about two pathways in glucose catabolism—glycolysis and the citric acid cycle—that generate ATP. Most of the ATP generated during the aerobic catabolism of glucose, however, is not generated directly from these pathways. Rather, it is derived from a process that begins with moving electrons through a series of electron transporters that undergo redox reactions. This causes hydrogen ions to accumulate within the matrix space.
-
- 7.5: Metabolism without Oxygen
- In aerobic respiration, the final electron acceptor is an oxygen molecule, O2. If aerobic respiration occurs, then ATP will be produced using the energy of high-energy electrons carried by NADH or FADH2 to the electron transport chain. If aerobic respiration does not occur, NADH must be reoxidized to NAD+ for reuse as an electron carrier for the glycolytic pathway to continue.
-
- 7.6: Connections of Carbohydrate, Protein, and Lipid Metabolic Pathways
- All of the catabolic pathways for carbohydrates, proteins, and lipids eventually connect into glycolysis and the citric acid cycle pathways. Metabolic pathways should be thought of as porous—that is, substances enter from other pathways, and intermediates leave for other pathways. These pathways are not closed systems. Many of the substrates, intermediates, and products in a particular pathway are reactants in other pathways.
-
- 7.7: Regulation of Cellular Respiration
- Cellular respiration must be regulated in order to provide balanced amounts of energy in the form of ATP. The cell also must generate a number of intermediate compounds that are used in the anabolism and catabolism of macromolecules. Without controls, metabolic reactions would quickly come to a stand still as the forward and backward reactions reached a state of equilibrium. Resources would be used inappropriately.
Thumbnail: The generalized structure of a prokaryotic cell. (CC BY 4.0; OpenStax ).


7.3: Cyclic Structures of Monosaccharides
- Describe the reaction between and an alcohol and an aldehyde or ketone to form furanose and pyranose rings in monosaccharides.
- Define what is meant by anomers and describe how they are formed.
- Explain what is meant by mutarotation.
Reaction of Aldehyde and Ketone with Alcohol
So far we have represented monosaccharides as linear molecules, but many of them also adopt cyclic structures. This conversion occurs because of the ability of aldehydes and ketones to react with alcohols:
Figure \(\PageIndex{1}\): Reaction of aldehyde and ketone with alcohol.
The aldehyde reacts with the OH group on the fifth carbon atom of the monosaccharide as in Figure 7.3.2. Cyclic compounds containing five or six carbon atoms in the ring are the most stable. Therefore, monosaccharides rings consisting of five or six carbon atoms are the most common. Rings that contain five carbons are called furanose and those that contain six carbons are called pyranose .
Figure \(\PageIndex{2}\): Cyclization of Glucose: a. Glucose is represented as straight chain, b. Open form of glucose prior to cyclization, c. By reacting the OH group on the fifth carbon atom with the aldehyde group, the cyclic monosaccharide is produced.
Cyclic Structures of Monosaccharides
When a straight-chain monosaccharide, such as glucose, forms a cyclic pyranose structure, the carbonyl oxygen atom may be pushed either up or down, giving rise to two isomers, as shown in Figure \(\PageIndex{3}\). The structure shown on the left side of Figure \(\PageIndex{3}\), with the OH group on the first carbon atom projected downward, represent what is called the alpha (α) form . The structures on the right side, with the OH group on the first carbon atom pointed upward, is the beta (β) form . These two isomers of a cyclic monosaccharide are known as anomers; they differ in structure around the anomeric carbon—that is, the carbon atom that was the carbonyl carbon atom in the straight-chain form.
It is possible to obtain a sample of crystalline glucose in which all the molecules have the α structure or all have the β structure. The α form melts at 146°C, while the β form melts at 150°C. When the sample is dissolved in water, however, a mixture is soon produced containing both anomers as well as the straight-chain form, in dynamic equilibrium (part (a) of Figure \(\PageIndex{3}\)). You can start with a pure crystalline sample of glucose consisting entirely of either anomer, but as soon as the molecules dissolve in water, they open to form the carbonyl group and then reclose to form either the α or the β anomer. The opening and closing repeats continuously in an ongoing interconversion between anomeric forms and is referred to as mutarotation (Latin mutare , meaning “to change”). At equilibrium, the mixture consists of about 36% α-D-glucose, 64% β-D-glucose, and less than 0.02% of the open-chain aldehyde form.
