10.1: Variables, Constants, and Real Numbers
- be able to distinguish between variables and constants
- be able to recognize a real number and particular subsets of the real numbers
- understand the ordering of the real numbers
Variables and Constants
A basic distinction between algebra and arithmetic is the use of symbols (usually letters) in algebra to represent numbers. So, algebra is a generalization of arithmetic. Let us look at two examples of situations in which letters are substituted for numbers:
- Suppose that a student is taking four college classes, and each class can have at most 1 exam per week. In any 1-week period, the student may have 0, 1, 2, 3, or 4 exams. In algebra, we can let the letter \(x\) represent the number of exams this student may have in a 1-week period. The letter \(x\) may assume any of the various values 0, 1, 2, 3, 4.
- Suppose that in writing a term paper for a biology class a student needs to specify the average lifetime, in days, of a male housefly. If she does not know this number off the top of her head, she might represent it (at least temporarily) on her paper with the letter \(t\) (which reminds her of time ). Later, she could look up the average time in a reference book and find it to be 17 days. The letter \(t\) can assume only the one value, 17, and no other values. The value \(t\) is constant .
- A letter or symbol that represents any member of a collection of two or more numbers is called a variable .
- A letter or symbol that represents one specific number, known or unknown, is called a constant .
In example 1, the letter \(x\) is a variable since it can represent any of the numbers 0, 1, 2, 3, 4. The letter \(t\) example 2 is a constant since it can only have the value 17.
Real Numbers
Real Number Line
The study of mathematics requires the use of several collections of numbers. The
real number line
allows us to visually display (graph) the numbers in which we are interested.
A line is composed of infinitely many points. To each point we can associate a unique number, and with each number, we can associate a particular point.
The number associated with a point on the number line is called the coordinate of the point.
The point on a number line that is associated with a particular number is called the graph of that number.
Constructing a Real Number Line
We construct a real number line as follows:
Draw a horizontal line.
Origin
Choose any point on the line and label it 0. This point is called the
origin
.
Choose a convenient length. Starting at 0, mark this length off in both directions, being careful to have the lengths look like they are about the same.
We now define a real number.
A real number is any number that is the coordinate of a point on the real number line.
Real numbers whose graphs are to the right of 0 are called positive real numbers , or more simply, positive numbers . Real numbers whose graphs appear to the left of 0 are called negative real numbers , or more simply, negative numbers .
The number 0 is neither positive nor negative.
Subsets of Real Numbers
The set of real numbers has many subsets. Some of the subsets that are of interest in the study of algebra are listed below along with their notations and graphs.
Natural Numbers, Counting Numbers
The
natural
or
counting numbers
\((N)\): 1, 2, 3, 4, . . . Read “and so on.”
Whole Numbers
The
whole numbers
\((W)\): 0, 1, 2, 3, 4, . . .
Notice that every natural number is a whole number.
Integers
The
integers
\((Z)\): . . . -3, -2, -1, 0, 1, 2, 3, . . .
Notice that every whole number is an integer.
Rational Numbers (Fractions)
The
rational numbers
\((Q)\): Rational numbers are sometimes called
fractions
. They are numbers that can be written as the
quotient
of two integers. They have decimal representations that either terminate or do not terminate but contain a repeating block of digits. Some examples are
\(\underbrace{\dfrac{-3}{4} = -0.75}_{text{Terminating}}\) \(\underbrace{8 \dfrac{11}{27} = 8.407407407...}_{\text{Nonterminating, but repeating.}}\)
Some rational numbers are graphed below.
Notice that every integer is a rational number .
Notice that there are still a great many points on the number line that have not yet been assigned a type of number. We will not examine these other types of numbers in this text. They are examined in detail in algebra. An example of these numbers is the number \(\pi\), whose decimal representation does not terminate nor contain a repeating block of digits. An approximation for \(\pi\) is 3.14.
Is every whole number a natural number?
Solution
No. The number 0 is a whole number but it is not a natural number.
Is there an integer that is not a natural number?
Solution
Yes. Some examples are 0, -1, -2, -3, and -4.
Is there an integer that is a whole number?
Solution
Yes. In fact, every whole number is an integer.
Practice Set A
Is every natural number a whole number?
- Answer
-
yes
Practice Set A
Is every whole number an integer?
- Answer
-
yes
Practice Set A
Is every integer a real number?
- Answer
-
yes
Practice Set A
Is there an integer that is a whole number?
- Answer
-
yes
Practice Set A
Is there an integer that is not a natural number?
- Answer
-
yes
Ordering Real Numbers
Ordering Real Numbers
A real number \(b\) is said to be
greater
than a real number \(a\), denoted \(b > a\), if \(b\) is to the right of \(a\) on the number line. Thus, as we would expect, \(5 > 2\) since 5 is to the right of 2 on the number line. Also, \(-2 > -5\) since -2 is to the right of -5 on the number line.
-5, and on the left side is 5 > 2." data-media-type="image/png" data-print-width="2.5in" width="400"<EMAIL_ADDRESS>If we let \(a\) and \(b\) represent two numbers, then \(a\) and \(b\) are related in exactly one of three ways: Either
Equality Symbol
\(a = b\) \(a\) and \(b\) are equal (8 = 8)
Inequality Symbols
\(\begin{cases} a > b & a \text{ is greater than }b & (8 > 5) \\ a < b & a \text{ is less than } b & (5 < 8) \\ \ & \text{Some variations of these symbols are} & \ \\ a \ne b & a \text{ is not equal to } b & (8 \ne 5) \\ a \ge b & a \text{ is greater than or equal to } b & (a \ge 8) \\ a \le b & a \text{ is less than or equal to } b & (a \le 8) \end{cases}\)
What integers can replace xx so that the following statement is true?
\(-3 \le x < 2\)
Solution
The integers are -3, -2, -1, 0, 1.
Draw a number line that extends from -3 to 5. Place points at all whole numbers between and including -1 and 3.
Solution
-1 is not a whole number
Practice Set B
What integers can replace \(x\) so that the following statement is true? \(-5 \le x < 2\)
- Answer
-
-5, -4, -3, -2, -1, 0
Practice Set B
Draw a number line that extends from -4 to 3. Place points at all natural numbers between, but not including, -2 to 2.
- Answer
-
Exercises
For the following 8problems, next to each real number, note all collections to which it belongs by writing \(N\) for natural number, \(W\) for whole number, or \(Z\) for integer. Some numbers may belong to more than one collection.
Exercise \(\PageIndex{1}\)
6
- Answer
-
N, W, Z
Exercise \(\PageIndex{2}\)
12
Exercise \(\PageIndex{3}\)
0
- Answer
-
W, Z
Exercise \(\PageIndex{4}\)
1
Exercise \(\PageIndex{5}\)
-3
- Answer
-
Z
Exercise \(\PageIndex{6}\)
-7
Exercise \(\PageIndex{7}\)
-805
- Answer
-
Z
Exercise \(\PageIndex{8}\)
-900
Exercise \(\PageIndex{9}\)
Is the number 0 a positive number, a negative number, neither, or both?
- Answer
-
Neither
Exercise \(\PageIndex{10}\)
An integer is an even integer if it is evenly divisible by 2. Draw a number line that extends from -5 to 5 and place points at all negative even integers and all positive odd integers.
Exercise \(\PageIndex{11}\)
Draw a number line that extends from -5 to 5. Place points at all integers that satisfy \(-3 \le x < 4\).
- Answer
-
Exercise \(\PageIndex{12}\)
Is there a largest two digit number? If so, what is it?
Exercise \(\PageIndex{13}\)
Is there a smallest two digit number? If so, what is it?
- Answer
-
Yes, 10
For the pairs of real numbers in the following 5 problems, write the appropriate symbol (<, >, =) in place of the □.
Exercise \(\PageIndex{14}\)
-7 □ -2
Exercise \(\PageIndex{15}\)
-5 □ 0
- Answer
-
<
Exercise \(\PageIndex{16}\)
-1 □ 4
Exercise \(\PageIndex{17}\)
6 □ -1
- Answer
-
>
Exercise \(\PageIndex{18}\)
10 □ 10
For the following 5 problems, what numbers can replace m so that the following statements are true?
Exercise \(\PageIndex{19}\)
\(-1 \le m \le -5\), \(m\) an integer.
- Answer
-
{-1, 0, 1, 2, 3, 4, 5}
Exercise \(\PageIndex{20}\)
\(-7 < m < -1\), \(m\) an integer.
Exercise \(\PageIndex{21}\)
\(-3 \le m < 2\), \(m\) a natural number.
- Answer
-
{1}
Exercise \(\PageIndex{22}\)
\(-15 < m \le -1\), \(m\) a natural number.
Exercise \(\PageIndex{23}\)
\(-5 \le m < 5\), \(m\) a whole number.
- Answer
-
{0, 1, 2, 3, 4}
For the following 10 problems, on the number line, how many units are there between the given pair of numbers?
Exercise \(\PageIndex{24}\)
0 and 3
Exercise \(\PageIndex{25}\)
-4 and 0
- Answer
-
4
Exercise \(\PageIndex{26}\)
-1 and 6
Exercise \(\PageIndex{27}\)
-6 and 2
- Answer
-
8
Exercise \(\PageIndex{28}\)
-3 and 3
Exercise \(\PageIndex{29}\)
Are all positive numbers greater than zero?
- Answer
-
yes
Exercise \(\PageIndex{30}\)
Are all positive numbers greater than all negative numbers?
Exercise \(\PageIndex{31}\)
Is 0 greater than all negative number?
- Answer
-
yes
Exercise \(\PageIndex{32}\)
Is there a largest natural number?
Exercise \(\PageIndex{33}\)
Is there a largest negative integer?
- Answer
-
yes, -1
Exercises for Review
Exercise \(\PageIndex{34}\)
Convert \(6 \dfrac{5}{8}\) to an improper fraction.
Exercise \(\PageIndex{35}\)
Find the value: \(\dfrac{3}{11}\) of \(\dfrac{33}{5}\).
- Answer
-
\(\dfrac{9}{5}\) or \(1 \dfrac{4}{5}\) or 1.8
Exercise \(\PageIndex{36}\)
Find the sum of \(\dfrac{4}{5} + \dfrac{3}{8}\).
Exercise \(\PageIndex{37}\)
Convert 30.06 cm to m.
- Answer
-
0.3006 m
Exercise \(\PageIndex{38}\)
Find the area of the triangle.


