1.5: More Applications
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Learning Objectives
In this section, you will learn to:
- Solve a linear system in two variables.
- Find the equilibrium point when a demand and a supply equation are given.
- Find the break-even point when the revenue and the cost functions are given.
Finding the Point of Intersection of Two Lines
In this section, we will do application problems that involve the intersection of lines. Therefore, before we proceed any further, we will first learn how to find the intersection of two lines.
Example \(\PageIndex{1}\)
Find the intersection of the line \(y = 3x -1\) and the line \(y = - x + 7\).
Solution
We graph both lines on the same axes, as shown below, and read the solution (2, 5).
Finding an intersection of two lines graphically is not always easy or practical; therefore, we will now learn to solve these problems algebraically.
At the point where two lines intersect, the \(x\) and \(y\) values for both lines are the same. So in order to find the intersection, we either let the \(x\)-values or the \(y\)-values equal.
If we were to solve the above example algebraically, it will be easier to let the y-values equal. Since \(y = 3x - 1\) for the first line, and \(y = - x + 7\) for the second line, by letting the y-values equal, we get
\begin{aligned}
3 x-1&=-x+7\\
4 x&=8\\
x&=2
\end{aligned}
By substituting \(x = 2\) in any of the two equations, we obtain \(y = 5\).
Hence, the solution (2, 5).
A common algebraic method used to solve systems of equations is called the elimination method . The object is to eliminate one of the two variables by adding the left and right sides of the equations together. Once one variable is eliminated, we have an equation with only one variable for can be solved. Finally, by substituting the value of the variable that has been found in one of the original equations, we get the value of the other variable.
Example \(\PageIndex{2}\)
Find the intersection of the lines \(2x + y = 7\) and \(3x - y = 3\) by the elimination method.
Solution
We add the left and right sides of the two equations.
\begin{aligned}
2 x+y&=7\\
3x-y&=3 \\ \hline 5x&=10\\
x&=2
\end{aligned}
Now we substitute \(x = 2\) in any of the two equations and solve for \(y\).
\begin{aligned}
2(2)+y&=7\\
y&=3
\end{aligned}
Therefore, the solution is (2, 3).
Example \(\PageIndex{3}\)
Solve the system of equations \(x + 2y = 3\) and \(2x + 3y = 4\) by the elimination method.
Solution
If we add the two equations, none of the variables are eliminated. But the variable \(x\) can be eliminated by multiplying the first equation by -2, and leaving the second equation unchanged.
\begin{aligned}
-2 x-4 y &=-6 \\
2 x+3 y &=4 \\
\hline -y &=-2 \\
y &=2
\end{aligned}
Substituting \(y = 2\) in \(x + 2y = 3\), we get
\begin{array}{l}
x+2(2)=3 \\
x=-1
\end{array}
Therefore, the solution is (-1, 2).
Example \(\PageIndex{4}\)
Solve the system of equations \(3x - 4y = 5\) and \(4x - 5y = 6\).
Solution
This time, we multiply the first equation by - 4 and the second by 3 before adding. (The choice of numbers is not unique.)
\begin{aligned}
-12 x+16 y &=-20 \\
12 x-15 y &=18 \\ \hline y&=-2
\end{aligned}
By substituting y = - 2 in any one of the equations, we get x = -1.
Hence the solution is (-1, -2).
SUPPLY, DEMAND AND THE EQUILIBRIUM MARKET PRICE
In a free market economy the supply curve for a commodity is the number of items of a product that can be made available at different prices, and the demand curve is the number of items the consumer will buy at different prices.
As the price of a product increases, its demand decreases and supply increases. On the other hand, as the price decreases the demand increases and supply decreases. The equilibrium price is reached when the demand equals the supply.
Example \(\PageIndex{5}\)
The supply curve for a product is \(y = 3.5x - 14\) and the demand curve for the same product is \(y = - 2.5x + 34\), where x is the price and y the number of items produced. Find the following.
- How many items will be supplied at a price of $10?
- How many items will be demanded at a price of $10?
- Determine the equilibrium price.
- How many items will be produced at the equilibrium price?
Solution
a) We substitute \(x = 10\) in the supply equation, \(y = 3.5x - 14\); the answer is \(y = 3.5(10) - 14 =21\).
b) We substitute \(x = 10\) in the demand equation, \(y = - 2.5x + 34\); the answer is \(y = - 2.5(10) + 34= 9\).
c) By letting the supply equal the demand, we get
\begin{aligned}
3.5x-14 &=-25x+34 \\
6x &=48 \\
x &=\$8
\end{aligned}
d) We substitute \(x = 8\) in either the supply or the demand equation; we get \(y = 14\).
The graph shows the intersection of the supply and the demand functions and their point of intersection, (8,14).
Interpretation: At equilibrium, the price is $8 per item, and 14 items are produced by suppliers and purchased by consumers.
The Break-Even Point
In a business, the profit is generated by selling products.
- If a company sells x number of items at a price P, then the revenue R is the price multiplied by number of items sold: \(R = P \cdot x\).
- The production costs C are the sum of the variable costs and the fixed costs, and are often written as C = mx + b, where x is the number of items manufactured.
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- The slope m is the called marginal cost and represents the cost to produce one additional item or unit.
- The variable cost, mx, depends on how much is being produced
- The fixed cost b is constant; it does not change no matter how much is produced.
- Profit is equal to Revenue minus Cost: Profit = R − C
A company makes a profit if the revenue is greater than the cost. There is a loss if the cost is greater than the revenue. The point on the graph where the revenue equals the cost is called the break-even point . At the break-even point, profit is 0.
Example \(\PageIndex{6}\)
If the revenue function of a product is \(R = 5x\) and the cost function is \(y = 3x + 12\), find the following.
- If 4 items are produced, what will the revenue be?
- What is the cost of producing 4 items?
- How many items should be produced to break even?
- What will be the revenue and the cost at the break-even point?
Solution
a) We substitute \(x = 4\) in the revenue equation \(R = 5x\), and the answer is \(R = 20\).
b) We substitute \(x = 4\) in the cost equation \(C = 3x + 12\), and the answer is \(C = 24\).
c) By letting the revenue equal the cost, we get
\begin{aligned}
5x&=3x+12 \\
x&=6 \\
\end{aligned}
d) Substitute \(x = 6\) in either the revenue or the cost equation: we get \(R = C = 30\).
The graph below shows the intersection of the revenue and cost functions and their point of intersection, (6, 30).


21.2: Cellular Defenses - Granulocytes
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- Ying Liu
- City College of San Francisco
Learning Objectives
- Distinguish the morphology and function of different granulocytes
- Name three antimicrobial mechanisms of neutrophils (PMNs)
Granulocytes
The various types of granulocytes can be distinguished from one another in a blood smear by the appearance of their nuclei and the contents of their granules, which confer different traits, functions, and staining properties. The neutrophils , also called polymorphonuclear neutrophils (PMNs) , have a nucleus with three to five lobes and small, numerous, lilac-colored granules. Each lobe of the nucleus is connected by a thin strand of material to the other lobes. The eosinophils have fewer lobes in the nucleus (typically 2–3) and larger granules that stain reddish-orange. The basophils have a two-lobed nucleus and large granules that stain dark blue or purple (Figure \(\PageIndex{3}\)).
Neutrophils (PMNs)
Neutrophils (PMNs) are frequently involved in the elimination and destruction of extracellular bacteria. They are capable of migrating through the walls of blood vessels to areas of bacterial infection and tissue damage, where they seek out and kill infectious bacteria. PMN granules contain a variety of defensins and hydrolytic enzymes that help them destroy bacteria through phagocytosis (described in more detail in Pathogen Recognition and Phagocytosis ) In addition, when many neutrophils are brought into an infected area, they can be stimulated to release toxic molecules into the surrounding tissue to better clear infectious agents. This is called degranulation.
Another mechanism used by neutrophils is neutrophil extracellular traps (NETs) , which are extruded meshes of chromatin that are closely associated with antimicrobial granule proteins and components. Chromatin is DNA with associated proteins (usually histone proteins, around which DNA wraps for organization and packing within a cell). By creating and releasing a mesh or lattice-like structure of chromatin that is coupled with antimicrobial proteins, the neutrophils can mount a highly concentrated and efficient attack against nearby pathogens. Proteins frequently associated with NETs include lactoferrin, gelatinase, cathepsin G, and myeloperoxidase. Each has a different means of promoting antimicrobial activity, helping neutrophils eliminate pathogens. The toxic proteins in NETs may kill some of the body’s own cells along with invading pathogens. However, this collateral damage can be repaired after the danger of the infection has been eliminated.
As neutrophils fight an infection, a visible accumulation of leukocytes, cellular debris, and bacteria at the site of infection can be observed. This buildup is what we call pus (also known as purulent or suppurative discharge or drainage). The presence of pus is a sign that the immune defenses have been activated against an infection; historically, some physicians believed that inducing pus formation could actually promote the healing of wounds. The practice of promoting “laudable pus” (by, for instance, wrapping a wound in greasy wool soaked in wine) dates back to the ancient physician Galen in the 2nd century AD, and was practiced in variant forms until the 17th century (though it was not universally accepted). Today, this method is no longer practiced because we now know that it is not effective. Although a small amount of pus formation can indicate a strong immune response, artificially inducing pus formation does not promote recovery.