Figure \(\PageIndex{3}\): Monosaccharides. In an aqueous solution, monosaccharides exist as an equilibrium mixture of three forms. The interconversion between the forms is known as mutarotation , which is shown for D-glucose (a) and D-fructose (b).
Even though only a small percentage of the molecules are in the open-chain aldehyde form at any time, the solution will nevertheless exhibit the characteristic reactions of an aldehyde.
The difference between the α and the β forms of sugars may seem trivial, but such structural differences are often crucial in biochemical reactions. This explains why we can get energy from the starch in potatoes and other plants but not from cellulose, even though both starch and cellulose are polysaccharides composed of glucose molecules linked together.
Pentose sugars such as ribose and 2-deoxyribose also exist in furanose cyclic forms shown below:
Figure \(\PageIndex{4}\): Pentose monosaccharides in their cyclic furanose form.
Summary
Monosaccharides that are pentoses or hexoses form cyclic structures in aqueous solution. Two cyclic isomers can form from each straight-chain monosaccharide; these are known as anomers. In an aqueous solution, an equilibrium mixture forms between the two anomers and the straight-chain structure of a monosaccharide in a process known as mutarotation.


8.3.1: Comparing Groups
Lesson
Let's compare two groups.
Exercise \(\PageIndex{1}\): Notice and Wonder: Comparing Heights
What do you notice? What do you wonder?
Exercise \(\PageIndex{2}\): More Team Heights
-
How much taller is the volleyball team than the gymnastics team?
- Gymnastics team’s heights (in inches) : 56, 59, 60, 62, 62, 63, 63, 63, 64, 64, 68, 69
- Volleyball team’s heights (in inches): 72, 75, 76, 76, 78, 79, 79, 80, 80, 81, 81, 81
-
Make dot plots to compare the heights of the tennis and badminton teams.
- Tennis team’s heights (in inches): 66, 67, 69, 70, 71, 73, 73, 74, 75, 75, 76
-
Badminton team’s heights (in inches): 62, 62, 65, 66, 68, 71, 73
What do you notice about your dot plots?
- Elena says the members of the tennis team were taller than the badminton team. Lin disagrees. Do you agree with either of them? Explain or show your reasoning.
Exercise \(\PageIndex{3}\): Family Heights
Compare the heights of these two families. Explain or show your reasoning.
- The heights (in inches) of Noah’s family members: 28, 39, 41, 52, 63, 66, 71
- The heights (in inches) of Jada’s family members: 49, 60, 68, 70, 71, 73, 77
Are you ready for more?
If Jada's family adopts newborn twins who are each 18 inches tall, does this change your thinking? Explain your reasoning.
Exercise \(\PageIndex{4}\): Track Length
Here are three dot plots that represent the lengths, in minutes, of songs on different albums.
-
One of these data sets has a mean of 5.57 minutes and another has a mean of 3.91 minutes.
- Which dot plot shows each of these data sets?
- Calculate the mean for the data set on the other dot plot.
-
One of these data sets has a mean absolute deviation of 0.30 and another has a MAD of 0.44.
- Which dot plot shows each of these data sets?
- Calculate the MAD for the other data set.
- Do you think the three groups are very different or not? Be prepared to explain your reasoning.
- A fourth album has a mean length of 8 minutes with a mean absolute deviation of 1.2. Is this data set very different from each of the others?
Summary
Comparing two individuals is fairly straightforward. The question "Which dog is taller?" can be answered by measuring the heights of two dogs and comparing them directly. Comparing two groups can be more challenging. What does it mean for the basketball team to generally be taller than the soccer team?