1.2: Historical Context
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The Romantic era was characterized by revolutions, including the American, the French, and the Industrial. The American Revolution had an impact on all of Europe. Its causes included the desire for political freedom and economic stability that the colonialists saw King Georgia III as menacing. England saw the American colonies as a source of materials and goods not in England proper and as a market for goods produced by England. Much against which the colonists objected were British laws endeavoring to maintain this economic balance. When England forcefully repressed protests and rebellion, the colonies directed their ire against King George III in their Declaration of Independence. And in the Declaration, individual freedom and independence were added to economic freedom as social and moral claims.
In addition to the American Revolution, England experienced its own economic revolution—commercial, agricultural, in transportation with new roads and canals, in industrialization. The Industrial Revolution became visible to many people about the mid-1700s. It was a revolution in methods, organization, and economic principles. Before industrialization, England functioned by a Medieval code of minute regulations in business and trade and restrictions on mobility and labor.
Comparatively few people in England at that time had actual, independent rights, particularly of possession. People who had lived on the land for centuries were tenants, not owners. With progress in manufacture, particularly in textiles, came the Enclosure movement, that is, the enclosing of land which previously had been available to everyone.  Agriculture consequently declined and tenants moved to cities to work in new factories and mills.
The shift in employment opportunities—or lack thereof—through increasing mechanization resulted in riots such as The Peterloo Massacre. Percy Bysshe Shelley (1792-1822) responded with poems like “England in 1819” that supported the working class. While working men suffered, women also faced restrictions, as they had almost no legal rights and few, if any, educational opportunities.
The French Revolution evoked the American Revolution and England’s Glorious Revolution during which Charles I was beheaded. The French Revolution smashed institutions, destroyed the monarchy and aristocracy, and built a new (though not permanent) order. An ideal of the French Revolution was to let the individual freely develop, so it opposed the institutions that checked individual rights.
Nations such as Austria and Prussia allied against the revolution and were defeated by the Revolutionary Army that spread over Italy and Germany. Under the impact of war, counter-revolutions sprung up, and the Committee of Public Safety (1793) was formed. Through its Reign of Terror (1793-94), the Committee suppressed revolt and counter-revolution. 20,000 heads were struck off by the guillotine. The bicameral legislative government, called the Directory (1795), came into power but fell to a coup d’etat (1799) run by its own general, Napoleon Bonaparte (1769-1821).
The early Romantic writers at first greatly sympathized with the French Revolution. They were convinced that a revolution for moral change would occur in England. It seemed to them that the new millennium had arrived. William Blake saw it as the creation of a new world and himself as its prophet. Coleridge and Wordsworth responded with peons of joy, declaring, “bliss was it in that dawn to be alive” (Wordsworth The Prelude). Both went to France and even fell in love with French women. They returned chastened by the Reign of Terror. Edmund Burke’s Reflections on the French Revolution condemned the Revolution as an attempt to methodize anarchy. Reaction in England soon set in. English freedom became increasingly restricted through such acts as the Proclamation Against Seditious Writing. Parliament suspended habeas corpus, making possible imprisonment without trial, and passed the Treasonable and Seditious Practices Act (1795). Reaction against reform was stiffened by the ensuing Napoleonic Wars.


13.5: Learning Activities
Learning Activities
(Answers to “Learning Activities” can be found in the “Answer Key” at the end of the book. Answers to interactive activity elements will be provided within the element as immediate feedback.)
Ms. Curtis is a 67-year-old patient admitted for a left total knee replacement. She is post-op Day 2 and is currently receiving care on the medical surgical unit. Ms. Curtis has been complaining of pain and refused her previous two physical therapy appointments. She agrees to sitting up in the chair, but declines walking.
- What focused assessments should the nurse perform and why?
- What complications could occur related to Ms. Curtis’ immobility?
- What SMART outcomes should the nurse plan in collaboration with Ms. Curtis?
- List interventions the nurse should plan for Ms. Curtis and their rationale.
- How will the nurse evaluate if the interventions are successful?
Query \(\PageIndex{2}\)
Query \(\PageIndex{3}\)
Query \(\PageIndex{4}\)
Mobility Case Study by Susan Jepsen for Lansing Community College is licensed under CC BY 4.0


10.3: Exercise- Examining the Grand Averages
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Ordinarily, you would decide exactly how to quantify and analyze the ERP amplitudes and latencies prior to seeing the data. If you first look at the grand average ERP waveforms, the analysis parameters you select will likely be influenced by noise in the data, and you’ll have a high likelihood of finding significant effects that reflect noise rather than true effects and are completely bogus. This is a super important point! I’m not going to dwell on it here, because I’ve written about it extensively elsewhere (see especially Luck & Gaspelin, 2017). However, keep this point in mind throughout the chapter (especially in this first exercise, where we are going to look at the data before we develop our analysis plan—exactly what you shouldn’t do!).
I’ve already created the averaged ERP waveforms for looking at the LRP. If you go to the Chapter_10 folder, you’ll see a subfolder named Data , and inside that subfolder you’ll see another subfolder named ERPsets that contains an ERPset for each of the 40 participants. To create these ERPsets, I referenced the data to the average of P9 and P10, high-pass filtered at 0.1 Hz (12 dB/octave), and then applied ICA-based artifact correction for blinks and horizontal eye movements (using the optimized approach described in the chapter on artifact correction). The next step was to add an EventList and then run BINLISTER to create 4 bins:
- Bin 1: Left-Pointing Target with Compatible Flankers, Followed by Left Response
- Bin 2: Right-Pointing Target with Compatible Flankers, Followed by Right Response
- Bin 3: Left-Pointing Target with Incompatible Flankers, Followed by Left Response
- Bin 4: Right-Pointing Target with Incompatible Flankers, Followed by Right Response
Note that only correct responses were included in these bins because we’re going to focus on the LRP rather than the ERN.
Next, I epoched the data from -200 to 800 ms relative to stimulus onset. I then performed artifact detection to mark trials with C.R.A.P., and finally I averaged the data, excluding the marked trials.
Let’s load the data and make a grand average. Quit and restart EEGLAB, and set Chapter_10 to be Matlab’s current folder. Select EEGLAB > ERPLAB > Load existing ERPset , navigate to the Chapter_10 > Data > ERPsets folder, select all 40 ERPset files at once, and click Open . You should then be able to see all 40 ERPsets in the ERPsets menu. To make a grand average, select EEGLAB > ERPLAB > Average across ERPsets (Grand Average) , and indicate that the routine should average across ERPsets 1:40 in the ERPsets menu. All the other options should be kept at their default values. Click RUN and name the resulting ERPset grand . Save it as a file named grand.erp , because you’ll need it for a later exercise. Now plot the ERPs ( EEGLAB > ERPLAB > Plot ERP > Plot ERP waveforms ), making one plot for Bins 1 and 2 (compatible trials) and another plot for Bins 3 and 4 (incompatible trials). Find the C3 and C4 channels (where the LRP is typically largest) and look for the contralateral negativity from ~200-400 ms.
The key waveforms are summarized in Figure 10.2.A. For the compatible trials, the voltage at C3 from ~200-400 ms is more negative on trials with a right-hand response than on trials with a left-hand response, and the voltage at C4 during this period is more negative on trials with a left-hand response than on trials with a right-hand response. The overall voltage is positive in this time range (because of the P3b component), and the LRP sums with the positive voltages to make the voltage more negative (less positive) over the contralateral hemisphere than over the ipsilateral hemisphere.
The pattern is a little more complicated for the incompatible trials. At approximately 200 ms, you can see an opposite-polarity effect, with a more negative voltage for left-hand than for right-hand responses at C3 and a more negative voltage for right-hand than for left-hand responses at C4. This then reverses beginning at approximately 250 ms.
It’s a little challenging to piece together everything that’s happening with the waveforms shown in Figure 10.2.A. There are just a lot of waveforms to look at. We can simplify things by using ERP Bin Operations to collapse the data into contralateral waveforms (left-hemisphere waveforms on right-response trials averaged with right-hemisphere waveforms on left-response trials) and ipsilateral waveforms (left-hemisphere waveforms on left-response trials averaged with right-hemisphere waveforms on right-response trials).
Making these collapsed ERPsets is a little tricky (and is explained in the ERP Bin Operations section of the ERPLAB Manual ). To save some of your time, I’ve already made these collapsed ERPsets for you. To open them, first clear out any existing ERPsets from ERPLAB using EEGLAB > ERPLAB > Clear ERPset(s) . You should have 41 ERPsets (which you can verify in the ERPsets menu), so enter 1:41 when asked which ERPsets to clear. Next, load the 40 ERPsets in the Chapter_10 > Data > ERPsets_CI folder. You can now make a grand average of these ERPsets and plot the results (with one plot for Bins 1 and 2, and a separate plot for Bins 3 and 4).
Figure 10.2.B shows the results from the C3 and C4 electrode sites (which are now combined, as indicated by the C3/C4 label). Now we have only two pairs of waveforms rather than four pairs of waveforms, which makes it easier to see the contralateral negativity.
To make things even easier, and to isolate the LRP from other overlapping voltages, we can use ERP Bin Operations make a contralateral-minus-ipsilateral difference wave (Bin 1 minus Bin 2 for the compatible trials, and Bin 3 minus Bin 4 for the ipsilateral trials). I’ve already done this for you. Clear out the ERPsets and load these difference wave files from the Chapter_10 > Data > ERPsets_CI_Diff folder. Make a grand average, and plot the results (in a single plot with Bins 1 and 2).
Figure 10.2.C. shows the results at C3/C4. Now we have only one pair of waveforms, making it much easier to compare the LRP for the compatible and incompatible trials. On the compatible trials, you can see a nice clear negativity from ~200-500 ms. On the incompatible trials, you can see an initial contralateral positivity (which is really a negativity relative to the incorrect response), followed by a delayed contralateral negativity.
This is pretty cool! Our main goal in including both compatible and incompatible trials in this experiment was to generate a sufficient number of errors for the ERN analysis (because errors are a lot more common on incompatible trials). We didn’t intend to do any comparisons of compatible and incompatible trials, so this is the first time anyone has looked at these effects. It’s gratifying to see that we found the same pattern as in prior studies (e.g., Gratton et al., 1988), with a delayed LRP on incompatible trials that is preceded by an opposite-polarity deflection.