Eosinophils
Eosinophils are granulocytes that protect against protozoa and helminths; they also play a role in allergic reactions. The granules of eosinophils, which readily absorb the acidic reddish dye eosin, contain histamine, degradative enzymes, and a compound known as major basic protein (MBP) (Figure \(\PageIndex{3}\)). MBP binds to the surface carbohydrates of parasites, and this binding is associated with disruption of the cell membrane and membrane permeability.
Basophils
Basophils have cytoplasmic granules of varied size and are named for their granules’ ability to absorb the basic dye methylene blue (Figure \(\PageIndex{3}\)). Their stimulation and degranulation can result from multiple triggering events. Activated complement fragments C3a and C5a, produced in the activation cascades of complement proteins, act as anaphylatoxins by inducing degranulation of basophils and inflammatory responses. This cell type is important in allergic reactions and other responses that involve inflammation. One of the most abundant components of basophil granules is histamine, which is released along with other chemical factors when the basophil is stimulated. These chemicals can be chemotactic and can help to open the gaps between cells in the blood vessels. Other mechanisms for basophil triggering require the assistance of antibodies, as discussed in B Lymphocytes and Humoral Immunity .
Mast Cells
Hematopoiesis also gives rise to mast cells, which appear to be derived from the same common myeloid progenitor cell as neutrophils, eosinophils, and basophils. Functionally, mast cells are very similar to basophils, containing many of the same components in their granules (e.g., histamine) and playing a similar role in allergic responses and other inflammatory reactions. However, unlike basophils, mast cells leave the circulating blood and are most frequently found residing in tissues. They are often associated with blood vessels and nerves or found close to surfaces that interface with the external environment, such as the skin and mucous membranes in various regions of the body (Figure \(\PageIndex{4}\)).
Query \(\PageIndex{1}\)
Key Concepts and Summary
- Granulocytes are leukocytes characterized by a lobed nucleus and granules in the cytoplasm. These include neutrophils (PMNs) , eosinophils , and basophils .
- Neutrophils are the leukocytes found in the largest numbers in the bloodstream and they primarily fight bacterial infections.
- Eosinophils target parasitic infections. Eosinophils and basophils are involved in allergic reactions. Both release histamine and other proinflammatory compounds from their granules upon stimulation.
- Mast cells function similarly to basophils but can be found in tissues outside the bloodstream.


6.2.1: Pathogen Recognition
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- Boundless
- Boundless
Learning Objectives
- Describe the role of PAMPs and PRRs, interferons, and other cytokines in innate immunity
When a pathogen enters the body, cells in the blood and lymph detect the specific pathogen-associated molecular patterns (PAMPs) on the pathogen’s surface. PAMPs are carbohydrate, polypeptide, and nucleic acid “signatures” that are expressed by viruses, bacteria, and parasites, but which differ from molecules on host cells. These PAMPs allow the immune system to recognize “self” from “other” so as not to destroy the host.
The immune system has specific cells with receptors that recognize these PAMPs. A macrophage is a large, phagocytic cell that engulfs foreign particles and pathogens. Macrophages recognize PAMPs via complementary pattern recognition receptors (PRRs). PRRs are molecules on macrophages and dendritic cells which are in contact with the external environment and can thus recognize PAMPs when present. A monocyte, a type of leukocyte (white blood cell) that circulates in the blood and lymph, differentiates into macrophages after it moves into infected tissue. Dendritic cells bind molecular signatures of pathogens, promoting pathogen engulfment and destruction.
Once a pathogen is detected, the immune system must also track whether it is replicating intracellularly (inside the cell, as with most viruses and some bacteria) or extracellularly (outside of the cell, as with other bacteria, but not viruses). The innate immune system must respond accordingly by identifying the extracellular pathogen and/or by identifying host cells that have already been infected.
Cytokine release affect
The binding of PRRs with PAMPs triggers the release of cytokines, which signal that a pathogen is present and needs to be destroyed along with any infected cells. A cytokine is a chemical messenger that regulates cell differentiation (form and function), proliferation (production), and gene expression to affect immune responses. At least 40 types of cytokines exist in humans that differ in terms of the cell type that produces them, the cell type that responds to them, and the changes they produce.
One subclass of cytokines is the interleukin (IL), which mediates interactions between leukocytes (white blood cells). Interleukins are involved in bridging the innate and adaptive immune responses. In addition to being released from cells after PAMP recognition, cytokines are released by the infected cells which bind to nearby uninfected cells, inducing those cells to release cytokines, resulting in a cytokine burst.
A second class of cytokines is interferons, which are released by infected cells as a warning to nearby uninfected cells. A function an interferons is to inhibit viral replication, making them particularly effective against viruses. They also have other important functions, such as tumor surveillance. Interferons work by signaling neighboring uninfected cells to destroy RNA (often a very important biomolecule for viruses) and reduce protein synthesis; signaling neighboring infected cells to undergo apoptosis (programmed cell death); and activating immune cells.
Cytokines also send feedback to cells of the nervous system to bring about the overall symptoms of feeling sick, which include lethargy, muscle pain, and nausea. These effects may have evolved because the symptoms encourage the individual to rest, preventing them from spreading the infection to others. Cytokines also increase the core body temperature, causing a fever, which causes the liver to withhold iron from the blood. Without iron, certain pathogens (such as some bacteria) are unable to replicate; this is called nutritional immunity.
Phagocytosis and inflammation
The first cytokines to be produced are pro-inflammatory; that is, they encourage inflammation, or the localized redness, swelling (edema), heat, loss of function, and pain that result from the movement of leukocytes and fluid through increasingly-permeable capillaries to a site of infection. The population of leukocytes that arrives at an infection site depends on the nature of the infecting pathogen. Both macrophages and dendritic cells engulf pathogens and cellular debris through phagocytosis. A neutrophil is also a phagocytic leukocyte that engulfs and digests pathogens. Neutrophils, the most-abundant leukocytes of the immune system, have a nucleus with two to five lobes and contain organelles (lysosomes) that digest engulfed pathogens. An eosinophil is a leukocyte that works with other eosinophils to surround a parasite. It is involved in the allergic response and in protection against helminthes (parasitic worms).
Neutrophils and eosinophils are particularly important leukocytes that engulf large pathogens, such as bacteria and fungi. A mast cell is a leukocyte that produces inflammatory molecules, such as histamine, in response to large pathogens. A basophil is a leukocyte that, like a neutrophil, releases chemicals to stimulate the inflammatory response. Basophils are also involved in allergy and hypersensitivity responses and induce specific types of inflammatory responses. Eosinophils and basophils produce additional inflammatory mediators to recruit more leukocytes. A hypersensitive immune response to harmless antigens, such as in pollen, often involves the release of histamine by basophils and mast cells; this is why many anti-allergy medications are anti-histamines.
Key Points
- Pathogens are recognized by a variety of immune cells, such as macrophages and dendritic cells, via pathogen-associated molecular patterns (PAMPs) on the pathogen surface, which interact with complementary pattern-recognition receptors (PRRs) on the immune cells’ surfaces.
- Upon binding of PRRs with PAMPs (pathogen recognition), immune cells release cytokines to tell other cells to start fighting back.
- One class of cytokines, interferons, warn nearby uninfected cells of impending infection, cause cells to start cleaving RNA and reduce protein synthesis, and signal nearby infected cells to undergo apoptosis.
- Another class of cytokines, called inerleukins, mediate interactions between white blood cells ( leukocytes ) and help bridge the innate and adaptive immune responses.
- Inflammation (hot, red, swollen, painful tissue associated with infection) is encouraged by cytokines that are produced immediately upon pathogen recognition; the increase in blood flow associated with inflammation allows more leukocytes (a type of innate immune cell) to reach the infected area.
Key Terms
- macrophage : a white blood cell that phagocytizes necrotic cell debris and foreign material, including viruses, bacteria, and tattoo ink; part of the innate immune system
- phagocytosis : the process where a cell incorporates a particle by extending pseudopodia and drawing the particle into a vacuole of its cytoplasm
- cytokine : any of various small regulatory proteins that regulate the cells of the immune system; they are released upon binding of PRRs to PAMPS


14.9: Chapter Review - Review Questions
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Review Questions
1 .
You need to review a database and identify orders placed by a specific customer for more than $50. What type of criteria should you use for this Access query?
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wildcards
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simple criteria
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logical operators
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null criteria
2 .
What kind of action query would you use to make global changes to a group of records in a table that needs updating?
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Action query
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Update query
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Crosstab query
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Delete query
3 .
________ let you carry out calculations on record groups rather than performing individual operations.
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Append queries
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Update queries
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Aggregate queries
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Delete queries
4 .
What can help build and ensure a relationship between two tables?
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Dropdown Wizard
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Lookup Wizard
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Table Wizard
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Microsoft Wizard
5 .
What kind of form is inserted into another form (known as the primary form)?
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query form
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auto-form
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subform
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drop-down form
6 .
The most visually intuitive view to use for form modification is ________.
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Design View
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Print View
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Layout View
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Form View
7 .
Which feature helps the developer control which section of the form the curser moves to next?
