5.3.1: Position, Speed, and Direction
Lesson
Let's use signed numbers to represent movement.
Exercise \(\PageIndex{1}\): Distance, Rate, Time
- An airplane moves at a constant speed of 120 miles per hour for 3 hours. How far does it go?
- A train moves at constant speed and travels 6 miles in 4 minutes. What is its speed in miles per minute?
- A car moves at a constant speed of 50 miles per hour. How long does it take the car to go 200 miles?
Exercise \(\PageIndex{2}\): Going Left, Going Right
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After each move, record your location in the table. Then write an expression to represent the ending position that uses the starting position, the speed, and the time. The first row is done for you.
starting position direction speed (units per second) time (seconds) ending position (units) expression \(0\) right \(5\) \(3\) \(+15\) \(0+5\cdot 3\) \(0\) left \(4\) \(6\) \(0\) right \(2\) \(8\) \(0\) right \(6\) \(2\) \(0\) left \(1.1\) \(5\) Table \(\PageIndex{1}\) - How can you see the direction of movement in the expression?
- Using a starting position \(p\), a speed \(s\), and a time \(t\), write two expressions for an ending position. One expression should show the result of moving right, and one expression should show the result of moving left.
Exercise \(\PageIndex{3}\): Velocity
A traffic safety engineer was studying travel patterns along a highway. She set up a camera and recorded the speed and direction of cars and trucks that passed by the camera. Positions to the east of the camera are positive, and to the west are negative.
Vehicles that are traveling towards the east have a positive velocity, and vehicles that are traveling towards the west have a negative velocity.
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Complete the table with the position of each vehicle if the vehicle is traveling at a constant speed for the indicated time period. Then write an equation.
velocity (meters per second) time after passing the camera (seconds) ending position (meters) equation describing the position \(+25\) \(+10\) \(+250\) \(25\cdot 10=250\) \(-20\) \(+30\) \(+32\) \(+40\) \(-35\) \(+20\) \(+28\) \(0\) Table \(\PageIndex{2}\) - If a car is traveling east when it passes the camera, will its position be positive or negative 60 seconds after it passes the camera? If we multiply two positive numbers, is the result positive or negative?
- If a car is traveling west when it passes the camera, will its position be positive or negative 60 seconds after it passes the camera? If we multiply a negative and a positive number, is the result positive or negative?
Are you ready for more?
In many contexts we can interpret negative rates as "rates in the opposite direction." For example, a car that is traveling -35 miles per hour is traveling in the opposite direction of a car that is traveling 40 miles per hour.
- What could it mean if we say that water is flowing at a rate of -5 gallons per minute?
- Make up another situation with a negative rate, and explain what it could mean.
Summary
We can use signed numbers to represent the position of an object along a line.  Positions to the right of zero are positive. Positions to the left of zero are negative.
When we combine speed with direction indicated by the sign of the number, it is called velocity . For example, if you are moving 5 meters per second to the right, then your velocity is +5 meters per second. If you are moving 5 meters per second to the left, then your velocity is -5 meters per second.
If you start at zero and move 5 meters per second for 10 seconds, you will be \(5\cdot 10=50\) meters to the right of zero. In other words, \(5\cdot 10=50\).
If you start at zero and move -5 meters per second for 10 seconds, you will be \(5\cdot 10=50\) meters to the left of zero. In other words,
\(-5\cdot 10=-50\)
In general, a negative number times a positive number is a negative number.
Practice
Exercise \(\PageIndex{4}\)
A number line can represent positions that are north and south of a truck stop on a highway. Decide whether you want positive positions to be north or south of the truck stop. Then plot the following positions on a number line.
- The truck stop
- \(5\) miles north of the truck stop
- \(3.5\) miles south of the truck stop
Exercise \(\PageIndex{5}\)
- How could you distinguish between traveling west at 5 miles per hour and traveling east at 5 miles per hour without using the words “east” and “west”?
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Four people are cycling. They each start at the same point. (0 represents their starting point.) Plot their finish points after five seconds of cycling on a number line.
- Lin cycles at 5 meters per second
- Diego cycles at -4 meters per second
- Elena cycles at 3 meters per second
- Noah cycles at -6 meters per second
Exercise \(\PageIndex{6}\)
Find the value of each expression.
- \(16.2+-8.4\)
- \(\frac{2}{5}-\frac{3}{5}\)
- \(-9.2+-7\)
- \(-4\frac{3}{8}-(-1\frac{1}{4})\)
(From Unit 5.2.5)
Exercise \(\PageIndex{7}\)
For each equation, write two more equations using the same numbers that express the same relationship in a different way.
- \(3+2=5\)
- \(7.1+3.4=10.5\)
- \(15-8=7\)
- \(\frac{3}{2}+\frac{9}{5}=\frac{33}{10}\)
(From Unit 5.2.4)
Exercise \(\PageIndex{8}\)
A shopper bought a watermelon, a pack of napkins, and some paper plates. In his state, there is no tax on food. The tax rate on non-food items is 5%. The total for the three items he bought was $8.25 before tax, and he paid $0.19 in tax. How much did the watermelon cost?
(From Unit 4.3.1)
Exercise \(\PageIndex{9}\)
Which graphs could not represent a proportional relationship? Explain how you decided.
(From Unit 2.4.1)


29.7A: Characteristics and Evolution of Primates
- Identify key characteristics of primates
Characteristics of Primates
All primate species possess adaptations for climbing trees, as they all descended from tree-dwellers. This arboreal heritage of primates has resulted in adaptations that include, but are not limited to: 1) a rotating shoulder joint; 2) a big toe that is widely separated from the other toes and thumbs, that are widely separated from fingers (except humans), which allow for gripping branches; and 3) stereoscopic vision, two overlapping fields of vision from the eyes, which allows for the perception of depth and gauging distance. Other characteristics of primates are brains that are larger than those of most other mammals (larger brain/body ratio than similar-sized non-primates), claws that have been modified into flattened nails, typically only one offspring per pregnancy, and a trend toward holding the body upright.
The Order Primates is divided into two groups: prosimians and anthropoids. Prosimians include the bush babies and pottos of Africa, the lemurs of Madagascar, and the lorises of Southeast Asia. Tarsier, also from Southeast Asia, show some prosimian-like and some anthropoid-like features. Anthropoids include monkeys, apes, and humans. In general, prosimians tend to be nocturnal (in contrast to diurnal anthropoids, excluding the nocturnal Aotus , owl monkey) and have a smaller brain/body ratio than anthropoids.