8.2: Introduction to Analysis As Critical Thinking
What you’ll learn to do: describe analysis
Analysis is a critical thinking skill that has been applied to academic study since the time of Aristotle (384–322 BCE). It is a foundational tool across disciplines, from chemistry to literature to business to philosophy. Understanding what analysis is will be of value to you throughout your college career.
Contributors and Attributions
CC licensed content, Original
- Outcome: Analysis As Critical Thinking. Provided by : University of Mississippi. License : CC BY: Attribution
CC licensed content, Shared previously
- Image of stone sculpture heads. Authored by : morhamedufmg. Provided by : Pixabay. Located at : pixabay.com/photos/bustos-filsofia-aristotle-756620/. License : Other . License Terms : pixabay.com/service/terms/#license


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12.3.2: Procedure- Tub or Shower Bath
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Explain the procedure to the patient.
-
Wash and dry hands according to proper hand washing guidelines.
-
Assemble equipment needed (soap, shampoo/conditioner, wash cloths, towels).
-
Ensure that the bathroom is warm and comfortable. Take care it is not too cold or too hot.
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Remove any fall risk hazards, such as loose rugs, from the floor.
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Place any safety devices in the shower as needed (e.g. shower chair, rubber mats).
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Ensure safety items such as handrails and grab bars are in good working order. Immediately inform a supervisor if they are not.
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Turn on the water and test water temperature using a bath thermometer. Water temperature should be no higher than 105 degrees Fahrenheit. If providing a tub bath, fill the bath and test the temperature before putting the patient in the tub. Tub baths or very warm showers can lead to a person feeling faint, nauseous, or tired. Baths should not last longer than 20 minutes and should be discontinued at the first sign of patient discomfort, weakness, or complaints of feeling faint.
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Allow the patient to test the water temperature for their comfort. Adjust as needed.
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Wash and dry hands. Put on gloves.
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Assist the patient to the bathroom. If the patient is ambulatory, assist the patient as needed to undress and then transfer them into the tub or shower. Undress the patient immediately before getting them into the shower or tub. This prevents them from chilling.
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If the patient is independent, give them privacy to bathe, if they prefer. If leaving a patient unattended, check on them every 5 minutes or more frequently as needed. Ensure the patient knows how to use safety items such as shower chairs and grab bars.
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If the patient is standing to shower, stay in the bathroom and monitor the patient’s need for assistance. If they are weak, always stay with them in the bathroom, providing privacy as able.
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Never let a weak person stand to bathe or leave them in the bath alone. You can stay in the bathroom and draw the shower curtain to provide privacy. Communicate with them frequently to let them know you are there to provide assistance.
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Water should be turned off and the tub drained before assisting the patient to transfer out of the tub.
To Transfer the Patient into the Tub:
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If the patient is in a wheelchair, face the patient and wheelchair toward tub, between the grab bars or safety rails.Lock the wheelchair brakes. Raise the wheelchair footrests. If using a
gait belt
, ensure it is secure and that the patient has a shirt or towel on, with the gait belt positioned over their clothing. This is to prevent skin irritation and breakdown. Instruct the patient or assist with placing their legs, one at a time, over edge of tub. Ensure feet are planted firmly onto tub floor before assisting them with transferring into the tub.
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Instruct the patient to grab onto the bars or the side of the tub and assist them into a sitting position on the edge of the tub. Use a gait belt to assist the patient into position and to provide a safe transfer.
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Bring patient to a sitting position at edge of tub. Lower the patient into the tub by holding around their waist or the gait belt. Instruct them to hold the edge of the tub or the grab bars for support and balance.
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If using a
slide board
position the slide board onto the shower chair and under the patient’s buttocks. Assist the patient to move across the slide board in small movements by lifting their bottom up and down, and moving slowly across the board until they are on the shower chair.
Never
drag
a
patient
across
a
slide board.
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Move the wheelchair away from the tub during bathing.
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Place all supplies to be used during the shower/tub bath within your reach and the reach of the patient. This is to avoid unnecessary stretching to retrieve items. If assisting the patient during the bath, avoid bending over with your back. Position yourself to a safe working level at patient height. You may kneel on the floor using a cushioned mat to protect your knees.
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Assist the patient to shampoo and condition hair, as necessary.
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Assist the patient, as necessary, with washing their body. Start with the patient’s eyes and then face, using a clean washcloth. Do not apply soap to the patient’s eyes.
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Assist the patient to clean their genital and anal areas. Use clean washcloths for these areas. Do not use these washcloths for other areas of the body.
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Wash the patient’s body from clean to dirty areas. This helps to avoid contaminating clean areas. Make sure all soap is rinsed off completely.
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If the patient is ambulatory, assist them with the transfer out of the shower/tub. Cover the patient with a towel or robe during transfer to prevent them from chilling.
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To assist the patient out of the tub if using a wheelchair, assist them to the edge of the tub. Bring the patients’ legs one at a time over the outer edge of tub. Assist them back into the wheelchair. Always ensure wheelchair locks are on during transfer.
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Help or complete the drying of the patient. Take care to carefully dry areas where there are skin folds, underneath breasts, and in the genital and anal areas. Assist them with dressing.
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Drain and clean tub/shower area. Discard used linens.
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Remove gloves. Wash and dry hands.
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Document completion of the task and record any changes in condition or behavior.


1.13.3: End-of-Chapter Material
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Key takeaways for this Chapter
- The immune system is constantly working to keep you healthy.
- There are about 1,400 known pathogens that cause disease in humans.
- There are steps you can take to break the chain of infection and stop disease transmission.
- The bodies first barrier to disease are the physical and chemical barriers.
- The innate and adaptive immune system work in tandem to protect you.
- The immune system has an incredible ability to remember past infections.
- The ability to remember pathogens is the foundation for Vaccines
- There are several different types of vaccines.
- STD’s are very common
- Most STDs are asymptomatic.
Media Attributions
- Immune_system101 © AIDSgov is licensed under a Public Domain license
- Chain_of_Infection © Genieieiop, is licensed under a CC BY (Attribution) license
- Cooperation_Between_Innate_and_Immune_Responses © OpenStax College is licensed under a CC BY (Attribution) license
- Innate-Immune-System-Cells © Modification of work by NIH is licensed under a Public Domain license
- Lymph_42 © Open Learning Initiative is licensed under a CC BY (Attribution) license
- Pandemics throughout the history, Sampath S, Khedr A, Qamar S, Tekin A, Singh R, Green R, Kashyap R. Pandemics Throughout the History. Cureus. 2021 Sep 20;13(9):e18136. doi: 10.7759/cureus.18136. PMID: 34692344; PMCID: PMC8525686.
References
- Balloux, F., van Dorp, L. Q&A: What are pathogens, and what have they done to and for us?. BMC Biol 15, 91 (2017). https://doi.org/10.1186/s12915-017-0433-z [1]
- Balloux, F., van Dorp, L. Q&A: What are pathogens, and what have they done to and for us?. BMC Biol 15, 91 (2017). https://doi.org/10.1186/s12915-017-0433-z [2]
- Piret J, Boivin G. Pandemics Throughout History. Front Microbiol. 2021 Jan 15;11:631736. doi: 10.3389/fmicb.2020.631736. PMID: 33584597; PMCID: PMC7874133. [3]


2.4: Spelling and Grammar Checker
Learning Objectives
- Simple instructions for using the spelling and grammar checking features of word processing.
Spelling and Grammar Checker
Many students, especially ESL students, hope to write an academic essay, paper, or any academic writing that is free of spelling or grammar mistakes. Sometimes when we revise our work, we might miss or cannot recognize some of those mistakes, and for that reason, Microsoft Office Word has provided the world an awesome feature called Spelling and Grammar Checker. Spelling and Grammar Checker helps you avoid many common spelling and grammar errors in your word documents, and at the same time you may correct some of them.
Types of Errors
There are three different wavy underline colors that have three different meanings: green, red, and blue; the green wavy underline indicates grammatical error(s), the red wavy underline refers to spelling error(s), and the blue wavy underline refers to contextual error(s).
Auto Corrections
Microsoft Office Word has a feature that corrects some spelling errors automatically; for example, if you type "teh" instead of "the", the word "teh" will be adjusted automatically to "the". However, the application cannot correct or find all grammar mistakes, so you have to review your document thoroughly before printing the final draft, and make sure that your document does not have any spelling, grammatical, or contextual errors.
There are many methods to identify misspelled words or questionable grammar in your document: you may print your document and give it to someone else to correct it using a marker, or you may read your document aloud that helps you find some mistakes.
Using Spelling and Grammar Checker
To start Spelling and Grammar Checker, do the following steps:
Then, choose the appropriate options. Once you finish, click the X button on the right top corner of the Spelling and Grammar dialog box to close the dialog box.