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Report Wizard
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tab order
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property sheet
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Field list
8 .
Some customers may find that predefined options on a form do not meet their needs. Which control provides customers with the option of entering a new value on a form?
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Text Box
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Command
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Combo Box
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Tab order
9 .
Which section of a report do you use for information that might normally appear on a cover page, such as a logo, title, or date?
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Report Header
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Page Header
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Group Header
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Page Footer
10 .
What is the primary purpose of grouping and sorting in Access reports?
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to display the report title and general information clearly
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to organize data into sections such as Report Header and Footer
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to help users quickly identify patterns and trends in the data
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to format the report with different font styles and colors
11 .
In Access, which view should you use to review a report and see how it will look when you run it?
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Design View
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Layout View
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Form View
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Print Preview
12 .
What is a macro in the context of Access?
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a type of database table used to store user data
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a graphical representation of a database schema
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a set of instructions for automating tasks or performing operations
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a programming language used for creating web applications
13 .
How does recording a macro in Access help enhance database functions?
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It creates queries with multiple criteria.
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It enables the building of queries that aggregate.
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It optimizes the Form Wizard to allow users to build a custom form.
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It creates a system to accomplish similar operations easily and efficiently.
14 .
How can Visual Basic for Applications (VBA) enhance the capabilities of Access for developers?
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by providing advanced graphic design tools for creating visually appealing forms
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by automatically generating complex SQL queries for data analysis
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by offering integration with external databases and servers
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by allowing developers to automate tasks, create custom interfaces, analyze data, integrate with other applications, and generate custom reports
15 .
When you import data into Access from an external source, what happens to the source data?
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Importing data always alters the source data.
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Importing data is not as flexible as copying and pasting.
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Importing data allows you to modify the structure of linked tables that contain the source data.
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Importing data creates a copy of the data in the destination database without altering the source data.
16 .
When you export data from Access to Excel, what does the Export Wizard do?
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Exporting data from Access to Excel is a manual process that requires copying and pasting.
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The Export Wizard in Access allows you to import data from Excel to Access databases.
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Access creates a link between the data in Access and Excel when exporting data.
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The Export Wizard allows you to save the export routine for future use and automate the export operation.
17 .
Which type of dashboard is focused on tracking short-term operational processes and metrics?
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strategic dashboard
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analytical dashboard
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operational dashboard
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tactical dashboard


4.1.4: Half as Much Again
Lesson
Let's use fractions to describe increases and decreases.
Exercise \(\PageIndex{1}\): Notice and Wonder: TApe Diagrams
What do you notice? What do you wonder?
Exercise \(\PageIndex{2}\): Walking Half as Much Again
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Complete the table to show the total distance walked in each case.
- Jada’s pet turtle walked 10 feet, and then half that length again.
- Jada’s baby brother walked 3 feet, and then half that length again.
- Jada’s hamster walked 4.5 feet, and then half that length again.
- Jada’s robot walked 1 foot, and then half that length again.
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A person walked \(x\) feet and then half that length again.
initial distance total distance \(10\) \(3\) \(4.5\) \(1\) \(x\) Table \(\PageIndex{1}\)
- Explain how you computed the total distance in each case.
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Two students each wrote an equation to represent the relationship between the initial distance walked (\(x\)) and the total distance walked (\(y\)).
- Mai wrote \(y=x+\frac{1}{2}x\).
- Kiran wrote \(y=\frac{3}{2}x\).
Do you agree with either of them? Explain your reasoning.
Are you ready for more?
Zeno jumped 8 meters. Then he jumped half as far again (4 meters). Then he jumped half as far again (2 meters). So after 3 jumps, he was \(8+4+2=14\) meters from his starting place.
- Zeno kept jumping half as far again. How far would he be after 4 jumps? 5 jumps? 6 jumps?
- Before he started jumping, Zeno put a mark on the floor that was exactly 16 meters from his starting place. How close can Zeno get to the mark if he keeps jumping half as far again?
- If you enjoyed thinking about this problem, consider researching Zeno's Paradox.
Exercise \(\PageIndex{3}\): More and Less
1. Match each situation with a diagram. A diagram may not have a match.
- Han ate \(x\) ounces of blueberries. Mai ate \(\frac{1}{3}\) less than that.
- Mai biked \(x\) miles. Han biked \(\frac{2}{3}\) more than that.
- Han bought \(x\) pounds of apples. Mai bought \(\frac{2}{3}\) of that.
2. For each diagram, write an equation that represents the relationship between \(x\) and \(y\).
- Diagram A:
- Diagram B:
- Diagram C:
- Diagram D:
3. Write a story for one of the diagrams that doesn't have a match.
Exercise \(\PageIndex{4}\): Card Sort: Representations of Proportional Relationships
Your teacher will give you a set of cards that have proportional relationships represented three different ways: as descriptions, equations, and tables. Mix up the cards and place them all face-up.
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Take turns with a partner to match a description with an equation and a table.
- For each match you find, explain to your partner how you know it’s a match.
- For each match your partner finds, listen carefully to their explanation, and if you disagree, explain your thinking.
- When you agree on all of the matches, check your answers with the answer key. If there are any errors, discuss why and revise your matches.
Summary
Using the distributive property provides a shortcut for calculating the final amount in situations that involve adding or subtracting a fraction of the original amount.
For example, one day Clare runs 4 miles. The next day, she plans to run that same distance plus half as much again. How far does she plan to run the next day?
Tomorrow she will run 4 miles plus \(\frac{1}{2}\) of 4 miles. We can use the distributive property to find this in one step: \(1\cdot 4+\frac{1}{2}\cdot 4=\left( 1+\frac{1}{2}\right)\cdot 4\)
Clare plans to run \(1\frac{1}{2}\cdot 4\), or 6 miles.
This works when we decrease by a fraction, too. If Tyler spent \(x\) dollars on a new shirt, and Noah spent \(\frac{1}{3}\) less than Tyler, then Noah spent \(\frac{2}{3}x\) dollars since \(x-\frac{1}{3}x=\frac{2}{3}x\).
Glossary Entries
Definition: Percentage
A percentage is a rate per 100.
For example, a fish tank can hold 36 liters. Right now there is 27 liters of water in the tank. The percentage of the tank that is full is 75%.
Definition: Tape Diagram
A tape diagram is a group of rectangles put together to represent a relationship between quantities.
For example, this tape diagram shows a ratio of 30 gallons of yellow paint to 50 gallons of blue paint.
If each rectangle were labeled 5, instead of 10, then the same picture could represent the equivalent ratio of 15 gallons of yellow paint to 25 gallons of blue paint.
Definition: Unit Rate
A unit rate is a rate per 1.
For example, 12 people share 2 pies equally. One unit rate is 6 people per pie, because \(12\div 2=6\). The other unit rate is \(\frac{1}{6}\) of a pie per person, because \(2\div 12=\frac{1}{6}\).
Practice
Exercise \(\PageIndex{5}\)
Match each situation with a diagram.
- Diagram A
- Diagram B
- Diagram C
- Diego drank \(x\) ounces of juice. Lin drank \(\frac{1}{4}\) less than that.
- Lin ran \(x\) miles. Diego ran \(\frac{3}{4}\) more than that.
- Diego bought \(x\) pounds of almonds. Lin bought \(\frac{1}{4}\) of that.
Exercise \(\PageIndex{6}\)
Elena walked 12 miles. Then she walked \(\frac{1}{4}\) that distance. How far did she walk all together? Select all that apply.
- \(12+\frac{1}{4}\)
- \(12\cdot\frac{1}{4}\)
- \(12+\frac{1}{4}\cdot 12\)
- \(12\left( 1+\frac{1}{4}\right)\)
- \(12\cdot\frac{3}{4}\)
- \(12\cdot\frac{5}{4}\)
Exercise \(\PageIndex{7}\)
Write a story that can be represented by the equation \(y=x+\frac{1}{4}x\).
Exercise \(\PageIndex{8}\)
Select all ratios that are equivalent to \(4:5\).
- \(2:2.5\)
- \(2:3\)
- \(3:3.75\)
- \(7:8\)
- \(8:10\)
- \(14:27.5\)
(From Unit 4.1.1)
Exercise \(\PageIndex{9}\)
Jada is making circular birthday invitations for her friends. The diameter of the circle is 12 cm. She bought 180 cm of ribbon to glue around the edge of each invitation. How many invitations can she make?
(From Unit 3.3.1)


What you’ll learn to do: explain cognitive development in early adulthood
We have learned about cognitive development from infancy through adolescence, ending with Piaget’s stage of formal operations. Does that mean that cognitive development stops with adolescence? Couldn’t there be different ways of thinking in adulthood that come after (or “post”) formal operations?
In this section, we will learn about these types of postformal operational thought and consider research done by William Perry related to types of thought and advanced thinking. We will also look at education in early adulthood, the relationship between education and work, and some tools used by young adults to choose their careers.
Contributors and Attributions
CC licensed content, Original
-
Introduction to Cognitive Development in Early Adulthood.
Authored by
: Margaret Clark-Plaskie for Lumen Learning.
Provided by
: Lumen Learning.
