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2e1c162da5ee88c13f2d3821c3c9addf | X:osx:astronomy-2e:m59982 | openstax-astronomy-2e | passage | Even if life did develop in a stronger-gravity universe, life forms would have to be tiny or they could not stand up or move around. What Had to Be, Had to Be
In summary, we see that a specific set of rules and conditions in the universe has allowed complexity and life on Earth to develop. As yet, we have no theory to ... | 63157f370b09c06a4cc12832384aaaf4de1ced3b | https://github.com/openstax/osbooks-astronomy/blob/63157f370b09c06a4cc12832384aaaf4de1ced3b/modules/m59982/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@63157f37 | [
"The Big Bang"
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5fc6a816eaa4ab9ebad181d21401caaa | X:osx:introduction-anthropology:m00035 | openstax-introduction-anthropology | passage | Meyer, Matthias, Juan-Luis Arsuaga, Cesare de Filippo, Sarah Nagel, Ayinuer Aximu-Petri, Birgit Nickel, Ignacio Martínez et al. 2016. “Nuclear DNA Sequences from the Middle Pleistocene Sima de los Huesos Hominins. Nature 531: 504–07. https://doi.org/10.1038/nature17405. Monfils, A., J. Allen, B. W. Goodner, and D. Lint... | f0f11fc382e1f8974f2b961d512369ac87d27e32 | https://github.com/openstax/osbooks-introduction-anthropology/blob/f0f11fc382e1f8974f2b961d512369ac87d27e32/modules/m00035/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@f0f11fc3 | [
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4e30489eae5631147d16ec3491ca82a1 | X:osx:introduction-anthropology:m00038 | openstax-introduction-anthropology | passage | Researchers Brent Berlin and Paul Kay analyzed the color term systems of 98 languages and found that the diversity of color term systems is governed by one set of rules. All of these color term systems are comprised of a few basic colors with specific colors added to the scheme over time (Kay 2015, Berlin and Kay 1969)... | f0f11fc382e1f8974f2b961d512369ac87d27e32 | https://github.com/openstax/osbooks-introduction-anthropology/blob/f0f11fc382e1f8974f2b961d512369ac87d27e32/modules/m00038/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@f0f11fc3 | [
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6116b02637b1b74aebbd26742a45190e | X:osx:introduction-anthropology:m00056 | openstax-introduction-anthropology | passage | In his ethnography Pathogenic Policing: Immigration Enforcement and Health in the US South (2019), medical and legal anthropologist Nolan Kline describes immigrant policing as a form of biopower that attempts to control and govern immigrants through tactics based on fear, making undocumented immigrants fearful as they ... | f0f11fc382e1f8974f2b961d512369ac87d27e32 | https://github.com/openstax/osbooks-introduction-anthropology/blob/f0f11fc382e1f8974f2b961d512369ac87d27e32/modules/m00056/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@f0f11fc3 | [
"Social Inequalities"
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1080bf47e191eeaaa8e7f818a4bc4967 | X:osx:principles-economics-3e:m64108 | openstax-principles-economics-3e | passage | (See the following Clear It Up feature on the relationship between compound growth rates and compound interest rates. If the rate of growth is 8%, young adults starting at age 20 will see the average standard of living in their country more than double by the time they reach age 30, and grow more than sixfold by the ti... | 020e54dbecb376f27b37c3498f9347a45961c11a | https://github.com/openstax/osbooks-principles-economics-bundle/blob/020e54dbecb376f27b37c3498f9347a45961c11a/modules/m64108/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@020e54db | [
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81eaa5f776da1f1a139eca0e223e71c3 | X:osx:principles-economics-3e:m64098 | openstax-principles-economics-3e | passage | It is not a physical and unchanging law of nature. Instead, it is only the “natural” rate because it is the unemployment rate that would result from the combination of economic, social, and political factors that exist at a time—assuming the economy was neither booming nor in recession. These forces include the usual p... | 020e54dbecb376f27b37c3498f9347a45961c11a | https://github.com/openstax/osbooks-principles-economics-bundle/blob/020e54dbecb376f27b37c3498f9347a45961c11a/modules/m64098/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@020e54db | [
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19c73a3b7c9ad76115f286dd73dc1285 | X:osx:principles-economics-3e:m64098 | openstax-principles-economics-3e | passage | Employers typically review wages only once or twice a year. In many modern jobs, it is difficult to measure productivity at the individual level. For example, how precisely would one measure the quantity produced by an accountant who is one of many people working in the tax department of a large corporation? Because pr... | 020e54dbecb376f27b37c3498f9347a45961c11a | https://github.com/openstax/osbooks-principles-economics-bundle/blob/020e54dbecb376f27b37c3498f9347a45961c11a/modules/m64098/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@020e54db | [
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e6c0edfdf3eda0c36e0b862ac7b01b04 | X:osx:principles-economics-3e:m63975 | openstax-principles-economics-3e | passage | Practical Problems with Discretionary Fiscal Policy
In the early 1960s, many leading economists believed that the problem of the business cycle, and the swings between cyclical unemployment and inflation, were a thing of the past. On the cover of its December 31, 1965, issue, Time magazine, then the premier news magazi... | 020e54dbecb376f27b37c3498f9347a45961c11a | https://github.com/openstax/osbooks-principles-economics-bundle/blob/020e54dbecb376f27b37c3498f9347a45961c11a/modules/m63975/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@020e54db | [
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fee4fa2c724f7093d09a7b011c30f8e0 | X:osx:principles-economics-3e:m63975 | openstax-principles-economics-3e | passage | It often takes some months before the economic statistics signal clearly that a downturn has started, and a few months more to confirm that it is truly a recession and not just a one- or two-month blip. Economists often call the time it takes to determine that a recession has occurred the recognition lag. After this la... | 020e54dbecb376f27b37c3498f9347a45961c11a | https://github.com/openstax/osbooks-principles-economics-bundle/blob/020e54dbecb376f27b37c3498f9347a45961c11a/modules/m63975/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@020e54db | [
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84e7baf97ac9201f78cffd06f334bb6f | X:osx:principles-economics-3e:m64133 | openstax-principles-economics-3e | passage | According to Central Intelligence Agency data in its CIA Factbook, as of 2021, 85% of Burundi’s population is agrarian, with bananas as the main income producing crop. Only one in two children attends school and, as shows, many are not in schools comparable to what occurs in developed countries. Political instability h... | 020e54dbecb376f27b37c3498f9347a45961c11a | https://github.com/openstax/osbooks-principles-economics-bundle/blob/020e54dbecb376f27b37c3498f9347a45961c11a/modules/m64133/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@020e54db | [
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4f71da0e70ab79fd7a23084415b275ca | X:osx:principles-economics-3e:m64133 | openstax-principles-economics-3e | passage | In her book Dead Aid: Why Aid Is Not Working and How There Is Another Way for Africa (2009), she lays out the failure of past aid, indicating that it typically ends up in the pockets of corrupt officials and has the adverse effect of minimizing other types of investment. At the time, Moyo proposed a complete stoppage o... | 020e54dbecb376f27b37c3498f9347a45961c11a | https://github.com/openstax/osbooks-principles-economics-bundle/blob/020e54dbecb376f27b37c3498f9347a45961c11a/modules/m64133/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@020e54db | [
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f9fe8cecd4148df8b4102eed6e0b03e1 | X:osx:principles-economics-3e:m64133 | openstax-principles-economics-3e | passage | They see opportunities all across Africa, Asia, and Latin America to set up health clinics and schools. They want to help with the task of building economic infrastructure: clean water, plumbing, electricity, and roads. Supporters of this aid include formal state-sponsored institutions like the United Kingdom’s Departm... | 020e54dbecb376f27b37c3498f9347a45961c11a | https://github.com/openstax/osbooks-principles-economics-bundle/blob/020e54dbecb376f27b37c3498f9347a45961c11a/modules/m64133/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@020e54db | [
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844ba4ed6a33691ccc83e1ca70a11f73 | X:osx:world-history-volume-2:m00050 | openstax-world-history-volume-2 | passage | To know history is to know ourselves, and understanding history’s nuances opens our imaginations to the possibilities each new situation creates. It is this knowledge of possibilities that allows the student of history to see the present with more clarity and prescience. World History as Preparation for Life After Coll... | 3e17beda9130380d24be881e6d1942dfcc1be845 | https://github.com/openstax/osbooks-world-history/blob/3e17beda9130380d24be881e6d1942dfcc1be845/modules/m00050/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@3e17beda | [