Evolution of Primates
The first primate-like mammals are referred to as proto-primates. They were roughly similar to squirrels and tree shrews in size and appearance. The existing fossil evidence (mostly from North Africa) is very fragmentary. These proto-primates will remain largely mysterious creatures until more fossil evidence becomes available. The oldest known primate-like mammal with a relatively robust fossil record is Plesiadapis (although some researchers do not agree that Plesiadapis was a proto-primate). Fossils of this primate have been dated to approximately 55 million years ago. Plesiadapiforms had some features of the teeth and skeleton in common with true primates. They were found in North America and Europe in the Cenozoic, going extinct by the end of the Eocene.
The first true primates were found in North America, Europe, Asia, and Africa in the Eocene Epoch. These early primates resembled present-day prosimians such as lemurs. Evolutionary changes continued in these early primates, with larger brains and eyes, and smaller muzzles being the trend. By the end of the Eocene Epoch, many of the early prosimian species went extinct due either to cooler temperatures or competition from the first monkeys.
Evidence shows that the anthropoid monkeys evolved from prosimians during the Oligocene Epoch. By 35 million years ago, evidence indicates that monkeys were present the Old World (Africa and Asia) and in the New World (South America) by 30 million years ago. New World monkeys are also called Platyrrhini: a reference to their broad noses. Old World monkeys (and apes) are called Catarrhini: a reference to their narrow noses. There is still quite a bit of uncertainty about the origins of the New World monkeys. At the time the platyrrhines arose, the continents of South American and Africa had drifted apart. Therefore, it is thought that monkeys arose in the Old World and reached the New World by drifting on log rafts or mangrove floating ‘islands’. Due to this reproductive isolation, New World monkeys and Old World monkeys underwent separate adaptive radiations over millions of years. The New World monkeys are all arboreal, whereas Old World monkeys include arboreal and ground-dwelling species.
Apes evolved from the catarrhines in Africa midway through the Cenozoic during the Miocene epoch, approximately 25 million years ago. Apes are generally larger than monkeys and do not possess a tail. All apes are capable of moving through trees, although many species spend most their time on the ground. Apes are more intelligent than monkeys as they have relatively larger brains proportionate to body size.
The apes are divided into two groups. The lesser apes comprise the family Hylobatidae, including gibbons and siamangs. The great apes include the genera Pan (chimpanzees and bonobos), Gorilla (gorillas), Pongo (orangutans), and Homo (humans). The very arboreal gibbons are smaller than the great apes; they have low sexual dimorphism (that is, the genders are not markedly different in size); and they have relatively longer arms used for swinging/brachiating through trees.
Key Points
- All primates are descended from tree-dwellers, exhibiting adaptations which allow for tree climbing that include: a rotating shoulder joint, separated big toes and thumb for grasping, and stereoscopic vision.
- Other primate characteristics include: having one offspring per pregnancy, claws evolved into flattened nails; and larger brain/body ratio than other mammals, and tendency to hold body upright.
- True primates, ancestral to prosimians, first appear in the fossil record in the Eocene epoch around 55 million years ago; they were similar in form to lemurs.
- Anthropoids ancestral to both Old World and New World monkeys appear in the fossil record in the Oligocene epoch around 35 million years ago.
- Anthropoids ancestral to apes appear in the Miocene epoch around 25 million years ago.
- Apes are divided into two main groups of hominoids: lesser apes or hylobatids (gibbons and siamangs) and great apes ( Pongo : orangutans, Gorilla : gorillas, Pan :chimpanzees, and Homo : humans).
Key Terms
- dimorphism : the occurrence in an animal species of two distinct types of individual
- adaptive radiation : the diversification of species into separate forms that each adapt to occupy a specific environmental niche


Learning Objectives
At the end of the module, students will be able to:
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explain the implications of culture on social status and stratification
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summarize the mechanisms used by dominant groups to develop and sustain culturalpower
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understand cultural hegemony
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describe the consequences of social conflicts over cultural power
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identify and evaluate cultural prejudice and discrimination
All humans are comprised of the same biological structure and matter. The unique distinctions among us stem from our culture (Kottak and Kozaitis 2012). The differences in our values, beliefs, norms, expressive language, practices, and artifacts is which stands us apart from each other. Being culturally unique projects exclusivity that draws attention to our variations and differences. People find cultural fit or acceptance from those who share uniqueness or the same cultural characteristics. Consequently, people may find or experience intolerance or rejection from those with different cultural traits.
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4.9.1: Cultural Hierarchies
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At the end of the module, students will be able to, explain the implications of culture on social status and stratification This chapter summarizes the mechanisms used by dominant groups to develop and sustain cultural power and helps to further understand cultural hegemony. Overall, it describes the consequences of social conflicts over cultural power as well as how to identify and evaluate cultural prejudice and discrimination
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4.9.2: Social and Cultural Capital
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Social and cultural relationships have productive benefits in society. Research defines social capital as a form of economic (e.g., money and property) and cultural (e.g., norms, fellowship, trust) assets central to a social network (Putnam 2000). The social networks people create and maintain with each other enable society to function. Sociologists find cultural capital or the social assets of person (including intellect, education, speech pattern, mannerisms, and dress) promote social mobility
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4.9.3: Cultural Hegemoney
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The very nature of cultural creation and production requires an audience to receive a cultural idea or product. Without people willing to receive culture, it cannot be sustainable or become an object.
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4.9.4: Prejudice and Discrimination
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Think about a time when you came across someone who did not fit the cultural “norm” either expressively or behaviorally. Were you compelled to understand the differences between you and the other person or were you eager to dismiss, confront, or ignore the other person? Prejudice is an attitude of thoughts and feelings directed at someone from prejudging or making negative assumptions. Discrimination is an action of unfair treatment against someone based on characteristics such as age, etc.
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4.9.S: Cultural Power (Summary)
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Thumbnail: Counter service in a McDonald's restaurant in Dukhan, Qatar. (CC BY-SA 3.0 Unported; Vincent van Zeijst).


8.4.2: Culture Media
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Learning Objectives
- Classify culture media
Culture medium or growth medium is a liquid or gel designed to support the growth of microorganisms. There are different types of media suitable for growing different types of cells. Here, we will discuss microbiological cultures used for growing microbes, such as bacteria or yeast.
