3.8: The Healthy People Initiative-2030
- 103637
The Healthy People Initiative began in 1979 due to another landmark surgeon general report titled: “Healthy People: The Surgeon General’s Report on Health Promotion and Disease Prevention” (Office of Disease Prevention and Health Promotion, n.d.-a) Each decade, the initiative sets targets for improving different areas of public health, and measures these outcomes to see if those targets have been hit. The overarching goals have changed over the years, but most have included decreasing or eliminating health disparities, and promoting health for all across the lifespan. The latest iteration - Healthy People 2030 - emphasizes the social determinants of health, including: economic stability, education access and quality, healthcare access and quality, neighborhood and built environment, and social and community context (more on these in Chapter 8). There is also a new focus in the 2030 objectives of health literacy - the ability to find, understand and use information to make well-informed health decisions. An emphasis is also placed on the responsibility of health organizations to provide equitable access to health information and support its use in individual decision-making. The Healthy People 2030 website offers descriptions and the latest data on each health-related objective. (Office of Disease Prevention and Health Promotion, n.d.-b).


6.6: Choose and draw coordinate systems
After and while sketching the objects and forces, one or more relevant coordinate systems should be chosen. The choice of the coordinate system (CS) and its orientation is important, since a smart choice can significantly simplify the analysis. In most cases Cartesian coordinates are preferred. If you know the direction of a force (like the gravitational force or the contact force with the ground), it is often smart to align one of the coordinate axes with that force. Cylindrical coordinates are useful when objects rotate about a fixed rotation axis and \(t, n, b\) coordinates can be useful when point masses move along a constrained path, e.g. via a constraining rail object. In some cases a combination of coordinate systems can be used. In Figure 6.3 one can use Cartesian coordinates and align the \(y\)-axis with the gravitational acceleration vector, however one can also choose to use natural \(t, n, b\) coordinates with path coordinate \(s\). For demonstration, both are shown in the figure. It will become clear that in this situation \(t, n, b\) coordinates are easier to use \({ }^{2}\). After having chosen the CS it is drawn in the sketch with unit vectors according the guidelines from Sec. 3.3.


27.1: Voice Leading Seventh Chords
27.1 Voice Leading Seventh Chords
There is one general rule for voice leading any seventh chord: resolve the 7th of the chord down by step. All other voices should move smoothly to the nearest chord tone in a voicing containing the appropriate doubling.
Principle 27.1.1. 7th chords.
Resolve the 7th of a 7th chord down by step.
The one exception to this is in the progression II–VV34–II6, which closes the theme of the first movement of Mozart’s Piano Sonata K. 331.
In the example below, one can see that the 7th resolves up by step.
Notice that parallel fifths occur in this progression because of the upward resolution of the 7th. These parallel fifths may have been deemed less objectionable because they consist of unequal fifths (where one of the fifths is in a case of parallel fifths is diminished).


12.3: The Papyrus
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Here are the translations of the central fragments of the 3rd-century BCE papyrus letter (translation with minor changes from Renberg and Naether 2010): [In Greek]
P.Cairo
10328,
recto
...it also (?) seemed good to me that I should fully inform you about my dream, so that you will know in what ways the gods know you. I have written below in Egyptian so that you will know precisely (
aigyptisti de hypegrapsa, hopôs akribôs eidêis
). When I was about to go to sleep, I wrote two short letters, the one concerning Taunchis the daughter of Thermou- this and the other concerning Tetimouthis the daughter of Taues, who is the daughter of Ptolemaios, and yet one more...
P.Cairo
30961,
recto
...pour a drink for (or anoint) yourself, in which manner I too celebrated a fine (
kalên
) day.
Farewell. Year 2, Phaophi 26.
[
At this point in P.Cairo 30961 recto, Ptolemaios starts to write in Demotic
] I saw myself in a dream in the following way: I am standing at the doorway of the sanctuary. A priest is sitting there, and many people (
~remetch
) are standing beside him. The priest spoke to the people who were standing there: “...”
P.Cairo
30961,
verso
...I spoke [to the] aforementioned [prie]st: “The man of Pamoun – who is it?” He said: “It is Nebwotis”. See, the answer which they gave me: the man of Pamoun whom he named: “He is /That’s life”. He says: “Taunchis”, (and) she said to me: “The man of Pamoun, who is it?” He said, “Nebwotis is it, who has said it”. The one who is there says: “A woman is it outside giving to me...”
This letter has been dated to the 3 rd century BCE, and has been conjectured to be from the Fayum region, although the most recent editors have cast doubt on this provenance (Bagnall and Derow 2004; Goodspeed 1902; Renberg and Naether 2010; Spiegelberg 1908; Wilcken and von Mitteis 1912; Witkowski 1911). If it is indeed of a 3rd-century date, it must be late, due to the use of the reed pen for writing the Egyptian, which suggests a date after 230 BCE (Depauw 1997: 83). The question of interest for this papyrus is why Ptolemaios switches from Greek to Egyptian in order to describe his dream. He writes “I have written below in Egyptian, so that you may accurately understand”. But does this mean that Akhilles’ Greek was not proficient? As Wilcken and von Mitteis suggested a century ago, such a conclusion would be absurd, since if Ptolemaios had thought Akhilles’ knowledge of Greek was inadequate, he would not have written him a Greek letter in the first place (Wilcken and von Mitteis 1912: 74). It seems that the reason for the language shift must be due to something other than language competence. One could identify cultural reasons for the shift (e.g. that when bilinguals discuss religious topics in Ptolemaic Egypt, either in spoken or written form, they might tend toward using Egyptian rather than Greek). Or one might identify linguistic reasons (e.g. that in order to interpret a dream properly one must look to the words themselves — a style of dream interpretation found in both Greek and Egyptian dream-interpretation manuals). I consider such possibilities elsewhere (Kidd 2011). Here, however, rather than pursuing linguistic or religious reasons, I would like to consider the physical influences that were present when Ptolemaios made this language shift, especially regarding the scripts themselves and the material practice of writing these two scripts. Arguably, the material of the writing surface, the pens, and the ink were just as entangled in Ptolemaios’ experience of writing as the immaterial, conceptualized words and sounds, so it is worth considering the materials more closely in their own right. If Greek and Egyptian were generally written with different tools via different embodied practices, could these physical differences inform the language shift? Although language-shifts are generally conceived of as cerebral events, the motions of the hand, the materiality of the pens, and the application of ink on papyrus may also drive the transitions of language, not as passive accompaniments, but active agents. It is to these materials I now turn.


6.1: Composition
Mineralogy
Carbonate sedimentary rocks are dominated by the Ca 2 + , Mg 2 + and CO 3 2 - ions. Although there are many carbonate minerals, the four most important ones are:
Calcite (CaCO 3 ) is the more stable polymorph of calcium carbonate; its atoms are arranged into a rhombohedral architecture. Mg can substitute for up to 16% of Ca in calcite; specimens with <4% are referred to as low-Mg calcite and those with 4-16% are referred to as high-Mg calcite.
Under atmospheric temperatures and pressures, aragonite (CaCO 3 ) is a less stable polymorph of calcium carbonate and given time it will often turn into calcite. The atoms are arranged into an orthorhombic configuration. Many invertebrate shells that have the “mother of pearl” luster are composed of aragonite.
Dolomite (CaMg(CO 3 ) 2 ) has equal parts Ca and Mg and is thus a different mineral than high-Mg calcite which has a maximum of 16% Mg substituting in for Ca. Although extremely common in the geologic record, direct precipitation at the Earth’s surface is unlikely because it can only form at high temperature and/or under conditions where the Mg/Ca ratio greatly exceeds typical ocean chemistry (see Figure 6.3.1 ).
Siderite (FeCO 3 ) is common in reducing, freshwater conditions and is often nucleated around organic material that causes localized reduction. It is uncommon as an early formed mineral in marine environments because the iron will preferentially bond with the sulfur (and thus form pyrite) that is abundant in marine settings.
Calcite and aragonite seas
The crystal structure of aragonite does not allow Mg to substitute for Ca easily. Conversely, calcite allows Mg to readily substitute, but increased Mg concentrations make the calcite unstable. The end result is that when the ocean is relatively enriched in Mg (as is the case when there is rapid seafloor spreading), aragonite and high-Mg calcite become the most abundant types of inorganic carbonate in the oceans (“aragonite seas”). Conversely, “calcite seas” exist at times of low Mg concentration. However, most ancient aragonite transforms into calcite during diagenesis.
Carbonate Rocks
Rocks that are made up of >50% calcite/aragonite are classified as limestones and those with >50% dolomite are called dolomite (or dolostones). Although there are numerous other carbonate minerals, calcite, aragonite, and dolomite make up approximately 98% of them and are the most important ones for rocks names. Please also keep in mind that other minerals can occur in accessory amounts in carbonate rocks; quartz grains, chert, and glauconite are particularly common.


10.7: Prenatal Care
Once pregnancy is confirmed, it is advised to seek prenatal care to assess the physical condition of the mother and what to expect in the coming months. It is typical to begin prenatal care at approximately 8-10 weeks gestation, and pregnancy care should continue until approximately 6 weeks postpartum. The main purpose of the prenatal visits is to perform preventative medicine. Most complications in pregnancy are best treated if they are caught early. A series of tests will be performed throughout the pregnancy to judge the mother and fetus' well-being including:
- Mother's history
- Urine tests for glucose, protein, blood cells and infection
- The mother's weight
- Blood tests such as a complete blood count, HIV test, or the triple screen which is the test used most commonly to look for neural tube defects and Down's Syndrome.
- Physical examination
- Blood pressure
- Fetal heart monitoring
- Ultrasound scans
- Non-stress tests
Continuous care is the best way to ensure a healthy mother and baby.