To compare two groups, we use the distribution of values for the two groups. Most importantly, a measure of center (usually mean or median ) and its associated measure of variability (usually mean absolute deviation or interquartile range) can help determine the differences between groups.
For example, if the average height of pugs in a dog show is 11 inches, and the average height of the beagles in the dog show is 15 inches, it seems that the beagles are generally taller. On the other hand, if the MAD is 3 inches, it would not be unreasonable to find a beagle that is 11 inches tall or a pug that is 14 inches tall. Therefore the heights of the two dog breeds may not be very different from one another.
Glossary Entries
Definition: Mean
The mean is one way to measure the center of a data set. We can think of it as a balance point. For example, for the data set 7, 9, 12, 13, 14, the mean is 11.
To find the mean, add up all the numbers in the data set. Then, divide by how many numbers there are. \(7+9+12+13+14=55\) and \(55\div 5=11\).
Definition: Mean Absolute Deviation (MAD)
The mean absolute deviation is one way to measure how spread out a data set is. Sometimes we call this the MAD. For example, for the data set 7, 9, 12, 13, 14, the MAD is 2.4. This tells us that these travel times are typically 2.4 minutes away from the mean, which is 11.
To find the MAD, add up the distance between each data point and the mean. Then, divide by how many numbers there are.
\(4+2+1+2+3=12\) and \(12\div 5=2.4\)
Definition: Median
The median is one way to measure the center of a data set. It is the middle number when the data set is listed in order.
For the data set 7, 9, 12, 13, 14, the median is 12.
For the data set 3, 5, 6, 8, 11, 12, there are two numbers in the middle. The median is the average of these two numbers. \(6+8=14\) and \(14\div 2=7\).
Practice
Exercise \(\PageIndex{5}\)
Compare the weights of the backpacks for the students in these three classes.
Exercise \(\PageIndex{6}\)
A bookstore has marked down the price for all the books in a certain series by 15%.
- How much is the discount on a book that normally costs $18.00?
- After the discount, how much would the book cost?
(From Unit 4.3.2)
Exercise \(\PageIndex{7}\)
Match each expression in the first list with an equivalent expression from the second list.
- \(6(x+2y)-2(y-2x)\)
- \(2.5(2x+4y)-5(4y-x)\)
- \(4(5x-3y)-10x+6y\)
- \(5.5(x+y)-2(x+y)+6.5(x+y)\)
- \(7.9(5x+3y)-4.2(5x+3y)-1.7(5x+3y)\)
- \(10(x-y)\)
- \(10(x+y)\)
- \(10x+6y\)
- \(10x-6y\)
(From Unit 6.4.5)
Exercise \(\PageIndex{8}\)
Angles \(C\) and \(D\) are complementary. The ratio of the measure of Angle \(C\) to the measure of Angle \(D\) is \(2:3\). Find the measure of each angle. Explain or show your reasoning.
(From Unit 7.1.2)


13.6: Pythagorean theorem
Recall that \(\cosh\) denotes hyperbolic cosine ; that is, the function defined by
\(\cosh x := \dfrac{e^x+e^{-x}}2.\)
Assume that \(ACB\) is an h-triangle with right angle at \(C\) . Set
\(a = BC_h,\) \(b = CA_h\) and \(c = AB_h\).
Then
\[\cosh c = \cosh a \cdot \cosh b.\]
The formula 13.6.1 will be proved by means of direct calculations. Before giving the proof, let us discuss the limit cases of this formula.
Note that \(\cosh x\) can be written using the Taylor expansion
\(\cosh x=1+\dfrac{1}{2}\cdot x^2+\dfrac{1}{24}\cdot x^4+\dots.\)
It follows that if \(a\) , \(b\) , and \(c\) are small, then
\(\begin{array} {rcl} {1 + \dfrac{1}{2} \cdot c^2} & \approx & {\cosh c = \cosh a \cdot \cosh b \approx} \\ {} & \approx & {(1 + \dfrac{1}{2} \cdot a^2)(1 + \dfrac{1}{2} \cdot b^2) \approx} \\ {} & \approx & {1 + \dfrac{1}{2} \cdot (a^2 + b^2).} \end{array}\)
In other words, the original Pythagorean theorem ( Theorem 6.2.1 ) is a limit case of the hyperbolic Pythagorean theorem for small triangles.