NUTRIENT BROTHS AND AGAR PLATES
These are the most common growth media, although specialized media are sometimes required for microorganism and cell culture growth. Some organisms, termed fastidious organisms, need specialized environments due to complex nutritional requirements. Viruses, for example, are obligate intracellular parasites and require a growth medium containing living cells. Many human microbial pathogens also require the use of human cells or cell lysates to grow on a media.
The most common growth media nutrient broths (liquid nutrient medium) or LB medium (Lysogeny Broth) are liquid. These are often mixed with agar and poured into Petri dishes to solidify. These agar plates provide a solid medium on which microbes may be cultured. They remain solid, as very few bacteria are able to decompose agar. Many microbes can also be grown in liquid cultures comprised of liquid nutrient media without agar.
DEFINED VS UNDEFINED MEDIA
This is an important distinction between growth media types. A defined medium will have known quantities of all ingredients. For microorganisms, it provides trace elements and vitamins required by the microbe and especially a defined carbon and nitrogen source. Glucose or glycerol are often used as carbon sources, and ammonium salts or nitrates as inorganic nitrogen sources. An undefined medium has some complex ingredients, such as yeast extract, which consists of a mixture of many, many chemical species in unknown proportions. Undefined media are sometimes chosen based on price and sometimes by necessity – some microorganisms have never been cultured on defined media.
There are many different types of media that can be used to grow specific microbes, and even promote certain cellular processes; such as wort, the medium which is the growth media for the yeast that makes beer. Without wort in certain conditions, fermentation cannot occur and the beer will not contain alcohol or be carbonated (bubbly).
COMMON BROADLY-DEFINED CULTURE MEDIA
Nutrient media – A source of amino acids and nitrogen (e.g., beef, yeast extract). This is an undefined medium because the amino acid source contains a variety of compounds with the exact composition being unknown. These media contain all the elements that most bacteria need for growth and are non-selective, so they are used for the general cultivation and maintenance of bacteria kept in laboratory-culture collections.
Minimal media – Media that contains the minimum nutrients possible for colony growth, generally without the presence of amino acids, and are often used by microbiologists and geneticists to grow “wild type” microorganisms. These media can also be used to select for or against the growth of specific microbes. Usually a fair amount of information must be known about the microbe to determine its minimal media requirements.
Selective media – Used for the growth of only selected microorganisms. For example, if a microorganism is resistant to a certain antibiotic, such as ampicillin or tetracycline, then that antibiotic can be added to the medium in order to prevent other cells, which do not possess the resistance, from growing.
Differential media – Also known as indicator media, are used to distinguish one microorganism type from another growing on the same media. This type of media uses the biochemical characteristics of a microorganism growing in the presence of specific nutrients or indicators (such as neutral red, phenol red, eosin y, or methylene blue) added to the medium to visibly indicate the defining characteristics of a microorganism. This type of media is used for the detection and identification of microorganisms.
These few examples of general media types provide some indication only; there are a myriad of different types of media that can be used to grow and control microbes.
Key Points
- Culture media contains the nutrients needed to sustain a microbe.
- Culture media can vary in many ingredients allowing the media to select for or against microbes.
- Glucose or glycerol are often used as carbon sources, and ammonium salts or nitrates as inorganic nitrogen sources in culture media.
Key Terms
- culture : The process of growing a bacterial or other biological entity in an artificial medium.
- lysogeny broth : Lysogeny broth (LB) is a nutritionally-rich medium; primarily used for the growth of bacteria.


12.5: Organizational Stress and Retention Cycle
The impact of inadequate stress management for health care personnel can greatly impact health care organizations. When harmful stress is not adequately addressed, burnout can rapidly become a burgeoning problem resulting in absenteeism, decreased productivity, decline in care quality, staff dissatisfaction, and employee turnover. Work environment and lack of workplace support often contribute to feelings of burnout and job attrition. [1] Organizations must recognize the significance of stress in regard to the cyclical nature it plays in the retention of employees. For example, if one employee experiences harmful stress resulting in depression and anxiety, this may influence their timeliness and attendance at work. If the employee begins to struggle, they may be more inclined to phone in as “sick time” for shifts or even be a “no show” for a scheduled shift. When this occurs, the burden of their absence is passed on to other employees on the unit. Calls for overtime, mandated stay, or increased client care assignments quickly increase the burden on the other members of the health care team. As a result, the team members experiencing increased workload feel an impact on their own job-related stress. The compounded stress can quickly overtax an individual who has been managing normal work-related stress. Many individuals who were previously self-managing stress may struggle under these increased role demands. When there is a decrease in an individual’s “downtime,” there is even less reprieve from the stressful work environment. As a result, the organization and health care system become even more overtaxed, and the cycle perpetuates itself among other staff. [2] Managers and directors often struggle with rehiring and orienting staff at a rate that is suitable to offset the stress cycle and decreased retention within the organization.
Promoting Nurse Retention
Nurse leaders must be proactive in finding solutions to address clinical nurse and nursing faculty shortages and high nurse turnover rates. The 2018 National Healthcare Retention and RN Staffing Report states the following data [3] :
- The U.S. Bureau of Labor Statistics reports that 233,000 new RN jobs will be created annually.
- Forty-five percent of hospitals anticipate increasing their RN staff.
- Hospital turnover is at 18.2%, an increase from previous years.
- RNs working in emergency care, step-down, and medical-surgical units experience high turnover rates, with the highest rate of turnover for certified nursing assistants.
- The average cost of each RN turnover is $49,500, resulting in an average hospital losing an estimated $4.4 to $7 million due to turnover.
- Each percent change in RN turnover will cost or save the average hospital $337,500.
- It takes approximately 2.5 months to recruit an experienced RN.
- More than half of hospitals would like to decrease reliance on supplemental staffing.
- For every 20 travel RNs eliminated, a hospital can save an average of $1,435,000.
Unfortunately, many nurse leaders struggle to receive organizational support for recruitment and hiring in a timely fashion. Demonstrating the need for staff replacement often cannot be established until a staff vacancy exists. As a result, the retention cycle is further compromised when workload is impacted due to staff vacancies during the recruitment and orientation process. Many frontline nursing staff may not be aware of the rigorous challenges that nurse leaders face when requesting administrative support for additional staff positions. Most organizations require executive-level approval for hiring, and unit productivity is examined for rationale that additional staff are needed. The time required for this investigation and executive-level approval can be very challenging for staff nurses who experience the workload burden during the vacancies. During this time frame, nurse leaders may struggle to maintain team morale while also acknowledging the organization’s need to be financially responsible in staff hiring.