3.E: Integers (Exercises)
3.1 - Introduction to Integers
Locate Positive and Negative Numbers on the Number Line
In the following exercises, locate and label the integer on the number line.
- 5
- −5
- −3
- 3
- −8
- −7
Order Positive and Negative Numbers
In the following exercises, order each of the following pairs of numbers, using < or >.
- 4__8
- −6__3
- −5__−10
- −9__−4
- 2__−7
- −3__1
Find Opposites
In the following exercises, find the opposite of each number.
- 6
- −2
- −4
- 3
In the following exercises, simplify.
- (a) −(8) (b) −(−8)
- (a) −(9) (b) −(−9)
In the following exercises, evaluate.
- −x, when (a) x = 32 (b) x = −32
- −n, when (a) n = 20 (b) n = −20
Simplify Absolute Values
In the following exercises, simplify.
- |−21|
- |−42|
- |36|
- −|15|
- |0|
- −|−75|
In the following exercises, evaluate.
- |x| when x = −14
- −|r| when r = 27
- −|−y| when y = 33
- |−n| when n = −4
In the following exercises, fill in <, >, or = for each of the following pairs of numbers.
- −|−4|__4
- −2__|−2|
- −|−6|__−6
- −|−9|__|−9|
In the following exercises, simplify.
- −(−55) and − |−55|
- −(−48) and − |−48|
- |12 − 5|
- |9 + 7|
- 6|−9|
- |14−8| − |−2|
- |9 − 3| − |5 − 12|
- 5 + 4|15 − 3|
Translate Phrases to Expressions with Integers
In the following exercises, translate each of the following phrases into expressions with positive or negative numbers.
- the opposite of 16
- the opposite of −8
- negative 3
- 19 minus negative 12
- a temperature of 10 below zero
- an elevation of 85 feet below sea level
3.2 - Add Integers
Model Addition of Integers
In the following exercises, model the following to find the sum.
- 3 + 7
- −2 + 6
- 5 + (−4)
- −3 + (−6)
Simplify Expressions with Integers
In the following exercises, simplify each expression.
- 14 + 82
- −33 + (−67)
- −75 + 25
- 54 + (−28)
- 11 + (−15) + 3
- −19 + (−42) + 12
- −3 + 6(−1 + 5)
- 10 + 4(−3 + 7)
Evaluate Variable Expressions with Integers
In the following exercises, evaluate each expression.
- n + 4 when (a) n = −1 (b) n = −20
- x + (−9) when (a) x = 3 (b) x = −3
- (x + y) 3 when x = −4, y = 1
- (u + v) 2 when u = −4, v = 11
Translate Word Phrases to Algebraic Expressions
In the following exercises, translate each phrase into an algebraic expression and then simplify.
- the sum of −8 and 2
- 4 more than −12
- 10 more than the sum of −5 and −6
- the sum of 3 and −5, increased by 18
Add Integers in Applications
In the following exercises, solve.
- Temperature On Monday, the high temperature in Denver was −4 degrees. Tuesday’s high temperature was 20 degrees more. What was the high temperature on Tuesday?
- Credit Frida owed $75 on her credit card. Then she charged $21 more. What was her new balance?
3.3 - Subtract Integers
Model Subtraction of Integers
In the following exercises, model the following.
- 6 − 1
- −4 − (−3)
- 2 − (−5)
- −1 − 4
Simplify Expressions with Integers
In the following exercises, simplify each expression.
- 24 − 16
- 19 − (−9)
- −31 − 7
- −40 − (−11)
- −52 − (−17) − 23
- 25 − (−3 − 9)
- (1 − 7) − (3 − 8)
- 3 2 − 7 2
Evaluate Variable Expressions with Integers
In the following exercises, evaluate each expression.
- x − 7 when (a) x = 5 (b) x = −4
- 10 − y when (a) y = 15 (b) y = −16
- 2n 2 − n + 5 when n = −4
- −15 − 3u 2 when u = −5
Translate Phrases to Algebraic Expressions
In the following exercises, translate each phrase into an algebraic expression and then simplify.
- the difference of −12 and 5
- subtract 23 from −50
Subtract Integers in Applications
In the following exercises, solve the given applications.
- Temperature One morning the temperature in Bangor, Maine was 18 degrees. By afternoon, it had dropped 20 degrees. What was the afternoon temperature?
- Temperature On January 4, the high temperature in Laredo, Texas was 78 degrees, and the high in Houlton, Maine was −28 degrees. What was the difference in temperature of Laredo and Houlton?
3.4 - Multiply and Divide Integers
Multiply Integers
In the following exercises, multiply.
- −9 • 4
- 5(−7)
- (−11)(−11)
- −1 • 6
Divide Integers
In the following exercises, divide.
- 56 ÷ (−8)
- −120 ÷ (−6)
- −96 ÷ 12
- 96 ÷ (−16)
- 45 ÷ (−1)
- −162 ÷ (−1)
Simplify Expressions with Integers
In the following exercises, simplify each expression.
- 5(−9) − 3(−12)
- (−2) 5
- −3 4
- (−3)(4)(−5)(−6)
- 42 − 4(6 − 9)
- (8 − 15)(9 − 3)
- −2(−18) ÷ 9
- 45 ÷ (−3) − 12
Evaluate Variable Expressions with Integers
In the following exercises, evaluate each expression.
- 7x − 3 when x = −9
- 16 − 2n when n = −8
- 5a + 8b when a = −2, b = −6
- x 2 + 5x + 4 when x = −3
Translate Word Phrases to Algebraic Expressions
In the following exercises, translate to an algebraic expression and simplify if possible.
- the product of −12 and 6
- the quotient of 3 and the sum of −7 and s
3.5 - Solve Equations using Integers; The Division Property of Equality
Determine Whether a Number is a Solution of an Equation
In the following exercises, determine whether each number is a solution of the given equation.
-
5x − 10 = −35
- x = −9
- x = −5
- x = 5
-
8u + 24 = −32
- u = −7
- u = −1
- u = 7
Using the Addition and Subtraction Properties of Equality
In the following exercises, solve.
- a + 14 = 2
- b − 9 = −15
- c + (−10) = −17
- d − (−6) = −26
Model the Division Property of Equality
In the following exercises, write the equation modeled by the envelopes and counters. Then solve it.
Solve Equations Using the Division Property of Equality
In the following exercises, solve each equation using the division property of equality and check the solution.
- 8p = 72
- −12q = 48
- −16r = −64
- −5s = −100
Translate to an Equation and Solve.
In the following exercises, translate and solve.
- The product of −6 and y is −42
- The difference of z and −13 is −18.
- Four more than m is −48.
- The product of −21 and n is 63.
Everyday Math
- Describe how you have used two topics from this chapter in your life outside of your math class during the past month.
PRACTICE TEST
- Locate and label 0, 2, −4, and −1 on a number line.
In the following exercises, compare the numbers, using < or > or =.
- (a) −6__3 (b) −1__−4
- (a) −5__|−5| (b) −|−2|__−2
In the following exercises, find the opposite of each number.
- (a) −7 (b) 8
In the following exercises, simplify.
- −(−22)
- |4 − 9|
- −8 + 6
- −15 + (−12)
- −7 − (−3)
- 10 − (5 − 6)
- −3 • 8
- −6(−9)
- 70 ÷ (−7)
- (−2) 3
- −4 2
- 16−3(5−7)
- |21 − 6| − |−8|
In the following exercises, evaluate.
- 35 − a when a = −4
- (−2r) 2 when r = 3
- 3m − 2n when m = 6, n = −8
- −|−y| when y = 17
In the following exercises, translate each phrase into an algebraic expression and then simplify, if possible.
- the difference of −7 and −4
- the quotient of 25 and the sum of m and n.
In the following exercises, solve.
- Early one morning, the temperature in Syracuse was −8°F. By noon, it had risen 12°. What was the temperature at noon?
- Collette owed $128 on her credit card. Then she charged $65. What was her new balance?
In the following exercises, solve.
- n + 6 = 5
- p − 11 = −4
- −9r = −54
In the following exercises, translate and solve.
- The product of 15 and x is 75.
- Eight less than y is −32.


