15.6: Family Adaptations during Labor and Birth
By the end of this section, you will be able to:
- Explain the importance of the partner or support person during the process of labor and birth
- Explain the importance of the family to the person who is laboring
Not so long ago, people birthing in hospitals in the United States experienced labor and birth without support people present, in a medicated state, and with little to no memory of their birth. The shift in our culture to include spouses or partners, trained birth support people like doulas, and even photographers or videographers has occurred slowly. Research shows that the presence of these support people, especially those experienced in birth like a doula, can improve the experience of the birthing person, reduce trauma, and improve health outcomes (Sobczak et al., 2023).
Partner and Support Person Adaptations during the Process of Labor and Birth
Some partners feel empowered in their role as a non-birthing partner; others may feel disempowered and unsure of their new role. Some partners rise to the challenge and provide excellent labor support that meets or exceeds the quality of a trained birth doula; others are less prepared or too overwhelmed to provide support in the way preferred by the birthing person (Saether et al., 2023). The experience of both the birthing person and their partner can be improved by taking preparatory classes on labor, birth, and the postpartum period and discussing the birth with experienced parents (Vanderlaan & Givens, n.d.). The planned support person should be prepared to experience the sights and sounds of birth, know their own limits or needs, maintain their own hydration and nutrition so that they are able to provide support, and have any unanswered questions addressed before the onset of labor so that they feel prepared. Nurses can support the birthing person’s desired level of involvement of the support person by asking the patient or by reading the birth plan .
Some birthing patients are unable to have their desired partner with them at the birth for multiple reasons (military, no longer in the relationship, unavailable). The nurse can be an emotional and physical support to the patient. A doula can also be the support person. Doulas often have basic training in physical and emotional support of laboring people and may have certification. Doulas can suggest position changes and comfort measures, as well as be a reassuring presence at the bedside. Research shows the addition of an experienced support person can improve birth experiences (Sobczak et al., 2023). In the current birth culture where trauma can occur, the necessity of support cannot be stressed enough. This is especially true if a birthing person is a person of color or belongs to another marginalized population.
Family Adaptations during the Process of Labor and Birth
Which family members are present during the four stages of labor is a very personal choice that may be impacted by the route of delivery, birthplace policies, health issues or the presence of infection, the health of each relationship with the birthing person, and cultural expectations. During the COVID-19 pandemic, restrictions on support people caused worsening of outcomes and an increase in negative experiences of birth as well as postpartum mood changes like depression, according to research (Shuman et al., 2022). Historically, family involvement during pregnancy included giving advice, helping prepare for birth, and attending the labor and birth; this involvement decreased stress and increased emotional security (Hawkins et al., 2021). Nurses should be prepared for supporting birthing people and their families by providing education, reassurance of the normality of labor and birth experiences, and family access to the extent the laboring person wishes it. Each family will have differing needs for their birth based on personal, societal, and cultural expectations. Prioritizing this support can improve outcomes and experiences for families.
Surrogacy
Surrogacy can be a significant ethical or legal issue with varying levels of complexity based on the circumstances and the state where the pregnancy occurs. Nurses need to be aware of surrogacy laws, facility policy, and plans for security around these very unpredictable pregnancies. For example, consider the following situation: Fetal heart rate decelerations are present, and the birthing person is a surrogate for two intended parents who are present for the delivery. The provider recommends moving to a cesarean birth immediately for fetal protection. The birthing person declines and requests alternative options due to the risks of surgery to their body. The intended parents demand the surgery begin immediately. What are the laws in the state? What are the facility policies, and what is included in the contract in this specific case? This is just one example of conflicts that can arise that nurses should be prepared to navigate or escalate through the proper chains of command.