"Understanding the Past"
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71c0a3ea7c9169862274071ea9ce723d | X:osx:world-history-volume-2:m00050 | openstax-world-history-volume-2 | passage | Features of This Textbook
This text is a great place to begin your journey into the world’s past. It has several features that will help you understand the history of world civilizations from the fifteenth century and the beginning of the early modern period until today. For the most part, it adopts a traditional chron... | 3e17beda9130380d24be881e6d1942dfcc1be845 | https://github.com/openstax/osbooks-world-history/blob/3e17beda9130380d24be881e6d1942dfcc1be845/modules/m00050/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@3e17beda | [
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9f8702402cba1bd8cbcfc5a4966c5050 | X:osx:world-history-volume-2:m00050 | openstax-world-history-volume-2 | passage | In Their Own Words
In Their Own Words feature boxes present a source composed in the period the chapter covers and allow you to examine it in context, learning how to critically analyze source material. A short series of questions will help to guide your analysis. Dueling Voices
Dueling Voices feature boxes present eit... | 3e17beda9130380d24be881e6d1942dfcc1be845 | https://github.com/openstax/osbooks-world-history/blob/3e17beda9130380d24be881e6d1942dfcc1be845/modules/m00050/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@3e17beda | [
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eed845b1071bf044c4fcdbe54900c360 | X:osx:college-success:m84281 | openstax-college-success | passage | If it’s someone else who’s emotional, again, ask yourself why. Can you see reasons that this person may feel attacked, belittled, or usurped? If you can recognize their emotion and address it, you may be able to get the communication back on solid footing. Think of what context and what communication tool you would con... | 4c04b87eb2753872c2d442fe9736859ddb27bb72 | https://github.com/openstax/osbooks-college-success-bundle/blob/4c04b87eb2753872c2d442fe9736859ddb27bb72/modules/m84281/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@4c04b87e | [
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35cfdda5ae19c549871a868037b6c3ef | X:osx:introduction-business-2e:m67754 | openstax-introduction-business-2e | passage | Management support systems are dynamic systems that allow users to analyze data to make forecasts, identify business trends, and model business strategies. Office automation systems improve the flow of communication throughout the organization. Each type of information system serves a particular level of decision-makin... | 2a839877ab89a207c9b9e501df438173013fa45c | https://github.com/openstax/osbooks-introduction-business/blob/2a839877ab89a207c9b9e501df438173013fa45c/modules/m67754/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@2a839877 | [
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386c8218678ca088ca470b6c8bc8539f | X:osx:introduction-business-2e:m67756 | openstax-introduction-business-2e | passage | For example, an unhappy employee in the purchasing department could get into the company’s computer system and delete information on past orders and future inventory needs. The sabotage could severely disrupt production and the accounts payable system. Willful acts to destroy or change the data in computers are hard to... | 2a839877ab89a207c9b9e501df438173013fa45c | https://github.com/openstax/osbooks-introduction-business/blob/2a839877ab89a207c9b9e501df438173013fa45c/modules/m67756/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@2a839877 | [
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53e59f1d24e79dbc877a997840d002dc | X:osx:introduction-business-2e:m67765 | openstax-introduction-business-2e | passage | The acid-test ratio is a good measure of liquidity when inventory cannot easily be converted to cash (for instance, if it consists of very specialized goods with a limited market). If inventory is liquid, the current ratio is better. Delicious Desserts’ acid-test ratio is 1.1 for 20XX. Because the bakery’s products are... | 2a839877ab89a207c9b9e501df438173013fa45c | https://github.com/openstax/osbooks-introduction-business/blob/2a839877ab89a207c9b9e501df438173013fa45c/modules/m67765/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@2a839877 | [
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4234e27f0db58fc1c20c00cc4ae3afd6 | X:osx:introduction-business-2e:m67773 | openstax-introduction-business-2e | passage | Would you be better off paying a monthly fee with unlimited check-writing privileges? Crunch the numbers to find the best deal. (Resources, Information)
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294880387f388e560d0964f72c11c32e | X:osx:preparing-for-college-success:m00013 | openstax-preparing-for-college-success | passage | The levels in which you “Analyze” and “Evaluate” require that you be able to examine the concepts in depth and be able to, for example, compare and contrast a concept with another concept (Analyze) or choose the best concept among others (Evaluate). The final level is “Create,” which, according to Bloom, is the pinnacl... | 4c04b87eb2753872c2d442fe9736859ddb27bb72 | https://github.com/openstax/osbooks-college-success-bundle/blob/4c04b87eb2753872c2d442fe9736859ddb27bb72/modules/m00013/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@4c04b87e | [
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dd924746cd397432dd47c72617e47a25 | X:osx:preparing-for-college-success:m00025 | openstax-preparing-for-college-success | passage | In some cases, your family may just not understand because they haven’t gone to college or they have not experienced what you have. You may just need to let go of the expectation that they will be able to provide the type of support that you want or need.
- Create boundaries. If you feel as though your family is overst... | 4c04b87eb2753872c2d442fe9736859ddb27bb72 | https://github.com/openstax/osbooks-college-success-bundle/blob/4c04b87eb2753872c2d442fe9736859ddb27bb72/modules/m00025/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@4c04b87e | [
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dd72e8431f0faa9c2ae29400a6f732d7 | X:osx:preparing-for-college-success:m00038 | openstax-preparing-for-college-success | passage | Loan Forgiveness Programs
Many income-based repayment options also have a loan forgiveness feature built into the repayment plan. If you make 100 percent of your payments on time and follow all of the other plan rules, any remaining loan balance at the end of the plan repayment term (typically 20 to 30 years) will be f... | 4c04b87eb2753872c2d442fe9736859ddb27bb72 | https://github.com/openstax/osbooks-college-success-bundle/blob/4c04b87eb2753872c2d442fe9736859ddb27bb72/modules/m00038/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@4c04b87e | [
"Understanding Financial Literacy"
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The complexity of the payment and forgiveness programs makes it difficult for non-experts to choose the best strategy to minimize costs. Additionally, the strict rules and pot... | 4c04b87eb2753872c2d442fe9736859ddb27bb72 | https://github.com/openstax/osbooks-college-success-bundle/blob/4c04b87eb2753872c2d442fe9736859ddb27bb72/modules/m00038/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@4c04b87e | [
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bc30ea8214f84156bef5b843ff35be81 | X:osx:preparing-for-college-success:m00038 | openstax-preparing-for-college-success | passage | Friends & Family Matter
Ana has several ideas for what to major in and because she has had to take out student loans to cover the costs of college, she is worried about getting a job after graduation that pays enough for her to afford the monthly loan payments. Fortunately, she has met with her financial aid advisor wh... | 4c04b87eb2753872c2d442fe9736859ddb27bb72 | https://github.com/openstax/osbooks-college-success-bundle/blob/4c04b87eb2753872c2d442fe9736859ddb27bb72/modules/m00038/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@4c04b87e | [
"Understanding Financial Literacy"
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ed7d62e57bb47dfb8116c0694e9689dd | X:osx:principles-microeconomics-3e:m63580 | openstax-principles-microeconomics-3e | passage | Why is this the case? It is because of scarcity. Let’s delve into the concept of scarcity a little deeper, because it is crucial to understanding economics. The Problem of Scarcity
Think about all the things you consume: food, shelter, clothing, transportation, healthcare, and entertainment. How do you acquire those it... | 020e54dbecb376f27b37c3498f9347a45961c11a | https://github.com/openstax/osbooks-principles-economics-bundle/blob/020e54dbecb376f27b37c3498f9347a45961c11a/modules/m63580/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@020e54db | [
"Welcome to Economics!"