8.18: Divisions of a Retail Business
- Name some key divisions of a retail business and the people who head them
Larger stores, such as national chains, will have multiple sectors where daily operations are handled. Depending on the retail organization, the exact terminology for each division and title held by each individual employee may vary but are typically similar in nature from store to store. “Titles demonstrate the importance of the business functions, either internally or externally.” [1] Executive, finance, operations and sales are integral parts of a large retail organizational structure. The executive level deals with preparation and planning. Finance would handle the bookkeeping and accounting aspects of the retail store. Sales, also called store operations, would be responsible for merchandising or customer service and regular procedures implemented within the store itself. Operations, also sometimes called regional operations consist of warehousing and transporting the merchandise.
Executive
As established in earlier this module, the CEO (or president) of a large retail company is the primary decision maker for the company. As with larger businesses the CEO reports to the shareholders and is the company’s principal decision maker. “Quick thinking, an ability to react swiftly to changing circumstances, knowing what to do immediately when faced with a challenging situation. What company can afford to have a CEO who does not fit that description?” [2] The executive division of a retail store will also consist of management and in the largest of companies’ corporate recruiters who are responsible for recruiting the top-level executives. These roles within a retail organization which handle planning and hiring are sometimes termed Central Operations. [3]
Finance
In many national chain and diversified retail markets the organizational structure may consist of a finance department. This department would house bookkeepers, accountants and sometimes tax attorneys who keep records of the financial dealings of a company. Accountants would record profit margins and losses as well as inventory costs. Tax attorneys would assist in financial planning, navigate complex tax codes and laws, handle disputes before the Internal Revenue Service (IRS) and oversee tax planning to legally minimize tax burdens. [4] Bookkeepers would also do a variety of tasks including print checks and keep track of employees’ hours in order to pay them their wages.
Operations and Sales
Operations consist of warehouse and distribution. A Warehouse Operations Manager might be one of the titles you would find in this sector of a retail organization. Not only do these types of managers oversee the housing and transport of merchandise but they also make decisions with regard to planning such as which software best functions for their warehouse operations. [5] Sales is another sector which deals with the day to day operations and functions of a retail store. In larger retail stores a Corporate Sales Manager (CSM) heads this division of a retail organization. CSM’s oversee the sales force which works within a retail business. These types of managers would spend time on the sales floor as well as behind the scenes in the office of a store.
-
Lee, H., & Scott, C. J. (2015). Marketing or sales: The executive decision.
The Journal of Business Strategy
, 36(5), 43–49.
↵
-
Meeks, M. D. (2015). STRATEGIC MANAGEMENT AND THE DISPARATE DUTIES OF THE CEO.
Academy of Strategic Management Journal
, 14(2), 93–116.
↵
-
https://study.com/academy/lesson/retail-organizational-structure-management-personnel-training.html
↵
-
Greenaway, T. D. (2015). Common threads and trends in tax.
The Tax Lawyer
, 68(2), 311–320.
↵
-
Faber, N., de Koster, M. B. M., & Smidts, A. (2013). Organizing warehouse management.
International Journal of Operations & Production Management
, 33(9), 1230–1256. doi:10.1108/IJOPM-12-2011-0471
↵
Contributors and Attributions
- Divisions of a Retail Business. Authored by : Freedom Learning Group. Provided by : Lumen Learning. License : CC BY: Attribution


5.5: Parentheses, Brackets, and Ellipses
- Demonstrate the proper use of parentheses, brackets, and ellipses
Parentheses
Interestingly, parentheses can do more than make smiley faces 🙂 and sad faces 🙁 like these. Although they are quite handy for these important emoticons, they serve an important function in formal writing as well.
Parentheses are used to set off information in a sentence that is important but not really a part of the main message. It’s important to remember that your sentence should make sense if you eliminate the parentheses and all that is contained between them.
Other punctuation marks used alongside parentheses need to take into account their context. If the parentheses enclose a full sentence beginning with a capital letter, then the end punctuation for the sentence falls inside the parentheses. For example:
Typically, suppliers specify air to cloth ratios of 6:1 or higher. (However, ratios of 4:1 should be used for applications involving silica or feldspathic minerals.)
If the parentheses indicate a citation at the end of a sentence, then the sentence’s end punctuation comes after the parentheses are closed:
In a study comparing three different building types, respirable dust concentrations were significantly lower in the open-structure building (Hugh et al., 2005).
Finally, if the parentheses appear in the midst of a sentence (as in this example), then any necessary punctuation (such as the comma that appeared just a few words ago) is delayed until the parentheses are closed.
You can also use parentheses to provide acronyms (or full names for acronyms). For example, “We use the MLA (Modern Language Association) style guide here” or “The Modern Language Association (MLA) style guide is my favorite to use.”
Remember, parentheses always appear in pairs. If you open a parenthesis, you need another to close it!
Note: In technical writing, there are additional rules for using parentheses, which can be more nuanced. While we won’t discuss those rules here, it’s important to bear their existence in mind, especially if you’re considering going into a more technical field.
You’ll probably use parentheses most often in your research papers because both APA and MLA formatting require in-text citations using parentheses. So right after a quote or any other borrowed information, you should include an in-text citation in parentheses, as illustrated in these examples:
- APA (Jones, 2011, p.131).
- MLA (Jones 131).
Brackets
Brackets are a fairly uncommon punctuation mark. Their main use is in quotations: they can be used to clarify quotes. For example, say you want to quote the following passage:
“I finally got to meet Trent today. I had a really great time with him. He was a lot taller than expected, though.”
However, you only want to relay the fact that Trent was taller than the speaker expected him to be. In order to do this, you would write the following: “[Trent] was a lot taller than expected.”
The brackets let the reader know that while the word Trent wasn’t in the original quote, his name was implied there. When using brackets, you need to be careful not to change the original meaning of the quote.
Another use of brackets is when there is a spelling or informational error in the original quote. For example, “Gabriel sat down on the river bank to fed [ sic ] the ducks.” (The term sic means that the typo was in the original source of this quote.)
Bracket Placement
See if you can correctly place the brackets in the following interactive.
https://lumenlearning.h5p.com/content/1290910655996694208/embed
Ellipses
An ellipsis (plural ellipses ) is a series of three periods, as you can see in the icon to the right.
As with most punctuation marks, there is some contention about its usage. The main point of contention is whether or not there should be a space between the periods (. . .) or not (…). MLA, APA, and Chicago , the most common style guides for students, support having spaces between the periods. Others you may encounter, such as in journalism, may not.
Quotes
Like the brackets we just learned about, you will primarily see ellipses used in quotes. They indicate a missing portion in a quote. Look at the following quote for an example:
Camarasaurus , with its more mechanically efficient skull, was capable of generating much stronger bite forces than Diplodocus . This suggests that Camarasaurus was capable of chomping through tougher plant material than Diplodocus , and was perhaps even capable of a greater degree of oral processing before digestion. This actually ties in nicely with previous hypotheses of different diets for each, which were based on apparent feeding heights and inferences made from wear marks on their fossilized teeth.
Diplodocus seems to have been well-adapted, despite its weaker skull, to a form of feeding known as branch stripping, where leaves are plucked from branches as the teeth are dragged along them. The increased flexibility of the neck of Diplodocus compared to other sauropods seems to support this too.
It’s a lengthy quote, and it contains more information than you want to include. Here’s how to cut it down:
Camarasaurus , with its more mechanically efficient skull, was capable of generating much stronger bite forces than Diplodocus . This suggests that Camarasaurus was capable of chomping through tougher plant material than Diplodocus. . . . This actually ties in nicely with previous hypotheses of different diets for each, which were based on apparent feeding heights and inferences made from wear marks on their fossilized teeth.
Diplodocus seems to have been well-adapted . . . to a form of feeding known as branch stripping, where leaves are plucked from branches as the teeth are dragged along them.
In the block quote above, you can see that the first ellipsis appears to have four dots. (“They are instantly recognized by their long, sweeping necks and whiplashed tails. . . .”) However, this is just a period followed by an ellipsis. This is because ellipses do not remove punctuation marks when the original punctuation still is in use; they are instead used in conjunction with original punctuation. This is true for all punctuation marks, including periods, commas, semi-colons, question marks, and exclamation points.
By looking at two sympatric species (those that lived together) from the fossil graveyards of the Late Jurassic of North America . . . , [David Button] tried to work out what the major dietary differences were between sauropod dinosaurs, based on their anatomy.
One of the best ways to check yourself is to take out the ellipsis. If the sentence or paragraph is still correctly punctuated, you’ve used the ellipsis correctly. (Just remember to put it back in!)
Quote the following passage, using ellipses to remove the bolded portions and using brackets for clarity where necessary.
 They are instantly recognized by their long, sweeping necks and whiplashed tails, and nearly always portrayed moving in herds, being stalked by hungry predators . In recent years, a huge amount of taxonomic effort from scientists has vastly increased the number of known species of sauropod. What we now know is that in many areas we had two or more species co-existing alongside each other. A question that arises from this, is how did we have animals that seem so similar, and with such high energy and dietary requirements, living alongside one another? Was there some sort of spinach-like super plant that gave them all Popeye-like physical boosts, or something more subtle?
[practice-area rows=”6″][/practice-area]
[reveal-answer q=”3662″]Show Answer[/reveal-answer]
[hidden-answer a=”3662″]The first ellipsis should follow a period, and the second should follow a comma. There are a couple of phrases that could be used in brackets, but we’ve chosen the phrase “research has shown.”
 They are instantly recognized by their long, sweeping necks and whiplashed tails. . . . In recent years, . . . [research has shown] that in many areas we had two or more species co-existing alongside each other. A question that arises from this, is how did we have animals that seem so similar, and with such high energy and dietary requirements, living alongside one another?
[/hidden-answer]
This is a part of Martin Luther King’s famous “I Have a Dream” speech from the March on Washington for Jobs and Freedom in 1963. Quote part of the following passage, using ellipses to remove the bolded passage and making sure that you use the appropriate punctuation surrounding it:
I have a dream that one day on the red hills of Georgia, the sons of former slaves and the sons of former slave owners will be able to sit down together at the table of brotherhood. I have a dream that one day even the state of Mississippi, a state sweltering with the heat of injustice, sweltering with the heat of oppression, will be transformed into an oasis of freedom and justice. I have a dream that my four little children will one day live in a nation where they will not be judged by the color of their skin but by the content of their character. I have a dream today.  I have a dream today.
[reveal-answer q=”713549″]Show Answer[/reveal-answer]
[hidden-answer a=”713549″]The first ellipses should NOT follow the comma, because the phrases that were removed make the comma meaningless. The second ellipses should follow the period. The third ellipses should follow the comma.
“I have a dream that one day on the red hills of Georgia, the sons of former slaves and the sons of former slave owners will be able to sit down together at the table of brotherhood. I have a dream that one day even the state of Mississippi . . . will be transformed into an oasis of freedom and justice. I have a dream that my four little children will one day live in a nation where they will not be judged by the color of their skin but by the content of their character. . . .  I have a dream today.”
[/hidden-answer]
The ellipsis can also indicate . . . a pause. This use is typically informal, and is only be used in casual correspondence (e.g., emails to friends, posts on social media, texting) or in literature. Because this use occurs in literature, you may find yourself quoting a passage that already has an ellipsis in it. For example, look at this passage spoken by Lady Bracknell, in The Importance of Being Ernest .
Well, I must say, Algernon, that I think it is high time that Mr. Bunbury made up his mind whether he was going to live or to die. This shilly-shallying with the question is absurd. Nor do I in any way approve of the modern sympathy with invalids. I consider it morbid. Illness of any kind is hardly a thing to be encouraged in others. Health is the primary duty of life. I am always telling that to your poor uncle, but he never seems to take much notice . . . as far as any improvement in his ailment goes. I should be much obliged if you would ask Mr. Bunbury, from me, to be kind enough not to have a relapse on Saturday, for I rely on you to arrange my music for me. It is my last reception, and one wants something that will encourage conversation, particularly at the end of the season when every one has practically said whatever they had to say, which, in most cases, was probably not much.
If you were to quote the passage, it may appear that something has been removed from the quote. So how can we indicate that this is not the case? If you think back to the bracket rules we just discussed, you may remember that [ sic ] can be used to show that an error was in the original. In a similar practice, we can enclose the ellipsis in brackets to show it appeared in the original work:
Well, I must say, Algernon, that I think it is high time that Mr. Bunbury made up his mind whether he was going to live or to die. This shilly-shallying with the question is absurd. Nor do I in any way approve of the modern sympathy with invalids. I consider it morbid. Illness of any kind is hardly a thing to be encouraged in others. Health is the primary duty of life. I am always telling that to your poor uncle, but he never seems to take much notice [. . .] as far as any improvement in his ailment goes. I should be much obliged if you would ask Mr. Bunbury, from me, to be kind enough not to have a relapse on Saturday, for I rely on you to arrange my music for me. It is my last reception, and one wants something that will encourage conversation, particularly at the end of the season when every one has practically said whatever they had to say, which, in most cases, was probably not much.
Contributors and Attributions
- Revision and Adaptation. Provided by : Lumen Learning. License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike
- Parentheses Practice. Provided by : Lumen Learning. License : CC BY: Attribution
- Text: Brackets. Provided by : Lumen Learning. License : CC BY: Attribution
- Modification of Mount Vesuvius (errors added). Provided by : Wikipedia. Located at : https://en.Wikipedia.org/wiki/Mount_Vesuvius . License : CC BY-SA: Attribution-ShareAlike
- Text: Ellipses. Provided by : Lumen Learning. License : CC BY: Attribution
- Style For Students Online. Authored by : Joe Schall. Provided by : The Pennsylvania State University. Located at : https://www.e-education.psu.edu/styleforstudents/ . Project : Penn State's College of Earth and Mineral Sciences' OER Initiative. License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike
- Modification of They might be giants, but how could they live with each other?. Authored by : Jon Tennant. Provided by : European Geosciences Union. Located at : http://blogs.egu.eu/network/palaeoblog/2015/03/05/they-might-be-giants-but-how-could-they-live-with-each-other . Project : Green Tea and Velociraptors. License : CC BY: Attribution
- Brackets Activity. Authored by : Excelsior OWL. Located at : https://owl.excelsior.edu/grammar-essentials/punctuation/brackets/brackets-try-it-out/ . License : CC BY: Attribution
- Introduction to Parentheses. Authored by : Excelsior OWL. Located at : https://owl.excelsior.edu/grammar-essentials/punctuation/parentheses/ . License : CC BY: Attribution
- The Importance of Being Earnest. Authored by : Oscar Wilde. Located at : https://www.gutenberg.org/ebooks/844 . Project : Project Gutenberg. License : Public Domain: No Known Copyright