For large \(a\) and \(b\) the terms \(e^{-a}\) , \(e^{-b}\) , and \(e^{-a-b+\ln 2}\) are neglectable. In this case we have the following approximations:
\(\begin{array} {\cosh a \cdot \cos h b} & \approx & {\dfrac{e^a}{2} \cdot \dfrac{e^b}{2} =} \\ {} & = & {\dfrac{e^{ a+b-\ln 2 }}{2} \approx} \\ {} & \approx & {\cosh ( a+b-\ln 2 )} \end{array}\)
Therefore \(c \approx a+b-\ln 2\) .
Assume that \(ACB\) is an h-triangle with right angle at \(C\) . Set \(a=BC_h\) , \(b=CA_h\) , and \(c=AB_h\) . Show that
\(c+\ln 2>a+b.\)
- Hint
-
Apply the hyperbolic Pythagorean theorem and the definition of hyperbolic cosine. The following observations should help:
- \(x \mapsto e^x\) is an increasing positive function.
- By the triangle inequality, we have \(-c \le a - b\) and \(-c \le b - a\)
In the proof of the hyperbolic Pythagorean theorem we use the following formula from Exercise 12.9.2 :
here \(A\) , \(B\) are h-points distinct from the center of absolute and \(A'\) , \(B'\) are their inversions in the absolute. This formula is derived in the hints.
Proof of Theorem \(\PageIndex{1}\). We assume that absolute is a unit circle. By the main observation ( Theorem 12.3.1 ) we can assume that \(C\) is the center of absolute. Let \(A'\) and \(B'\) denote the inverses of \(A\) and \(B\) in the absolute.
Set \(x=BC\) , \(y=AC\) . By Lemma Theorem 12.3.2
\(a = \ln \dfrac{1 + x}{1 - x}\), \(b = \ln \dfrac{1 + y}{1 - y}.\)
Therefore
\[\begin{array} {rclcrcl} {\cosh a} & = & {\dfrac{1}{2} \cdot (\dfrac{1 + x}{1 - x} + \dfrac{1 - x}{1 + x}) =} & \ \ \ \ & {\cosh b} & = & {\dfrac{1}{2} \cdot (\dfrac{1 + y}{1 - y} + \dfrac{1 - y}{1 + y}) =} \\ {} & = & {\dfrac{1 + x^2}{1-x^2},} & \ \ \ \ & {} & = & {\dfrac{1 + y^2}{1 - y^2}.} \end{array}\]
Note that
\(B'C = \dfrac{1}{x},\) \(A'C = \dfrac{1}{y}.\)
Therefore
\(BB' = \dfrac{1}{x} - x\), \(AA' = \dfrac{1}{y} - y.\)
Since the triangles \(ABC\), \(A'BC\), \(AB'C\), \(A'B'C\) are right, the original Pythagoran theorem ( Theorem 6.2.1 ) implies
\(\begin{array} {rcl} {AB} & = & {\sqrt{x^2 + y^2}} \\ {A'B} & = & {\sqrt{x^2 + \dfrac{1}{y^2}},} \end{array}\) \(\begin{array} {rcl} {AB'} & = & {\sqrt{\dfrac{1}{x^2} + y^2,}} \\ {A'B'} & = & {\sqrt{\dfrac{1}{x^2} + \dfrac{1}{y^2}}.} \end{array}\)
According to Exercise 12.9.2 ,
\[\begin{array} {rcl} {\cosh c} & = & {\dfrac{AB \cdot A'B' + AB' \cdot A'B}{AA' \cdot BB'} = } \\ {} & = & {\dfrac{\sqrt{x^2 + y^2} \cdot \sqrt{\dfrac{1}{x^2} + \dfrac{1}{y^2}} + \sqrt{\dfrac{1}{x^2} + y^2} \cdot \sqrt{x^2 + \dfrac{1}{y^2}}}{(\dfrac{1}{y} - y) \cdot (\dfrac{1}{x} - x)} =} \\ {} & = & {\dfrac{x^2 + y^2 + 1 + x^2 \cdot y^2}{(1 - y^2) \cdot (1 - x^2)} =} \\ {} & = & {\dfrac{1 + x^2}{1 - x^2} \cdot \dfrac{1 + y^2}{1 - y^2}.} \end{array}\]
Finally note that 13.6.2 and 13.6.3 imply 13.6.1.