It is important for all parties to remain engaged in their current work roles during the recruitment, hiring, and orientation periods of new nurses. Trust in one another during this time is critical, and all parties must remember the needs of clients receive top priority. Providing optimal care to the best of one’s ability is of the utmost importance even when experiencing staffing challenges. Additionally, staff, nursing leaders, and administrators within the organization must unite to find actionable solutions that acknowledge the impact of stress and reduce the impact of harmful stress contributing to the burnout of colleagues. There is no simple solution. All individuals must be united in exploring strategies to reduce the occurrence of burnout and seek to make change to enhance the health and well-being of all involved.
- Mercado. (2022). A cross‐sectional analysis of factors associated with stress, burnout and turnover intention among healthcare workers during the COVID‐19 pandemic in the United States. Health & Social Care in the Community . https://doi.org/10.1111/hsc.13712 ↵
- Chegini, Z., Asghari Jafarabadi, M. and Kakemam, E. (2019), Occupational stress, quality of working life and turnover intention amongst nurses. Nursing Critical Care, 24 : 283-289. https://doi-org.ezproxy.liberty.edu/10.1111/nicc.12419 ↵
- Kroning, M., & Hopkins, K. (2019). Healthcare organizations thrive with shared governance. Nursing Management, 50 (5), 13-15. https://doi.org/10.1097/01.numa.0000557781.40049.2d ↵


14.6: Characteristics of the Diels-Alder Reaction
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Objectives
After completing this section, you should be able to
- determine whether or not a given compound would behave as a reactive dienophile in a Diels-Alder reaction.
- predict the stereochemistry of the product obtained from the reaction of a given diene with a given dienophile.
- recognize that in order to undergo a Diels-Alder reaction, a diene must be able to assume an s -cis geometry, and determine whether or not a given diene can assume this geometry.
Key Terms
Make certain that you can define, and use in context, the key terms below.
- dienophile
- dimerization
Study Notes
Make sure that you understand that the s -cis and s -trans forms of a diene such as 1,3-butadiene are conformers, not isomers. Note that some textbooks can confuse the issue further by referring to a compound such as (2Z, 4Z)-hexadiene as cis, cis-2,4-hexadiene, and saying that the most stable form of this compound is its s -trans conformer!
In fulfilling Objective 2, above, you must recognize that the Diels-Alder reaction is stereospecific.
Finally, note reaction B in the reading shows 1,3-cyclopentadiene reacting with another molecule of 1,3-cyclopentadiene. When the same compound acts as both diene and dienophile in a Diels-Alder reaction to couple it is a dimerization .
The Dienophile
In general, Diels-Alder reactions proceed fastest with electron-withdrawing groups on the dienophile (diene lover). Ethylene reacts slowly while propenal, ethyl propenoate, and other molecules shown below are highly reactive in a Diels-Alder reaction.
In much the same manner as electron-withdrawing substituents on a benzene ring, these are typically a double or triple bond in conjugation with the double bond in the dienophile. A resonance form can be drawn which places a positive charge in the dienophile double bond. This results in the double bond being less electron rich (greater electron density shown in Red/Orange) than ethylene. Electrostatic potential maps show that the electron-withdrawing groups pull electron density away from the double bond.
Stereochemistry of Diels-Alder (dienophile)
The Diels-Alder reaction is enormously useful for synthetic organic chemists, not only because ring-forming reactions are useful in general but also because in many cases multiple new stereocenters are formed, and the reaction is inherently stereospecific. During a Diels-Alder reaction the stereochemistry of the dienophile is retained in the product. A cis dienophile will generate a cyclohexene ring with cis (syn) substitution on the two carbons from the dienophile. Likewise a trans dienophile will generate a cyclohexene ring with trans (anti) substitution on these two carbon.
Example \(\PageIndex{1}\)
The retention of stereochemistry is due to the planar nature of both reactants and that the forming process is suprafacial (i.e. to or from the same face of each plane). This stereospecificity also confirms the concerted nature of the Diels-Alder mechanism. The drawing below illustrates this fact for the reaction of 1,3-butadiene with (E)-dicyanoethene. The trans relationship of the cyano groups in the dienophile is preserved in the six-membered ring of the adduct.
Another facet of the stereochemical retention of the dienophile is that only the endo product, rather than the alternative exo product, is formed. The words endo and exo are used to indicate relative stereochemistry when referring to bicyclic structures like substituted norbornanes. The endo position on a bicyclic structure refers to the position that is inside the concave shape of the larger (six-membered) ring. As you might predict, the exo position refers to the outside position. Diels-Alder reactions with cyclic dienes favor the formation of bicyclic structures in which substituents are in the endo position . Preference of the endo position is also a facet of the suprafacial nature of the Diels-Alder reaction. The orbital overlap required for the reaction is greater when the dienophile lies directly underneath the diene.
Alkynes can also serve as dienophiles in Diels-Alder reactions:
The Diene
In general, Diels-Alder reactions proceed fastest with electron-donating groups on the diene (eg. alkyl groups). The Diels-Alder reaction is a single step process, so the diene component must adopt an s-cis conformation in order for the end carbon atoms (#1 & #4) to bond simultaneously to the dienophile. For many acyclic dienes the s-trans conformer is more stable than the s-cis conformer (due to steric crowding of the end groups), but the two are generally in rapid equilibrium, permitting the use of all but the most hindered dienes as reactants in Diels-Alder reactions.
For some dienes, extreme steric hindrance causes the s-cis conformation to be highly strained, and for this reason such dienes do not readily undergo Diels-Alder reactions.
Cyclic dienes, on the other hand, are ‘locked’ in the s-cis conformation, and are especially reactive. The result of a Diels-Alder reaction involving a cyclic diene is a bicyclic structure:
Stereochemistry of Diels-Alder (diene)
The 1 and 4 Carbons in the diene have the possibility of forming two new stereocenters in the cyclohexene product. Similarly to the effects of dienophile stereochemistry, the positioning of substituents on the 1 and 4 carbons in the diene determine the stereochemistry in the product. The diene substituents can be thought of as being either cis (both facing in or both facing out) or trans and the stereochemistry is retained to form a cis or trans cyclohexene product.