10.2: Introduction to The Americas
Generally, historians have promoted different ideas as to how the Americas became population.
- A land migration over Beringia (via a land bridge that would have separated modern-day Russia and Alaska in the United States)
- A seaborne migration from Asia
- A “Solutrean” migration from Europe ten thousand years before an ice-free corridor opened up in North America
In this chapter, our task is to admire pre-Columbian history. In a little over 15,000 years, migrants from Asia (probably) populated the Americas by foot, built hundreds of major cities, supported a population in the tens of millions, and constructed two of the most impressive empires the world has ever known. Fortunately, recent advances in archaeology and calendrics have helped us uncover much of this past.


22.5: Additional Exercises- Error Correction for BCH Codes
BCH codes have very attractive error correction algorithms. Let \(C\) be a BCH code in \(R_n\text{,}\) and suppose that a code polynomial \(c(t) = c_0 + c_1 t + \cdots + c_{n-1} t^{n-1}\) is transmitted. Let \(w(t) = w_0 + w_1 t + \cdots w_{n-1} t^{n-1}\) be the polynomial in \(R_n\) that is received. If errors have occurred in bits \(a_1, \ldots, a_k\text{,}\) then \(w(t) = c(t) + e(t)\text{,}\) where \(e(t) = t^{a_1} + t^{a_2} + \cdots + t^{a_k}\) is the error polynomial . The decoder must determine the integers \(a_i\) and then recover \(c(t)\) from \(w(t)\) by flipping the \(a_i\)th bit. From \(w(t)\) we can compute \(w( \omega^i ) = s_i\) for \(i = 1, \ldots, 2r\text{,}\) where \(\omega\) is a primitive \(n\)th root of unity over \({\mathbb Z}_2\text{.}\) We say the syndrome of \(w(t)\) is \(s_1, \ldots, s_{2r}\text{.}\)
Show that \(w(t)\) is a code polynomial if and only if \(s_i = 0\) for all \(i\text{.}\)
Show that
\[ s_i = w( \omega^i) = e( \omega^i) = \omega^{i a_1} + \omega^{i a_2} + \cdots + \omega^{i a_k} \nonumber \]
for \(i = 1, \ldots, 2r\text{.}\) The error-locator polynomial is defined to be
\[ s(x) = (x + \omega^{a_1})(x + \omega^{a_2}) \cdots (x + \omega^{a_k})\text{.} \nonumber \]
Recall the \((15,7)\)-block BCH code in Example \(22.19\). By Theorem \(8.13\), this code is capable of correcting two errors. Suppose that these errors occur in bits \(a_1\) and \(a_2\text{.}\) The error-locator polynomial is \(s(x) = (x + \omega^{a_1})(x + \omega^{a_2})\text{.}\) Show that
\[ s(x) = x^2 + s_1 x + \left( s_1^2 + \frac{s_3}{s_1} \right)\text{.} \nonumber \]
Let \(w(t) = 1 + t^2 +t^4 + t^5 + t^7 + t^{12} + t^{13}\text{.}\) Determine what the originally transmitted code polynomial was.