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a99ddf433e048d4c3aec21d736143493 | X:osx:principles-microeconomics-3e:m63596 | openstax-principles-microeconomics-3e | passage | A change in the wage or salary will result in a change in the quantity demanded of labor. If the wage rate increases, employers will want to hire fewer employees. The quantity of labor demanded will decrease, and there will be a movement upward along the demand curve. If the wages and salaries decrease, employers are m... | 020e54dbecb376f27b37c3498f9347a45961c11a | https://github.com/openstax/osbooks-principles-economics-bundle/blob/020e54dbecb376f27b37c3498f9347a45961c11a/modules/m63596/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@020e54db | [
"Labor and Financial Markets"
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3c48aa160ceeb5f226627ab2c315d7ed | X:osx:writing-guide:m00062 | openstax-writing-guide | passage | Citizens must demand that their elected officials at the local, state, and national levels accept responsibility to take action on both mitigation and adaptation. Without full governmental support, good intentions fall short of reaching net-zero emissions and cannot achieve the adaptation in attitude and lifestyle nece... | a6c95528390e3a2936f5bf87c49ac1a4995a0a6e | https://github.com/openstax/osbooks-writing-guide/blob/a6c95528390e3a2936f5bf87c49ac1a4995a0a6e/modules/m00062/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@a6c95528 | [
"Proposal: Writing About Problems and Solutions"
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9631653c037bed291eb8c26f19f46969 | X:osx:writing-guide:m00093 | openstax-writing-guide | passage | Use a blogging site or platform such as WordPress or Tumblr to explore the blogging genre, which includes video clips, images, hyperlinks, and other media to further your discussion. Because this genre is less formal than written text, your tone can be conversational. However, you still will be required to provide the ... | a6c95528390e3a2936f5bf87c49ac1a4995a0a6e | https://github.com/openstax/osbooks-writing-guide/blob/a6c95528390e3a2936f5bf87c49ac1a4995a0a6e/modules/m00093/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@a6c95528 | [
"Rhetorical Analysis: Interpreting the Art of Rhetoric"
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9107e7237b56d8041b111f1a6c4e5b5a | X:osx:writing-guide:m00093 | openstax-writing-guide | passage | Explain your reasoning in the right-hand column of this or a similar chart. The introductory paragraph or paragraphs should serve to move the reader into the body of the analysis and signal what will follow. Body
Your next step is to start supporting your thesis statement—that is, how Octavio Peterson, or the writer of... | a6c95528390e3a2936f5bf87c49ac1a4995a0a6e | https://github.com/openstax/osbooks-writing-guide/blob/a6c95528390e3a2936f5bf87c49ac1a4995a0a6e/modules/m00093/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@a6c95528 | [
"Rhetorical Analysis: Interpreting the Art of Rhetoric"
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2bf3def9efc79cb44ace4e9c93ac7045 | X:osx:writing-guide:m00150 | openstax-writing-guide | passage | In this way, artists who work with the medium of language become the prophets. This conclusion looks to the future, which is a productive rhetorical or persuasive technique to give the audience an idea about what they can take away from this project. Works Cited
Ali, Lorraine. “‘Such a Nasty Woman’: Trump’s Debate Dig ... | a6c95528390e3a2936f5bf87c49ac1a4995a0a6e | https://github.com/openstax/osbooks-writing-guide/blob/a6c95528390e3a2936f5bf87c49ac1a4995a0a6e/modules/m00150/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@a6c95528 | [
"Print or Textual Analysis: What You Read"
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1f71439c0788004ce186f724a8599ca7 | X:osx:writing-guide:m00150 | openstax-writing-guide | passage | Calixta was preparing supper. She had set the table and was dripping coffee at the hearth. She sprang up as they came in. “Oh, Bobinôt! You back! My! but I was uneasy. W’ere you been during the rain? An’ Bibi? he ain’t wet? he ain’t hurt? She had clasped Bibi and was kissing him effusively. Bobinôt’s explanations and a... | a6c95528390e3a2936f5bf87c49ac1a4995a0a6e | https://github.com/openstax/osbooks-writing-guide/blob/a6c95528390e3a2936f5bf87c49ac1a4995a0a6e/modules/m00150/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@a6c95528 | [
"Print or Textual Analysis: What You Read"
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cbf741a137303d583f6c29aa077c6213 | X:osx:writing-guide:m00007 | openstax-writing-guide | passage | Evaluation: Transitions
Learning Outcomes
By the end of this section, you will be able to:
- Implement conventions from a variety of modes and media to address a range of audiences.
- Match the capacities of different genres to various rhetorical situations. Ask a peer to use the rubric below to read through your draft... | a6c95528390e3a2936f5bf87c49ac1a4995a0a6e | https://github.com/openstax/osbooks-writing-guide/blob/a6c95528390e3a2936f5bf87c49ac1a4995a0a6e/modules/m00007/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@a6c95528 | [
"Multimodal and Online Writing: Creative Interaction between Text and Image"
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b5d9de38df7f6d8f8ff43c5ec749e406 | X:osx:college-algebra-corequisite-support-2e:m49432 | openstax-college-algebra-corequisite-support-2e | passage | See .
- The decomposition of P(x)Q(x) with repeated linear factors must account for the factors of the denominator in increasing powers. See .
- The decomposition of P(x)Q(x) with a nonrepeated irreducible quadratic factor needs a linear numerator over the quadratic factor, as in Ax+Bx+C(ax2+bx+c). See .
- In the decom... | 4922e46ebc04326979e19392ccc2384cb8b9076c | https://github.com/openstax/osbooks-college-algebra-bundle/blob/4922e46ebc04326979e19392ccc2384cb8b9076c/modules/m49432/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@4922e46e | [
"Systems of Equations and Inequalities"
] | 239 | f2321f6836ef6dc46bbd6d5fe931c6ed25bbedcee18a7f2e45c70b81222431f6 | 0 | 0 | true |
68c00212d7ccd09c4592b74a4cdd763e | X:osx:college-algebra-corequisite-support-2e:m49438 | openstax-college-algebra-corequisite-support-2e | passage | Access these online resources for additional instruction and practice with ellipses.
- Conic Sections: The Ellipse
- Graph an Ellipse with Center at the Origin
- Graph an Ellipse with Center Not at the Origin
Key Equations
Key Concepts
- An ellipse is the set of all points (x,y) in a plane such that the sum of their di... | 4922e46ebc04326979e19392ccc2384cb8b9076c | https://github.com/openstax/osbooks-college-algebra-bundle/blob/4922e46ebc04326979e19392ccc2384cb8b9076c/modules/m49438/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@4922e46e | [
"Analytic Geometry"
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ddce0ae28d252fe464a537484e49a4ce | X:osx:college-algebra-corequisite-support-2e:m49440 | openstax-college-algebra-corequisite-support-2e | passage | The endpoints of the latus rectum lie on the curve. By definition, the distance d from the focus to any point P on the parabola is equal to the distance from P to the directrix. To work with parabolas in the coordinate plane, we consider two cases: those with a vertex at the origin and those with a vertex at a point ot... | 4922e46ebc04326979e19392ccc2384cb8b9076c | https://github.com/openstax/osbooks-college-algebra-bundle/blob/4922e46ebc04326979e19392ccc2384cb8b9076c/modules/m49440/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@4922e46e | [
"Analytic Geometry"
] | 231 | 4628ecef5455c9185c28261daad04c4d20989838fea1276170f17860da168bd6 | 0 | 0 | true |
3fadc87bb2bfdcfc5fef9a7c6a3dd912 | X:osx:entrepreneurship:m71115 | openstax-entrepreneurship | passage | This vision is about creating community, helping each other, and strengthening communities. The business model encourages homeless people to create short Miracle Messages through video, audio, or text, with messages then uploaded to social media and other methods to find that person’s loved one. Globalizing Miracle Mes... | c1fa2c872ba07dc864c3aeb5a510b08b4f657288 | https://github.com/openstax/osbooks-entrepreneurship/blob/c1fa2c872ba07dc864c3aeb5a510b08b4f657288/modules/m71115/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@c1fa2c87 | [
"The Entrepreneurial Perspective"
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e7184f4a2deaa0d6a115cca12412fba4 | X:osx:entrepreneurship:m71144 | openstax-entrepreneurship | passage | Note that key features and the value proposition are already addressed through three simple slides.