Examples \(\PageIndex{1}\)
The Essential Characteristics of the Diels-Alder Cycloaddition Reaction:
- The reaction always creates a new six-membered ring.
- The diene component must be able to assume an s-cis conformation.
- Electron withdrawing groups on the dienophile facilitate reaction.
- Electron donating groups on the diene facilitate reaction.
- Steric hindrance at the bonding sites may inhibit or prevent reaction.
- The reaction is stereospecific with respect to substituent configuration in both the dienophile and the diene.
Examples \(\PageIndex{2}\)
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Predicting the Product of a Diels-Alder Reaction
Start by rotating the diene until it is in the s-cis conformation then point it towards the double bond of the dienophile. Remove the double bonds present in the diene and dieneophile. Connect carbons 1 and 4 of the the diene to a carbon in the dienophile double bond using a sigma bond to create a six-membered ring. Create a double bond between carbons 2 and 3 of diene.
Determine if any substituents attached to either the double bond of the dieneophile or carbons 1 and 4 of the diene have a cis / trans conformation. If so make sure the substituents have the same configuration in the cycloalkene product.
Predict the product of the following reaction:
The diene is locked into an s-cis configuration which will promote the reaction. The ring portion of the diene will act as electron donating groups which will also promote the reaction. Because the diene already contained a ring the product will be bicyclic. The dienophile has two nitriles attached to it both of which are electron withdrawing. Since the two nitriles in the dieneophile are cis to each other the the two nitriles will be cis to each other in the product.
Predict the product of the following reaction:
A particularly rapid Diels-Alder reaction takes place between cyclopentadiene and maleic anhydride. Cyclopentadiene is held in the required s-cis configuration so it will make a good diene for a Diels-Alder reaction. Maleic anhydride is also a very good dienophile, because the electron-withdrawing effect of the carbonyl groups causes the two alkene carbons to be electron-poor, and thus a good target for attack by the pi electrons in the diene. Since it is part of a ring, the double bond of maleic anhydride is in a cis configuration so the cyclohexene ring will also have a cis configuration. Lastly, the product will prefer the endo position.
7) Of the following dienes, which are S-trans and which are s-cis? Of those that are s-trans, are they able to rotate to become s-cis?
8) Predict the product of the following reaction.
7)
A) s-trans, unable to rotate to become s-cis
B) s-cis
C) s-trans, can rotate to become s-cis.
8)
Exercise \(\PageIndex{1}\)


19.4: Cost of Living
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Introduction to Inflation
Inflation is a persistent increase in the general price level, and has three varieties: demand-pull, cost-push, and built-in.
learning objectives
- Distinguish between demand-pull and cost-push inflation
In economics, inflation is a persistent increase in the general price level of goods and services in an economy over a period of time. When the general price level rises, each unit of currency buys fewer goods and services. Consequently, inflation reflects a reduction in the purchasing power per unit of money; it is a loss of real value, as a single dollar is able to purchase fewer goods than it previously could.
Types of Inflation
The reasons for inflation depend on supply and demand. Depending on the type of inflation, changes in either supply or demand can create an increase in the price level of goods and services. In Keynesian economics, there are three types of inflation.
Demand-Pull Inflation
Demand-pull inflation is inflation that occurs when total demand for goods and services exceeds the economy’s capacity to produce those goods. Put another way, there is “too much money chasing too few goods. ” Typically, demand-pull inflation occurs when unemployment is low or falling. The increases in employment raise aggregate demand, which leads to increased hiring to expand the level of production. Eventually, production cannot keep pace with aggregate demand because of capacity constraints, so prices rise.
Demand-Pull Inflation : Demand-pull inflation is caused by an increase in aggregate demand. As demand increases, so does the price level.
Cost-Push Inflation
Cost-push inflation occurs when there is an increase in the costs of production. Unlike demand-pull inflation, cost-push inflation is not “too much money chasing too few goods,” but rather, a decrease in the supply of goods, which raises prices.
Cost-Push Inflation : As the costs of production inputs rises, aggregate supply can decrease, which increases price levels.
The reason for decreases in supply are usually related to increases in the prices of inputs. One major reason for cost-push inflation are supply shocks. A supply shock is an event that suddenly changes the price of a commodity or service. (sudden supply decrease) will raise prices and shift the aggregate supply curve to the left. One historical example of this is the oil crisis of the 1970’s, when the price of oil in the U.S. surged. Because oil is integral to many industries, the price increase led to large increases in the costs of production, which translated to higher price levels.
Built-In Inflation
Built-in inflation is the result of adaptive expectations. If workers expect there to be inflation, they will negotiate for wages increasing at or above the rate of inflation (so as to avoid losing purchasing power). Their employers then pass the higher labor costs on to customers through higher prices, which actually reflects inflation. Thus, there is a cycle of expectations and inflation driving one another.
Defining and Calculating CPI
The consumer price index (CPI) is a statistical estimate of the change in prices of goods and services bought for consumption.
learning objectives
- Assess the uses and limitations of the Consumer Price Index
Consumer Price Index
The consumer price index (CPI) is a statistical estimate of the level of prices of goods and services bought for consumption by households. It measures changes in the price level of a market basket of goods and services used by households. The CPI is calculated by collecting the prices of a sample of representative items over a specific period of time. Goods and services are divided into categories, sub categories, and sub indexes. All of the information is combined to produce the overall index of consumer expenditures. The annual percentage change in a CPI is used to measure inflation. The CPI can be used to index the real value of wages, salaries, pensions, and price regulation. It is one of the most closely watched national economic statistics.
Consumer Price Index : The graph shows the consumer price index in the United States from 1913 – 2004. The x-axis indicates year, the left y-axis indicates the Consumer Price Index, and the right y-axis indicates annual percentage change in Consumer Price Index, which can be used to measure inflation.
Calculating CPI using a Single Item
In order to calculate the CPI using a single item the following equation is used:
\[\text{Current CPI}=\text{Current item price} \times \text{Base year price} \times \dfrac{\text{Current CPI}}{\text{Base year CPI}}\]
Calculating the CPI for Multiple Items
When calculating the CPI for multiple items, it must be noted that many but not all price indices are weighted averages using weights that sum to 1 or 100. When calculating the average for a large number of products, the price is given a weighted average between 1 and 100 to simplify calculation. The weighting determines the importance of the quantity of the product on average. The equation for calculating the CPI for multiple items is:
CPI for multiple items=Cost of CPI market basket at current period pricesCost of CPI market basket at base period prices×100.CPI for multiple items=Cost of CPI market basket at current period pricesCost of CPI market basket at base period prices×100.