1.6: Anatomical Terminology
By the end of the section, you will be able to:
- Demonstrate the anatomical position
- Describe the human body using directional and regional terms
- Identify three planes most commonly used in the study of anatomy
- Distinguish between the posterior (dorsal) and anterior (ventral) body cavities, identifying their subdivisions and representative organs found in each
- Describe a serous membrane and explain its function
Anatomists and health care providers use terminology that can be bewildering to the uninitiated. However, the purpose of this language is not to confuse, but rather to increase precision and reduce medical errors. For example, is a scar “above the wrist” located on the forearm two or three inches away from the hand? Or is it at the base of the hand? Is it on the palm-side or back-side? By using precise anatomical terminology, we eliminate ambiguity. Anatomical terms derive from ancient Greek and Latin words. Because these languages are no longer used in everyday conversation, the meaning of their words does not change.
Anatomical terms are made up of roots, prefixes, and suffixes. The root of a term often refers to an organ, tissue, or condition, whereas the prefix or suffix often describes the root. For example, in the disorder hypertension, the prefix “hyper-” means “high” or “over,” and the root word “tension” refers to pressure, so the word “hypertension” refers to abnormally high blood pressure.
Anatomical Position
To further increase precision, anatomists standardize the way in which they view the body. Just as maps are normally oriented with north at the top, the standard body “map,” or anatomical position , is that of the body standing upright, with the feet at shoulder width and parallel, toes forward. The upper limbs are held out to each side, and the palms of the hands face forward as illustrated in Figure \(\PageIndex{1}\). Using this standard position reduces confusion. It does not matter how the body being described is oriented, the terms are used as if it is in anatomical position. For example, a scar in the “anterior (front) carpal (wrist) region” would be present on the palm side of the wrist. The term “anterior” would be used even if the hand were palm down on a table.
A body that is lying down is described as either prone or supine. Prone describes a face-down orientation, and supine describes a face up orientation. These terms are sometimes used in describing the position of the body during specific physical examinations or surgical procedures.
Regional Terms
The human body’s numerous regions have specific terms to help increase precision. Figure \(\PageIndex{1}\) has labeled each region with the correct anatomical term (seen in bold), while also listing the common name of the region. Additionally, the adjective form of the regional term is listed in parenthesis. Keep in mind that in the study of human anatomy, it is the bold terms listed in the figure that are used. Notice that the term “brachium” is reserved for the “upper arm” and “antebrachium” is used rather than “lower arm.” Similarly, “femur” designates the upper portion of the lower limb and “crus” is reserved for the portion of the lower limb between the knee and the ankle. You will be able to describe the body’s regions using the terms from the figure.
Directional Terms
Certain directional anatomical terms appear throughout this and any other anatomy textbook (Figure \(\PageIndex{2}\)). These terms are essential for describing the relative locations of different body structures. For instance, an anatomist might describe one band of tissue as “inferior to” another or a physician might describe a tumor as “superficial to” a deeper body structure. Commit these terms to memory to avoid confusion when you are studying or describing the locations of particular body parts.
- Anterior (or ventral ) describes the front or direction toward the front of the body. The toes are anterior to the foot.
- Posterior (or dorsal ) describes the back or direction toward the back of the body. The popliteus is posterior to the patella.
- Superior (or cranial ) describes a position above or higher than another part of the body proper. The orbits are superior to the oris.
- Inferior (or caudal ) describes a position below or lower than another part of the body proper; near or toward the tail (in humans, the coccyx, or lowest part of the spinal column). The pelvis is inferior to the abdomen.
- Lateral describes the side or direction toward the side of the body. The pollex (thumb) is lateral to the digits.
- Medial describes the middle or direction toward the middle of the body. The hallux (big toe) is the medial toe.
- Proximal describes a position in a limb that is nearer to the point of attachment or the trunk of the body. The brachium is proximal to the antebrachium.
- Distal describes a position in a limb that is farther from the point of attachment or the trunk of the body. The crus is distal to the femur.
- Superficial describes a position closer to the surface of the body. The skin is superficial to the bones.
- Deep describes a position farther from the surface of the body. The brain is deep to the skull.
Body Planes
A section is a two-dimensional surface of a three-dimensional structure that has been cut. Modern medical imaging devices enable clinicians to obtain “virtual sections” of living bodies. We call these scans. Body sections and scans can be correctly interpreted, however, only if the viewer understands the plane along which the section was made. A plane is an imaginary two-dimensional surface that passes through the body. There are three planes commonly referred to in anatomy and medicine, as illustrated in Figure \(\PageIndex{3.a,b}\).
- The sagittal plane is the plane that divides the body or an organ vertically into right and left sides. If this vertical plane runs directly down the middle of the body, it is called the midsagittal or median plane. If it divides the body into unequal right and left sides, it is called a parasagittal plane or less commonly a longitudinal section.
- The frontal plane is the plane that divides the body or an organ vertically into an anterior (front) portion and a posterior (rear) portion. The frontal plane is also referred to as a coronal plane. (“Corona” is Latin for “crown.”)
- The transverse plane is the plane that divides the body or organ horizontally into upper and lower portions. Transverse planes produce images referred to as cross sections.
Body Cavities and Serous Membranes
The body maintains its internal organization by means of membranes, sheaths, and other structures that separate compartments. The dorsal (posterior) cavity and the ventral (anterior) cavity are the largest body compartments (Figure \(\PageIndex{4}\)). These cavities contain and protect delicate internal organs, and the ventral cavity allows for significant changes in the size and shape of the organs as they perform their functions. The lungs, heart, stomach, and intestines, for example, can expand and contract without distorting other tissues or disrupting the activity of nearby organs.
Subdivisions of the Posterior (Dorsal) and Anterior (Ventral) Cavities
The posterior (dorsal) and anterior (ventral) cavities are each subdivided into smaller cavities. In the posterior (dorsal) cavity, the cranial cavity houses the brain, and the spinal cavity (or vertebral cavity) encloses the spinal cord. Just as the brain and spinal cord make up a continuous, uninterrupted structure, the cranial and spinal cavities that house them are also continuous.
The anterior (ventral) cavity has two main subdivisions: the thoracic cavity and the abdominopelvic cavity (see Figure \(\PageIndex{4}\)). The thoracic cavity is the more superior subdivision of the anterior cavity, and it is enclosed by the rib cage. It contains the pleural cavities, which house the lungs, and the mediastinum, the space between the lungs in the thoracic cavity. The mediastinum has a superior portion, which contains the trachea and esophagus, and an inferior portion containing the pericardial cavity, which surrounds the heart. The diaphragm forms the floor of the thoracic cavity and separates it from the more inferior abdominopelvic cavity. The abdominopelvic cavity is the largest cavity in the body. Although no membrane physically divides the abdominopelvic cavity into more specific compartments, it can be useful to distinguish between the abdominal cavity, the division that houses the digestive organs, and the pelvic cavity, the division that houses the organs of reproduction.
Abdominal Regions and Quadrants
To promote clear communication, for instance about the location of a patient’s abdominal pain or a suspicious mass, health care providers typically divide up the cavity into either nine regions or four quadrants (Figure \(\PageIndex{5}\)).
The more detailed regional approach subdivides the cavity with one horizontal line immediately inferior to the ribs and one immediately superior to the pelvis, and two vertical lines drawn as if dropped from the midpoint of each clavicle (collarbone). There are nine resulting regions:
- Right hypochondriac region containing a portion of liver.
- Right lumbar region containing the ascending colon and a portion of the small intestine.
- Right iliac region containing the appendix, the cecum and a portion of the small intestine.
- Epigastric region containing the pancreas, gall bladder, and portions of the stomach and liver.
- Umbilical region containing the transverse colon and a portion of the small intestine.
- Hypogastric region containing a portion of the small intestine and the bladder.
- Left hypochondriac region containing the spleen and portion of the stomach
- Left lumbar region containing the descending colon and a portion of the small intestine.
- Left iliac region containing the sigmoid colon and a portion of the small intestine.
The simpler quadrants approach, which is more commonly used in medicine, subdivides the cavity with one horizontal and one vertical line that intersect at the patient’s umbilicus (navel). This results in four quadrants:
- Right upper quadrant (RUQ) containing the right lobe of liver, the gall bladder, the duodenum, head of the pancreas, the right kidney and adrenal gland, portions of the colon.
- Right lower quadrant (RLQ) containing the cecum, the appendix, the ascending colon, and the right ureter.
- Left upper quadrant (LUQ) containing the stomach, the spleen, left lobe of the liver, body of the pancreas, the left kidney and adrenal gland, and portions of the colon.
- Left lower quadrant (LLQ) containing the descending colon, the sigmoid colon, portions of the small intestine, and the left ureter.
Membranes of the Anterior (Ventral) Body Cavity
A serous membrane (also referred to a serosa) is one of the thin membranes that cover the walls and organs in the thoracic and abdominopelvic cavities. The parietal layers of the membranes line the walls of the body cavity (pariet- refers to a cavity wall). The visceral layer of the membrane covers the organs (the viscera). Between the parietal and visceral layers is a very thin, fluid-filled serous space, or cavity (Figure \(\PageIndex{6}\)).
There are three serous cavities and their associated membranes. The pleura is the serous membrane that surrounds the lungs in the pleural cavity; the pericardium is the serous membrane that surrounds the heart in the pericardial cavity; and the peritoneum is the serous membrane that surrounds several organs in the abdominopelvic cavity. The serous fluid produced by the serous membranes reduces friction between the walls of the cavities and the internal organs when they move, such as when the lungs inflate or the heart beats. Both the parietal and visceral serosa secrete the thin, slippery serous fluid that prevents friction when an organ slides past the walls of a cavity. In the pleural cavities, pleural fluid prevents friction between the lungs and the walls of the cavity. In the pericardial sac, pericardial fluid prevents friction between the heart and the walls of the pericardial sac. And in the peritoneal cavity, peritoneal fluid prevents friction between abdominal and pelvic organs and the wall of the cavity. The serous membranes therefore provide additional protection to the viscera they enclose by reducing friction that could lead to inflammation of the organs.
Concept Review
A standard reference position for mapping the body’s structures is the normal anatomical position. Regions of the body are identified using terms such as “occipital” that are more precise than common words and phrases such as “the back of the head.” Directional terms such as anterior and posterior are essential for accurately describing the relative locations of body structures. Images of the body’s interior commonly align along one of three planes: the sagittal, frontal, or transverse. The body’s organs are organized in one of two main cavities — dorsal and ventral — which are further sub-divided according to the structures present in each area. The serous membranes have two layers — parietal and visceral — surrounding a fluid filled space. Serous membranes cover the lungs (pleural serosa), heart (pericardial serosa), and some abdominopelvic organs (peritoneal serosa).
Review Questions
Q. What is the position of the body when it is in the “normal anatomical position?”
A. The person is prone with upper limbs, including palms, touching sides and lower limbs touching at sides.
B. The person is standing facing the observer, with upper limbs extended out at a ninety-degree angle from the torso and lower limbs in a wide stance with feet pointing laterally
C. The person is supine with upper limbs, including palms, touching sides and lower limbs touching at sides.
D. None of the above
- Answer
-
Answer: D
Q. To make a banana split, you halve a banana into two long, thin, right and left sides along the ________.
A. coronal plane
B. longitudinal plane
C. midsagittal plane
D. transverse plane
- Answer
-
Answer: C
Q. The epigastric region is ________.
A. inferior to the hypogastric region
B. inferior to the right hypochondriac region
C. superior to the hypogastric region
D. superior to the left hypochondriac region
- Answer
-
Answer: C
Q. The heart is within the ________.
A. cranial cavity
B. mediastinum
C. posterior (dorsal) cavity
D. All of the above
- Answer
-
Answer: B
Critical Thinking Question
Q. If a bullet were to penetrate a lung, which three anterior thoracic body cavities would it enter, and which layer of the serous membrane would it encounter first?
- Answer
-
A. The bullet would enter the ventral, thoracic, and pleural cavities, and it would encounter the parietal layer of serous membrane first.
Glossary
- abdominopelvic cavity
- division of the anterior (ventral) cavity that houses the abdominal and pelvic viscera
- anatomical position
- standard reference position used for describing locations and directions on the human body
- anterior
- describes the front or direction toward the front of the body; also referred to as ventral
- anterior cavity
- larger body cavity located anterior to the posterior (dorsal) body cavity; includes the serous membrane-lined pleural cavities for the lungs, pericardial cavity for the heart, and peritoneal cavity for the abdominal and pelvic organs; also referred to as ventral cavity
- caudal
- describes a position below or lower than another part of the body proper; near or toward the tail (in humans, the coccyx, or lowest part of the spinal column); also referred to as inferior
- cranial
- describes a position above or higher than another part of the body proper; also referred to as superior
- cranial cavity
- division of the posterior (dorsal) cavity that houses the brain
- deep
- describes a position farther from the surface of the body
- distal
- describes a position farther from the point of attachment or the trunk of the body
- dorsal
- describes the back or direction toward the back of the body; also referred to as posterior
- dorsal cavity
- posterior body cavity that houses the brain and spinal cord; also referred to the posterior body cavity
- frontal plane
- two-dimensional, vertical plane that divides the body or organ into anterior and posterior portions
- inferior
- describes a position below or lower than another part of the body proper; near or toward the tail (in humans, the coccyx, or lowest part of the spinal column); also referred to as caudal
- lateral
- describes the side or direction toward the side of the body
- medial
- describes the middle or direction toward the middle of the body
- pericardium
- sac that encloses the heart
- peritoneum
- serous membrane that lines the abdominopelvic cavity and covers the organs found there
- plane
- imaginary two-dimensional surface that passes through the body
- pleura
- serous membrane that lines the pleural cavity and covers the lungs
- posterior
- describes the back or direction toward the back of the body; also referred to as dorsal
- posterior cavity
- posterior body cavity that houses the brain and spinal cord; also referred to as dorsal cavity
- prone
- face down
- proximal
- describes a position nearer to the point of attachment or the trunk of the body
- sagittal plane
- two-dimensional, vertical plane that divides the body or organ into right and left sides
- section
- in anatomy, a single flat surface of a three-dimensional structure that has been cut through
- serous membrane
- membrane that covers organs and reduces friction; also referred to as serosa
- serosa
- membrane that covers organs and reduces friction; also referred to as serous membrane
- spinal cavity
- division of the dorsal cavity that houses the spinal cord; also referred to as vertebral cavity
- superficial
- describes a position nearer to the surface of the body
- superior
- describes a position above or higher than another part of the body proper; also referred to as cranial
- supine
- face up
- thoracic cavity
- division of the anterior (ventral) cavity that houses the heart, lungs, esophagus, and trachea
- transverse plane
- two-dimensional, horizontal plane that divides the body or organ into superior and inferior portions
- ventral
- describes the front or direction toward the front of the body; also referred to as anterior
- ventral cavity
- larger body cavity located anterior to the posterior (dorsal) body cavity; includes the serous membrane-lined pleural cavities for the lungs, pericardial cavity for the heart, and peritoneal cavity for the abdominal and pelvic organs; also referred to as anterior body cavity
Contributors and Attributions
-
OpenStax Anatomy & Physiology (CC BY 4.0). Access for free at https://openstax.org/books/anatomy-and-physiology