4.1: Introduction to Subgroups
Sometimes groups are too complicated to understand directly. One method that can be used to identify a group's structure is to study its subgroups .
Definition: Subgroup
A subgroup of a group \(G\) is a subset of \(G\) that is also a group under \(G\)'s operation. If \(H\) is a subgroup of \(G\text{,}\) we write \(H \leq G\text{;}\) if \(H\subseteq G\) is not a subgroup of \(G\text{,}\) we write \(H\not\leq G\text{.}\)
Note
Do not confuse sub groups with sub sets ! All subgroups of a group \(G\) are, by definition, subsets of \(G\text{,}\) but not all subsets of \(G\) are subgroups of \(G\) (see Example \(4.1.1\), Parts 2–5, below). Whether or not a subset of \(G\) is a subgroup of \(G\) depends on the operation of \(G\text{.}\)
Example \(\PageIndex{1}\)
-
Consider the subset \(\mathbb{Z}\) of the group \(\mathbb{Q}\text{,}\) assuming that \(\mathbb{Q}\) is equipped with the usual addition of real numbers (as we indicated above that we would assume, by default). Since we already know that \(\mathbb{Z}\) is a group under this operation, \(\mathbb{Z}\) is not just a subset but in fact a subgroup of \(\mathbb{Q}\) (under addition).
-
Instead, consider the subset \(\mathbb{Q}^+\) of the group \(\mathbb{Q}\text{.}\) This subset is not a group under \(\mathbb{Q}\)'s operation \(+\text{,}\) since it does not contain an identity element for \(+\text{.}\) Therefore, \(\mathbb{Q}^+\) is a subset but not a subgroup of \(\mathbb{Q}\text{.}\)
-
Let \(I\) be the subset
\begin{equation*} I=\mathbb{R}-\mathbb{Q}=\{x\in \mathbb{R}: x \text{ is irrational} \} \end{equation*}
of the group \(\mathbb{R}\text{.}\) The set \(I\) is not a group under \(\mathbb{R}\)'s operation \(+\) since it is not closed under addition: for instance, \(\pi, -\pi \in I\text{,}\) but \(\pi+(-\pi)=0\not\in I\text{.}\) So \(I\) is a subset but not a subgroup of \(\mathbb{R}\text{.}\)
-
Consider the subset \(\mathbb{Z}^+\) of the group \(\mathbb{R}^+\text{.}\) The set \(\mathbb{Z}^+\) is closed under multiplication, multiplication is associative on \(\mathbb{Z}^+\text{,}\) and \(\mathbb{Z}^+\) does contain an identity element (namely, \(1\)). However, most elements of \(\mathbb{Z}^+\) do not have inverses in \(\mathbb{Z}^+\) under multiplication: for instance, the inverse of \(3\) would have to be \( \dfrac{1}{3}\text{,}\) but \(\dfrac{1}{3}\not\in \mathbb{Z}^+\text{.}\) Therefore, \(\mathbb{Z}^+\) is a subset but not a subgroup of \(\mathbb{R}^+\text{.}\)
-
Consider the subset \(GL(n,\mathbb{R})\) of \(\mathbb{M}_n(\mathbb{R})\text{.}\) We know that \(GL(n,\mathbb{R})\) is a group, so it might be tempting to say that it is a subgroup of \(\mathbb{M}_n(\mathbb{R})\text{;}\) to be a subgroup of \(\mathbb{M}_n(\mathbb{R})\text{,}\) \(GL(n,\mathbb{R})\) must be a group under \(\mathbb{M}_n(\mathbb{R})\)'s operation, which is matrix addition. While \(GL(n,\mathbb{R})\) is a group under matrix multiplication, it is not a group under matrix addition: for instance, it is not closed under matrix addition, since \(I_n, -I_n\in GL(n,\mathbb{R})\) but \(I_n+(-I_n)\) is the matrix consisting of all zeros, which is not in \(GL(n,\mathbb{R})\text{.}\) So \(GL(n,\mathbb{R})\) is a subset but not a subgroup of \(\mathbb{M}_n(\mathbb{R})\text{.}\)