- Slide 4: To establish product-market fit, you first have to have a market. The Airbnb pitch deck notes that at the time there were 630,000 users on couchsurfing.com and that there were 17,000 temporary housing listings... | c1fa2c872ba07dc864c3aeb5a510b08b4f657288 | https://github.com/openstax/osbooks-entrepreneurship/blob/c1fa2c872ba07dc864c3aeb5a510b08b4f657288/modules/m71144/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@c1fa2c87 | [
"Telling Your Entrepreneurial Story and Pitching the Idea"
] | 222 | 8df10668295d64e2cdd5f4c17693849f17664453fa1aa9685dbff1484a97c4fc | 0 | 0 | true |
c543ff282cba71d470bb48b6bf280da6 | X:osx:entrepreneurship:m71150 | openstax-entrepreneurship | passage | Talking to the focus group can uncover possible research questions to undertake. Merkadoteknia Research and Consulting is a Hispanic-owned company that conducts research for different industries that cater to Hispanic consumers. This company helps fast-food companies, retailers, and pharmaceutical companies, among othe... | c1fa2c872ba07dc864c3aeb5a510b08b4f657288 | https://github.com/openstax/osbooks-entrepreneurship/blob/c1fa2c872ba07dc864c3aeb5a510b08b4f657288/modules/m71150/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@c1fa2c87 | [
"Entrepreneurial Marketing and Sales"
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bd201eecc1daf276cbbe354c888fea94 | X:osx:entrepreneurship:m71150 | openstax-entrepreneurship | passage | In addition to identifying competition and determining growth and profit potential, a good market analysis will identify the total available market (TAM) for a specific product, which is the total perceived demand for a product or service within the marketplace. It will also identify the serviceable available market (S... | c1fa2c872ba07dc864c3aeb5a510b08b4f657288 | https://github.com/openstax/osbooks-entrepreneurship/blob/c1fa2c872ba07dc864c3aeb5a510b08b4f657288/modules/m71150/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@c1fa2c87 | [
"Entrepreneurial Marketing and Sales"
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dabe306be57382975ab6cb117b2e4877 | X:osx:entrepreneurship:m71172 | openstax-entrepreneurship | passage | In addition to improving their products, they also created new ones out of their original scents by adding them to body sprays, lotions, lip shimmer, and candles that smell exactly like the original. Read this Forbes article on Phlur perfume and see how Phlur sold thousands of bottles of its perfume before customers co... | c1fa2c872ba07dc864c3aeb5a510b08b4f657288 | https://github.com/openstax/osbooks-entrepreneurship/blob/c1fa2c872ba07dc864c3aeb5a510b08b4f657288/modules/m71172/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@c1fa2c87 | [
"Launch for Growth to Success"
] | 248 | f38ccbeaa31f1e1f95838f9a1565f7a1ba5814d4b451c887f739f4ba3ea52d14 | 0 | 0 | true |
81b57f36874cd841103e8ea50e704e05 | X:osx:entrepreneurship:m71172 | openstax-entrepreneurship | passage | Franchising is a form of licensing that allows the business (franchisor) to share its business model to expand the business through various distributors (franchisees) for a fee. In turn, the franchisor provides the training, marketing, know-how, management, and support to help the franchisee fulfill its sales objective... | c1fa2c872ba07dc864c3aeb5a510b08b4f657288 | https://github.com/openstax/osbooks-entrepreneurship/blob/c1fa2c872ba07dc864c3aeb5a510b08b4f657288/modules/m71172/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@c1fa2c87 | [
"Launch for Growth to Success"
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91c454a7eb9b5a8d5a5a2221baaf9ff9 | X:osx:entrepreneurship:m80316 | openstax-entrepreneurship | passage | Some investors might prefer out-of-state incorporation, and the entrepreneur needs to remember that the corporation will be subject to taxes, filing requirements, and other fees imposed by each state of operation and the state of incorporation. Delaware is a particularly popular state in which to incorporate due to the... | c1fa2c872ba07dc864c3aeb5a510b08b4f657288 | https://github.com/openstax/osbooks-entrepreneurship/blob/c1fa2c872ba07dc864c3aeb5a510b08b4f657288/modules/m80316/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@c1fa2c87 | [
"Business Structure Options: Legal, Tax, and Risk Issues"
] | 229 | ee6d831b0285cd3f7dbfe1335f6ec1b0173fdd85e5e0ee791c4c2c65e69f5b80 | 0 | 0 | true |
6b411bec41193fc41b7db955031d5a34 | X:osx:entrepreneurship:m80316 | openstax-entrepreneurship | passage | Therefore, your online business may have to collect and remit sales tax to as many as forty-five states (five states do not have a sales tax). All entrepreneurs need to develop an understanding of how the Internet and the related tax laws and regulations will affect their planned business operations. Creating a company... | c1fa2c872ba07dc864c3aeb5a510b08b4f657288 | https://github.com/openstax/osbooks-entrepreneurship/blob/c1fa2c872ba07dc864c3aeb5a510b08b4f657288/modules/m80316/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@c1fa2c87 | [
"Business Structure Options: Legal, Tax, and Risk Issues"
] | 245 | c2466346ef0e212bd24fadcf9d20e703d8bf96c7fd2def5af7ac859b5267c53b | 0 | 0 | true |
4501f23e0b210644796ffc25ed833e24 | X:osx:entrepreneurship:m71190 | openstax-entrepreneurship | passage | It has a wealth of helpful information for entrepreneurs on this topic: https://erm.ncsu.edu/library/article/coso-erm-framework | c1fa2c872ba07dc864c3aeb5a510b08b4f657288 | https://github.com/openstax/osbooks-entrepreneurship/blob/c1fa2c872ba07dc864c3aeb5a510b08b4f657288/modules/m71190/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@c1fa2c87 | [
"Business Structure Options: Legal, Tax, and Risk Issues"
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7a6733f4aa8ceb1f9024d5466e2f4b94 | X:osx:entrepreneurship:m71192 | openstax-entrepreneurship | passage | Check the laws and regulations of your local and state governments to ensure your business meets the legal requirements for licensing and permits. You can do this by contacting the secretary of state in your state and also by contacting your local chamber of commerce. Importantly, these licenses and permits often carry... | c1fa2c872ba07dc864c3aeb5a510b08b4f657288 | https://github.com/openstax/osbooks-entrepreneurship/blob/c1fa2c872ba07dc864c3aeb5a510b08b4f657288/modules/m71192/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@c1fa2c87 | [
"Fundamentals of Resource Planning"
] | 250 | 3a0c0635d63473f38f9f32a43150aeef486e61f791af3438cf2a1f1110a7d23c | 0 | 0 | true |
fdb9338cf53c57c50d275816a5b45f28 | X:osx:entrepreneurship:m71192 | openstax-entrepreneurship | passage | If you don’t make your list first, then you run the risk of ending up in a facility that is not suitable. and provide starting points for thinking through the tangible and intangible resources needs for your venture. Business owners are constantly faced with difficult decisions about resources. A decision tree is a ben... | c1fa2c872ba07dc864c3aeb5a510b08b4f657288 | https://github.com/openstax/osbooks-entrepreneurship/blob/c1fa2c872ba07dc864c3aeb5a510b08b4f657288/modules/m71192/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@c1fa2c87 | [
"Fundamentals of Resource Planning"
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2ef1b8d3641cf44f92cdb8e6f98f52be | X:osx:entrepreneurship:m71192 | openstax-entrepreneurship | passage | Once you have figured out what interest you are willing to give up in return for the investment, make it professional by giving a presentation about the business and signing a contract to ensure that they will get paid back, whether in money or shares of stock. This safeguards the relationship by holding you accountabl... | c1fa2c872ba07dc864c3aeb5a510b08b4f657288 | https://github.com/openstax/osbooks-entrepreneurship/blob/c1fa2c872ba07dc864c3aeb5a510b08b4f657288/modules/m71192/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@c1fa2c87 | [
"Fundamentals of Resource Planning"
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f54016a70f9c3c32fef62d1e5c2abb3c | X:osx:entrepreneurship:m71200 | openstax-entrepreneurship | passage | Depending on your business model, you might need licenses or permits, and your local SBA office will be well informed on these topics and can help you acquire what is needed to support the success of your venture. Watch this video explaining various services offered by the Small Business Administration to learn about r... | c1fa2c872ba07dc864c3aeb5a510b08b4f657288 | https://github.com/openstax/osbooks-entrepreneurship/blob/c1fa2c872ba07dc864c3aeb5a510b08b4f657288/modules/m71200/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@c1fa2c87 | [
"Next Steps"
] | 239 | 3d243786effadd7be9e3ec09ea26825ee682c1463871947f62139d875f30c3d4 | 0 | 0 | true |
ba0196ced06b6c2c7b71c5638fbf5866 | X:osx:physics:m54290 | openstax-physics | passage | If two objects at different temperatures are brought in contact with each other, energy is transferred from the hotter object (that is, the object with the greater temperature) to the colder (lower temperature) object, until both objects are at the same temperature. There is no net heat transfer once the temperatures a... | dfdfd7a5356ecdd42e504de3df50d9153e33ea49 | https://github.com/openstax/osbooks-physics/blob/dfdfd7a5356ecdd42e504de3df50d9153e33ea49/modules/m54290/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@dfdfd7a5 | [
"Thermal Energy, Heat, and Work"
] | 233 | e3cef00a6a799a66033ad76f6c2511bb721287e178c8443322401c198106d5df | 0 | 0 | true |
d1e34c6d989a22a2bdb7b93bd870f5a9 | X:osx:physics:m54290 | openstax-physics | passage | Values of specific heat must be looked up in tables, because there is no simple way to calculate them. gives the values of specific heat for a few substances as a handy reference. We see from this table that the specific heat of water is five times that of glass, which means that it takes five times as much heat to rai... | dfdfd7a5356ecdd42e504de3df50d9153e33ea49 | https://github.com/openstax/osbooks-physics/blob/dfdfd7a5356ecdd42e504de3df50d9153e33ea49/modules/m54290/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@dfdfd7a5 | [
"Thermal Energy, Heat, and Work"
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2a3ba589905bfc34fc0c04923ab0ba23 | X:osx:physics:m54342 | openstax-physics | passage | In addition, the High School Physics Laboratory Manual addresses content in this section in the lab titled: Light and Color, as well as the following standards:
- (7) Science concepts. The student knows the characteristics and behavior of waves. The student is expected to (C) compare characteristics and behaviors of tr... | dfdfd7a5356ecdd42e504de3df50d9153e33ea49 | https://github.com/openstax/osbooks-physics/blob/dfdfd7a5356ecdd42e504de3df50d9153e33ea49/modules/m54342/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@dfdfd7a5 | [
"Light"
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9735efa522b76a3652677e6d8b9677a8 | X:osx:physics:m54342 | openstax-physics | passage | Point out how these three fields are similar, and how they differ.