2.5: Confronting Objections to the Economic Approach
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Learning Objectives
- Analyze arguments against economic approaches to decision-making
- Interpret a tradeoff diagram
- Contrast normative statements and positive statements
It is one thing to understand the economic approach to decision-making and another thing to feel comfortable applying it. The sources of discomfort typically fall into two categories: that people do not act in the way that fits the economic way of thinking, and that even if people did act that way, they should try not to. Let’s consider these arguments in turn.
First Objection: People, Firms, and Society Do Not Act Like This
The economic approach to decision-making seems to require more information than most individuals possess and more careful decision-making than most individuals actually display. After all, do you or any of your friends draw a budget constraint and mutter to yourself about maximizing utility before you head to the shopping mall? Do members of the U.S. Congress contemplate production possibilities frontiers before they vote on the annual budget? The messy ways in which people and societies operate somehow doesn’t look much like neat budget constraints or smoothly curving production possibilities frontiers.
However, the economics approach can be a useful way to analyze and understand the tradeoffs of economic decisions even so. To appreciate this point, imagine for a moment that you are playing basketball, dribbling to the right, and throwing a bounce-pass to the left to a teammate who is running toward the basket. A physicist or engineer could work out the correct speed and trajectory for the pass, given the different movements involved and the weight and bounciness of the ball. But when you are playing basketball, you do not perform any of these calculations. You just pass the ball, and if you are a good player, you will do so with high accuracy.
Someone might argue: “The scientist’s formula of the bounce-pass requires a far greater knowledge of physics and far more specific information about speeds of movement and weights than the basketball player actually has, so it must be an unrealistic description of how basketball passes are actually made.” This reaction would be wrongheaded. The fact that a good player can throw the ball accurately because of practice and skill, without making a physics calculation, does not mean that the physics calculation is wrong.
Similarly, from an economic point of view, someone who goes shopping for groceries every week has a great deal of practice with how to purchase the combination of goods that will provide that person with utility, even if the shopper does not phrase decisions in terms of a budget constraint. Government institutions may work imperfectly and slowly, but in general, a democratic form of government feels pressure from voters and social institutions to make the choices that are most widely preferred by people in that society. So, when thinking about the economic actions of groups of people, firms, and society, it is reasonable, as a first approximation, to analyze them with the tools of economic analysis. For more on this, read about behavioral economics in the chapter on Consumer Choices.
Second Objection: People, Firms, and Society Should Not Act This Way
The economics approach portrays people as self-interested. For some critics of this approach, even if self-interest is an accurate description of how people behave, these behaviors are not moral. Instead, the critics argue that people should be taught to care more deeply about others. Economists offer several answers to these concerns.
First, economics is not a form of moral instruction. Rather, it seeks to describe economic behavior as it actually exists. Philosophers draw a distinction between positive statements , which describe the world as it is, and normative statements , which describe how the world should be. For example, an economist could analyze a proposed subway system in a certain city. If the expected benefits exceed the costs, he concludes that the project is worth doing—an example of positive analysis. Another economist argues for extended unemployment compensation during the Great Depression because a rich country like the United States should take care of its less fortunate citizens—an example of normative analysis.
Even if the line between positive and normative statements is not always crystal clear, economic analysis does try to remain rooted in the study of the actual people who inhabit the actual economy.  In fact, we need to look no further than to Adam Smith , the very father of modern economics to find evidence of this. The opening sentence of his book, The Theory of Moral Sentiments, puts it very clearly: “How selfish soever man may be supposed, there are evidently some principles in his nature, which interest him in the fortune of others, and render their happiness necessary to him, though he derives nothing from it except the pleasure of seeing it.” Clearly, individuals are both self-interested and altruistic.
Second, self-interested behavior and profit-seeking can be labeled with other names, such as personal choice and freedom. The ability to make personal choices about buying, working, and saving is an important personal freedom. Some people may choose high-pressure, high-paying jobs so that they can earn and spend a lot of money on themselves. Others may earn a lot of money and give it to charity or spend it on their friends and family. Others may devote themselves to a career that can require a great deal of time, energy, and expertise but does not offer high financial rewards, like being an elementary school teacher or a social worker. Still others may choose a job that does not take lots of their time or provide a high level of income, but still leaves time for family, friends, and contemplation. Some people may prefer to work for a large company; others might want to start their own business. People’s freedom to make their own economic choices has a moral value worth respecting.
Example \(\PageIndex{1}\): Is a diagram by any other name the same?
When you study economics, you may feel buried under an avalanche of diagrams: diagrams in the text, diagrams in the lectures, diagrams in the problems, and diagrams on exams. Your goal should be to recognize the common underlying logic and pattern of the diagrams, not to memorize each of the individual diagrams.
This chapter uses only one basic diagram, although it is presented with different sets of labels. The consumption budget constraint and the production possibilities frontier for society, as a whole, are the same basic diagram. Figure \(\PageIndex{1}\) shows an individual budget constraint and a production possibilities frontier for two goods, Good 1 and Good 2. The tradeoff diagram always illustrates three basic themes: scarcity, tradeoffs, and economic efficiency.
The first theme is scarcity . It is not feasible to have unlimited amounts of both goods. But even if the budget constraint or a PPF shifts, scarcity remains—just at a different level. The second theme is tradeoffs . As depicted in the budget constraint or the production possibilities frontier, it is necessary to give up some of one good to gain more of the other good. The details of this tradeoff vary. In a budget constraint, the tradeoff is determined by the relative prices of the goods: that is, the relative price of two goods in the consumption choice budget constraint. These tradeoffs appear as a straight line. However, the tradeoffs in many production possibilities frontiers are represented by a curved line because the law of diminishing returns holds that as resources are added to an area, the marginal gains tend to diminish. Regardless of the specific shape, tradeoffs remain.
The third theme is economic efficiency , or getting the most benefit from scarce resources. All choices on the production possibilities frontier show productive efficiency because in such cases, there is no way to increase the quantity of one good without decreasing the quantity of the other. Similarly, when an individual makes a choice along a budget constraint, there is no way to increase the quantity of one good without decreasing the quantity of the other. The choice on a production possibilities set that is socially preferred, or the choice on an individual’s budget constraint that is personally preferred, will display allocative efficiency.
The basic budget constraint/production possibilities frontier diagram will recur throughout this book. Some examples include using these tradeoff diagrams to analyze trade, labor supply versus leisure, saving versus consumption, environmental protection and economic output, equality of incomes and economic output, and the macroeconomic tradeoff between consumption and investment. Do not be confused by the different labels. The budget constraint/production possibilities frontier diagram is always just a tool for thinking carefully about scarcity, tradeoffs, and efficiency in a particular situation.
The Tradeoff Diagram
Third, self-interested behavior can lead to positive social results. For example, when people work hard to make a living, they create economic output. Consumers who are looking for the best deals will encourage businesses to offer goods and services that meet their needs. Adam Smith, writing in The Wealth of Nations, christened this property the invisible hand . In describing how consumers and producers interact in a market economy, Smith wrote:
"Every individual…generally, indeed, neither intends to promote the public interest, nor knows how much he is promoting it. By preferring the support of domestic to that of foreign industry, he intends only his own security; and by directing that industry in such a manner as its produce may be of the greatest value, he intends only his own gain. And he is in this, as in many other cases, led by an invisible hand to promote an end which was no part of his intention…By pursuing his own interest he frequently promotes that of the society more effectually than when he really intends to promote it."
The metaphor of the invisible hand suggests the remarkable possibility that broader social good can emerge from selfish individual actions.
Fourth, even people who focus on their own self-interest in the economic part of their life often set aside their own narrow self-interest in other parts of life. For example, you might focus on your own self-interest when asking your employer for a raise or negotiating to buy a car. But then you might turn around and focus on other people when you volunteer to read stories at the local library, help a friend move to a new apartment, or donate money to a charity. Self-interest is a reasonable starting point for analyzing many economic decisions, without needing to imply that people never do anything that is not in their own immediate self-interest.
Example \(\PageIndex{2}\): Choices ... To What Degree?
What have we learned? We know that scarcity impacts all the choices we make. So, an economist might argue that people do not go on to get bachelor’s degrees or master’s degrees because they do not have the resources to make those choices or because their incomes are too low and/or the price of these degrees is too high. A bachelor’s degree or a master’s degree may not be available in their opportunity set.
The price of these degrees may be too high not only because the actual price, college tuition (and perhaps room and board), is too high. An economist might also say that for many people, the full opportunity cost of a bachelor’s degree or a master’s degree is too high. For these people, they are unwilling or unable to make the tradeoff of giving up years of working, and earning an income, to earn a degree.
Finally, the statistics introduced at the start of the chapter reveal information about intertemporal choices . An economist might say that people choose not to get a college degree because they may have to borrow money to go to college, and the interest they have to pay on that loan in the future will affect their decisions today. Also, it could be that some people have a preference for current consumption over future consumption, so they choose to work now at a lower salary and consume now, rather than putting that consumption off until after they graduate college.
Key Concepts and Summary
The economic way of thinking provides a useful approach to understanding human behavior. Economists make the careful distinction between positive statements, which describe the world as it is, and normative statements, which describe how the world should be. Even when economics analyzes the gains and losses from various events or policies, and thus draws normative conclusions about how the world should be, the analysis of economics is rooted in a positive analysis of how people, firms, and governments actually behave, not how they should behave.
References
Smith, Adam. “Of Restraints upon the Importation from Foreign Countries.” In The Wealth of Nations. London: Methuen & Co., 1904, first pub 1776), I.V. 2.9.
Smith, Adam. “Of the Propriety of Action.” In The Theory of Moral Sentiments. London: A. Millar, 1759, 1.
Glossary
- invisible hand
- idea that self-interested behavior by individuals can lead to positive social outcomes
- normative statement
- statement which describes how the world should be
- positive statement
- statement which describes the world as it is