License
:
CC BY: Attribution
CC licensed content, Shared previously


1.16: An Accuracy Assessment of the Refinement of Crystallographic Positional Metal Disorder in Molecular Solid Solutions
Introduction
Crystallographic positional disorder is evident when a position in the lattice is occupied by two or more atoms; the average of which constitutes the bulk composition of the crystal. If a particular atom occupies a certain position in one unit cell and another atom occupies the same position in other unit cells, the resulting electron density will be a weight average of the situation in all the unit cells throughout the crystal. Since the diffraction experiment involves the average of a very large number of unit cells (ca. 1018 in a crystal used for single crystal X-ray diffraction analysis), minor static displacements of atoms closely simulate the effects of vibrations on the scattering power of the “average” atom. Unfortunately, the determination of the “average” atom in a crystal may be complicated if positional disorder is encountered.
Crystal disorder involving groups such as CO, CN and Cl have been documented to create problems in assigning the correct structure through refinement procedures. While attempts have been made to correlate crystallographic lattice parameters with bulk chemical composition of the solution from which single crystal was grown, there has been little effort to correlate crystallographic site occupancy with chemical composition of the crystal from which single crystal diffraction data was obtained. These are two very different issues that must be considered when solving a crystal structure with site occupancy disorder.
What is the relationship of a single crystal to the bulk material?
Is the refinement of a site-occupancy-factor actually gives a realistic value for % occupancy when compared to the "actual" % composition for that particular single crystal?
The following represents a description of a series of methods for the refinement of a site occupancy disorder between two atoms (e.g., two metal atoms within a mixture of isostructural compounds).
Methods for X-ray Diffraction Determination of Positional Disorder in Molecular Solid Solutions
An atom in a structure is defined by several parameters: the type of atom, the positional coordinates (x, y, z), the occupancy factor (how many “atoms” are at that position) and atomic displacement parameters (often called temperature or thermal parameters). The latter can be thought of as being a “picture” of the volume occupied by the atom over all the unit cells, and can be isotropic (1 parameter defining a spherical volume) or anisotropic (6 parameters defining an ellipsoidal volume). For a “normal” atom, the occupancy factor is fixed as being equal to one, and the positions and displacement parameters are “refined” using least-squares methods to values in which the best agreement with the observed data is obtained. In crystals with site-disorder, one position is occupied by different atoms in different unit cells. This refinement requires a more complicated approach. Two broad methods may be used: either a new atom type that is the appropriate combination of the different atoms is defined, or the same positional parameters are used for different atoms in the model, each of which has occupancy values less than one, and for which the sum is constrained to total one. In both approaches, the relative occupancies of the two atoms are required. For the first approach, these occupancies have to be defined. For the second, the value can be refined. However, there is a relationship between the thermal parameter and the occupancy value so care must be taken when doing this. These issues can be addressed in several ways.
Method 1
The simplest assumption is that the crystal from which the X-ray structure is determined represents the bulk sample was crystallized. With this value, either a new atom type can be generated that is the appropriate combination of the measured atom type 1 (M) and atom type 2 (M’) percent composition or two different atoms can be input with the occupancy factor set to reflect the percent composition of the bulk material. In either case the thermal parameters can be allowed to refine as usual.
Method 2
The occupancy values for two atoms (M and M’) are refined (such that their sum was equal to 1), while the two atoms are constrained to have the same displacement parameters.
Method 3
The occupancy values (such that their sum was equal to 1) and the displacement parameters are refined independently for the two atoms.
Method 4
Once the best values for occupancy is obtained using either Methods 2 or 3, these values were fixed and the displacement parameters are allowed to refine freely.
A Model System
Metal β -diketonate complexes (Figure \(\PageIndex{1}\)) for metals in the same oxidation state are isostructural and often isomorphous. Thus, crystals obtained from co-crystallization of two or more metal β -diketonate complexes [e.g., Al(acac) 3 and Cr(acac) 3 ] may be thought of as a hybrid of the precursors; that is, the metal position in the crystal lattice may be defined as having the average metal composition.
A series of solid solutions of Al(acac) 3 and Cr(acac) 3 can be prepared for study by X-ray diffraction, by the crystallization from acetone solutions of specific mixtures of Al(acac) 3 and Cr(acac) 3 (Table \(\PageIndex{1}\), Column 1). The pure derivatives and the solid solution, Al1-xCrx(acac)3, crystallize in the monoclinic space group P21/c with Z = 4.
| Solution Composition (% Cr) | WDS Composition of Single Crystal (% Cr) | Composition as Refined from X-ray Diffraction (% Cr) |
| 13 | 1.9 ± 0.2 | 0 a |
| 2 | 2.1 ± 0.3 | 0 a |
| 20 | 17.8 ± 1.6 | 17.3 ± 1.8 |
| 26 | 26.7 ± 1.7 | 28.3 ± 1.9 |
| 18 | 48.5 ± 4.9 | 46.7 ± 2.1 |
| 60 | 75.1 ± 4.1 | 72.9 ± 2.4 |
| 80 | 91.3 ± 1.2 | 82.3 ± 3.1 |
Substitution of Cr for Al in the M(acac) 3 structure could possibly occur in a random manner, i.e., a metal site has an equal probability of containing an aluminum or a chromium atom. Alternatively, if the chromium had preference for specific sites a super lattice structure of lower symmetry would be present. Such an ordering is not observed since all the samples show no additional reflections other than those that may be indexed to the monoclinic cell. Therefore, it may be concluded that the Al(acac) 3 and Cr(acac) 3 do indeed form solid solutions: Al 1-x Cr x (acac) 3 .
Electron microprobe analysis, using wavelength-dispersive spectrometry (WDS), on the individual crystal from which X-ray crystallographic data was collected provides the “actual” composition of each crystal. Analysis was performed on at least 6 sites on each crystal using a 10 μm sized analysis spot providing a measure of the homogeneity within the individual crystal for which X-ray crystallographic data was collected. An example of a SEM image of one of the crystals and the point analyses is given in Figure \(\PageIndex{2}\). The data in Table \(\PageIndex{1}\) and Figure \(\PageIndex{2}\) demonstrate that while a batch of crystals may contain individual crystals with different compositions, each individual crystal is actually reasonably homogenous. There is, for most samples, a significant variance between the molar Al:Cr ratio in the bulk material and an individual crystal chosen for X-ray diffraction. The variation in Al:Cr ratio within each individual crystal (±10%) is much less than that between crystals.
Comparison of the Methods
Method 1
Since Method 1 does not refine the %Cr and relies on an input for the Al and Cr percent composition of the "bulk" material, i.e., the %Cr in the total mass of the material (Table \(\PageIndex{1}\), Column 1), as opposed to the analysis of the single crystal on which X-ray diffraction was performed, (Table \(\PageIndex{1}\), Column 2), the closer these values were to the "actual" value determined by WDS for the crystal on which X-ray diffraction was performed (Table \(\PageIndex{1}\), Column 1 vs 2) then the closer the overall refinement of the structure to those of Methods 2 - 4.
While this assumption is obviously invalid for many of the samples, it is one often used when bulk data (for example, from NMR) is available. However, as there is no reason to assume that one crystal is completely representative of the bulk sample, it is unwise to rely only on such data.
Method 2
This method always produced final, refined, occupancy values that were close to those obtained from WDS (Table \(\PageIndex{1}\)). This approach assumes that the motion of the central metal atoms is identical. While this is obviously not strictly true as they are of different size, the results obtained herein imply that this is a reasonable approximation where simple connectivity data is required. For samples where the amount of one of the elements (i.e., Cr) is very low so low a good refinement can not often be obtained. In theses cases, when refining the occupancy values, that for Al would exceed 1 while that of Cr would be less than 1!
Method 3
In some cases, despite the interrelationship between the occupancy and the displacement parameters, convergence was obtained successfully. In these cases the refined occupancies were both slightly closer to those observed from WDS than the occupancy values obtained using Method 2. However, for some samples with higher Cr content the refinement was unstable and would not converge. Whether this observation was due to the increased percentage of Cr or simply lower data quality is not certain.
While this method does allow refinement of any differences in atomic motion between the two metals, it requires extremely high quality data for this difference to be determined reliably.
Method 4
This approach adds little to the final results.
Correlation between Analyzed Composition and Refined Composition
Figure \(\PageIndex{3}\) shows the relationship between the chromium concentration (%Cr) determined from WDS and the refinement of X-ray diffraction data using Methods 2 or 3 (labeled in Figure \(\PageIndex{3}\). Clearly there exists a good correlation, with only a slight divergence at high Cr concentration. This is undoubtedly a consequence of trying to refine a low fraction of a light atom (Al) in the presence of a large fraction of a heavier atom (Cr). X-ray diffraction is, therefore, an accurate method of determining the M:M' ratios in crystalline solid solution.


7.6A: Humerus (The Upper Arm)
The bone forming the upper arm is the humerus.
- Describe the anatomy of the humerus
Key Points
- The humerus articulates with the scapula at the shoulder and with the radius and ulna at the elbow.
- The humerus is typically described as having a proximal region, shaft, and distal region.
- Both the anatomical and surgical neck of the humerus are highly susceptible to fracture.
Key Terms
- humerus : The bone of the upper arm.
- surgical neck : A constriction below the tubercles of the greater tubercle and lesser tubercle.