[AL]Describe vectors as having magnitude and direction, and explain that fields are vector quantities. In these cases, the fields are made up of forces acting in a direction. Electromagnetic radiation is generated by a moving electric charge, that is, b... | dfdfd7a5356ecdd42e504de3df50d9153e33ea49 | https://github.com/openstax/osbooks-physics/blob/dfdfd7a5356ecdd42e504de3df50d9153e33ea49/modules/m54342/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@dfdfd7a5 | [
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7330f16cecc572e381285e19b4c978c9 | X:osx:physics:m54342 | openstax-physics | passage | Television, radio, cell phone, and remote-control devices all broadcast and/or receive signals with these wavelengths. AM and FM radio signals are both low-frequency radiation. They are in different regions of the spectrum, but that is not their basic difference. AM and FM are abbreviations for amplitude modulation and... | dfdfd7a5356ecdd42e504de3df50d9153e33ea49 | https://github.com/openstax/osbooks-physics/blob/dfdfd7a5356ecdd42e504de3df50d9153e33ea49/modules/m54342/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@dfdfd7a5 | [
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1198b091e202e0d024db63a93442b82b | X:osx:physics:m54437 | openstax-physics | passage | Teacher Support
Point out that the charge carriers in this sketch are positive, so they move in the same direction as the electric current. Assume each particle q in carries a charge q=1nC, in which case the total charge shown would be ΔQ=5q=5nC . If these charges move past the area A in a time Δt=1ns, then the current... | dfdfd7a5356ecdd42e504de3df50d9153e33ea49 | https://github.com/openstax/osbooks-physics/blob/dfdfd7a5356ecdd42e504de3df50d9153e33ea49/modules/m54437/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@dfdfd7a5 | [
"Electrical Circuits"
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847d665a36f6e35bcd093633ef76653b | X:osx:physics:m54437 | openstax-physics | passage | See how the current is affected by modifying the resistance and/or the voltage. Note that the resistance is modeled as an element containing small scattering centers. These represent impurities or other obstacles that impede the passage of the current. Resistance of a Headlight
Determine Resistance from Current-Voltage... | dfdfd7a5356ecdd42e504de3df50d9153e33ea49 | https://github.com/openstax/osbooks-physics/blob/dfdfd7a5356ecdd42e504de3df50d9153e33ea49/modules/m54437/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@dfdfd7a5 | [
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90ac81047e9f95db53de234ce1735135 | X:osx:physics:m54437 | openstax-physics | definition | alternating current: electric current whose direction alternates back and forth at regular intervals
ampere: unit for electric current; one ampere is one coulomb per second ( 1A=1C/s )
conventional current: flows in the direction that a positive charge would flow if it could move
direct current: electric current that f... | dfdfd7a5356ecdd42e504de3df50d9153e33ea49 | https://github.com/openstax/osbooks-physics/blob/dfdfd7a5356ecdd42e504de3df50d9153e33ea49/modules/m54437/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@dfdfd7a5 | [
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5fc40be09b62e7331fc6930c735b4718 | X:osx:college-physics-ap-courses-2e:m42102 | openstax-college-physics-ap-courses-2e | passage | Falling Objects
Learning Objectives
By the end of this section, you will be able to:
- Describe the effects of gravity on objects in motion.
- Describe the motion of objects that are in free fall.
- Calculate the position and velocity of objects in free fall. Falling objects form an interesting class of motion problems... | f98d7a792138a6133fe7267d17e70aa04e9ccbed | https://github.com/openstax/osbooks-college-physics-bundle/blob/f98d7a792138a6133fe7267d17e70aa04e9ccbed/modules/m42102/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@f98d7a79 | [
"Kinematics"
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06adff0f9176e52da94df80bc70c648c | X:osx:college-physics-ap-courses-2e:m42132 | openstax-college-physics-ap-courses-2e | passage | The bathroom scale is an excellent example of a normal force acting on a body. It provides a quantitative reading of how much it must push upward to support the weight of an object. But can you predict what you would see on the dial of a bathroom scale if you stood on it during an elevator ride? Will you see a value gr... | f98d7a792138a6133fe7267d17e70aa04e9ccbed | https://github.com/openstax/osbooks-college-physics-bundle/blob/f98d7a792138a6133fe7267d17e70aa04e9ccbed/modules/m42132/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@f98d7a79 | [
"Dynamics: Force and Newton's Laws of Motion"
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4065200e52076b981d6f2eed91e5c00d | X:osx:college-physics-ap-courses-2e:m55108 | openstax-college-physics-ap-courses-2e | passage | Enduring Understanding 3.D A force exerted on an object can change the momentum of the object. Essential Knowledge 3.D.2 The change in momentum of an object occurs over a time interval. Big Idea 4: Interactions between systems can result in changes in those systems. Enduring Understanding 4.B Interactions with other ob... | f98d7a792138a6133fe7267d17e70aa04e9ccbed | https://github.com/openstax/osbooks-college-physics-bundle/blob/f98d7a792138a6133fe7267d17e70aa04e9ccbed/modules/m55108/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@f98d7a79 | [
"Linear Momentum and Collisions"
] | 244 | 1a7e494b59ca04cb59af9487eacc8eceb6333807e10b2665a6bcb441f25eda89 | 0 | 0 | true |
3c38f132f5c3372f5c84890b0d556364 | X:osx:college-physics-ap-courses-2e:m42165 | openstax-college-physics-ap-courses-2e | passage | Collisions of Point Masses in Two Dimensions
Learning Objectives
By the end of this section, you will be able to:
- Discuss two dimensional collisions as an extension of one dimensional analysis.
- Define point masses.
- Derive an expression for conservation of momentum along x-axis and y-axis.
- Describe elastic colli... | f98d7a792138a6133fe7267d17e70aa04e9ccbed | https://github.com/openstax/osbooks-college-physics-bundle/blob/f98d7a792138a6133fe7267d17e70aa04e9ccbed/modules/m42165/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@f98d7a79 | [
"Linear Momentum and Collisions"
] | 239 | 3a09cfc27920fbdb86a67fa371247422252490979dd545c0a6cc2505f2834aeb | 0 | 0 | true |
f806500dae4c8fb29439315dcb9560f3 | X:osx:college-physics-ap-courses-2e:m42226 | openstax-college-physics-ap-courses-2e | definition | conduction: heat transfer through stationary matter by physical contact
convection: heat transfer by the macroscopic movement of fluid
radiation: heat transfer which occurs when microwaves, infrared radiation, visible light, or other electromagnetic radiation is emitted or absorbed | f98d7a792138a6133fe7267d17e70aa04e9ccbed | https://github.com/openstax/osbooks-college-physics-bundle/blob/f98d7a792138a6133fe7267d17e70aa04e9ccbed/modules/m42226/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@f98d7a79 | [
"Heat and Heat Transfer Methods",
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"radiation"
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c9d77946d6b75e9ec7545b87e9e9e1ff | X:osx:college-physics-ap-courses-2e:m42444 | openstax-college-physics-ap-courses-2e | passage | Here a carrier wave having the basic frequency of the radio station, perhaps 105.1 MHz, is modulated in frequency by the audio signal, producing a wave of constant amplitude but varying frequency. Since audible frequencies range up to 20 kHz (or 0.020 MHz) at most, the frequency of the FM radio wave can vary from the c... | f98d7a792138a6133fe7267d17e70aa04e9ccbed | https://github.com/openstax/osbooks-college-physics-bundle/blob/f98d7a792138a6133fe7267d17e70aa04e9ccbed/modules/m42444/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@f98d7a79 | [
"Electromagnetic Waves"
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3ed55a80e7ebc3c1d0c8a2ec6c281525 | X:osx:college-physics-ap-courses-2e:m42444 | openstax-college-physics-ap-courses-2e | passage | Most lasers used for this type of eye surgery have an average power rating of about one watt. For our example, if we assume that each laser burst from this pulsed laser lasts for 10 ns, and there are 400 bursts per second, then the average power is Qtot×400=150mW. Optics is the study of the behavior of visible light an... | f98d7a792138a6133fe7267d17e70aa04e9ccbed | https://github.com/openstax/osbooks-college-physics-bundle/blob/f98d7a792138a6133fe7267d17e70aa04e9ccbed/modules/m42444/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@f98d7a79 | [
"Electromagnetic Waves"
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98c6f890f35b6c34dfeb3448452bda35 | X:osx:college-physics-ap-courses-2e:m55362 | openstax-college-physics-ap-courses-2e | passage | This chapter supports Big Idea 6 in its coverage of wave optics by presenting explanations and examples of many phenomena that can only be explained by the wave aspect of light. You will learn how only waves can exhibit diffraction and interference patterns that we observe in light (Enduring Understanding 6.C). As expl... | f98d7a792138a6133fe7267d17e70aa04e9ccbed | https://github.com/openstax/osbooks-college-physics-bundle/blob/f98d7a792138a6133fe7267d17e70aa04e9ccbed/modules/m55362/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@f98d7a79 | [
"Wave Optics"
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61db8c54bf5611072999eecb378de541 | X:osx:college-physics-ap-courses-2e:m42542 | openstax-college-physics-ap-courses-2e | passage | Relativistic Momentum
Learning Objectives
By the end of this section, you will be able to:
- Calculate relativistic momentum.