14.1: Intro to Environmental Health
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Environmental health is the branch of public health that is concerned with all aspects of the natural and built environment that may affect human health. Health is the science, practice, and study of a human's well-being and their health and preventing illnesses and human injuries. Other terms referring to or concerning environmental health are environmental public health, and public health protection/environmental health protection. Environmental health and environmental protection are very much related. Environmental health is focused on the natural and built environments for the benefit of human health, whereas environmental protection is concerned with protecting the natural environment for the benefit of human health and the ecosystem. Research in the environmental health field tries to limit the harmful exposures through natural things such as soil, water, air food, etc.
The natural environment encompasses all living and non-living things occurring naturally, meaning in this case not artificial. The term is most often applied to the Earth or some parts of Earth. This environment encompasses the interaction of all living species, climate, weather, and natural resources that affect human survival and economic activity. The concept of the natural environment can be distinguished as components:
- Complete ecological units that function as natural systems without massive civilized human intervention, including all vegetation, microorganisms, soil, rocks, atmosphere, and natural phenomena that occur within their boundaries and their nature
- Universal natural resources and physical phenomena that lack clear-cut boundaries, such as air, water, and climate, as well as energy, radiation, electric charge, and magnetism, not originating from civilized human activity
In contrast to the natural environment is the built environment. In such areas where man has fundamentally transformed landscapes such as urban settings and agricultural land conversion, the natural environment is greatly modified into a simplified human environment. Even acts which seem less extreme, such as building a mud hut or a photovoltaic system in the desert, modify the natural environment into an artificial one. Though many animals build things to provide a better environment for themselves, they are not human, hence beaver dams and the works of Mound-building termites are thought of as natural.
People seldom find absolutely natural environments on Earth, and naturalness usually varies in a continuum, from 100% natural in one extreme to 0% natural in the other. More precisely, we can consider the different aspects or components of an environment, and see that their degree of naturalness is not uniform. If, for instance, in an agricultural field, the mineralogic composition and the structure of its soil are similar to those of an undisturbed forest soil, but the structure is quite different.
The carrying capacity of a biological species in an environment is the maximum population size of the species that the environment can sustain indefinitely, given the food, habitat, water, and other necessities available in the environment. In population biology, carrying capacity is defined as the environment's maximal load, which is different from the concept of population equilibrium. Its effect on population dynamics may be approximated in a logistic model, although this simplification ignores the possibility of overshoot which real systems may exhibit.
Carrying capacity was originally used to determine the number of animals that could graze on a segment of land without destroying it. Later, the idea was expanded to more complex populations, like humans. For the human population, more complex variables such as sanitation and medical care are sometimes considered as part of the necessary establishment. As population density increases, birth rate often decreases and death rate typically increases. The difference between the birth rate and the death rate is the "natural increase". The carrying capacity could support a positive natural increase or could require a negative natural increase. Thus, the carrying capacity is the number of individuals an environment can support without significant negative impacts to the given organism and its environment. Below carrying capacity, populations typically increase, while above, they typically decrease. A factor that keeps population size at equilibrium is known as a regulating factor. Population size decreases above carrying capacity due to a range of factors depending on the species concerned, but can include insufficient space, food supply, or sunlight. The carrying capacity of an environment may vary for different species and may change over time due to a variety of factors including: food availability, water supply, environmental conditions and living space. The origins of the term "carrying capacity" are uncertain, with researchers variously stating that it was used "in the context of international shipping" or that it was first used during 19 th -century laboratory experiments with micro-organisms. A recent review finds the first use of the term in an 1845 report by the US Secretary of State to the US Senate.


15.3: Glance at Genre- Observation, Description, and Analysis
By the end of this section, you will be able to:
- Identify the structural components of case studies.
- Determine the objectivity of case studies.
- Apply the genre conventions of case studies in your own research.
The goal of case study authors is to expand knowledge in a field of study. In many case studies, researchers look for “blind spots”: areas of investigation that the current research is not addressing or not addressing sufficiently. Sometimes the authors of a study will explicitly state what they believe are the gaps in their research and call on other researchers to fill in those gaps.
Components of Case Studies
Case studies generally have five main parts. They begin by presenting an overview of previous case studies on the topic. Sometimes called a literature review , this part of the case study provides background and helps readers understand where the current study fits within previous research. The second component of a case study is a detailed description of the participants and the observation environment . These descriptions of the individuals being studied and the conditions under which they are being studied provide additional background and context. The third component is the methods section, in which the author explains the ways in which data will be collected, such as interviews, surveys, observations, document analysis, and so on. The fourth component, following the methods section, is an organized presentation of the data collected, or the findings of the study. Finally, an analysis of the results concludes the case study. In this section, the author provides an interpretation of the collected data. This section usually includes an explanation of the limitations of and gaps in the case study’s data, methods, or anything else the author believes is important.
Similar to academic essays, case studies adhere to a formal structure and voice. They are organized clearly, edited carefully, and reflect objectivity. As with all academic work, sources are documented and cited, usually using APA Documentation and Format.
Key Terms
A case study, at its most basic level, is about close observation as a basis for analysis. By observing individuals or groups in a particular setting, researchers attempt to learn something about the participants’ thoughts, actions, behavior, or feelings. To conduct a case study, you should be familiar with the following terms.
- Analysis: Interpretation of data gathered in a case study.
- Data: Information gathered from observation, interviews, research, or any other part of a case study.
- field observations: Observations made while participants are engaged in “real” activities at “real” places. Usually these are the workplace, school, or home. Other locations might be athletic or social venues or any other setting in which participants can be observed acting as they would if they were not being observed.
- Results: What collected data reveals about the research question.
- Participants: The human or, in some cases, nonhuman subjects observed in specific settings for the purpose of collecting data and evidence.
- Observation environment: The location and conditions under which participants are observed.
- qualitative research: Subjective information based on observations or elements that are difficult to replicate.
- quantitative research: Specific data that can be replicated in a controlled environment.
- Research question: Focused question about the topic being researched. A research question is the basis of a case study.
- Survey or Interview: Questions that the author of a case study asks participants in order to elicit relevant information


6: Composition of Substances and Solutions
Quantitative aspects of the composition of substances and mixtures are the subject of this chapter.
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- 6.2: Formula Mass
- The formula mass of a substance is the sum of the average atomic masses of each atom represented in the chemical formula and is expressed in atomic mass units. The formula mass of a covalent compound is also called the molecular mass. A convenient amount unit for expressing very large numbers of atoms or molecules is the mole. Experimental measurements have determined the number of entities composing 1 mole of substance to be \(6.022 \times 10^{23}\), a quantity called Avogadro’s number.
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- 6.3: Determining Empirical and Molecular Formulas
- The chemical identity of a substance is defined by the types and relative numbers of atoms composing its fundamental entities (molecules in the case of covalent compounds, ions in the case of ionic compounds). A compound’s percent composition provides the mass percentage of each element in the compound, and it is often experimentally determined and used to derive the compound’s empirical formula.
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- 6.4: Molarity
- Solutions are homogeneous mixtures. Many solutions contain one component, called the solvent, in which other components, called solutes, are dissolved. An aqueous solution is one for which the solvent is water. The concentration of a solution is a measure of the relative amount of solute in a given amount of solution. Concentrations may be measured using various units, with one very useful unit being molarity, defined as the number of moles of solute per liter of solution.
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- 6.5: Other Units for Solution Concentrations
- In addition to molarity, a number of other solution concentration units are used in various applications. Percentage concentrations based on the solution components’ masses, volumes, or both are useful for expressing relatively high concentrations, whereas lower concentrations are conveniently expressed using ppm or ppb units. These units are popular in environmental, medical, and other fields where mole-based units such as molarity are not as commonly used.


7.2: The Central Limit Theorem for Sample Means
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The sampling distribution is a theoretical distribution. Specifically, the sampling distribution is the probability distribution of the mean of a random sample. Since the sample is obtained randomly, the value of the sample mean is a random variable. The sampling distribution is created by taking many samples of size \(n\) from a population. Each sample mean is then treated like a single observation of this new distribution, the sampling distribution. The genius of thinking this way is that it recognizes that when we sample we are creating an observation and that observation must come from some particular distribution. The Central Limit Theorem answers the question: from what distribution did a sample mean come? If this is discovered, then we can treat a sample mean just like any other random variable and calculate probabilities about what values it might take on. We have effectively moved from the world of statistics where we know only what we have from the sample, to the world of probability where we know the distribution from which the sample mean came and the parameters of that distribution.
The reasons that one samples a population are obvious. The time and expense of checking every invoice to determine its validity or every shipment to see if it contains all the items may well exceed the cost of errors in billing or shipping. For some products, sampling would require destroying them, called destructive sampling. One such example is measuring the ability of a metal to withstand saltwater corrosion for parts on ocean going vessels.
Sampling thus raises an important question; just which sample was drawn. Even if the sample were randomly drawn, there are theoretically an almost infinite number of samples. With just 100 items, there are more than 75 million unique samples of size 5 that can be drawn. If 6 are in the sample, the number of possible samples increases to just more than one billion. Of the 75 million possible samples, then, which one did you get? If there is variation in the items to be sampled, there will be variation in the samples. One could draw an "unlucky" sample and make very wrong conclusions concerning the population. This recognition that any sample we draw is really only one from a distribution of samples provides us with what is probably the single most important theorem is statistics: the Central Limit Theorem . Without the Central Limit Theorem it would be impossible to proceed to inferential statistics from simple probability theory. In its most basic form, the Central Limit Theorem states that regardless of the underlying probability density function of the population data, the theoretical distribution of the means of samples from the population will be normally distributed. In essence, this says that the mean of a sample should be treated like an observation drawn from a normal distribution. The Central Limit Theorem only holds if the sample size is "large enough" which has been shown to be only 30 or more.
Figure \(\PageIndex{1}\) graphically displays this very important proposition.
Notice that the horizontal axis in the top panel is labeled \(x\). These are the individual observations of the population. This is the unknown distribution of the population values. The graph is purposefully drawn all squiggly to show that it does not matter just how odd ball it really is. Remember, we will never know what this distribution looks like, or its mean or standard deviation for that matter.
The horizontal axis in the bottom panel is labeled \(\overline{x}\)'s. This is the theoretical distribution called the sampling distribution of the sample mean. Each observation on this distribution is a sample mean. All these sample means were calculated from individual samples with the same sample size. The theoretical sampling distribution contains all of the sample mean values from all the possible samples that could have been taken from the population. Of course, no one would ever actually take all of these samples, but if they did this is how they would look. And the Central Limit Theorem says that they will be normally distributed.
The Central Limit Theorem goes even further and tells us the mean and standard deviation of this theoretical distribution, as detailed in Table \(\PageIndex{1}\).
| Parameter | Population distribution | Sample | Sampling distribution of \(\overline{X}\) |
|---|---|---|---|
| Mean | \(\mu\) | \(\overline{X}\) | \(\mu_{\overline{X}} = \mathrm{E}\left[\overline{X}\right]=\mu\) |
| Standard deviation | \(\sigma\) | \(s\) | \(\sigma_{\overline{X}}=\frac{\sigma}{\sqrt{n}}\) |
The practical significance of The Central Limit Theorem is that now we can compute probabilities for drawing a sample mean, \(\overline{X}\), in just the same way as we did for drawing specific observations, \(X\)'s, when we knew the population mean and standard deviation and that the population data were normally distributed. The standardizing formula has to be amended to recognize that the mean and standard deviation of the sampling distribution, sometimes, called the standard error of the mean, are different from those of the population distribution, but otherwise nothing has changed. The new standardizing formula is
\[Z=\frac{\overline{X}-\mu_{\overline{X}}}{\sigma_{\overline{X}}}=\frac{\overline{X}-\mu}{\frac{\sigma}{\sqrt{n}}}\nonumber\]
Notice that \(\mu_{\overline{X}}\) in the first formula has been changed to simply \(\mu\) in the second version. The reason is that mathematically it can be shown that the expected value of \(\overline{X}\), the mean of \(\overline{X}\), is equal to \(\mu\). This was stated in Table \(\PageIndex{1}\) above. This formula will be used in the next chapter to provide interval estimates of the unknown population parameter \(\mu\).