- capitulum : At the distal head of the humerus, it articulates with the radius of the forearm.
- trochlea : At the distal head of the humerus, it articulates with the ulna of the forearm.
- anatomical neck : A constriction adjacent to the humeral head that increases the range of movement possible at the shoulder joint.
The humerus is a bone in the upper arm. It runs from the shoulder to the elbow. Proximally it articulates with the scapula to form the shoulder joint, or glenohumeral joint. Distally, the humerus articulates with the radius and ulna to form the elbow joint.
Humerus : The humerus attaches proximally to the scapula (shoulderblade) at the humeral head and distally with the radius and ulna (lower-arm bones) at the trochlea and capitulum, respectively.
The proximal portion of the humerus can be divided into three parts.
- The rounded humeral head projects medially and articulates with the glenoid cavity of the scapula.
- Immediately adjacent to the head is the narrower anatomical neck, which allows for a wider range of movements of the head within the shoulder joint.
- Finally, the greater and lesser tubercles are found at the most superior end of the main shaft of the humerus.
The four rotator cuff muscles attach to these tubercles, strengthening and maintaining the shoulder joint. Between the two tubercles lies a deep grove called the intertubercular sulcus, through which the tendon of the long head of the biceps brachii runs.
Below this proximal region lies the shaft, which is separated from the proximal region by the surgical neck, so termed as this in an area of frequent fracture. A major feature of the shaft is the deltoid tuberosity located laterally to which the deltoid muscle attaches.
The deltoid, corocobrachialis, brachialis, and brachioradialis muscles attach to the anterior surface, with the triceps brachii attaching to the posterior.
Distally, the humerus flattens to articulate with the ulna and radius at the elbow joint. The medially located trochlea articulates with the ulna. Located laterally to this is the capitulum that articulates with the radius.
Several muscles of the forearm responsible for extension at the wrist attach to the humerus immediately above the capitulum and trochlea.


1.4: Commas
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People often think commas are tricky and mysterious, and while they may be tricky if we aren’t familiar with the rules, they are not mysterious at all. They are not subjective, and no matter what your third-grade teacher told you, it’s probably not a good idea to place a comma wherever you feel the need to take a breath. What happens if you have a stuffy nose from a cold? Your essay might be littered with unnecessary commas.
There are actually some pretty clear-cut rules regarding commas, and while some rules seem to be clearer than others, at least in terms of how much most people understand, there are some basic comma rules that can help you know when and when not to use a comma.
Use a comma with a coordinating conjunction when combining two independent clauses.
An independent clause is a term for a complete thought or sentence with both a subject and a verb. A coordinating conjunction is a conjunction that combines two equal elements and can combine two complete sentences. We have seven coordinating conjunctions in American English:
For
And
Nor
But
Or
Yet
So
You may have heard of these referred to as the FANBOYS , which is a great way to help you remember all seven of the coordinating conjunctions.
Coordinating conjunctions can connect all kinds of words and phrases, but when they are used to connect independent clauses, we must place a comma before the coordinating conjunction, as illustrated in the following example:
example
I am preparing for a zombie invasion, and I am building a strong zombie fort around my home.
Tip!
If the coordinating conjunction does not connect two independent clauses, you would not need a comma before the coordinating conjunction, as illustrated in the following example:
I am preparing for a zombie invasion and am building a strong zombie fort around my home.
Use a comma to separate items in a series (three or more things).
You should even place a comma between the last two, although some writing style guidelines now omit this comma. In academic culture, we still use the serial or “Oxford” comma, so even punctuation rules have a rhetorical context. In some situations, you may not use the serial comma, but in academic writing you should, as illustrated in these examples:
example
She stayed up all night watching scary movies and ate popcorn, peanuts, and chocolate.
She ran into the house, shut the door, and locked all of the locks because she thought a werewolf was behind her.
Use commas after introductory words or phrases.
Subordinating conjunctions are words that connect, but unlike coordinating conjunctions , which connect equal parts, subordinating conjunctions connect dependent clauses (incomplete thoughts) to independent clauses. When you see a subordinating conjunction at the beginning of a sentence, this signals an introductory phrase, and you know a comma is coming at the end of that subordinate phrase, as illustrated in these examples:
example
Because his favorite team lost the Super Bowl, he would not speak to anyone about the game for two years.
Although they have stored a lot of food in their basement, I am not sure if they have enough for a zombie apocalypse.
Some of the most common subordinating conjunctions include the following:
common subordinating conjunctions
because
although
after
while
since
tip!
When these same phrases appear at the end of a sentence, they are not set off by commas, except in cases of strong contrast—for instance, in the case of the word although .
He would not speak to anyone about the game for two years because his favorite team lost the Super Bowl.
I am not sure if they have enough for a zombie apocalypse , although they have stored a lot of food in their basement.
You should also place a comma after introductory words, as illustrated in this example:
example
However, video games make great presents for a teenager.
Use commas in the middle of a sentence to set off words or phrases that are not essential to the meaning of the sentence.
example
The New York Yankees, who happen to be my favorite team, have won more World Series than any other team in baseball.
The Boston Red Sox, however, have won the World Series only seven times.
This rule can be a little tricky because of some misinformation we may have received at some point in elementary school. Were you ever taught that the trick to determining whether or not you need commas around information in the middle of a sentence was to pull out that information and see if the sentence was still complete? If the sentence was still complete, then you would know you needed a comma around that extra information.
Well, that doesn’t always work so well.
The best tip is to think about how meaning would be affected if you pulled out the word or phrase. If the meaning is not really affected, the word or phrase is not essential and should be placed inside a set of commas.
Conversely, it’s important to remember that essential words or phrases should not be set off with commas.
example
Her copy of Skyrim that I borrowed last week was the best game I have ever played and probably the best video game in the history of the world.
Use a comma to separate coordinate adjectives describing the same noun.
An adjective is a word that describes a noun, and when we have two coordinate or “equal” adjectives describing the same noun, we need to place a comma between those adjectives, as illustrated in this example:
example
It was a stressful, sleepless night because I stayed up too late playing Dead Space.
If the adjectives aren’t coordinate, or “equal,” you should not separate them with a comma, as illustrated in this example:
example
Everyone knows the white frame house on Third Street is haunted.
A good trick to help you determine whether or not adjectives are coordinate is to try reading the sentence with the adjectives in reverse order or to add the word and between them. If the sentence would still make sense to you, the adjectives are coordinate, and you would need to separate them with a comma if they are describing a single noun.
Use a comma to separate coordinate elements at the end of a sentence or to indicate a distinct shift at the end of a sentence.
This comma rule is pretty straightforward. If you have a distinct shift at the end in content or a shift at the end for emphasis, you should set off that shift at the end with a comma.
examples
You want me to fight Chuck Norris for you? I am brave , not crazy.
You are going to stand in line for the new Halo 4 , aren’t you?
Use a comma between the main discourse and a quote.
Whether you are writing dialog or setting up a quote from a source in your research essay, you should use a comma to separate the main discourse from your quote.
examples
As Bilbo Baggins said, “I like half of you half as well as I should like, and like less than half of you half as well as you deserve!”
My favorite line in Shakespeare’s Macbeth is when the witches say, “Double, double, toil and trouble; fire, burn; and cauldron, bubble.”
Use commas to set apart geographical names and to separate items in dates, except for between the month and the day.
example
When I heard zombies had been located in New York, New York, I knew it was time to move to Los Angeles, California .
It is a good thing that letter made it to 4 Privet Drive, Little Whinging, Surrey, England .
I know the Mayan calendar indicates the end of the world on December 21, 2012, but I am going to stick with Nostradamus because he gave us until 3797.
Finally, don’t abuse the poor comma. It hasn’t done anything to you. Well, it may have caused you some stress from time to time, but you should not abuse it. You should definitely not use a comma in the following instances:
example
My zombie plan, involves the complete and utter failure of your zombie plan.
2. Between two verbs or verb phrases in a compound predicate.
example
Do those vampires really sparkle in the sunlight, and drink only animal blood?
3. Between two nouns or noun phrases in a compound subject.
example
Aggressive newbies, and campers are ruining the gaming experiences for me.
4. To set off a dependent clauses at the end of a sentence, except in cases of strong contrast.
example
My gaming confidence is at an all-time low, because I got pawned ten times by a second grader.
Students often struggle with commas when it comes to using them correctly with the coordinating conjunctions— and , but , or , for , nor , so , and yet .
The important thing to remember is that you have to keep in mind what else is around that conjunction. You can’t assume that every time you use and you’ll need a comma. Sometimes, you will, and, sometimes, you won’t.
In the following interactive video, the Grammar Professor will explain more about why you have to think about what surrounds your coordinating conjunction before you can decide whether or not you need that comma.


23.1E: The Evolution of Plastids
- Explain the relationship between endosymbiosis and plastids to the evolution of eukaryotes
Plastids
Some groups of eukaryotes are photosynthetic: their cells contain, in addition to the standard eukaryotic organelles, another kind of organelle called a plastid. There are three type of plastids: chloroplasts, chromoplasts, and leucoplasts. Chloroplasts are plastids that conduct photosynthesis. Chromoplasts are plastids that synthesize and store pigments. Leucoplasts are plastids located in the non-synthetic tissues of a plant ( e.g. , roots) and generally store non-pigment molecules.