4.10: Sex Offender Treatment and Civil Commitment
Many sex offenders are placed on probation, with requirements that they attend a sex offender treatment program, report regularly to a probation officer, do not contact their victims, do not use the internet, and do not live or work in certain areas. Sex offender treatment programs can be inpatient (residential) or outpatient (non-residential) and generally use cognitive-behavioral therapy, counseling, and other approaches to reduce the likelihood that the person will commit another sex offense. About 20 states also have “civil commitment” programs, which place sex offenders in secure hospitals or residential treatment facilities for treatment.  Offenders can be required to stay on civil commitment indefinitely, which means the programs can cost up to four times what it costs to keep an offender in prison.


4.3: Addition and Subtraction in Base Systems
- Add and subtract in bases 2–9 and 12.
- Identify errors in adding and subtracting in bases 2–9 and 12.
Once we decide on a system for counting, we need to establish rules for combining the numbers we’re using. This begins with the rules for addition and subtraction. We are familiar with base 10 arithmetic, such as or . How does that change if we instead use a different base? A larger base? A smaller one? In particular, computers use base 2 for all number representation. When your calculator adds or subtracts, multiplies or divides, it uses base 2. This is because the circuitry recognizes only two things, high current and low current, which means the system is uses only has two symbols. Which is what base 2 is.
In this section, we use addition and subtraction in bases other than 10 by referencing the processes of base 10, but applied to a new base system.
Addition in Bases Other Than Base 10
Now that we understand what it means for numbers to be expressed in a base other than 10, we can look at arithmetic using other bases, starting with addition. When you think back to when you first learned addition, it is very likely you learned the addition table. Once you knew the addition table, you moved on to addition of numbers with more than one digit. The same process holds for addition in other bases. We begin with an addition table, and then move on to adding numbers with two or more digits.
We worked with base 6 earlier, and have the numbers in base 6 up to 100 6 . Using that table of values, we can create the base 6 addition table.
Here’s the beginning of the base 6 addition table:
| + | 0 | 1 | 2 | 3 | 4 | 5 |
| 0 | 0 | 1 | 2 | 3 | 4 | 5 |
| 1 | 1 | 2 | 3 | 4 | 5 | ? |
| 2 | 2 | 3 | 4 | 5 | ? | ? |
| 3 | 3 | 4 | 5 | ? | ? | ? |
| 4 | 4 | 5 | ? | ? | ? | ? |
| 5 | 5 | ? | ? | ? | ? | ? |
Many of the cells are not filled out. The ones filled in are values that never get past 5, which is the largest legal symbol in base 6, so they are acceptable symbols. But what do we do with 5 + 3 in base 6? We can’t represent the answer as “8” since “8” is not a symbol available to us. Let’s go back to the list of numbers we have for base 6.
| 0 | 1 | 2 | 3 | 4 | 5 |
| 10 | 11 | 12 | 13 | 14 | 15 |
| 20 | 21 | 22 | 23 | 24 | 25 |
| 30 | 31 | 32 | 33 | 34 | 35 |
| 40 | 41 | 42 | 43 | 44 | 45 |
| 50 | 51 | 52 | 53 | 54 | 55 |
So, what is 5 + 1 equal to in base 6? Well, start at the 5, and jump ahead one step. You land on 10.
This means that, in base 6, 5 + 1 = 10.
So, what is 5 + 2 in base 6? Well, 5 + 2 = 5 + 1 + 1, so 10 + 1…jump one more space and you land on 11. So, 5 + 2 = 11 in base 6.
And so it goes. Using that process, stepping one more along the list, we can fill in the remainder of the base 6 addition table (Table 4.4).
| + | 0 | 1 | 2 | 3 | 4 | 5 |
| 0 | 0 | 1 | 2 | 3 | 4 | 5 |
| 1 | 1 | 2 | 3 | 4 | 5 | 10 |
| 2 | 2 | 3 | 4 | 5 | 10 | 11 |
| 3 | 3 | 4 | 5 | 10 | 11 | 12 |
| 4 | 4 | 5 | 10 | 11 | 12 | 13 |
| 5 | 5 | 10 | 11 | 12 | 13 | 14 |
With this table, and with our understanding of “carrying the one,” we can then use the addition table to do addition in base 6 for numbers with two or more digits, using the same processes you learned for addition when you did it by hand.