For example, imagine you buy five sandwiches, two magazines, and two pairs of jeans. In the first period, sandwiches are $6 each, magazines are $4 each, and jeans are $35 each. This will be our base period. In the second period, sandwiches are $7, magazines are $6, and jeans are $45.
\(\text{Market basket at base period prices} = 5(6.00) + 2(4.00) + 2(35.00) = 108.00.\)
\(\text{Market basket at current period prices} = 5(7.00) + 2(6.00) + 2(45.00) = 137.00.\)
\(\text{CPI for multiple items}=\frac{137}{108} \times 100=127\)
The CPI based on consumption is 127.
CPI Limitations
The CPI is a convenient way to calculate the cost of living and price level for a certain period of time. However, the CPI does not provide a completely accurate estimate for the cost of living. Issues that impede the accuracy of the CPI include substitution bias (consumers substituting goods for others), introducing new products, and changes in quality. The CPI can also overstate inflation because it does not always account for quality improvements or new goods and services.
GDP Deflator vs. CPI
The GDP deflator is a measure of the level of prices of all new, domestically produced, final goods and services in an economy. Unlike the CPI, the GDP deflator is a measure of price inflation or deflation for a specific base year. The GDP deflator differs from the CPI because it is not based on a fixed basket of goods and services. The GDP deflator “basket” changes from year to year depending on people’s consumption and investment patterns. Unlike the CPI, the GDP deflator is not impacted by substitution biases. Despite the GDP being more flexible, the CPI is a more accurate reflection of the changes in the cost of living.
Key Points
- Inflation is an increase in price levels, which decreases the real value, or purchasing power, of money.
- Demand -pull inflation is an increase in price levels due to an increase in aggregate demand when the employment level is full or close to full.
- Cost -push inflation is an increase in price levels due to a decrease in aggregate supply. Generally, this occurs due to supply shocks, or an increase in the price of production inputs.
- The CPI is calculated by collecting the prices of a sample of representative items over a specific period of time.
- The CPI can be used to index the real value of wages, salaries, pensions, and price regulation. It is one of the most closely watched national economic statistics.
- The equation to calculate a price index using a single item is: Current CPI=Current item price×Base year price×Current CPIBase year CPICurrent CPI=Current item price×Base year price×Current CPIBase year CPI.
- The equation for calculating the CPI for multiple items is: CPI for multiple items=Cost of CPI market basket at current period pricesCost of CPI market basket at base period prices×100.CPI for multiple items=Cost of CPI market basket at current period pricesCost of CPI market basket at base period prices×100..
Key Terms
- inflation : An increase in the general level of prices or in the cost of living.
- demand-pull inflation : A rise in the price level for goods and services in an economy due to greater demand than the economy’s ability to produce those goods and services.
- cost-push inflation : A rise in the price level for goods and services in an economy due to increases in the costs of production.
- consumer price index : A statistical estimate of the level of prices of goods and services bought for consumption purposes by households.
- market basket : A list of items used specifically to track the progress of inflation in an economy or specific market.
LICENSES AND ATTRIBUTIONS
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- Types of Inflation. Provided by : econ101-powers-sectione Wikispace. Located at : econ101-powers-sectione.wikis...s+of+Inflation . License : CC BY-SA: Attribution-ShareAlike
- Inflation. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Inflation . License : CC BY-SA: Attribution-ShareAlike
- Cost-push inflation. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Cost-push_inflation . License : CC BY-SA: Attribution-ShareAlike
- Types of Inflation. Provided by : econ101-powers-sectionc Wikispace. Located at : econ101-powers-sectionc.wikis...s+of+Inflation . License : CC BY-SA: Attribution-ShareAlike
- Demand-pull inflation. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Demand-pull_inflation . License : CC BY-SA: Attribution-ShareAlike
- Supply shock. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Supply_shock . License : CC BY-SA: Attribution-ShareAlike
- Inflation. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Inflation . License : CC BY-SA: Attribution-ShareAlike
- Boundless. Provided by : Boundless Learning. Located at : www.boundless.com//economics/...push-inflation . License : CC BY-SA: Attribution-ShareAlike
- Boundless. Provided by : Boundless Learning. Located at : www.boundless.com//economics/...pull-inflation . License : CC BY-SA: Attribution-ShareAlike
- inflation. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/inflation . License : CC BY-SA: Attribution-ShareAlike
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4: Linear Functions
Recall that a function is a relation that assigns to every element in the domain exactly one element in the range. Linear functions are a specific type of function that can be used to model many real-world applications, such as plant growth over time. In this chapter, we will explore linear functions, their graphs, and how to relate them to data.
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- 4.1: Introduction to Linear Functions
- Imagine placing a plant in the ground one day and finding that it has doubled its height just a few days later. Although it may seem incredible, this can happen with certain types of bamboo species. These members of the grass family are the fastest-growing plants in the world. One species of bamboo has been observed to grow nearly 1.5 inches every hour. A constant rate of change, such as the growth cycle of this bamboo plant, is a linear function.
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- 4.2: Linear Functions
- The ordered pairs given by a linear function represent points on a line. Linear functions can be represented in words, function notation, tabular form, and graphical form. The rate of change of a linear function is also known as the slope. An equation in the slope-intercept form of a line includes the slope and the initial value of the function. The initial value, or y-intercept, is the output value when the input of a linear function is zero.
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- 4.3: Modeling with Linear Functions
- We can use the same problem strategies that we would use for any type of function. When modeling and solving a problem, identify the variables and look for key values, including the slope and y-intercept. Draw a diagram, where appropriate. Check for reasonableness of the answer. Linear models may be built by identifying or calculating the slope and using the y-intercept. The x-intercept may be found by setting y=0, which is setting the expression mx+b equal to 0.
Contributors and Attributions
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Jay Abramson (Arizona State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at https://openstax.org/details/books/precalculus .