17.5: Appendix E to Applied Probability - Properties of Mathematical Expectation
\[E[g(X)] = \int g(X)\ dP \nonumber\]
We suppose, without repeated assertion, that the random variables and Borel functions of random variables or random vectors are integrable. Use of an expression such as \(I_M (X)\) involves the tacit assumption that \(M\) is a Borel set on the codomain of \(X\).
(E1): \(E[aI_A] = aP(A)\), any constant \(a\), any event \(A\)
(E1a): \(E[I_M (X)] = P(X \in M)\) and \(E[I_M (X) I_N (Y)] - P(X \in M, Y \in N)\) for any Borel sets \(M, N\) (Extends to any finite product of such indicator functions of random vectors)
(E2):
Linearity
. For any constants \(a, b\), \(E[aX + bY) = aE[X] + bE[Y]\) (Extends to any finite linear combination)
(E3):
Positivity; monotonicity.
a. \(X \ge 0\) a.s. implies \(E[X] \ge 0\), with equality iff \(X = 0\) a.s.
b. \(X \ge Y\) a.s. implies \(E[X] \ge E[Y]\), with equality iff \(X = Y\) a.s.
(E4):
Fundamental lemma
. If \(X \ge 0\) is bounded, and \(\{X_n: 1 \le n\}\) is a.s. nonnegative, nondecreasing, with \(\text{lim}_n X_n (\omega) \ge X(\omega)\) for a.e. \(\omega\), then \(\text{lim}_n E[X_n] \ge E[X]\)
(E4a):
Monotone convergence
. If for all \(n\), \(0 \le X_n \le X_{n + 1}\) a.s. and \(X_n \to X\) a.s.,then \(E[X_n] \to E[X]\) (The theorem also holds if \(E[X] = \infty\))
******
(E5):
Uniqueness
. * is to be read as one of the symbols \(\le, =\), or \(\ge\)
a. \(E[I_M(X) g(X)]\) * \(E[I_M(X) h(X)]\) for all \(M\) iff \(g(X)\) * \(h(X)\) a.s.
b. \(E[I_M(X) I_N (Z) g(X, Z)] = E[I_M (X) I_N (Z) h(X,Z)]\) for all \(M, N\) iff \(g(X, Z) = h(X, Z)\) a.s.
(E6): Fatou's lemma. If \(X_n \ge 0\) a.s., for all \(n\), then \(E[ \text{lim inf } X_n] \le [\text{lim inf } E[X_n]\)
(E7): Dominated convergence. If real or complex \(X_n \to X\) a.s., \(|X_n| \le Y\) a.s. for all \(n\), and \(Y\) is integrable, then \(\text{lim}_n E[X_n] = E[X]\)
(E8):
Countable additivity and countable sums
.
a. If \(X\) is integrable over \(E\), and \(E = \bigvee_{i = 1}^{\infty} E_i\) (disjoint union), then \(E[I_E X] = \sum_{i = 1}^{\infty} E[I_{E_i} X]\)
b. If \(\sum_{n = 1}^{\infty} E[|X_n|] < \infty\), then \(\sum_{n = 1}^{\infty} |X_n| < \infty\), a.s. and \(E[\sum_{n = 1}^{\infty} X_n] = \sum_{n = 1}^{\infty} E[X_n]\)
(E9):
Some integrability conditions
a. \(X\) is integrable iff both \(X^{+}\) and \(X^{-}\) are integrable iff \(|X|\) is integrable.
b. \(X\) is integrable iff \(E[I_{\{|X| > a\}} |X|] \to 0\) as \(a \to \infty\)
c. If \(X\) is integrable, then \(X\) is a.s. finite
d. If \(E[X]\) exists and \(P(A) = 0\), then \(E[I_A X] = 0\)
(E10):
Triangle inequality
. For integrable \(X\), real or complex, \(|E[X]| \le E[|X|]\)
(E11):
Mean-value theorem
. If \(a \le X \le b\) a.s. on \(A\), then \(aP(A) \le E[I_A X] \le bP(A)\)
(E12): For nonnegative, Borel \(g\), \(E[g(X)] \ge aP(g(X) \ge a)\)
(E13):
Markov's inequality
. If \(g \ge 0\) and nondecreasing for \(t \ge 0\) and \(a \ge 0\), then
\(g(a)P(|X| \ge a) \le E[g(|X|)]\)
(E14):
Jensen's inequality
. If \(g\) is convex on an interval which contains the range of random variable \(X\), then \(g(E[X]) \le E[g(X)]\)
(E15):
Schwarz' inequality
. For \(X, Y\) real or complex, \(|E[XY]|^2 \le E[|X|^2] E[|Y|^2]\), with equality iff there is a constant \(c\) such that \(X = cY\) a.s.
(E16):
Hölder's inequality
. For \(1 \le p, q\), with \(\dfrac{1}{p} + \dfrac{1}{q} = 1\), and \(X, Y\) real or complex.
\(E[|XY|] \le E[|X|^p]^{1/p} E[|Y|^q]^{1/q}\)
(E17): Hölder's inequality . For \(1 < p\) and \(X, Y\) real or complex,
\(E[|X + Y|^p]^{1/p} \le E[|X|^p]^{1/p} + E[|Y|^p]^{1/p}\)
(E18):
Independence and expectation
. The following conditions are equivalent.
a. The pair \(\{X, Y\}\) is independent
b. \(E[I_M (X) I_N (Y)] = E[I_M (X)] E[I_N (Y)]\) for all Borel \(M, N\)
c. \(E[g(X)h(Y)] = E[g(X)] E[h(Y)]\) for all Borel \(g, h\) such that \(g(X)\), \(h(Y)\) are integrable.
(E19):
Special case of the Radon-Nikodym theorem
If \(g(Y)\) is integrable and \(X\) is a random vector, then there exists a real-valued Borel function \(e(\cdot)\), defined on the range of \(X\), unique a.s. \([P_X]\), such that \(E[I_M(X) g(X)] = E[I_M (X) e(X)]\) for all Borel sets \(M\) on the codomain of \(X\).
(E20):
Some special forms of expectation
a. Suppose \(F\) is nondecreasing, right-continuous on \([0, \infty)\), with \(F(0^{-}) = 0\). Let \(F^{*} (t) = F(t - 0)\). Consider \(X \ge 0\) with \(E[F(X)] < \infty\). Then,
(1) \(E[F(X)] = \int_{0}^{\infty} P(X \ge t) F\ (dt)\) and (2) \(E[F^{*} (X)] = \int_{0}^{\infty} P(X > t) F\ (dt)\)
b. If \(X\) is integrable, then \(E[X] = \int_{-\infty}^{\infty} [u(t) - F_X (t)]\ dt\)
c. If \(X, Y\) are integrable, then \(E[X - Y] = \int_{-\infty}^{\infty} [F_Y (t) - F_X (t)]\ dt\)
d. if \(X \ge 0\) is integrable, then
\(\sum_{n = 0}^{\infty} P(X \ge n + 1) \le E[X] \le \sum_{n = 0}^{\infty} P(X \ge n) \le N \sum_{k = 0}^{\infty} P(X \ge kN)\), for all \(N \ge 1\)
e. If integrable \(X \ge 0\) is integer-valued, then
\(E[X] = \sum_{n = 1}^{\infty} P(X \ge n) = \sum_{n = 0}^{\infty} P(X > n) E[X^2] = \sum_{n = 1}^{\infty} (2n - 1) P(X \ge n) = \sum_{n = 0}^{\infty} (2n + 1) P(X > n)\)
f. If \(Q\) is the quantile function for \(F_X\), then \(E[g(X)] = \int_{0}^{1} g[Q(u)]\ du\)