Calculate 251 6 + 133 6 .
- Answer
-
Step 1: Let’s set up the addition using columns.
2 5 1 + 1 3 3 Step 2: Let’s do the one’s place first. According to the base 6 addition table (Table 4.4), 1 + 3 = 4.
2 5 1 + 1 3 3 4
Step 3: Now, we do the “tens” place (it’s really the sixes place). According to the base 6 addition table (Table 4.4), we have 5 + 3 = 12. So, like in base 10, we use the 2 and carry the 1.
| 1 | |||
| 2 | 5 | 1 | |
| + | 1 | 3 | 3 |
| 2 | 4 |
Step 4: Now the “hundreds” place (really, thirty-sixes place). There, we have 1 + 2 + 1 = 3 + 1 = 4.
| 1 | |||
| 2 | 5 | 1 | |
| + | 1 | 3 | 3 |
| 4 | 2 | 4 |
So, 251 6 + 133 6 = 424 6 .
As you can see, the process is the same as when you learned base 10 addition, just a different symbol set.
Calculate 453 6 + 345 6 .
- Create the addition table for base 7.
- Create the addition table for base 2.
- Answer
-
-
We begin with the table below.
+ 0 1 2 3 4 5 6 0 0 1 2 3 4 5 6 1 1 2 3 4 5 6 2 2 3 4 5 6 3 3 4 5 6 4 4 5 6 5 5 6 6 6 In base 7, the number that follows 6 is 10 (since we’ve run out of symbols!). So, 6 7 + 1 7 = 10 7 . Once that is established, 6 7 + 2 7 will be two numbers past 6, which is 11 in base 7.
+ 0 1 2 3 4 5 6 0 0 1 2 3 4 5 6 1 1 2 3 4 5 6 10 2 2 3 4 5 6 11 3 3 4 5 6 4 4 5 6 5 5 6 6 6 10 11
-
We begin with the table below.
Continuing, we can fill in the rows as we would in base 10, but being aware that we are working in base 7 (Table 4.5).
| + | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| 0 | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| 1 | 1 | 2 | 3 | 4 | 5 | 6 | 10 |
| 2 | 2 | 3 | 4 | 5 | 6 | 10 | 11 |
| 3 | 3 | 4 | 5 | 6 | 10 | 11 | 12 |
| 4 | 4 | 5 | 6 | 10 | 11 | 12 | 13 |
| 5 | 5 | 6 | 10 | 11 | 12 | 13 | 14 |
| 6 | 6 | 10 | 11 | 12 | 13 | 14 | 15 |
-
We revisit base 2 here. Begin with the table:
+ 0 1 0 0 1 1 1 Table 4.6 In base 2, the number that follows 1 is 10 (since we’ve run out of symbols!). So, 1 2 + 1 2 = 10 2 . The complete table for base two then is below.
+ 0 1 0 0 1 1 1 10 This demonstrates that the rules necessary for base 2 addition are as small as possible: four rules.
Create the addition table for base 4.
To summarize the creation of the addition tables for a given base, do the following.
Step 1: Set up the table.
Step 2: Fill in all the additions that use the “legal” symbols for the base. The diagonal that goes from upper left to lower right that is immediately next to the filled boxes all get the value 10, regardless of base.
Step 3: Enter the values that are in the “teens.” This can all be done on one table without creating multiple copies of previously done work.
Calculate 536 7 + 433 7 .
- Answer
-
Step 1: Let’s set up the addition using columns.
5 3 6 + 4 3 3 Step 2: Let’s do the one’s place first. According to the base 7 addition table in the solution for Example 4.29, 6 + 3 = 12. We will carry the 1.