- Explain why the only mass it makes sense to talk about is rest mass. In classical physics, momentum is a simple product of mass and velocity. However, we saw in the last section that when spec... | f98d7a792138a6133fe7267d17e70aa04e9ccbed | https://github.com/openstax/osbooks-college-physics-bundle/blob/f98d7a792138a6133fe7267d17e70aa04e9ccbed/modules/m42542/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@f98d7a79 | [
"Special Relativity"
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6b0891087da487be80a5f5455912d139 | X:osx:college-physics-ap-courses-2e:m42568 | openstax-college-physics-ap-courses-2e | definition | photon momentum: the amount of momentum a photon has, calculated by p=hλ=Ec
Compton effect: the phenomenon whereby x rays scattered from materials have decreased energy | f98d7a792138a6133fe7267d17e70aa04e9ccbed | https://github.com/openstax/osbooks-college-physics-bundle/blob/f98d7a792138a6133fe7267d17e70aa04e9ccbed/modules/m42568/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@f98d7a79 | [
"Quantum Physics",
"photon momentum",
"Compton effect"
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85ce5ffde5419632500a3a041a8d3e87 | X:osx:college-physics-ap-courses-2e:m42627 | openstax-college-physics-ap-courses-2e | passage | Ionizing radiation passing through the tube produces free ion pairs (each pair consisting of one positively charged particle and one negatively charged particle) that are attracted to the wire and cylinder, forming a current that is detected as a count. The word count implies that there is no information on energy, cha... | f98d7a792138a6133fe7267d17e70aa04e9ccbed | https://github.com/openstax/osbooks-college-physics-bundle/blob/f98d7a792138a6133fe7267d17e70aa04e9ccbed/modules/m42627/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@f98d7a79 | [
"Radioactivity and Nuclear Physics"
] | 241 | f0ceaab8d74d3edea90e477ed6d7684b36c7a80f12d8fcb9ff0f53c37683b648 | 0 | 0 | true |
8c074b0bbe6c3bf565f917368b7b14e2 | X:osx:college-physics-ap-courses-2e:m42680 | openstax-college-physics-ap-courses-2e | passage | Not only were three particles having spin 1 predicted, the mass of the W+ and W− was predicted to be 81GeV/c2, and that of the Z0 was predicted to be 90GeV/c2. (Their masses had to be about 1000 times that of the pion, or about 100GeV/c2, since the range of the weak force is about 1000 times less than the strong force ... | f98d7a792138a6133fe7267d17e70aa04e9ccbed | https://github.com/openstax/osbooks-college-physics-bundle/blob/f98d7a792138a6133fe7267d17e70aa04e9ccbed/modules/m42680/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@f98d7a79 | [
"Particle Physics"
] | 226 | 6000cdf9862fa15e1caf982fa36d95d0296427141045bf4557d95cfe29c9a45f | 0 | 0 | true |
b1e7a139ad77e51bd751d76343750f17 | X:osx:college-physics-ap-courses-2e:m42680 | openstax-college-physics-ap-courses-2e | passage | Taken together, QCD and the electroweak theory are widely accepted as the Standard Model of particle physics.
- Unification of the strong force is expected at such high energies that it cannot be directly tested, but it may have observable consequences in the as-yet unobserved decay of the proton and topics to be discu... | f98d7a792138a6133fe7267d17e70aa04e9ccbed | https://github.com/openstax/osbooks-college-physics-bundle/blob/f98d7a792138a6133fe7267d17e70aa04e9ccbed/modules/m42680/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@f98d7a79 | [
"Particle Physics"
] | 107 | ca4f7cf97a13a8dd2594c5a9cae625ef7f968b90d0f5d157914023d2e81299af | 0 | 0 | true |
dc6f6abbbdf36b8f1032c25dd43d4f75 | X:osx:life-liberty-and-pursuit-happiness:m76321 | openstax-life-liberty-and-pursuit-happiness | passage | In 1613, Powhatan’s daughter, Pocahontas, was lured aboard an English ship and held hostage at Jamestown. While living there, she converted to Christianity, took the name Rebecca, and married a colonist named John Rolfe (). Powhatan supported the marriage. For Europeans and American Indians, marriage was a traditional ... | acb6fbe2744dd112187b6aff5946cfe969410fca | https://github.com/openstax/osbooks-life-liberty-and-pursuit-happiness/blob/acb6fbe2744dd112187b6aff5946cfe969410fca/modules/m76321/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@acb6fbe2 | [
"1607–1763"
] | 248 | d53acb6a6f81d3a9dde18899c58e57c03b690019af7d9355946638eb29693233 | 0 | 0 | true |
7b35fbb43d53ce0bee1d8f5f58b3c690 | X:osx:life-liberty-and-pursuit-happiness:m80579 | openstax-life-liberty-and-pursuit-happiness | passage | 🔎 The Election of 1860
Standards
Topic: 5.7 Election of 1860 and Secession
Theme: PCE Politics and Power
Learning Objective: Unit 5H Describe the effects of Lincoln’s election
Historical Development: 5.2.II.D
Historical Thinking Skills: HTS-2 Sourcing and Situation, HTS-3 Source Claims and Evidence, HTS-4 Contextualiz... | acb6fbe2744dd112187b6aff5946cfe969410fca | https://github.com/openstax/osbooks-life-liberty-and-pursuit-happiness/blob/acb6fbe2744dd112187b6aff5946cfe969410fca/modules/m80579/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@acb6fbe2 | [
"1844–1860"
] | 252 | b38c4c7ba7c2a1f200e8036522f3c6091f1991a45e5bb1b84daf98ab61eaf188 | 0 | 0 | true |
94f8534f56c36d09bfc84056d38a96a9 | X:osx:life-liberty-and-pursuit-happiness:m80591 | openstax-life-liberty-and-pursuit-happiness | passage | How did they differ?
- How did Lecouvreur’s immigrant status influence his perception of mining life?
- As an educated American woman from the East Coast, how did Clappe’s experiences influence her perception of mining life?
- How did Lecouvreur and Clappe describe the class relations and ethnic diversity in California... | acb6fbe2744dd112187b6aff5946cfe969410fca | https://github.com/openstax/osbooks-life-liberty-and-pursuit-happiness/blob/acb6fbe2744dd112187b6aff5946cfe969410fca/modules/m80591/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@acb6fbe2 | [
"1844–1860"
] | 229 | e48ca2c2cb50dd92a583c7aa93bac8d0da9f77c05a5dd326d9baff87409ba4a8 | 0 | 0 | true |
380ab85533f1cd55ba9742aa2b8e12d4 | X:osx:life-liberty-and-pursuit-happiness:m83507 | openstax-life-liberty-and-pursuit-happiness | passage | They lynched black men and set their bodies afire. For three days the riot raged on, until state militia and U.S. Army troops arrived and restored order. The violence left more than 100 dead, at least 2,000 injured, and more than 50 buildings destroyed. It was one of the worst riots in American history and demonstrated... | acb6fbe2744dd112187b6aff5946cfe969410fca | https://github.com/openstax/osbooks-life-liberty-and-pursuit-happiness/blob/acb6fbe2744dd112187b6aff5946cfe969410fca/modules/m83507/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@acb6fbe2 | [
"1860–1877"
] | 242 | 6f4f380f7a021d4c11b92e522503fc73e8628838bde7ffd10fa411fa5ac0a4ab | 0 | 0 | true |
49bb96bf22dcc2c24e6872daef2f58e5 | X:osx:life-liberty-and-pursuit-happiness:m80605 | openstax-life-liberty-and-pursuit-happiness | passage | When the line crossed into the Utah Territory, it hired many Mormon workers to complete the line (and tried to cheat them on their wages). Finally, on May 10, 1869, the two railroads met at Promontory Summit, Utah, and a golden spike was driven in by Leland Stanford to commemorate one of the great engineering feats of ... | acb6fbe2744dd112187b6aff5946cfe969410fca | https://github.com/openstax/osbooks-life-liberty-and-pursuit-happiness/blob/acb6fbe2744dd112187b6aff5946cfe969410fca/modules/m80605/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@acb6fbe2 | [
"1877–1898"
] | 206 | 043746bcbffb6360f9e9d86e5692ef0e6562a90f5351dd859063d3e1d55fdbd4 | 0 | 0 | true |
9ec64e80650377f014642fa830e8ae65 | X:osx:life-liberty-and-pursuit-happiness:m80607 | openstax-life-liberty-and-pursuit-happiness | passage | An even larger force of 1,300 cavalry and Indian allies left Fort Fetterman under General George Crook and were searching for Sitting Bull’s village on the Rosebud River. Although Sitting Bull had ordered the warriors to adopt a defensive posture, the young warriors rushed out to attack the column and assaulted it seve... | acb6fbe2744dd112187b6aff5946cfe969410fca | https://github.com/openstax/osbooks-life-liberty-and-pursuit-happiness/blob/acb6fbe2744dd112187b6aff5946cfe969410fca/modules/m80607/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@acb6fbe2 | [
"1877–1898"
] | 217 | c9181c4bcb5e84bf7c46c223a9230a7dd63627787bf5dc6b42a1e3ae6237df69 | 0 | 0 | true |