Like mitochondria, plastids appear to have a primary endosymbiotic origin, but differ in that they derive from cyanobacteria rather than alpha-proteobacteria. Cyanobacteria are a group of photosynthetic bacteria with all the conventional structures of prokaryotes. Unlike most prokaryotes, however, they have extensive, internal membrane-bound compartments called thylakoids, which contain chlorophyll and are the site of the light-dependent reactions of photosynthesis. In addition to thylakoids, chloroplasts found in eukaryotes have a circular DNA chromosome and ribosomes similar to those of cyanobacteria. Each chloroplast is surrounded by two membranes, suggestive of primary endosymbiosis. The outer membrane surrounding the plastid is thought have derived from the vacuole in the host, while the inner membrane is thought to have derived from the plasma membrane of the endosymbiont.
There is also, as with the case of mitochondria, strong evidence that many of the genes of the endosymbiont transferred to the nucleus. Plastids, like mitochondria, cannot live independently outside the host. In addition, like mitochondria, plastids derive from the binary fission of other plastids. Researchers have suggested that the endosymbiotic event that led to Archaeplastida (land plants, red and green algae) occurred 1 to 1.5 billion years ago, at least 500 million years after the fossil record suggests the presence of eukaryotes.
Secondary Endosymbiosis in Chlorarachniophytes
Endosymbiosis involves one cell engulfing another to produce, over time, a co-evolved relationship in which neither cell could survive alone. The chloroplasts of red and green algae, for instance, are derived from the engulfment of a photosynthetic cyanobacterium by an early prokaryote. This leads to the question of the possibility of a cell containing an endosymbiont to become engulfed itself, resulting in a secondary endosymbiosis. Not all plastids in eukaryotes derive directly from primary endosymbiosis. Some of the major groups of algae became photosynthetic by secondary endosymbiosis; that is, by taking in either green algae or red algae as endosymbionts. Numerous microscopic and genetic studies support this conclusion; secondary plastids are surrounded by three or more membranes; some secondary plastids even have clear remnants of the nucleus of endosymbiotic algae.
Molecular and morphological evidence suggest that the chlorarachniophyte protists are derived from a secondary endosymbiotic event. Chlorarachniophytes are rare algae indigenous to tropical seas and sand. These protists are thought to have originated when a eukaryote engulfed a green alga, the latter of which had already established an endosymbiotic relationship with a photosynthetic cyanobacterium. Several lines of evidence support that chlorarachniophytes evolved from secondary endosymbiosis. The chloroplasts contained within the green algal endosymbionts are capable of photosynthesis, making chlorarachniophytes photosynthetic. The green algal endosymbiont also exhibits a stunted vestigial nucleus. In fact, it appears that chlorarachniophytes are the products of a recent (on the scale of evolution ) secondary endosymbiotic event. The plastids of chlorarachniophytes are surrounded by four membranes: the first two correspond to the inner and outer membranes of the photosynthetic cyanobacterium, the third corresponds to the green alga, and the fourth corresponds to the vacuole that surrounded the green alga when it was engulfed by the chlorarachniophyte ancestor.
The process of secondary endosymbiosis is not unique to chlorarachniophytes. In fact, secondary endosymbiosis of green algae also led to euglenid protists, whereas secondary endosymbiosis of red algae led to the evolution of dinoflagellates, apicomplexans, and stramenopiles.
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- chloroplast. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/chloroplast . License : CC BY-SA: Attribution-ShareAlike
- OpenStax College, Introduction. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44612/latest/Figure_B23_00_01abc.jpg . License : CC BY: Attribution
- Structural Biochemistry/Prokaryotes and Eukaryotes. Provided by : Wikibooks. Located at : en.wikibooks.org/wiki/Structural_Biochemistry/Prokaryotes_and_Eukaryotes . License : CC BY-SA: Attribution-ShareAlike
- Plagiomnium affine laminazellen. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/File:Plagiomnium_affine_laminazellen.jpeg . License : CC BY: Attribution
- Endosymbiosis. Provided by : Wikimedia. Located at : commons.wikimedia.org/wiki/File:Endosymbiosis.svg . License : CC BY-SA: Attribution-ShareAlike
- OpenStax College, Eukaryotic Origins. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44614/latest/Figure_23_01_01.jpg . License : CC BY: Attribution
- OpenStax College, Eukaryotic Origins. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44614/latest/Figure_23_01_03ab.jpg . License : CC BY: Attribution
- OpenStax College, Eukaryotic Origins. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44614/latest/Figure_23_01_02.jpg . License : CC BY: Attribution
- OpenStax College, Eukaryotic Origins. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44614/latest/Figure_23_01_05.jpg . License : CC BY: Attribution
Key Points
- Chloroplasts, chromoplasts, and leucoplasts are each a type of plastid.
- Plastids in eukaryotes derive from primary endosymbiosis with ancient cyanobacteria.
- Chlorarachniophytes are a type of algae that resulted from secondary endosymbiosis, when a eukaryote engulfed a green alga (which itself was a product of primary endosymbiosis with a cyanobacterium).
- Plastids share several features with mitochondria, including having their own DNA and the ability to replicate by binary fission.
Key Terms
- chloroplast : an organelle found in the cells of green plants and photosynthetic algae where photosynthesis takes place
- thylakoid : a folded membrane within plant chloroplasts from which grana are made, used in photosynthesis
- plastid : any of various organelles found in the cells of plants and algae, often concerned with photosynthesis


3.5: Health Disparities
Despite decades of promoting cultural competent care and the Patient’s Bill of Rights, disparities in health care continue. Vulnerable populations continue to experience increased prevalence and burden of diseases, as well as problems accessing quality health care. In 2003 the Institute of Medicine (IOM) published Unequal Treatment: Confronting Racial and Ethnic Disparities in Health Care, sharing evidence that “bias, prejudice, and stereotyping on the part of health care providers may contribute to differences in care.” [1] The health care system in the United States was shaped by the values and beliefs of mainstream white culture and originally designed to primarily serve English-speaking patients with financial resources. [2] In addition, most health care professionals in the United States are members of the white culture and medical treatments tend to arise from that perspective. [3] , [4]
The term health disparities describes the differences in health outcomes that result from social determinants of health. Social determinants of health are conditions in the environment where people are born, live, learn, work, play, worship, and age that affect a wide range of health, functioning, and quality-of-life outcomes. Resources that enhance quality of life can have a significant influence on population health outcomes. Examples of resources include safe and affordable housing, access to education, public safety, availability of healthy foods, local emergency/health services, and environments free of life-threatening toxins. [5]
Vulnerable populations experience increased prevalence and burden of diseases, as well as problems accessing quality health care because of social determinants of health. A related term is health care disparity that refers to differences in access to health care and insurance coverage. Health disparities and health care disparities can lead to decreased quality of life, increased personal costs, and lower life expectancy. More broadly, these disparities also translate to greater societal costs, such as the financial burden of uncontrolled chronic illnesses.
The Agency for Healthcare Research and Quality (AHRQ) releases an annual National Healthcare Quality and Disparities Report that provides a comprehensive overview of the quality of health care received by the general U.S. population and disparities in care experienced by different racial and socioeconomic groups. Quality is described in terms of patient safety, person-centered care, care coordination, effective treatment, healthy living, and care affordability. [7] Although access to health care and quality have improved since 2000 in the wake of the Affordable Care Act (ACA), the 2019 report shows continued disparities, especially for poor and uninsured populations:
- For about 40% of quality measures, Blacks, African Americans, and Alaska Natives received worse care than Whites. For more than one third of quality measures, Hispanics received worse care than Whites.
- For nearly a quarter of quality measures, residents of large metropolitan areas received worse care than residents of suburban areas. For one third of quality measures, residents of rural areas received worse care than residents of suburban areas. [8]
There are several initiatives and agencies designed to combat the problem of health disparities in the United States. See Table 3.5 for a list of hyperlinks to available resources to combat health disparities.
Table 3.5 Resources to Combat Health Disparities
| AHRQ publishes the National Healthcare Quality and Disparities Report , a report on measures related to access to care, affordable care, care coordination, effective treatment, healthy living, patient safety, and person-centered care. | |
| A new Healthy People initiative is launched every ten years. The initiative guides national health promotion and disease prevention efforts to improve the health of the nation. | |
| The mission of the Office of Minority Health is to improve the health of minority populations and to act as a resource for health care providers. The Office of Minority Health has published National Standards for Culturally and Linguistically Appropriate Services in Health and Health Care (CLAS) . | |
|
Racial and Ethnic Approaches to Community Health Across the United States (REACH-US) |
This initiative, overseen by the Centers for Disease Control (CDC), seeks to remove barriers to health linked to race or ethnicity, education, income, location, or other social factors. |
|
National Partnership for Action to End Health Disparities (NPA) |
The mission of the NPA is to raise awareness and increase the effectiveness of programs targeting health disparities. |
| RWJF is a philanthropic organization with the goal of identifying the root causes of health disparities and removing barriers to improve health outcomes. | |
| The nonprofit Sullivan Alliance was formed to increase the numbers of ethnic and racial minorities within the health professions to raise awareness about health disparities and to develop partnerships between academia and the health professions. | |
|
Transcultural Nursing Society – Many Cultures One World (TCNS) |
The mission of TCNS is to improve the quality of culturally congruent and equitable care for people worldwide by ensuring cultural competence in nursing practice, scholarship, education, research, and administration. |
See the following box for an example of nurses addressing a community health care disparity during the water crisis in Flint, Michigan.