Ethical Use and Citing Sources
It’s helpful to understand why to cite your sources.
You likely know that research projects always need a reference or a works cited page (also called a bibliography). But have you ever wondered why?
There are some big picture reasons that don’t often get articulated that might help you get better at meeting the citation needs of research projects. It’s helpful to understand both the theory behind citing, as well as the mechanics of it, to really become a pro.
Tip: How to Cite Sources
This section introduces the concept of citing source, so you can begin your search for sources with it in mind. See the next section, How to Cite Sources for examples and the steps for citing appropriately.
In everyday life, we often have conversations where we share new insights with each other. Sometimes these are insights we’ve developed on our own through the course of our own everyday experiences, thinking, and reflection. Sometimes these insights come after talking to other people and learning from additional perspectives. When we relate the new things we have learned to our family, friends, or co-workers, we may or may not fill them in on how these thoughts came to us.
In everyday conversation and political speeches, evidence
for arguments is often not provided. (Image source:
XKDC
)
Academic research leads us to the insight that comes from gaining perspectives and understandings from other people through what we read, watch, and hear. In academic work we must tell our readers who and what led us to our conclusions. Documenting our research is important because people rely on academic research to be authoritative, so it is essential for academic conversation to be as clear as possible. Documentation for clarity is a shared and respected practice, and it represents a core value of the academy called “academic integrity.” It is a way to distinguish academic conversations (or discourse) from everyday conversations (or discourse).
It is hard to talk about citation practices without considering some related concepts. Here are some definitions of those concepts that are often mentioned in assignments when citation is required.
What Is Academic Integrity?
Different colleges and universities have different definitions. Irvine Valley College states a commitment to academic integrity by the following statement from the 2020-2021 IVC Catalog:
Irvine Valley College actively promotes academic and institutional honesty. Academic dishonesty runs counter to a healthy intellectual environment and tarnishes the educational opportunities offered.
Please take a few moments to read the Policies and Standards under Academic Honesty and Dishonesty in the
2020-2021 IVC Catalog
that describes the consequences of falsification, plagiarism, and cheating in more detail.
In other words, you must take full responsibility for your work, acknowledge your own efforts, and acknowledge the contributions of others’ efforts. Working/Writing with integrity requires accurately representing what you contributed, as well as acknowledging how others have influenced your work. When you are a student, an accurate representation of your knowledge is important because it will allow both you and your professors to know the extent to which you have developed as a scholar. Part of that development is evidenced by how you apply the ruler for acknowledging the work of others.
What Is Academic Misconduct?
As you might imagine, academic misconduct is when you do not use integrity in your academic work. Academic misconduct includes many different unacceptable behaviors, but the one most relevant to what we are discussing here is submitting plagiarized work:
Submitting plagiarized work for an academic requirement. Plagiarism is the representation of another’s work or ideas as one’s own; it includes the unacknowledged word-for-word use and/or paraphrasing of another person’s work, and/or the inappropriate unacknowledged use of another person’s ideas.
To see the full definition of academic misconduct, refer to the
Irvine Valley College Student Code of Conduct
.
What Is Plagiarism?
Plagiarism is defined by the
2020-2021 IVC Course Catalog
in this way:
Students should be advised to state the source of ideas when these are known, since this lends strength to their answers and is part of the ethics of scholarship.
Plagiarism is any conduct in academic work or programs involving misrepresentation of someone else’s words, ideas or data as one’s original work, including, but not limited to, the following:
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intentionally representing as one’s own work the work, words, ideas or arrangement of ideas, research, formulae, diagrams, statistics, or evidence of another.
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taking sole credit for ideas and/or written work that resulted from collaboration with others.
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paraphrasing or quoting material without citing the source.
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submitting as one’s own a copy of or the actual work of another person, either in part or in entirety, without appropriate citation (e.g., term-paper mill or internet derived products).
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sharing computer files and programs or written papers and then submitting individual copies of the results as one’s own individual work.
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submitting substantially the same material in more than one course without prior authorization from each instructor involved.
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modifying another’s work and representing it as one’s own work.
Plagiarism can be intentional (knowingly using someone else’s work and presenting it as your own) or unintentional (inaccurately or inadequately citing ideas and words from a source). It may be impossible for your professor to determine whether plagiarized work was intentional or unintentional. But in either case, plagiarism puts both you and your professor in a compromising position.
While academic integrity calls for work resulting from your own effort, scholarship requires that you learn from others. So in the world of academic scholarship you are actually expected to learn new things from others AND come to new insights on your own. There is an implicit understanding that as a student you will be both using other’s knowledge as well as your own insights to create new scholarship. To do this in a way that meets academic integrity standards you must acknowledge the part of your work that develops from others’ efforts. You do this by citing the work of others. You plagiarize when you fail to acknowledge the work of others and do not follow appropriate citation guidelines.
What Is Citing?
Citing, or citation, is a practice of documenting specific influences on your academic work. See How to Cite Sources for details.
In other words, you must cite all the sources you quote directly, paraphrase, or summarize as you:
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Answer your research question
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Convince your audience
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Describe the situation around your research question and why the question is important
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Report what others have said about your question


2.1: Introductory Information- Demographic and Biographic Data
“Introductory information” refers to the demographic and biographic data that you collect from the client. This data provides you with basic characteristics about the client, such as their name, contact information, birthdate and age, gender and preferred pronouns, allergies, languages spoken and preferred language, relationship status, occupation, and resuscitation status.
Although this data is brief and succinct, the intent of collecting it is not to be reductionist or to label clients. Rather, it is meant as a brief overview of the client and to provide the information you need to reach next of kin in an emergency, to be attentive to allergies at a glance, and to tend to the client in a caring manner. See Film Clip 2.1 of a nurse conducting an assessment of a client’s demographic and biographic data. See Table 2.1 for suggested questions and statements you can use to collect this data in an inclusive and caring manner, as well as an example of a demographic and biographic form below.
| Data | Questions and Statements |
|---|---|
|
Name/contact information and emergency information |
|
| Birthdate and age |
|
| Gender |
|
| Allergies |
Note: You may need to prompt for information on medications, foods, etc. |
| Languages spoken and preferred language |
Note : You may need to inquire and document if the client requires an interpreter. |
| Relationship status |
Tell me about your relationship status. Note : Avoid questions such as “Are you married?” or “Do you have boyfriend?” or “Do you have a wife?” as they assume normative behaviour and heterosexuality. |
| Occupation/school status |
Note : Reassure the client that this information provides insight into the nature of their work (e.g., the physical or mental impact) and environmental exposures, and that the question is not intended to evaluate the client. |
| Resuscitation status |
Note : Depending on the client’s answer, you will need to collaborate with the broader healthcare team, explore the details of the client’s wishes further, and have them complete a requisite resuscitation form. |
Demographic Information Form (Example)
Clicking the hyperlinked question mark (?) next to the example form fields will take you to some suggested questions to ask your patient.
Interview Date: _______________________
Client Name: _______________________ (?)
Date of Birth: _______________________ (?)
Age: _____ Sex: Male / Female / Another Option _____________
Gender You Self Identify With: ______________ (?) Preferred Pronouns: ________________
Healthcard Number: _______________________
Primary Language: _______________________ (?)
Relationship Status: _______________________ (?)
Phone Number: _______________________
Address: ______________________________________________
Allergies: _______________________ (?)
Occupation/Education: _______________________ (?)
Resuscitation Status: ______________________________________________(?)
Emergency Contact: Relationship to Patient:
Phone Number:
Information from: Patient / Other
Patient Accompanied: Yes / No Accompanied’s Details:
Test Yourself
Query \(\PageIndex{1}\)