6.3: Some Details of Glycolysis
A. Glycolysis, Stage 1
Reaction 1: In the first reaction of glycolysis, the enzyme hexokinase rapidly phosphorylates glucose entering the cell, forming glucose-6-phosphate ( G-6-P ). As shown below, the overall reaction is exergonic ; the free energy change for the reaction is -4 Kcal per mole of G-6-P synthesized.
This is a coupled reaction , in which phosphorylation of glucose is coupled to ATP hydrolysis. The free energy of ATP hydrolysis (an energetically favorable reaction) fuels the glucose phosphorylation (an energetically un favorable reaction). The reaction is also biologically irreversible , as shown by the single vertical arrow. Excess dietary glucose can be stored in most cells (especially liver and kidney cells) as a highly branched polymer of glucose monomers called glycogen . In green algae and plants, glucose made by photosynthesis is stored as polymers of starch. When glucose is necessary for energy, glycogen and starch hydrolysis forms glucose-1- phosphate ( G-1-P ) which is then converted to G-6-P .
Let’s look at the energetics (free energy flow) of the hexokinase-catalyzed reaction. This reaction can be seen as the sum of two reactions shown below.
Recall that ATP hydrolysis is an exergonic reaction , releasing ~7 Kcal/mole (rounding down!) in a closed system under standard conditions. The condensation reaction of glucose phosphorylation occurs with a DGo of +3 Kcal/mole. This is an endergonic reaction under standard conditions. Summing up the free energy changes of the two reactions, we can calculate the overall DGo of -4 Kcal/mole for the coupled reaction under standard conditions in a closed system.
The reactions above are written as if they are reversible. However, we said that the overall coupled reaction is biologically irreversible . Where’s the contradiction? To explain, we say that an enzyme-catalyzed reaction is biologically irreversible when the products have a relatively low affinity for the enzyme active site, making catalysis (acceleration) of the reverse reaction very inefficient. Enzymes catalyzing biologically irreversible reactions don’t allow going back to reactants, but they are often allosterically regulated. This is the case for hexokinase. Imagine a cell that slows its consumption of G-6-P because its energy needs are being met. What happens when G-6-P levels rise in cells? You might expect the hexokinase reaction to slow down so that the cell doesn’t unnecessarily consume a precious nutrient energy resource. The allosteric regulation of hexokinase is illustrated below.
As G-6-P concentrations rise in the cell, excess G-6-P binds to an allosteric site on hexokinase. The conformational change in the enzyme is then transferred to the active site, inhibiting the reaction.
152 Glycolysis Stage 1, Reaction 1
Reaction 2: In this slightly endergonic and reversible reaction, isomerase catalyzes the isomerization of G-6-P to fructose-6-P ( F-6-P ), as shown below.
Reaction 3: In this biologically irreversible reaction, 6-phosphofructokinase (6-P- fructokinase) catalyzes the phosphorylation of F-6-P to make fructose 1,6 di- phosphate ( F1,6 diP ). This is also a coupled reaction , in which ATP provides the second phosphate. The overall reaction is written as the sum of two reactions, as shown below.
Like the hexokinase reaction, the 6-P-fructokinase reaction is a coupled, exergonic and allosterically regulated reaction. Multiple allosteric effectors , including ATP, ADP and AMP and long-chain fatty acids regulate this enzyme.
Reactions 4 and 5: These are the last reactions of the first stage of glycolysis. In reaction 4 , F1,6 diP (a 6-C sugar) is reversibly split into dihydroxyacetone phosphate ( DHAP ) and glyceraldehyde-3-phosphate ( G-3-P ). In reaction 5 (also reversible), DHAP is converted into another G-3-P. Here are the reactions:
The net result is the formation of two molecules of G-3-P in the last reactions of Stage 1 of glycolysis. The enzymes F-diP aldolase and triose-P-isomerase both catalyze freely reversible reactions. Also, both reactions proceed with a positive free energy change and are therefore endergonic . The sum of the free energy changes for the splitting of F1,6 diP into two G-3-Ps is a whopping +7.5 Kcal per mole, a very energetically unfavorable process.
Summing up, by the end of Stage 1 of glycolysis, we have consumed two ATP molecules, and split one 6C carbohydrate into two 3-C carbohydrates. We have also seen two biologically irreversible and allosterically regulated enzymes.
B. Glycolysis, Stage 2
We will follow just one of the two molecules of G-3-P generated by the end of Stage 1 of glycolysis, but remember that both are proceeding through Stage 2 of glycolysis .
Reaction 6: This is a redox reaction. G-3-P is oxidized to 1,3, diphosphoglyceric acid ( 1,3, diPG ) and NAD+ is reduced to NADH. The reaction catalyzed by g lyceraldehyde-3-phopsphate dehydrogenase is shown below.
In this freely reversible endergonic reaction, a hydrogen molecule ( H 2 ) is removed from G-3-P, leaving behind phosphoglyceric acid. This short-lived oxidation intermediate is phosphorylated to make 1,3 diphosphoglyceric acid ( 1,3diPG ). At the same time, the hydrogen molecule is split into a hydride ion ( H - ) and a proton ( H + ). The H- ions reduce NAD + to NADH, leaving the protons behind in solution. Remember that all of this is happening in the active site of the same enzyme!
Even though it catalyzes a reversible reaction, G-3-P dehydrogenase is allosterically regulated. However, in contrast to the regulation of hexokinase, that of G-3-P dehydrogenase is more complicated! The regulator is NAD+ and the mechanism of allosteric regulation of G-3-P dehydrogenase by NAD+ is called negative cooperativity . It turns out that the higher the [NAD+] in the cell, the lower the affinity of the enzyme for more NAD+ and the faster the reaction in the cell! The mechanism is discussed at the link below.
154 Glycolysis Stage 2; Reaction 6
Reaction 7: The reaction shown below is catalyzed by phosphoglycerate kinase . It is freely reversible and exergonic , yielding ATP and 3-phosphoglyceric acid ( 3PG ).
Catalysis of phosphate group transfer between molecules by kinases is called substrate-level phosphorylation , often the phosphorylation of ADP to make ATP. In this coupled reaction the free energy released by hydrolyzing a phosphate from 1,3 diPG is used to make ATP. Remember that this reaction occurs twice per starting glucose. Two ATPs have been synthesized to this point in glycolysis. We call 1,3 diPG a very high-energy phosphate compound .
Reaction 8: This freely reversible endergonic reaction moves the phosphate from the number 3 carbon of 3PG to the number 2 carbon as shown below.
Mutases like phoshoglycerate mutase catalyze transfer of functional groups within a molecule.
Reaction 9: In this reaction (shown below), enolase catalyzes the conversion of 2PG to phosphoenol pyruvate ( PEP ).
Reaction 10: This reaction results in the formation of pyruvic acid ( pyruvate ), as shown below. Remember again , two pyruvates are produced per starting glucose molecule.
The enzyme pyruvate kinase couples the biologically irreversible, exergonic hydrolysis of a phosphate from PEP and transfer of the phosphate to ADP in a coupled reaction . The reaction product, PEP, is another very high-energy phosphate compound.
155 Glycolysis Stage 2; Reactions 7-10
Pyruvate kinase is allosterically regulated by ATP, citric acid, long-chain fatty acids, F1,6 diP, and one of its own substrates, PEP.
In incomplete (aerobic) glycolysis , pyruvate is oxidized in mitochondria during respiration (see the Alternate Fates of Pyruvate above). Fermentations are called complete glycolysis because pyruvate is reduced to one or another end product. Recall that muscle fatigue results when skeletal muscle uses anaerobic fermentation to get energy during vigorous exercise. When pyruvate is reduced to lactic acid ( lactate ), lactic acid accumulation causes muscle fatigue. The enzyme Lactate Dehydrogenase ( LDH ) that catalyzes this reaction is regulated, but not allosterically. Instead different muscle tissues regulate LDH by making different versions of the enzyme! Click the Link below for an explanation.
156 Fermentation: Regulation of Pyruvate Reduction is NOT Allosteric!
C. A Chemical and Energy Balance Sheet for Glycolysis
Compare the balance sheets for complete glycolysis (fermentation) to lactic acid and incomplete (aerobic) glycolysis, showing chemical products and energy transfers.
There are two reactions in Stage 2 of glycolysis that each yield a molecule of ATP. Since each of these reactions occurs twice per starting glucose molecule, Stage 2 of glycolysis produces four ATP molecules. Since Stage 1 consumed two ATPs, the net yield of chemical energy as ATP by the end of glycolysis is two ATPs, whether complete to lactate or incomplete to pyruvate! Because they can’t make use of oxygen, anaerobes have to settle for the paltry 15 Kcal worth of ATP that they get from a fermentation. Since there are 687 Kcal potentially available from the complete combustion of a mole of glucose, there is a lot more free energy left to be captured during the rest of respiration.
157 Balance Sheet of Glycolysis
Remember also that the only redox reaction in aerobic glycolysis is in Stage 2. This is the oxidation of G-3-P, a 3C glycolytic intermediate. Now check out the redox reaction a fermentation pathway. Since pyruvate, also a 3C intermediate, was reduced, there has been no net oxidation of glucose (i.e., glycolytic intermediates) in complete glycolysis.
By this time, you will have realized that glycolysis is a net energetically favorable ( downhill , spontaneous ) reaction pathway in a closed system, with an overall negative ΔGo. Glycolysis is also normally spontaneous in most of our cells, driven by a constant need for energy to do cellular work. Thus the actual free energy of glycolysis, or ΔG’, is also negative. In fact, glycolysis in actively respiring cells proceeds with release of more free energy than it would in a closed system. In other words, the ΔG’ for glycolysis in active cells is more negative than the ΔGo of glycolysis!
Now, for a moment, let’s look at gluconeogenesis, the Atkins Diet and some not-so- normal circumstances when glycolysis essentially goes in reverse, at least in a few cell types. Under these conditions, glycolysis is energetically unfavorable, and those reverse reactions are the ones proceeding with a negative ΔG’!