-
Consider the subset \(H=\{0,2\}\) of \(\mathbb{Z}_4\text{.}\) The subset \(H\) is closed under addition modulo \(4\) (\(0+0=0\text{,}\) \(0+2=2+0=2\text{,}\) \(2+2=0\)), addition modulo \(4\) is always associative, \(H\) contains an identity element (namely, \(0\)) under addition modulo \(4\), and both \(0\) and \(2\) have inverses in \(\mathbb{Z}_4\) under this operation (\(0\) and \(2\) are each their own inverses). Thus, \(H\) is a subgroup of \(\mathbb{Z}_4\text{.}\)
-
Let \(G\) be a group. Then \(\{e_G\}\) and \(G\) are clearly both subgroups of \(G\text{.}\)
Definition: Trivial, Nontrivial, Proper, and Improper Subgroup
Let \(G\) be a group. The subgroups \(\{e_G\}\) and \(G\) of \(G\) are called the trivial subgroup and the improper subgroup of \(G\text{,}\) respectively. Not surprisingly, if \(H\leq G\) and \(H\neq \{e_G\}\text{,}\) \(H\) is called a nontrivial subgroup of \(G\text{,}\) and if \(H\leq G\) and \(H\neq G\text{,}\) \(H\) is called a proper subgroup of \(G\text{.}\)
Remark
Sometimes the notation \(H\lt G\) is used to indicate that \(H\) is a proper subgroup of \(G\text{,}\) but sometimes it is simply used to mean that \(H\) is a subgroup—proper or improper—of \(G\text{.}\) We will not use the notation \(H\lt G\) in this text.
Notice that in the cases above, we saw subsets of groups fail to be subgroups because they were not closed under the groups' operations; because they did not contain identity elements; or because they didn't contain an inverse for each of their elements. None, however, failed because the relevant group's operation was not associative on them. This is not a coincidence: rather, since any element of a subset of a group \(G\) also lives in \(G\text{,}\) any associative operation on \(G\) is of necessity associative on any closed subset of \(G\text{.}\) Therefore, when we are checking to see if \(H\subseteq G\) is a subgroup of group \(G\text{,}\) we need only check for closure, an identity element, and inverses.
Lemma \(\PageIndex{1}\)
Let \(G\) be a group.
- If \(H\) is a subgroup of \(G\) then the identity element \(e_H\) of \(H\) is \(e_G\text{,}\) the identity element of \(G\text{.}\)
- If \(H\) is a subgroup of \(G\) and \(a\in H\) has inverse \(a^{-1}\) in \(G\text{,}\) then \(a\)'s inverse in \(H\) is also \(a^{-1}\text{.}\)
- Proof
-
For Part 1: Since \(e_H\) is in both \(H\) and \(G\), by the definition of \(e_H\), we have \(e_He_H=e_H\), and by the definition of \(e_G\) we have \(e_Ge_H=e_H\). So \(e_He_H=e_Ge_H\), and thus by right cancellation, \(e_H=e_G\).
Next, for Part 2, let \(b\) be the inverse of \(a\) in \(H\). Then using Part 1 of this lemma and the definition of an inverse, \(ab=e_H=e_G=aa^{−1}\). By left cancellation, then, we have that \(b=a^{−1}\).