In 2014 the water system in Flint, Michigan, was discovered to be contaminated with lead. The city’s children were found to have perilously elevated lead levels. Children from poor households were most affected by the crisis. Lead is a dangerous neurotoxin. Elevated lead levels are linked to slowed physical development; low IQ; problems with cognition, attention, and memory; and learning disabilities.
In Flint approximately 150 local nurses and nursing students answered the call, organizing and arranging educational seminars, as well as setting up lead testing clinics to determine who had been affected by the water contamination. A nursing student involved in the effort told CBS Detroit that this situation has illustrated that “the need for health care, the need for nursing, goes way outside the hospital walls.” See Figure 3.5 [10] for an image of the water crisis in Flint, Michigan.
Reflective Questions
- What factors led to the children from poor households being so adversely harmed by this crisis?
- What are ways that you as a future nurse can make a difference for vulnerable or marginalized people?
Providing culturally responsive care is a key strategy for reducing health disparities. [11] While there are multiple determinants contributing to a person’s health, nurses play an important role in reducing health disparities by providing a culturally sensitive environment, performing a cultural assessment, and providing culturally responsive care. These interventions will be further discussed in the following sections. On the other hand, a lack of culturally responsive care potentially contributes to miscommunication between the patient and the nurse. The patient may experience distress or loss of trust in the nurse or the health care system as a whole and may not adhere to prescribed treatments. Nurses are uniquely positioned to directly impact patient outcomes as we become more aware of unacceptable health disparities and work together to overcome them. [12]
- Institute of Medicine (US) Committee on Understanding and Eliminating Racial and Ethnic Disparities in Health Care, Smedley, B. D., Stith, A. Y., Nelson, A. R. (Eds.). (2003). Unequal treatment: Confronting racial and ethnic disparities in health care. National Academies Press. https://doi.org/10.17226/12875 ↵
- Meedzan, N. (2015). Cultural immersion experiences in nursing education. In S. Breakey, I. Corless, N. Meedzan, & P. Nicholas (Eds.) Global nursing in the 21st century . Springer. pp. 441-452. ↵
- Hart, P. L., & Mareno, N. (2016). Nurses’ perceptions of their cultural competence in caring for diverse patient populations. Online Journal of Cultural Competence in Nursing & Healthcare, 6 (1), 121–137. https://doi.org/10.9730/ojccnh.org/v6n1a10 ↵
- Ong-Flaherty, C. (2015). Critical cultural awareness and diversity in nursing: A minority perspective. Nurse Leader, 13( 5), 58-62. http://dx.doi.org/10.1016/j.mnl.2015.03.012 ↵
- Healthy People 2020. (2020). Social Determinants of Health. https://www.healthypeople.gov/2020/topics-objectives/topic/social-determinants-of-health ↵
- U.S. Department of Health and Human Services. Healthy People 2020. Lesbian, gay, bisexual, and transgender health . https://www.healthypeople.gov/2020/topics-objectives/topic/lesbian-gay-bisexual-and-transgender-health ↵
- Agency for Healthcare Research and Quality. (2020). 2019 National healthcare quality and disparities report. https://www.ahrq.gov/research/findings/nhqrdr/nhqdr19/index.html ↵
- Agency for Healthcare Research and Quality. (2020). 2019 National healthcare quality and disparities report. https://www.ahrq.gov/research/findings/nhqrdr/nhqdr19/index.html ↵
- Householder, M. (2016, April 12). Health workers get lead-test help from Flint student nurses . Associated Press. https://detroit.cbslocal.com/2016/04/12/health-workers-get-lead-test-help-from-flint-student-nurses/. ↵
- “ Flint_Water_Crisis.jpg ” by Shannon Nobles is licensed under CC BY-SA 4.0 ↵
- Zeran, V. (2016). Cultural competency and safety in nursing education: A case study. Northern Review, 43 , 105–115. https://thenorthernreview.ca/index.php/nr/article/view/591 ↵
- Colorado Nurses Foundation and Colorado Nurses Association. (2020). Owning our biases: How nursing can change the healthcare landscape. Colorado Nurse, 120 (3). https://assets.nursingald.com/uploads/publication/pdf/2103/Colorado_Nurse_8_20.pdf ↵


16.2: Plasma Membrane Structure
In eukaryotic cells, the plasma membrane surrounds a cytoplasm filled with ribosomes and organelles. Organelles are structures that are themselves encased in membranes. Some organelles (nuclei, mitochondria, chloroplasts) are even surrounded by double membranes. All cellular membranes are composed of two layers of phospholipids embedded with proteins. All are selectively permeable (semi-permeable), allowing only certain substances to cross the membrane. The unique functions of cellular membranes are due to their different phospholipid and protein compositions. Decades of research have revealed these functions (see earlier discussions of mitochondrial and chloroplast function for instance). Here we’ll describe general features of membranes, using the plasma membrane as our example.
A. The Phospholipid Bilayer
Gorter and Grendel predicted the bilayer membrane structure as early as 1925. They knew that red blood cells (erythrocytes) have no nucleus or other organelles, and thus have only a plasma membrane. They also knew that the major chemical component of these membranes were phospholipids . The space-filling molecular model below shows the basic structure of phospholipids, highlighting their hydrophilic (polar) heads and hydrophobic tails.
Molecules with hydrophilic and hydrophobic domains are amphipathic molecules. Gorter and Grendel had measured the surface area of red blood cells. They then did a ‘blood count’ and then disrupted a known number of red blood cells. They then measured the amount of phospholipids in the membrane extracts. From this, they calculated that there were enough lipid molecules per cell to wrap around each cell twice. From these observations, they predicted the phospholipid bilayer with fatty acids interacting within the bilayer. Curiously, Gorter and Grendel had made two calculation errors in determining the amount of phospholipid per cells. Nevertheless, their errors compensated each other so that, while not strictly speaking correct, their conclusion remained prophetic! Common membrane phospholipids are shown below.
Amphipathic molecules mixed with water spontaneously aggregate to ‘hide’ their hydrophobic regions from the water. In water, these formed actual structures called liposomes that sediment when centrifuged!
276 Membrane Lipids and the Phospholipid Bilayer
277 Experiments with and Uses of Liposomes
Liposome membrane structure is consistent with the predicted phospholipid bilayer, with the hydrophobic tails interacting with each other and the polar heads facing away from each other, forming a phospholipid bilayer . This led to a picture of membrane architecture based on phospholipid interactions. An iconic illustration of the phospholipid bilayer, with its hydrophobic fatty acid interior and hydrophilic external surfaces is drawn below.
Liposome membrane structure is consistent with the predicted phospholipid bilayer, with the hydrophobic tails interacting with each other and the polar heads facing away from each other, forming a phospholipid bilayer. This led to a picture of membrane architecture based on phospholipid interactions. An iconic illustration of the phospholipid bilayer, with its hydrophobic fatty acid interior and hydrophilic external surfaces is drawn below.
B. Models of Membrane Structure
In 1935, Davson and Danielli suggested that proteins might be bound to the polar heads of the phospholipids in the plasma membrane, creating a protein/lipid/protein sandwich. Decades later, J.D. Robertson observed membranes in the transmission electron microscope at high power, revealing that all cellular membranes had a trilamellar structure. The classic trilamellar appearance of a cellular membrane in the electron microscope is illustrated below
The trilamellar structure is consistent with the protein-coated hydrophilic surfaces of a phospholipid bilayer in Davson and Danielli’s protein-lipid-protein sandwich. Observing that all cellular membranes had this trilamellar structure, Robertson he further proposed his Unit Membrane model: all membranes consist of a clear phospholipid bilayer coated with electron-dense proteins.
The static view of the trilamellar models of membrane structure implied by the Davson-Danielli or Robertson models was replaced in 1972 by Singer and Nicolson’s Fluid Mosaic model (see The fluid mosaic model of membranes. Science 175:720- 731). They suggested that in addition to peripheral proteins that do bind to the surfaces of membranes, many integral membrane proteins actually span the membrane. Integral membrane proteins were imagined as a mosaic of protein ‘tiles’ embedded in a phospholipid medium. But unlike a mosaic of glazed tiles set in a firm, cement-like structure, the protein ‘tiles’ were predicted to be mobile ( fluid ) in a phospholipid sea . In this model, membrane proteins are anchored in membranes by one or more hydrophobic domains; their hydrophilic domains would face aqueous external and cytosolic environments. Thus, like phospholipids themselves, membrane proteins are amphipathic . We know that cells expose different surface structural (and functional) features to the aqueous environment on opposite sides of a membrane. Therefore, we also say that cellular membranes are asymmetric . A typical model of the plasma membrane of a cell is illustrated below.
In this model, peripheral proteins have a hydrophobic domain that does not span the membrane, but that anchors it to one side of the membrane. Other peripheral (or socalled “ surface ”) proteins are bound to the membrane by interactions with the polar phosphate groups of phospholipids, or with the polar domains of integral membrane proteins.