17.4: Putting It Together- Corporate Social Responsibility
Corporate responsibility—whether approached from a sustainability or CSR perspective—is the new normal; that is, the new expectation of stakeholders broadly. In “Reset: Business and Society in the New Social Landscape,” co-authors and University of Virginia Darden School of Business faculty James Rubin and Barie Carmichael note that what’s new is a “growing expectation of business’s role in society on a global basis. [1] People are shifting their attention from products and services to the companies behind those products and services.” [2] The authors state that how companies manage their impacts determines whether they will be perceived as pariahs or progressive, labels that are associated with either failure or success.
In his article “Social Accountability: The Business World’s New Role in Social Change,” writer Adam Uzialko summarized the key outtakes from Carmichael & Rubin’s research:
- 71% of people said their expectations for companies have increased.
- 68% said it’s more important to know how companies operate than what they sell.
- 94%of those surveyed said companies have the ability to shape a better society.
- 87% said most companies exist to create value for multiple interests in society, rather than just profit. [3]
- 75% said they converted their opinions of a company into action. [4]
These statistics matter because they not only influence purchasing and recommendation decisions, they influence employment decisions. The importance of building an employer brand—being an employer of choice—will become increasingly critical with demographic changes. For example: factor into our full-employment economy the statistic that Baby Boomers are leaving the workforce at a rate of approximately 10,000 per day—a pace that can’t be replaced with Gen-X, Millennial and post- Millennial workers. That will translate into increased competition for talent and, as the Cone and Millennial surveys reflect and Carmichael states, “workers are paying attention not just to professed core values, but to which companies put their money where their mouth is.” [5] What is exciting—and, perhaps, daunting—is the role that human resource professionals play in evolving culture, policies and practices to accommodate this new reality. To achieve this end, human resource professionals will need to embrace their role and not only as guardians and champions, but changemakers.
-
Rubin, James and Barie Carmichael. "Reset: Business and Society in the New Social Landscape." Columbia University Press. 2018. ↵
-
Uzialko, Adam C. "
Social Accountability: The Business World's New Role in Social Change
." Business News Daily. December 28, 2017. Accessed July 19, 2019. ↵
-
Ibid. ↵
-
Ibid. ↵
-
Ibid. ↵
Contributors and Attributions
- Untitled. Authored by : rawpixel. Provided by : Pixabay. Located at : pixabay.com/photos/adu /. License : CC0: No Rights Reserved . License Terms : Pixabay License


12.2: Conductor Size
Two Basic Varieties of Electrical Wire: Solid and Stranded
Electrical wire is usually round in cross-section (although there are some unique exceptions to this rule), and comes in two basic varieties: solid and stranded. Solid copper wire is just as it sounds: a single, solid strand of copper the whole length of the wire. Stranded wire is composed of smaller strands of solid copper wire twisted together to form a single, larger conductor. The greatest benefit of stranded wire is its mechanical flexibility, being able to withstand repeated bending and twisting much better than solid copper (which tends to fatigue and break after time).
Wire size can be measured in several ways. We could speak of a wire’s diameter, but since its really the cross-sectional area that matters most regarding the flow of electrons, we are better off designating wire size in terms of area.
The wire cross-section picture shown above is, of course, not drawn to scale. The diameter is shown as being 0.1019 inches. Calculating the area of the cross-section with the formula Area = πr 2 , we get an area of 0.008155 square inches:
These are fairly small numbers to work with, so wire sizes are often expressed in measures of thousandths-of-an-inch, or mils . For the illustrated example, we would say that the diameter of the wire was 101.9 mils (0.1019 inch times 1000). We could also, if we wanted, express the area of the wire in the unit of square mils, calculating that value with the same circle-area formula, Area = πr 2 :
Calculating the Circular-mil Area of a Wire
However, electricians and others frequently concerned with wire size use another unit of area measurement tailored specifically for wire’s circular cross-section. This special unit is called the circular mil (sometimes abbreviated cmil ). The sole purpose for having this special unit of measurement is to eliminate the need to invoke the factor π (3.1415927 . . .) in the formula for calculating area, plus the need to figure wire radius when you’ve been given diameter . The formula for calculating the circular-mil area of a circular wire is very simple:
Because this is a unit of area measurement, the mathematical power of 2 is still in effect (doubling the width of a circle will always quadruple its area, no matter what units are used, or if the width of that circle is expressed in terms of radius or diameter). To illustrate the difference between measurements in square mils and measurements in circular mils, I will compare a circle with a square, showing the area of each shape in both unit measures:
And for another size of wire:
Obviously, the circle of a given diameter has less cross-sectional area than a square of width and height equal to the circle’s diameter: both units of area measurement reflect that. However, it should be clear that the unit of “square mil” is really tailored for the convenient determination of a square’s area, while “circular mil” is tailored for the convenient determination of a circle’s area: the respective formula for each is simpler to work with. It must be understood that both units are valid for measuring the area of a shape, no matter what shape that may be. The conversion between circular mils and square mils is a simple ratio: there are π (3.1415927 . . .) square mils to every 4 circular mils.
Measuring Cross-Sectional Wire Area with Gauge
Another measure of cross-sectional wire area is the gauge . The gauge scale is based on whole numbers rather than fractional or decimal inches. The larger the gauge number, the skinnier the wire; the smaller the gauge number, the fatter the wire. For those acquainted with shotguns, this inversely-proportional measurement scale should sound familiar.
The table at the end of this section equates gauge with inch diameter, circular mils, and square inches for solid wire. The larger sizes of wire reach an end of the common gauge scale (which naturally tops out at a value of 1), and are represented by a series of zeros. “3/0” is another way to represent “000,” and is pronounced “triple-ought.” Again, those acquainted with shotguns should recognize the terminology, strange as it may sound. To make matters even more confusing, there is more than one gauge “standard” in use around the world. For electrical conductor sizing, the American Wire Gauge (AWG), also known as the Brown and Sharpe (B&S) gauge, is the measurement system of choice. In Canada and Great Britain, the British Standard Wire Gauge (SWG) is the legal measurement system for electrical conductors. Other wire gauge systems exist in the world for classifying wire diameter, such as the Stubs steel wire gauge and the Steel Music Wire Gauge (MWG), but these measurement systems apply to non-electrical wire use.
The American Wire Gauge (AWG) measurement system, despite its oddities, was designed with a purpose: for every three steps in the gauge scale, wire area (and weight per unit length) approximately doubles. This is a handy rule to remember when making rough wire size estimations!
For very large wire sizes (fatter than 4/0), the wire gauge system is typically abandoned for cross-sectional area measurement in thousands of circular mils (MCM), borrowing the old Roman numeral “M” to denote a multiple of “thousand” in front of “CM” for “circular mils.” The following table of wire sizes does not show any sizes bigger than 4/0 gauge, because solid copper wire becomes impractical to handle at those sizes. Stranded wire construction is favored, instead.
For some high-current applications, conductor sizes beyond the practical size limit of round wire are required. In these instances, thick bars of solid metal called busbars are used as conductors. Busbars are usually made of copper or aluminum, and are most often uninsulated. They are physically supported away from whatever framework or structure is holding them by insulator standoff mounts. Although a square or rectangular cross-section is very common for busbar shape, other shapes are used as well. Cross-sectional area for busbars is typically rated in terms of circular mils (even for square and rectangular bars!), most likely for the convenience of being able to directly equate busbar size with round wire.
REVIEW:
- Electrons flow through large-diameter wires easier than small-diameter wires, due to the greater cross-sectional area they have in which to move.
- Rather than measure small wire sizes in inches, the unit of “mil” (1/1000 of an inch) is often employed.
- The cross-sectional area of a wire can be expressed in terms of square units (square inches or square mils), circular mils, or “gauge” scale.
- Calculating square-unit wire area for a circular wire involves the circle area formula:
- Calculating circular-mil wire area for a circular wire is much simpler, due to the fact that the unit of “circular mil” was sized just for this purpose: to eliminate the “pi” and the d/2 (radius) factors in the formula.
- There are π (3.1416) square mils for every 4 circular mils.
- The gauge system of wire sizing is based on whole numbers, larger numbers representing smaller-area wires and vice versa. Wires thicker than 1 gauge are represented by zeros: 0, 00, 000, and 0000 (spoken “single-ought,” “double-ought,” “triple-ought,” and “quadruple-ought.”
- Very large wire sizes are rated in thousands of circular mils (MCM’s), typical for busbars and wire sizes beyond 4/0.
- Busbars are solid bars of copper or aluminum used in high-current circuit construction. Connections made to busbars are usually welded or bolted, and the busbars are often bare (uninsulated), supported away from metal frames through the use of insulating standoffs.


5.13: What is Blood Pressure?
Blood pressure is the force of blood exerted against the arterial walls, and is reported in millimetres of mercury (mm Hg). Try turning your kitchen tap on just a little bit, and then full blast. Compare the varying forces of water pressure as you adjust the tap. This comparison will give you a better sense of blood pressure.
The pressure against the arterial walls (the blood pressure) changes depending on whether the heart is contracting and pushing blood out into the arteries or whether the heart is in a resting phase and filling with blood. There is always force against the arterial walls, even when the heart is in a resting phase. The systolic pressure is the maximum pressure on the arteries during left ventricular contraction (systole) (OER #1). The left ventricle is a lower chamber of the heart responsible for pumping blood out to the body. The diastolic pressure is the resting pressure on the arteries between each cardiac contraction (OER #1) when the heart’s chambers are filling with blood (diastole).
Stroke volume is the amount of blood ejected from the left ventricle in a single contraction. Stroke volume provides information about the functioning of the heart. Stroke volume is influenced by age and typically ranges from 5–80 mL. Newborns have a stroke volume of about 5 mL per contraction while adults have a stroke volume of about 30–70 mL per contraction; the stroke volume increases as individuals grow and their hearts become stronger and can pump more volume per contraction. Direct measurement of stroke volume involves an invasive approach in which a catheter is passed into the pulmonary artery via a large neck vein; this monitoring device is only used during critical care situations.
Indirect measurement of stroke volume involves assessing the pulse pressure, which is the difference between the systolic and diastolic values and signifies the force required by the heart each time it contracts. For example, if someone’s blood pressure is 120/80 mm Hg, the pulse pressure is 40 mm Hg. A higher pulse pressure can indicate arterial stiffness, which often happens as a result of aging or cardiovascular disease. A higher pulse pressure can also be indicative of aortic valvular insufficiency where the diastolic pressure is unusually low and the systolic pressure is mildly elevated or unchanged. A lower pulse pressure can be a marker of poor heart function, where cardiac output is decreased.
_________________________________________________________________________
Part of this content was adapted from OER #1 (as noted in brackets above):
© 2015 British Columbia Institute of Technology (BCIT). Clinical Procedures for Safer Patient Care by Glynda Rees Doyle and Jodie Anita McCutcheon, British Columbia Institute of Technology. Licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted. Download this book for free at http://open.bccampus.ca


3.15: Conclusion
The aim of this chapter has been to deepen our understanding of the capability approach, by analysing some questions of clarification that are often posed, and by reconstructing and synthesizing some developments that have taken place in the capability literature over time.
The next chapter will focus on a range of critiques that have been put to the capability approach. Of course, it is not always entirely clear whether a certain question or debate is purely a matter of clarification, or rather a matter of debate and dispute; put differently, there is no neat demarcation between the main focus of this chapter and that of the next. Still, in this chapter I have tried to be as neutral and even-handed as possible in describing the literature, whereas in the next chapter I will take a more active role in arguing for or against certain views or claims.