6.8: Student-Run, Their Way
Student-run, their way: EcoTech Marine
Amid all the talk in this section about elevator pitches and equity, burn rate and liquidation, preferred stock and venture fairs, we present to you one simple and reassuring fact: you don’t have to get fancy angel or VC funding to succeed. In fact, in certain situations you might be better off without it. Such is the story of EcoTech Marine: a team of students with enough entrepreneurial spirit and drive to take a product all the way to market themselves, with a minimum of private investment. This profile follows EcoTech’s story from idea to prototype to successful company, detailing exactly how they got the money at each step along the way.
Humble beginnings
But first we need to back up—way up, to when EcoTech co-founder Tim Marks was in eighth grade. After getting “fish fever” and maintaining freshwater aquariums for several years, Marks set up a ten-gallon “reef” aquarium, nurturing live corals and other organisms in a saltwater environment. But Marks soon discovered that maintaining a reef aquarium is a complex task that practically requires a chemistry degree, to say nothing of time and effort invested. When the demands of the tank overwhelmed his eighth-grade education, Marks dismantled it and quit the hobby altogether.
Fast-forward to his senior year in high school, when, thanks in part to the Internet, Marks caught fish fever again. He was mentored online by Rick Dickens, webmaster of reefs.org, a popular online resource for reef keepers. The following year, as a freshman at Lehigh University, Marks met Justin Lawyer, a physics student at Oklahoma State University, in a chat room for reef enthusiasts. The two students realized they shared a vision of equipment that would automate the difficult task of reef aquarium maintenance, and they traded ideas and 3-D models of potential products. Before Marks finished his freshman year, using nothing but small amounts of their own personal funding he and Lawyer launched a full-fledged company, calling it EcoTech Marine.2 Their goal? Become a provider of innovative, high-end, automated equipment for serious aqua hobbyists.
Hard work and grant writing
There was much work to be done, however. Doing most of the prototyping in the basement workshop of Marks’ home, the team built a prototype of its first product: the Kalkwasser Reactor, a device that automatically replenishes and maintains an aquarium’s calcium and alkalinity levels, vital to the health of corals.3 It was a rough alpha version, though: they needed several thousand more dollars to develop the device fully. “We’d been funding the venture ourselves for several years,” said Patrick Clasen, a fellow student entrepreneur at Lehigh who quickly caught reef fever and joined EcoTech. “But that was no longer cutting it.”
The team decided to submit the reactor in the Invitation to Innovate contest sponsored by the Integrated Product Development (IPD) program at Lehigh. IPD is a comprehensive entrepreneurship training program in which teams of engineering, arts, and business students collaborate for one year to make and market products. EcoTech won the contest, getting $2,000 and the chance to work with business and engineering students for two semesters, all in preparation to submit an NCIIA Advanced E-Team grant proposal.
They did submit, and received $8,380 in NCIIA funding, mostly for prototyping. By the end of his sophomore year at Lehigh, Marks and his team had sold twenty reactors and seemed well on their way. But at the same time Marks knew that EcoTech needed more than just one product to be a viable business. “As it turned out,” says Marks, “the reactor project didn’t go as far as we hoped. But it did get our foot in the door in terms of business, manufacturing, and design experience. And, most importantly, it was the stepping-stone in terms of the next product we developed, which has been very successful.”
VorTech™ to the fore
Like so many other entrepreneurial successes, the turning point for EcoTech came when it made contact with an industry player. At a local reef club meeting Marks met Andy Howard, President of IceCap, Inc., a well known name in the reef aquarium hobby. Marks and Howard connected, and Marks mentioned an idea for what he called the VorTech, a new circulating pump for aquariums that would mimic a natural wave-like water flow and minimize the intrusion of heat and bulky equipment inside the tank. Howard, it turned out, was working on an idea for a battery-powered backup circulating system for aquariums, which would require a pump. The two ideas meshed: as a new company, EcoTech needed industry support to launch the product successfully, and IceCap wanted a discrete, high-end pump for their backup system. Marks and Howard arranged a formal meeting, signed nondisclosure agreements, and Marks brought to the table two different pump ideas. Says Marks, “IceCap immediately gravitated toward the VorTech, saying, ‘We want that, build us that!’ That’s when we really turned it into high gear and started product development.”
Meanwhile
In the meantime the EcoTech team members had completed their undergraduate degrees. But the project was far from over: they both stayed at Lehigh and continued to work on EcoTech, with Marks enrolled in the master of engineering in mechanical engineering program with a focus in IPD, while Clasen pursued a master’s in materials science and engineering. Their tuition was paid for, and they received stipends. Marks even became an IPD teaching assistant, helping undergraduates with their entrepreneurial projects.
More news came in on the money front: EcoTech received another Advanced E-Team grant from the NCIIA, this time for $18,738; through Lehigh they won a $9,000 “Agile Manufacturing” grant to help with tooling and production; they won $15,000 from the State of Pennsylvania as part of the Keystone Innovation Zone (KIZ) program, designed to prevent brain-drain and keep Pennsylvania-based ideas within state boundaries; and lastly, they secured a line of credit from a local bank. The line of credit, Marks says, is especially nice as a fall-back plan. “Because of the line of credit, we’re assured that if we need more money, we can get it. If we need to increase production quantities, or if things slow down, the line of credit gives us that insurance. It’s a good thing to have.”
And while not every team at Lehigh receives free office space and lab equipment, EcoTech did. According to Marks, EcoTech secured the space and equipment “just based on the fact that we had been doing this so long and were so dedicated.”
The ramp-up
In partnership with IceCap, EcoTech developed a polished prototype of the VorTech pump and debuted it on the market successfully in 2005. The specialized pump is now sold through a variety of online reef equipment companies, and the future of the product and the company is bright. “We’re getting our first product out the door now,” says Marks. “Product has shipped and more product will ship soon.”
And EcoTech isn’t stopping at the VorTech. “We’re developing a remote control for the VorTech right now,” says Marks, “and we have a number of other products in mind. Eventually we want to launch a complete line of products for advanced aquarists, a line of products that will completely automate the reef-keeping experience.”
Using a mish-mash of funding sources—NCIIA grants, personal money, Lehigh prize money, State of Pennsylvania money, bank money, and finally corporate partner money—EcoTech grew their venture from the ground up, their way.