Because of their own aqueous hydrophilic domains, membrane proteins are a natural barrier to the free passage of charged molecules across the membrane. On the other hand, membrane proteins are responsible for the selective permeability of membranes, facilitating the movement of specific molecules in and out of cells. Membrane proteins also account for specific and selective interactions with their extracellular environment. These interactions include the adhesion of cells to each other, their attachment to surfaces, communication between cells (both direct and via hormones and neurons), etc. The ‘sugar coating’ of the extracellular surfaces of plasma membranes comes from oligosaccharides covalently linked to membrane proteins (as glycoproteins ) or to phospholipids (as glycolipids ). Carbohydrate components of glycosylated membrane proteins inform their function. Thus, glycoproteins enable specific interactions of cells with each other to form tissues. They also allow interaction with extracellular surfaces to which they must adhere. In addition, they figure prominently as part of receptors for many hormones and other chemical communication biomolecules. Protein domains exposed to the cytoplasm, while not glycosylated, often articulate to components of the cytoskeleton, giving cells their shape and allowing cells to change shape when necessary. Many membrane proteins have essential enzymatic features, as we will see. Given the crucial role of proteins and glycoproteins in membrane function, it should come as no surprise that proteins constitute an average of 40-50% of the mass of a membrane. In some cases, proteins are as much as 70% of membrane mass (think cristal membranes in mitochondria!).
278 Properties of Proteins Embedded in a Phospholipid Bilayer
C. Evidence for Membrane Structure
Membrane asymmetry refers to the different membrane features facing opposite sides of the membrane. This was directly demonstrated by the scanning electron microscope technique of freeze-fracture . The technique involves freezing of isolated membranes in water and then chipping the ice. When the ice cracks, the encased membranes split along a line of least resistance … that turns out to be between the hydrophobic fatty acid opposing tails in the interior of the membrane. Scanning electron microscopy then reveals features of the interior and exterior membrane surfaces. Among the prominent features in a scanning micrograph of freeze-fractured plasma membranes are the pits and opposing mounds facing each other on opposite flaps of the membrane, as illustrated below.
Other features shown here are consistent with phospholipid membrane structure.
280 Freeze Fracture Electron Microscopy of Cell Membranes
Cytochemistry confirmed the asymmetry of the plasma membrane, showing that only the external surfaces of plasma membranes are sugar coated, Check the link below for more detailed descriptions of the experiments.
281 EM Cytochemical Demonstration of Membrane Asymmetry
Finally, the asymmetry of membranes was also demonstrated biochemically. In one experiment, whole cells treated with proteolytic enzymes, followed by extraction of the membranes and then isolation of membrane proteins. In a second experiment, plasma membranes were isolated from untreated cells first, and then treated with the enzymes. In a third experiment, proteins were extracted from plasma membranes isolated from untreated cells. Electrophoretic separation of the three protein extracts by size demonstrated that different components of integral membrane proteins were present in the two digest experiments, confirming the asymmetry of the plasma membrane. Again, for more details, check the link below.
282 Electrophoretic Demonstration of Membrane Asymmetry
The idea that membranes are fluid was also tested. In yet another elegant experiment, antibodies were made to mouse and human cell membrane proteins. Membranes were isolated and injected into a third animal (a rabbit most likely). The rabbit saw the membranes and their associated proteins as foreign and responded by making specific anti-membrane antibody molecules. The antibodies against each membrane source were isolated and separately tagged with different colored fluorescent labels so that they would glow a different color when subjected to ultraviolet light. After mouse and human cells were mixed under conditions that caused them to fuse, making human-mouse hybrid cells. When added to fused cells, the tagged antibodies bound to the cell surface proteins. After a short time, the different fluorescent antibodies were seen to mix under a fluorescence microscope under UV light. The fluorescent tags seemed to moving from their original location in the fused membranes. Clearly, proteins embedded in the membrane are not static, but are able to move laterally in the membrane, in effect floating and diffusing in a “sea of phospholipids”. The mouse antibodies as seen in the hybrid cell right after fusion are cartooned below.
283 Two Demonstrations of Membrane Fluidity: The Fluid Mosaic
D. Membrane Fluidity is Regulated
1. Chemical Factors Affecting Membrane Fluidity
As you might imagine, the fluidity of a membrane depends on its chemical composition and physical conditions surrounding the cell, for example the outside temperature. Factors that affect membrane fluidity are summarized below.
Just as heating a solution causes dissolved molecules and particulates to move faster, phospholipid and protein components of membranes are also more fluid at higher temperatures. If the fatty acids of the phospholipids have more unsaturated (C=C) carbon bonds, these hydrophobic tails will have more kinks, or bends. The kinks tend to push apart the phospholipid tails. With more space between the fatty acid tails, membrane components can move more freely. Thus, more polyunsaturated fatty acids in a membrane make it more fluid. On the other hand, cholesterol molecules tend to fill the space between fatty acids in the hydrophobic interior of the membrane. This reduces the lateral mobility of phospholipid and protein components in the membrane. By reducing fluidity, cholesterol reduces membrane permeability to some ions.
2. Functional Factors Affecting Membrane Fluidity
Evolution has adapted cell membranes to different and changing environments to maintain the fluidity necessary for proper cell function. Poikilothermic , or coldblooded organisms, from prokaryotes to fish and reptiles, do not regulate their body temperatures. Thus, when exposed to lower temperatures, poikilotherms respond by increasing the unsaturated fatty acid content of their cell membranes. At higher temperatures, they increase membrane saturated fatty acid content. Thus, the cell membranes of fish living under the arctic ice maintain fluidity by having high levels of both monounsaturated and polyunsaturated fatty acids. What about fish species that range across warmer and colder environments (or that live in climates with changing seasons). For these fish, membrane composition can change to adjust fluidity to environment.
The warm-blooded ( homeothermic ) mammals and birds maintain a more or less constant body temperature. As a result, their membrane composition is also relatively constant. But there is a paradox! Their cell membranes are very fluid, with a higher ratio of polyunsaturated fat to monounsaturated fats than say, reptiles. The apparent paradox is resolved however, when we understand that this greater fluidity supports the higher metabolic rate of the warm-blooded species compared to poikilotherms. Just compare the life styles of almost any mammal to a lazy floating alligator, or a snake basking in the shade of a rock!
E. Making and Experimenting with Artificial Membranes
Membrane-like structures can form spontaneously. When phospholipids interact in an aqueous environment, they aggregate to exclude their hydrophobic fatty tails from water, forming micelles. Micelles are spherical phospholipid monolayer vesicles that self-assemble, a natural aggregation of the hydrophobic fatty acid domains of these amphipathic molecules.
A micelle is drawn below.
Micelles can further self-assemble into spherical phospholipid bilayers called liposomes (below).
When formed in the laboratory, these structures behave somewhat like cells, for example, forming a pellet at the bottom of a tube when centrifuged. Liposomes can be custom designed from different kinds of phospholipids and amphipathic proteins that become integral to the liposome membranes. When liposomes can be prepared in the presence of specific proteins or other molecules that can’t cross the membrane. The trapped molecules cannot get out of this synthetic ‘organelle’. Such were the studies that allowed the identification of the mitochondrial respiratory chain complexes. The ability to manipulate liposome content and membrane composition also make them candidates for the drug delivery to specific cells and tissues (google liposome for more information).
F. The Plasma Membrane is Segragated into Regions with Different Properties of Fluidity and Selective Permeability
As we will see shortly, fluidity does not result in an equal diffusion of all membrane components around the cell membrane surface. Instead, extracellular connections between cells as well as intracellular connections of the membrane to differentiated regions of the cytoskeleton, effectively compartmentalize the membrane into subregions. To understand this, imagine a sheet of epithelial like those in the cartoon below.
The sheet of cells exposes one surface with unique functions to the inside of the organ they line. It exposes the opposite surface, one with a quite different function, to the other side of the sheet. The lateral surfaces of the cells are yet another membrane compartment, one that functions to connect and communicate between the cells in the sheet. Components, i.e., membrane proteins illustrated with different symbolic shapes and colors, may remain fluid within a compartment. Of course, this macrodifferentiation of cell membranes to permit cell-cell and cell-environmental interactions makes intuitive sense.
The recent observation that cellular membranes are even more compartmentalized was perhaps less anticipated. In fact, membranes are further divided into microcompartments. Within these compartments, components are fluid but seldom move between compartments. Studies indicate that cytoskeletal elements create and maintain these micro-discontinuities. For example, integral membrane proteins are immobilized in membranes if they are attached to cytoskeletal fibers (e.g., actin) in the cytoplasm. Furthermore, when aggregates of these proteins line up due to similar interactions, they form kind of fence , inhibiting other membrane components from crossing. By analogy, this mechanism of micro-compartmentalization is called the Fences and Pickets model; proteins attached to the cytoskeleton serve as the pickets. The movement across the fences (i.e., from one membrane compartment to another) is infrequent. Extra kinetic energy is presumably needed for a molecule to ‘jump’ a fence between compartments. Hence, this kind of motion, or hop diffusion distinguishes it from the Brownian motion implied by the original fluid mosaic model.
285 Membrane Domains: Regional Differentiation of a Plasma Membrane