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2.1: The Independent-Molecule Approximation
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Because the energies that characterize the interactions of atoms within a molecule are much greater than the energies that characterize the interaction of one molecule with another, the energy of the system can be viewed as the sum of two terms. One term is a sum of the energies that the component molecules would have if they were all infinitely far apart. The other term is a sum of the energies of all of the intermolecular interactions.
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2.2: The Probability of An Energy Level at Constant N, V, and T
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2.3: The Population Sets of a System at Equilibrium at Constant N, V, and T
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In developing Boltzmann statistics, we assume that we can tell different molecules of the same substance apart. We say that the molecules are distinguishable. This assumption is valid for molecules that occupy lattice sites in a crystal. In a crystal, we can specify a particular molecule by specifying its position in the lattice. In other systems, we may be unable to distinguish between different molecules of the same substance.
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2.4: How can Infinitely Many Probabilities Sum to Unity?
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2.5: The Total Probability Sum at Constant N, V, and T
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2.6: The Most Probable Population Set at Constant N, V, and T
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2.7: The Microstates of a Given Population Set
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Thus far, we have considered only the probabilities associated with the assignments of distinguishable molecules to the allowed energy levels.
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2.8: The Probabilities of Microstates that Have the Same Energy
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Our development of statistical thermodynamics relies on the principle of equal a priori probabilities. The equal-probability idea is useful only if it leads us to theoretical models that successfully mirror the behavior of real macroscopic systems. This it does. Accordingly, we recognize that the equal-probability idea is really a fundamental postulate about the behavior of quantum-mechanical systems.
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2.9: The Probabilities of the Population Sets of an Isolated System
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In principle, the energy of an equilibrium system that is in contact with a constant-temperature heat reservoir can vary slightly with time. In contrast, the energy of an isolated system is constant. A more traditional and less general statement of the equal a priori probability principle focuses on isolated systems, for which all possible microstates necessarily have the same energy: All microstates of an isolated (constant energy) system occur with equal probability.
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2.10: Entropy and Equilibrium in an Isolated System
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If an isolated system can undergo change, and we re-examine it at after a few molecules have moved to different energy levels, we expect to find it in one of the microstates of a more-probable population set. Evidently, the largest- W population set characterizes the equilibrium state. Either the system can undergo change until W reaches a maximum. Thereafter, it is at equilibrium and can undergo no further macroscopically observable change.
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2.11: Thermodynamic Probability and Equilibrium in an Isomerization Reaction
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To relate these ideas to a change in a more specific macroscopic system, let us consider isomeric substances A and B. In principle, we can solve the Schrödinger equation for a molecule of isomer A and for a molecule of isomer B . We obtain all possible energy levels for a molecule of each isomer. If we list these energy levels in order, beginning with the lowest, some of these levels belong to isomer A and the others belong to isomer B.
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2.12: The Degeneracy of an Isolated System and Its Entropy
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The sum of the thermodynamic probabilities over all allowed population sets is just the number of microstates that have energy E . This sum is just the degeneracy of the system energy, E .
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2.13: The Degeneracy of an Isolated System and its Entropy
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2.14: Effective Equivalence of the Isothermal and Constant-energy Conditions
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In principle, an isolated system is different from a system with identical macroscopic properties that is in equilibrium with its surroundings. We emphasize this point, because this distinction is important in the logic of our development. However, our development also depends on the assumption that, when N is a number that approximates the number molecules in a macroscopic system, the constant-temperature and constant-energy systems are functionally equivalent.
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2.15: Problems
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4.1: Ultrarelativistic particles
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Ultrarelativistic objects are objects moving at nearly c . A good way of thinking about an ultrarelativistic particle is that it’s a particle with a very small mass. For example, the subatomic particle called the neutrino has a very small mass, thousands of times smaller than that of the electron.
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4.2: E=mc²
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We now know the relativistic expression for kinetic energy in the limiting case of an ultrarelativistic particle: its energy is proportional to the “stretch factor” D of the Lorentz transformation. What about intermediate cases?
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4.3: Relativistic Momentum
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Since mass and energy are equivalent, we must stop talking about a material object’s kinetic energy and consider instead its total energy E, which includes a contribution from its mass. Massless particles always move at v=c , while massive ones always move at v<c .
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4.4: Systems with internal structure
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E=mc2 and the four-vector nature of p are both valid for systems with ﬁnite spatial extent, provided that the systems are isolated.
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4.5: Force
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Force is a concept that is seldom needed in relativity, and that’s why this section is optional.
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4.6: Two Applications
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4.7: Tachyons and Faster-than-Light (FTL)
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A tachyons are hypothetical particle that always moves faster than light. Most physicists believe that faster-than-light (FTL) particles cannot exist because superluminal transmission of information would violate causality, since it would allow a causal relationship between events that were spacelike in relation to one another, and the timeordering of such events is diﬀerent according to diﬀerent observers.
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4.E: Dynamics (Exercises)
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23.4: Assessment- Post-Tests and Activity Logs
Purpose
Now that you have completed your fitness program, it is time to evaluate your progress for the last time. Again, your CR posttest must be the same as your CR pretest.
Directions
- Click the President’s Challenge Fitness Test link to take the tests.
- See “Fitness Test Instructions” at the beginning of Unit Two for directions to submit the assignment
- When you submit the posttests, also submit your pretest report (you do not need to submit the midsemester updates).
- Write a brief reflection and compare your pretest scores with your posttest scores.
- For your physical activity logs, go to the Super Tracker website and click on “My Reports” then “History Charts” at the top of the page.
- Select “Physical Activity” on the left side of the page, enter your time period and dates (weekly), select chart type (bar or line graph), then create your report.
- Export or save the report as a PDF file. If your computer will not allow you to do this, copy and paste the chart (only the chart, not the entire page) into a document and save.
- This assignment will have two documents: your posttest report (submit as a Word document) and your physical activity report. Upload both directly into the course as one submission.
Grading
This assignment is worth 15 points maximum. Your work will be assessed using the Post-Test and Activity Logs Grading
Rubric:
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Criteria |
Absent |
Present |
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Post-tests |
0 points |
3 points
Must include results for aerobic endurance, flexibility, muscular endurance (half sit-ups and push-ups), BMI, and waist circumference. |
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Pre-tests |
0 points |
3 points Must include results for aerobic endurance, flexibility, muscular endurance (half sit-ups and push-ups), BMI, and waist circumference. |
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Reflection |
0 points |
4 points
Well-constructed reflection comparing your pre-test scored with your post-test scores and submitted by the deadline. Posting must be at least 2 sentences long. |
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Activity tracker report |
0 points |
5 points Physical activity report including 8 weeks of exercise program |
- Lifetime Fitness and Wellness. Provided by : Extended Learning Institute of Northern Virginia Community College. Located at : https://eli.nvcc.edu/ . License : CC BY: Attribution


13.5: Interest Rate and Reinvestment Rate Risks
An additional, clarifying word about interest rate and reinvestment rate risks is warranted at this time.
If in general, interest rates go up, market prices for existing, “older” bonds will go down – and vice versa. General interest rates and bond prices are inversely related. In an environment where market rates have gone up, bond investors holding “old” bonds will receive less interest income than if they had purchased “new” bonds that were issued more recently – at higher (coupon) rates. This will cause market values for existing bonds to go down; they are simply worth less competitively. Rising rates are “bad” news for (existing) bondholders in terms of interest rate risk.
However, bondholders will be able to reinvest their interest proceeds at higher rates than before if rates rise. Investors receive regular, periodic interest payments over the life of the bond, which upon receipt, is assumed to be reinvested into other alternatives that pay higher rates than before. Thus, rising rates are “good” news for bondholders – in terms of reinvestment risk.
In short, interest rate and reinvestment risks are inversely related to one another. The table below summarizes the relationships vis á vis the bond investor.