2.15: Nubia- The Kingdoms of Kerma and Kush
The region south of Aswan, at the first cataract of the Nile River, is commonly called Nubia . Nubia is notable for its long-term, dynamic relationship with ancient Egypt. Just as importantly, Nubia was also the site of an early civilization. The kingdoms of Kerma (c. 2400 BCE to 1500 BCE) and Kush (c. 1000 BCE to 300 CE) emerged along the Nile River. These kingdoms prospered especially due to their productive agriculture and the region’s copious natural resources. At certain points, both Kerma and Kush were strong enough to successfully invade Egypt. These kingdoms in Nubia also developed their own religious and cultural traditions, including a written script, Meroitic. While the people of this region, known collectively as Nubians, borrowed heavily from the Egyptians, Nubians also had distinctive practices that set their civilization apart from that of their northern neighbors.
Scholars generally link the origins of ancient Kerma (in present-day Sudan) back to the desiccation of the Sahara Desert and the rise of dynastic Egypt. Similarly to ancient Egypt, the drying out of the region encouraged people to move closer to the Nile River in the years between 5,000 and 4,000 BCE. Rock paintings, showing cattle in areas that have been desert for thousands of years, attest to the environmental changes in Nubia and also the development of a cattle culture that dates back to at least the fourth millennium BCE. Just as in Egypt, the desiccation of the Sahara desert drew together people from all directions. As people settled closer to the Nile River in Nubia, they brought their cattle, their agricultural traditions, and their languages, building settlements with higher population densities.
Additionally, Egyptian elites desired ivory, animal skins, incense, and other luxury goods prompting trade between Nubia and Egypt that pre-dated the unification of Egypt. With increased demand for luxury goods as social stratification grew, the Egyptians even ran military forays into Nubia. After unification, the Egyptians continued to invade Nubia to trade and raid for slaves and cattle. Likely, Nubian desires to control trade and protect themselves from Egyptian raids further compelled state formation in Nubia. Without Nubian records from the third millennium BCE, it is difficult to identify additional reasons why the state arose. However, archeological evidence does clearly indicate that by about 2400 BCE, Nubians had formed the Kingdom of Kerma between the third and fourth cataracts of the Nile River.
Kerma (c. 2400 BCE to c. 1500 BCE)
Kerma endured in Upper Nubia for almost a thousand years. The kingdom is named after its capital city at Kerma at the third cataract, but excavations at other sites (where similar pottery styles and burial sites have been found) suggest that at its height Kerma’s reach may have extended more than 200 miles southward past the fifth cataract of the Nile River. So far, archaeological evidence indicates that, with the exception of the capital and perhaps one or two other cities, most of the people in Kerma lived in smaller villages. They grew crops like barley, and kept goats, sheep, and cattle, sending tribute to their capital. The people of Kerma also developed industries, especially in mining, metalworking, and pottery. Kerma was linked interregionally through trade to its tributary villages, to dynastic Egypt, and to sub-Saharan Africa. Egyptian pharaohs and elites wanted the gold, copper, slaves, ivory, exotic animals, and more that they obtained from Kerma.
The people of Kerma also made use of their location on the Nile and proximity to Egypt as they imported textiles, jewelry, and other manufactured goods. Presumably, one reason that Nubian leaders built their ancient capital at Kerma was to oversee river trade. At the impassable cataract, boat owners unloaded their cargo and took it overland past the shallows and rocks before again proceeding on the water. This location at the cataract gave the leaders at Kerma the chance to tax, divert, and register goods being transported between Kerma and Egypt.
Agricultural surpluses and other tributary payments supported the rulers and elites of the capital. Archaeologists have shown that the capital had defenses, including ditches, ramparts, and massive walls with towers. There were also palaces within the city and on its outskirts. However, the most famous structure is the Western Deffufa (Figure \(\PageIndex{1}\)) made of mud-bricks, which likely served as a temple. Two other deffufa, large mud-brick structures with spaces for rituals on top, have been at least partially excavated within the vicinity of Kerma. Another notable archaeological find is the Eastern Cemetery, which lies a couple of miles to the east of the city. It served as the burial site for Kerma’s rulers for almost a thousand years and contains over 30,000 tombs. Some of the tombs were covered with large mounds. Demonstrating the cattle culture of the region, dozens of cattle skulls encircle a number of the tombs. Tombs also contain the remains of human sacrifices and other symbols of wealth and status, like jewelry made of gold and silver. The largest tomb found to date is 300 feet in diameter and covered with black granite, white quartz pebbles, and a marble top. Its interior burial suite contains semi-precious stones, bronze weapons, and lavish furniture. In the corridor leading into the underground burial site, archaeologists unearthed the remains of horses, dogs, and about 400 human sacrificial victims. The cattle skulls, mounds, and the remains of human sacrifices have led scholars to suggest that the Kerma elite had their own styles for monumental structures like the Western Deffufa and their tombs, even though they sometimes employed Egyptian artisans to complete the construction of these grand projects.
It appears that Kerma was strongest when neighboring Egypt was weak. As a case in point, during Egypt’s Second Intermediate Period, Kerma, at the height of its power, successfully invaded parts of Upper Egypt and established diplomatic relations with the occupying Hyksos. Once reunified during the New Kingdom, Egypt retaliated by conquering Kerma to the fourth cataract. Then, Egypt occupied Kerma for the next 500 years. During the Egyptian occupation, the elite classes of Kerma adopted many elements of Egyptian culture, including Egyptian gods, styles of dress, Hieroglyphics, and the Egyptian language. However, scholars believe that the Nubian masses retained their own distinctive identity with their local language and customs.
The Kingdom of Kush
As Egypt entered its Third Intermediate Period, Nubians gradually established their independence, eventually creating a new state, the Kingdom of Kush in the eighth century BCE. The initial capital of the Kingdom of Kush was Napata (c. 750 BCE to 593 BCE). From Napata, the Nubians took control of Upper Egypt, establishing the “Ethiopian Dynasty,” which ruled for 60 years from Thebes. Assyrian invasions destabilized the Nubian rulers in Thebes, causing the last pharaoh of the Ethiopian Dynasty to flee to Napata. Then, once strengthened, the Egyptians pushed back. The Egyptian army sacked Napata in 593 BCE and, in response, the Nubian rulers moved their capital farther south to Meroe. (See Map \(\PageIndex{1}\).) At this southern location, they further developed their civilization, which lasted until the fourth century CE.
With the new capital at Meroe , a location with well-watered farmland and some distance between it and Egypt, the Kingdom of Kush flourished. Meroe got more rainfall than Napata and was not as dependent on the Nile floods. Nubians were able to extend the areas under cultivation and grow a wider variety of crops, like cotton, sorghum, and millet. They were also able to easily graze their livestock and, as a result, during this period cattle became even more important as a symbol of their culture and wealth.
After moving the capital to Meroe, the culture of Kush showed more independence from Egypt as well. Particularly as Egypt’s power declined, the people of Kush put more emphasis on their own deities and pushed Egyptian gods to the background. For example, temples devoted to a Nubian war god, Apedamak, “the Lion of the South,” received more support and even used live lions for rituals. Gold had long been mined in the region and remained important while the people of Kush continued to develop additional industries. The area was rich in iron ore and the hardwoods used to make charcoal, which encouraged the growth of a booming iron industry. They made iron weapons and tools that they used for defense and to increase their crop yields. They were able to trade their agricultural surpluses, iron, cattle, and exotic things like elephants from sub-Saharan Africa, with Egypt, Greece, Rome, and India, bringing great wealth and prestige to Meroe. Also, the rulers of Meroe commissioned pyramids but had them built in a local style. As evident in Figure 2.14, their pyramids were smaller and had a unique shape. Kush burial practices were different than those used in dynastic Egypt, as corpses were not always mummified and were buried in the fetal position. Finally, a new locally-created written script, Meroitic , replaced the use of Egyptian Hieroglyphics by 300 BCE. Modern scholars have not yet translated Meroitic, and students of their culture will surely learn even more about the Kingdom of Kush once scholars have done so. As for now, we know that very productive agriculture, local rituals and burial practices, the growth of industries, social stratification facilitated by Meroe’s wealth and extensive trade networks, and the written script Meroitic, were some of the distinctive elements of the civilization at Kush.
While the Greeks and Romans occasionally sent raiding parties into Nubia, for a while, Meroe’s southern location helped isolate it from conquest. Legends also emphasize the strength of Meroe’s army and the physical prowess of its soldiers. Environmental changes, internal rivalries, and the rise of Axum (a new state to the East) likely all contributed to the fairly abrupt collapse of Meroe in the fourth century CE.
Egyptian sources were generally very derogatory in their portrayal of Nubians and even a few early twentieth century archaeologists carelessly (and incorrectly) identified these Nubian kingdoms as slave colonies of the Egyptians. However, the kingdoms of Kerma and Kush were known in the ancient world for their wealth and industries. The wealth garnered through productive agriculture and trade supported a ruling class, great artists, and monumental architecture. Egyptian culture was influential, but Nubians adapted Egyptian practices to meet their own needs and sensibilities. Often entangled with Egypt and sometimes defending themselves from other invaders as well, these two kingdoms persisted for hundreds of years, creating an independent civilization along the southern stretches of the Nile River.