9.1: Academic Learning Centers
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436 Business Building
817-272-7029
wweb.uta.edu/accounting/default.aspx?folder=lab& page=tutorlab_home.html
The Accounting Tutoring Lab is operated by UT Arlington’s chapter of Beta Alpha Psi Financial Information Society. The lab offers space for students to receive assistance from trained tutors on accounting and finance assignments and one-on-one help in 20-minute sessions. Assistance is given on a first come-first served basis.
318 Science Hall
817-272-5431
www.uta.edu/chemistry
Operated by the Department of Chemistry and Biochemistry, this clinic seeks to support students in all chemistry and biochemistry courses.
411 Central Library
817-272-2601
www.uta.edu/owl
The English Writing Center offers students both face-to-face tutoring offered in the Central Library and an online interaction through Skype. Appointments may be made on the English Writing Center Web site where you will also find other tips and resources for improving your papers.
303 Trimble Hall
817-272-3161
uta.edu/modl/LAC.php
The Language Acquisition Center (LAC) is dedicated to helping students succeed as they seek to master languages other than their own. A multimedia center serving the UTA community, the LAC features Mac computers, TV/VCR/DVD viewing stations, and CD/cassette listening stations. The LAC also maintains an extensive collection of analog and digital media as well as course-related software and self-study software.
325 Pickard Hall
817-272-5674
www.uta.edu/math/clinic
308 Pickard Hall
817-272-1749
http://www.uta.edu/math/emporium/
The Math Clinic and Math Emporium are drop-in tutoring centers located in Pickard Hall that offer assistance for students in specific undergraduate math courses and final review sessions before exams. For a complete list of courses served by the Math Clinic and Emporium, visit their Web site.
007 Science Hall
817-272-2266
www.uta.edu/physics/pages/department/clinics/helpclinics.html
The Physics Department operates a clinic for students desiring help in solving physics problems, understanding physics concepts, and anything relevant to being successful in their physics courses at UTA. For much of the day during the school week, an advanced undergraduate student is available to provide individualized assistance with course work or assisting in the better under- standing of course concepts.
106 Life Science
817-272-2129
www.uta.edu/cos/SECC
The Science Education and Career Center offers resource materials and study aids for students in Biology, Chemistry and Biochemistry, Mathematics, Physics, and Psychology classes. The center features lounge space, a computer lab, and information ranging from course-specific study mate- rials to information about pursuing particular career paths in the sciences.
206 Ransom Hall
817-272-3684
www.uta.edu/sss
Student Support Services provides free academic support to U.S. citizens or permanent residents who are either first generation, low income, and/or disabled. Free services include tutoring, coun- seling, advising, a private computer lab, seminars, cultural events, and a laptop, calculator, and textbook lending program.
205 Ransom Hall
817-272-2617
www.uta.edu/tutoring www.uta.edu/si
This University Tutorial offers individualized tutoring by high-quality, nationally certified tutors to students in a variety of subjects at the low price of $6.50 per hour. Supplemental Instruction is an internationally recognized student assistance program aimed at improving student performance in historically difficult courses. SI offers students regularly scheduled discussion sections led by specially trained upperclassmen and graduate students. These discussion sections are designed to help students master the concepts of an academic course and, at the same time, increase their competency in the learning strategies relevant to the course. SI is free to all students.


9.8: Women and World War II
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President Franklin D. Roosevelt and his administration had encouraged all able-bodied American women to help the war effort. He considered the role of women in the war critical for American victory, and the public expected women to assume various functions to free men for active military service. While most women opted to remain at home or volunteer with charitable organizations, many went to work or donned a military uniform.
World War II brought unprecedented labor opportunities for American women. Industrial labor, an occupational sphere dominated by men, shifted in part to women for the duration of wartime mobilization. Women applied for jobs in converted munitions factories. The iconic illustrated image of Rosie the Riveter, a muscular woman dressed in coveralls with her hair in a kerchief and inscribed with the phrase We Can Do It! , came to stand for female factory labor during the war. But women also worked in various auxiliary positions for the government. Although such jobs were often traditionally gendered female, over a million administrative jobs at the local, state, and national levels were transferred from men to women for the duration of the war. 19
For women who elected not to work, many volunteer opportunities presented themselves. The American Red Cross, the largest charitable organization in the nation, encouraged women to volunteer with local city chapters. Millions of women organized community social events for families, packed and shipped almost half a million tons of medical supplies overseas, and prepared twenty-seven million care packages of nonperishable items for American and other Allied prisoners of war. The American Red Cross further required all female volunteers to certify as nurse’s aides, providing an extra benefit and work opportunity for hospital staffs that suffered severe personnel losses. Other charity organizations, such as church and synagogue affiliates, benevolent associations, and social club auxiliaries, gave women further outlets for volunteer work.
Military service was another option for women who wanted to join the war effort. Over 350,000 women served in several all-female units of the military branches. The Army and Navy Nurse Corps Reserves, the Women’s Army Auxiliary Corps, the Navy’s Women Accepted for Volunteer Emergency Service, the Coast Guard’s SPARs (named for the Coast Guard motto, Semper Paratus , “Always Ready”), and Marine Corps units gave women the opportunity to serve as either commissioned officers or enlisted members at military bases at home and abroad. The Nurse Corps Reserves alone commissioned 105,000 army and navy nurses recruited by the American Red Cross. Military nurses worked at base hospitals, mobile medical units, and onboard hospital “mercy” ships. 20
Jim Crow segregation in both the civilian and military sectors remained a problem for black women who wanted to join the war effort. Even after President Roosevelt signed Executive Order 8802 in 1941, supervisors who hired black women still often relegated them to the most menial tasks on factory floors. Segregation was further upheld in factory lunchrooms, and many black women were forced to work at night to keep them separate from whites. In the military, only the Women’s Army Auxiliary Corps and the Nurse Corps Reserves accepted black women for active service, and the army set a limited quota of 10 percent of total end strength for black female officers and enlisted women and segregated black units on active duty. The American Red Cross, meanwhile, recruited only four hundred black nurses for the Army and Navy Nurse Corps Reserves, and black army and navy nurses worked in segregated military hospitals on bases stateside and overseas.
And for all of the postwar celebration of Rosie the Riveter, after the war ended the men returned and most women voluntarily left the workforce or lost their jobs. Meanwhile, former military women faced a litany of obstacles in obtaining veteran’s benefits during their transition to civilian life. The nation that beckoned the call for assistance to millions of women during the four-year crisis hardly stood ready to accommodate their postwar needs and demands.