18a17102bb73dd2cf1f354fb44825e67 | X:osx:life-liberty-and-pursuit-happiness:m83549 | openstax-life-liberty-and-pursuit-happiness | passage | The vast majority of black soldiers (89 percent) were classified as noncombatants and worked long days loading and unloading ships, building training camps and roads, or burying the dead. The 369th Infantry Regiment, the Harlem Hellfighters, was one of four black combatant regiments that gained acclaim by fighting unde... | acb6fbe2744dd112187b6aff5946cfe969410fca | https://github.com/openstax/osbooks-life-liberty-and-pursuit-happiness/blob/acb6fbe2744dd112187b6aff5946cfe969410fca/modules/m83549/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@acb6fbe2 | [
"1898–1919"
] | 217 | d4088d0cb5bff785dc74fbedfaaae6ba0c38012432788c3bf12553c8e48a8272 | 0 | 0 | true |
85398ae9827939331353e765692908e1 | X:osx:life-liberty-and-pursuit-happiness:m83549 | openstax-life-liberty-and-pursuit-happiness | passage | “I hope that you have not arrived too late,” the U.S. ambassador to France told Pershing when he arrived overseas. In March 1918, the Germans launched a series of breakthrough attacks intended to win the war while they still had a numerical advantage on the battlefield. Russia had just left the war after signing a sepa... | acb6fbe2744dd112187b6aff5946cfe969410fca | https://github.com/openstax/osbooks-life-liberty-and-pursuit-happiness/blob/acb6fbe2744dd112187b6aff5946cfe969410fca/modules/m83549/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@acb6fbe2 | [
"1898–1919"
] | 225 | c166b010f0ef6843424f80eac39533ebbf2a54cdc512c580d6bbd2bdc82082c1 | 0 | 0 | true |
3a6f0762c77aae5c041880167fcb9fbd | X:osx:life-liberty-and-pursuit-happiness:m83549 | openstax-life-liberty-and-pursuit-happiness | passage | “What I dread is that Germany doesn’t know that she was licked, had they given us another week, we’d have taught them,” he remarked. Correcting this mistake took another world war, fought by commanders including Douglas MacArthur, George Patton, and George Marshall who had learned their craft by serving under Pershing ... | acb6fbe2744dd112187b6aff5946cfe969410fca | https://github.com/openstax/osbooks-life-liberty-and-pursuit-happiness/blob/acb6fbe2744dd112187b6aff5946cfe969410fca/modules/m83549/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@acb6fbe2 | [
"1898–1919"
] | 237 | d9f4f40968eeb8163f5b0a02453be26eba6f022883ba0fb6169b39a0ae942de6 | 0 | 0 | true |
84e3e8dcc29d8cae471f75cf536cf2a6 | X:osx:life-liberty-and-pursuit-happiness:m84370 | openstax-life-liberty-and-pursuit-happiness | passage | A crowd of African Americans gathered, and when one fired at the police who surrounded them, the police shot and killed him. By 9:00 that night, white gangs were roaming the black neighborhood, beating, stabbing, and terrorizing African Americans. The next morning, white men killed two black workers on their way to the... | acb6fbe2744dd112187b6aff5946cfe969410fca | https://github.com/openstax/osbooks-life-liberty-and-pursuit-happiness/blob/acb6fbe2744dd112187b6aff5946cfe969410fca/modules/m84370/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@acb6fbe2 | [
"1920–1932"
] | 229 | a056797d2f5420833e57e63df1fa42362c77daee6c17e24e667669e0559019d5 | 0 | 0 | true |
f662ea85a0f8ca8b8f44f74c7c999566 | X:osx:life-liberty-and-pursuit-happiness:m84519 | openstax-life-liberty-and-pursuit-happiness | passage | Kennedy refused, and in August, Khrushchev ordered the Berlin Wall to be built separating East and West Berlin. This stemmed the large flow of emigrants from East to West that had characterized the city since its division. The building of the wall represented an admission on the part of the Soviet Union that the United... | acb6fbe2744dd112187b6aff5946cfe969410fca | https://github.com/openstax/osbooks-life-liberty-and-pursuit-happiness/blob/acb6fbe2744dd112187b6aff5946cfe969410fca/modules/m84519/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@acb6fbe2 | [
"1960–1968"
] | 233 | b7f1ea0310a9eee03f0cdb2b578086e31fcccf8e2f325dfe66cfab77a28c9cbd | 0 | 0 | true |
71766e4b56db796f998f091abb2c1ad8 | X:osx:life-liberty-and-pursuit-happiness:m84566 | openstax-life-liberty-and-pursuit-happiness | passage | NASA proposed the space shuttle as the successor to Apollo in 1969, though the program was not formally adopted and announced to the public until 1972, a few months before the final manned landing on the moon via Apollo 17. In one respect, the shuttle program represented a scaling back of America’s space exploration am... | acb6fbe2744dd112187b6aff5946cfe969410fca | https://github.com/openstax/osbooks-life-liberty-and-pursuit-happiness/blob/acb6fbe2744dd112187b6aff5946cfe969410fca/modules/m84566/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@acb6fbe2 | [
"1980–Present"
] | 249 | 90c1c4648f4b41d66f85b55ba8499961d7b2e91b614c105103f5fc0a33421cab | 0 | 0 | true |
d85744ff2da95f630603b3e40207f296 | X:osx:life-liberty-and-pursuit-happiness:m84586 | openstax-life-liberty-and-pursuit-happiness | passage | Claim B
Terrorist threats do not justify infringing on individual freedom and privacy rights, nor do they justify the relaxation of legal checks on surveillance. The U.S. Constitution includes numerous protections of civil rights and liberties, from the First Amendment’s guarantee of freedom of speech to the Fourth Ame... | acb6fbe2744dd112187b6aff5946cfe969410fca | https://github.com/openstax/osbooks-life-liberty-and-pursuit-happiness/blob/acb6fbe2744dd112187b6aff5946cfe969410fca/modules/m84586/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@acb6fbe2 | [
"1980–Present"
] | 222 | c6e2deffa9b0670e046e03a13758c2c8c11f32e6cbbddb9a84ddd869919f8bc0 | 0 | 0 | true |
26211cfda77906aca082675ab2a1a8c5 | X:osx:life-liberty-and-pursuit-happiness:m84586 | openstax-life-liberty-and-pursuit-happiness | passage | Individuals should be notified of searches so they can notify an attorney and file a court challenge if they believe they have been wrongly targeted. Another example of government overreach is the use of National Security Letters (NSLs) authorized by the USA PATRIOT Act. Unlike sneak-and-peek searches that require a wa... | acb6fbe2744dd112187b6aff5946cfe969410fca | https://github.com/openstax/osbooks-life-liberty-and-pursuit-happiness/blob/acb6fbe2744dd112187b6aff5946cfe969410fca/modules/m84586/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@acb6fbe2 | [
"1980–Present"
] | 245 | ad70d32b786e78dc04f7f9d3061537a3e4724cb1aa1f3ce327fa68e3b7fa8803 | 0 | 0 | true |
a93d74276ff7f6386aeb69397c9abf1b | X:osx:life-liberty-and-pursuit-happiness:m84626 | openstax-life-liberty-and-pursuit-happiness | passage | In the unanimous decision, the court determined that the act was unconstitutional because it shifted the power to regulate commerce from the legislative branch to the executive branch and regulated intrastate commerce within a state contrary to the Commerce Clause in Article I, section 8. Korematsu v. U.S., 323 U.S. 21... | acb6fbe2744dd112187b6aff5946cfe969410fca | https://github.com/openstax/osbooks-life-liberty-and-pursuit-happiness/blob/acb6fbe2744dd112187b6aff5946cfe969410fca/modules/m84626/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@acb6fbe2 | [] | 237 | 2658cceb0c957bfb1f3809317c23266e80dd199dd8f9482953f6f95fd6423be3 | 0 | 0 | true |
ed04753077cfce94158e895847e74c4b | X:osx:chemistry-atoms-first-2e:m68733 | openstax-chemistry-atoms-first-2e | passage | It was demonstrated in the 1920s that when hydrogen-line spectra are examined at extremely high resolution, some lines are actually not single peaks but, rather, pairs of closely spaced lines. This is the so-called fine structure of the spectrum, and it implies that there are additional small differences in energies of... | 32c719622fbb7a0ca729cd645c1df4cf4e7d5b3a | https://github.com/openstax/osbooks-chemistry-bundle/blob/32c719622fbb7a0ca729cd645c1df4cf4e7d5b3a/modules/m68733/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@32c71962 | [
"Electronic Structure and Periodic Properties of Elements"
] | 246 | b7db97197b893ffd4813c5e9a8419bd8ffa4e0619c32a18b280aaa5ffee41d63 | 0 | 0 | true |
4cbafc674cb3a0b5b2335a4f4fe0204f | X:osx:chemistry-atoms-first-2e:m68742 | openstax-chemistry-atoms-first-2e | passage | The two lone pairs are on opposite sides of the octahedron (180° apart), giving a square planar molecular structure that minimizes lone pair-lone pair repulsions (). Predicting Electron Pair Geometry and Molecular Structure