Corollary \(\PageIndex{1}\)
Let \(H\subseteq G\text{.}\) If the identity element of \(G\) is not in \(H\text{,}\) then \(H\not\leq G\text{.}\)


19.7: Summary
19.1 Fundamental Units of Distance
Early measurements of length were based on human dimensions, but today, we use worldwide standards that specify lengths in units such as the meter. Distances within the solar system are now determined by timing how long it takes radar signals to travel from Earth to the surface of a planet or other body and then return.
19.2 Surveying the Stars
For stars that are relatively nearby, we can “triangulate” the distances from a baseline created by Earth’s annual motion around the Sun. Half the shift in a nearby star’s position relative to very distant background stars, as viewed from opposite sides of Earth’s orbit, is called the parallax of that star and is a measure of its distance. The units used to measure stellar distance are the light-year, the distance light travels in 1 year, and the parsec (pc), the distance of a star with a parallax of 1 arcsecond (1 parsec = 3.26 light-years). The closest star, a red dwarf, is over 1 parsec away. The first successful measurements of stellar parallaxes were reported in 1838. Parallax measurements are a fundamental link in the chain of cosmic distances. The Hipparcos satellite has allowed us to measure accurate parallaxes for stars out to about 300 light-years, and the Gaia mission will result in parallaxes out to 30,000 light-years.
19.3 Variable Stars: One Key to Cosmic Distances
Cepheids and RR Lyrae stars are two types of pulsating variable stars. Light curves of these stars show that their luminosities vary with a regularly repeating period. RR Lyrae stars can be used as standard bulbs, and cepheid variables obey a period-luminosity relation, so measuring their periods can tell us their luminosities. Then, we can calculate their distances by comparing their luminosities with their apparent brightnesses, and this can allow us to measure distances to these stars out to over 60 million light-years.
19.4 The H–R Diagram and Cosmic Distances
Stars with identical temperatures but different pressures (and diameters) have somewhat different spectra. Spectral classification can therefore be used to estimate the luminosity class of a star as well as its temperature. As a result, a spectrum can allow us to pinpoint where the star is located on an H–R diagram and establish its luminosity. This, with the star’s apparent brightness, again yields its distance. The various distance methods can be used to check one against another and thus make a kind of distance ladder which allows us to find even larger distances.


2.1: Introduction
The Interview
Many of us have or will sit in a waiting room with our best clothes on awaiting a job (or school) interview. You can feel your palms sweat and thoughts race as you wait for your name to be called. You look around at the office environment and imagine yourself walking through those doors everyday. People walk by and smile, and overall, you have a really good first impression of the organization.  You tell yourself to remember to smile, while recalling all your experience that makes you the perfect person for this job. A moment of self-doubt may occur, as you wonder about the abilities of the other people being interviewed and hope you have more experience and make a better impression than they do.  The interview has begun.
As she walks you back to a conference room, you think you see encouraging smiles as you pass by people. She asks you to take a chair and then tells you what the interview process will be like. She then asks the first question, “Tell me about yourself.” As you start discussing your experience, you feel yourself relax, just a little bit. After the interview finishes, she asks you to take a quick cognitive test, which you feel good about. She tells you she will be doing reference checks and will let you know by early next week.
To get to this point, the hiring manager may have reviewed hundreds of résumés and developed criteria she would use for selection of the right person for the job. She has probably planned a time line for hiring, developed hiring criteria, determined a compensation package for the job, and enlisted help of other managers to interview candidates. She may have even performed a number of phone interviews before bringing only a few of the best candidates in for interviews. It is likely she has certain qualities in mind that she is hoping you or another candidate will possess. Much work goes into the process of hiring someone, with selection being an important step in that process. A hiring process done correctly is time-consuming and precise. The interviewer should already have questions determined and should be ready to sell the organization to the candidate as well. This chapter will discuss the main components to the selection process.