The following procedure uses VSEPR theory to determine the electron pair geometries and the mole... | 32c719622fbb7a0ca729cd645c1df4cf4e7d5b3a | https://github.com/openstax/osbooks-chemistry-bundle/blob/32c719622fbb7a0ca729cd645c1df4cf4e7d5b3a/modules/m68742/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@32c71962 | [
"Chemical Bonding and Molecular Geometry"
] | 245 | b87f6e19843ff479a7932474ce8b5b72396ffb5436657c1e92aa85d0eedb6aa9 | 0 | 0 | true |
09279b80cf9612f6427bb001bcea44cc | X:osx:chemistry-atoms-first-2e:m68742 | openstax-chemistry-atoms-first-2e | passage | The five atoms are all in the same plane and have a square planar molecular structure. Check Your Learning In a certain molecule, the central atom has three lone pairs and two bonds. What will the electron pair geometry and molecular structure be? Answer:
electron pair geometry: trigonal bipyramidal; molecular structur... | 32c719622fbb7a0ca729cd645c1df4cf4e7d5b3a | https://github.com/openstax/osbooks-chemistry-bundle/blob/32c719622fbb7a0ca729cd645c1df4cf4e7d5b3a/modules/m68742/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@32c71962 | [
"Chemical Bonding and Molecular Geometry"
] | 218 | 1e9c35c38015da8b6e9c31a3f429e258a15d83a80903746cd8e5ebf83aa1d57f | 0 | 0 | true |
86fa182a6ddb2be48f52b4aadf849225 | X:osx:chemistry-atoms-first-2e:m71828 | openstax-chemistry-atoms-first-2e | passage | Solution The ratio of the volumes of C3H8 and O2 will be equal to the ratio of their coefficients in the balanced equation for the reaction:
From the equation, we see that one volume of C3H8 will react with five volumes of O2:
A volume of 13.5 L of O2 will be required to react with 2.7 L of C3H8. Check Your Learning An... | 32c719622fbb7a0ca729cd645c1df4cf4e7d5b3a | https://github.com/openstax/osbooks-chemistry-bundle/blob/32c719622fbb7a0ca729cd645c1df4cf4e7d5b3a/modules/m71828/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@32c71962 | [
"Gases"
] | 231 | 1e2906cbe5f0a9ead03f2610c00c0f7c872f68c1b3b606ac88985d896f894e02 | 0 | 0 | true |
aa19c2d58ee0a4465b1f2200f09abfd3 | X:osx:chemistry-atoms-first-2e:m68821 | openstax-chemistry-atoms-first-2e | definition | electrode potential (EX): the potential of a cell in which the half-cell of interest acts as a cathode when connected to the standard hydrogen electrode
half cell: component of a cell that contains the redox conjugate pair (“couple”) of a single reactant | 32c719622fbb7a0ca729cd645c1df4cf4e7d5b3a | https://github.com/openstax/osbooks-chemistry-bundle/blob/32c719622fbb7a0ca729cd645c1df4cf4e7d5b3a/modules/m68821/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@32c71962 | [
"Electrochemistry",
"electrode potential (EX)",
"half cell"
] | 57 | 30e9546ba31357b0202fd26ffc1cfb9449036f77aaaefb14ba7e4b639f68ffba | 0 | 0 | true |
820db651b9478f9f9d85def132164a4c | X:osx:intermediate-algebra-2e:m81373 | openstax-intermediate-algebra-2e | passage | For each ordered pair in the relation, each x-value is matched with only one y-value. Function
A function is a relation that assigns to each element in its domain exactly one element in the range. The birthday example from helps us understand this definition. Every person has a birthday but no one has two birthdays. It... | 77a933c672e9c48c746eb802d588a9a7ddfd6e0d | https://github.com/openstax/osbooks-prealgebra-bundle/blob/77a933c672e9c48c746eb802d588a9a7ddfd6e0d/modules/m81373/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@77a933c6 | [
"Graphs and Functions"
] | 241 | d2581574976ff715ac1f2eae3cd28753e0a106a8cac531f774c59be19fb97a9a | 0 | 0 | true |
341bde4df87f438baf3f07ac3e931b05 | X:osx:intermediate-algebra-2e:m81373 | openstax-intermediate-algebra-2e | passage | Access this online resource for additional instruction and practice with relations and functions.
- Introduction to Functions
Key Concepts
- Function Notation: For the function y=f(x) f is the name of the function x is the domain value f(x) is the range value y corresponding to the value x We read f(x) as f of x or the... | 77a933c672e9c48c746eb802d588a9a7ddfd6e0d | https://github.com/openstax/osbooks-prealgebra-bundle/blob/77a933c672e9c48c746eb802d588a9a7ddfd6e0d/modules/m81373/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@77a933c6 | [
"Graphs and Functions"
] | 221 | 95815b7a0d53c35ed8745d9682bcf69b273a74a29fb7433b2050265f4d355c56 | 0 | 0 | true |
3a538e0fdcb620276ed5b540ca458cf3 | X:osx:intermediate-algebra-2e:m81439 | openstax-intermediate-algebra-2e | passage | Add and Subtract Rational Expressions
Before you get started, take this readiness quiz. Add and Subtract Rational Expressions with a Common Denominator
What is the first step you take when you add numerical fractions? You check if they have a common denominator. If they do, you add the numerators and place the sum over... | 77a933c672e9c48c746eb802d588a9a7ddfd6e0d | https://github.com/openstax/osbooks-prealgebra-bundle/blob/77a933c672e9c48c746eb802d588a9a7ddfd6e0d/modules/m81439/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@77a933c6 | [
"Rational Expressions and Functions"
] | 244 | 8c355e85333a1e66cece38e250d860652b4e799aa7672423731083d0fa06c72a | 0 | 0 | true |
d8440434a0f1ce83635255872763fa39 | X:osx:intermediate-algebra-2e:m81439 | openstax-intermediate-algebra-2e | passage | What value of x should be excluded in the next example? To subtract rational expressions, they must also have a common denominator. When the denominators are the same, you subtract the numerators and place the difference over the common denominator. Be careful of the signs when you subtract a binomial or trinomial. Add... | 77a933c672e9c48c746eb802d588a9a7ddfd6e0d | https://github.com/openstax/osbooks-prealgebra-bundle/blob/77a933c672e9c48c746eb802d588a9a7ddfd6e0d/modules/m81439/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@77a933c6 | [
"Rational Expressions and Functions"
] | 242 | 7aebc312db8a930e288365329f03ae543d274ea0cb2f865740582651b5763d34 | 0 | 0 | true |
ae5717b1f918d466a28e56deaa354223 | X:osx:intermediate-algebra-2e:m81439 | openstax-intermediate-algebra-2e | passage | No – Rewrite each rational expression with the LCD. Find the LCD. Rewrite each rational expression as an equivalent rational expression with the LCD. Add or subtract the rational expressions. Simplify, if possible. Practice Makes Perfect
Add and Subtract Rational Expressions with a Common Denominator
In the following e... | 77a933c672e9c48c746eb802d588a9a7ddfd6e0d | https://github.com/openstax/osbooks-prealgebra-bundle/blob/77a933c672e9c48c746eb802d588a9a7ddfd6e0d/modules/m81439/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@77a933c6 | [
"Rational Expressions and Functions"
] | 231 | 3e77172f74f4df6e76d9cf8643c0fa76b3d19a52d213104eaa50ccd365da7d1e | 0 | 0 | true |
28d3e158e02ea1d88570c62a4720576f | X:osx:intermediate-algebra-2e:m81409 | openstax-intermediate-algebra-2e | passage | The graphs of f(x)=(12)x and g(x)=(13)x as well as the graphs of f(x)=(14)x and g(x)=(15)x all have the same basic shape. While this is the shape we expect from an exponential function where 0<a<1, the graphs go down from left to right while the previous graphs, when a>1, went from up from left to right. We notice that... | 77a933c672e9c48c746eb802d588a9a7ddfd6e0d | https://github.com/openstax/osbooks-prealgebra-bundle/blob/77a933c672e9c48c746eb802d588a9a7ddfd6e0d/modules/m81409/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@77a933c6 | [
"Exponential and Logarithmic Functions"
] | 246 | 966a5af47d73209fe4a7a780cb854d981b72d74c19ef5aa9781686f3a7a446a0 | 0 | 0 | true |
5314b6610c0a302aa315556ea884276a | X:osx:population-health:m00134 | openstax-population-health | passage | The following are examples of how implicit racial bias manifests in the health care setting:
- BIPOC clients receive fewer cardiovascular interventions than their White counterparts, resulting in higher cardiovascular mortality rates (Bridges, 2018; Eberly et al., 2021; Emory University, 2023; Quach, 2020).
- BIPOC cli... | f0124920c65609137effe2333dea327d1c77accc | https://github.com/openstax/osbooks-nursing-external-bundle/blob/f0124920c65609137effe2333dea327d1c77accc/modules/m00134/index.cnxml | 2026-08-02 | null | CC-BY-4.0 | per-record-metadata:LICENSE@f0124920 | [
"Structural Racism and Systemic Inequities"
] | 250 | 7492fc88f4074ca018f31d3df9fcfd16254dd80aa99412692ecf91bd494a4911 | 0 | 0 | true |
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