1 5 3 6 + 4 3 3 2
Step 3: Now, we do the “tens” place (it’s really the sevens place). According to the base 7 addition table in the solution for Example 4.29, we have 1 + 3 + 3 = 10. So, like in base 10, we use the 0 and carry the 1.
| 1 | |||
| 5 | 3 | 6 | |
| + | 4 | 3 | 3 |
| 0 | 2 |
Step 4: Now the “hundreds” place (really, forty-ninths place). There, we have 1 + 5 + 4 = 6 + 4 = 13.
| 1 | |||
| 5 | 3 | 6 | |
| + | 4 | 3 | 3 |
| 1 | 3 | 0 | 2 |
So, 536 7 + 333 7 = 1302 7 .
Calculate 461 7 + 142 7.
As seen previously, when performing addition in another base, set up the problem exactly as you would for addition in base 10. At each step, check the addition table for the base. As in base 10 addition, move right to left, adding down the columns using the rules in the addition table. When necessary and just as in base 10, be sure to carry the 1.
Create the addition table for base 12.
- Answer
-
Step 1: Recall, in base 12, the symbol set is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, and B. So, the addition table begins as shown below.
+ 0 1 2 3 4 5 6 7 8 9 A B 0 0 1 2 3 4 5 6 7 8 9 A B 1 1 2 3 4 5 6 7 8 9 A B 2 2 3 4 5 6 7 8 9 A B 3 3 4 5 6 7 8 9 A B 4 4 5 6 7 8 9 A B 5 5 6 7 8 9 A B 6 6 7 8 9 A B 7 7 8 9 A B 8 8 9 A B 9 9 A B A A B B B Step 2: The diagonal immediately to the right of the filled in boxes is where the 10 goes for this base.
+ 0 1 2 3 4 5 6 7 8 9 A B 0 0 1 2 3 4 5 6 7 8 9 A B 1 1 2 3 4 5 6 7 8 9 A B 10 2 2 3 4 5 6 7 8 9 A B 10 3 3 4 5 6 7 8 9 A B 10 4 4 5 6 7 8 9 A B 10 5 5 6 7 8 9 A B 10 6 6 7 8 9 A B 10 7 7 8 9 A B 10 8 8 9 A B 10 9 9 A B 10 A A B 10 B B 10
Step 3: Using the pattern we’re familiar with, and counting in base 12, we can fill in the other cells.
| + | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B |
| 0 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B |
| 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | 10 |
| 2 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | 10 | 11 |
| 3 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | 10 | 11 | 12 |
| 4 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | 10 | 11 | 12 | 13 |
| 5 | 5 | 6 | 7 | 8 | 9 | A | B | 10 | 11 | 12 | 13 | 14 |
| 6 | 6 | 7 | 8 | 9 | A | B | 10 | 11 | 12 | 13 | 14 | 15 |
| 7 | 7 | 8 | 9 | A | B | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
| 8 | 8 | 9 | A | B | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 |
| 9 | 9 | A | B | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
| A | A | B | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |
| B | B | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 1A |
Notice that the lower-right entry is 1A 12 , as this is the number one past 19 12 .
Create the addition table for base 14.
Calculate 3A7 12 + 9BA 12 .
- Answer
-
Step 1: Using the process established in the earlier addition problem, set up the columns.
3 A 7 + 9 B A Step 2: Using the rules from the base 12 addition table in the solution for Example 4.31, and being careful to carry the 1 when necessary, we get the following:
1 1 3 A 7 + 9 B A 1 1 A 5
The ones that were carried are located over the columns.
So, 3A7 12 + 9BA 12 = 11A5 12 .
Calculate 4B3 12 + B06 12 .
We again return to base 2, the base used by computers. Calculate 1001 2 + 11011 2 .
- Answer
-
Step 1: Using the process established in the earlier addition problem, set up the columns.
1 0 0 1 + 1 1 0 1 1 Step 2: Using the rules from the base 2 addition table in the solution for Example 4.29, and being careful to carry the 1 when necessary (and shown at the top of the grid), we get the following:
1 1 1 1 0 0 1 + 1 1 0 1 1 1 0 0 1 0 0
Step 3: Calculate 1001 2 + 11011 2 = 100100 2 .
So, 1001 2 + 11011 2 = 100100 2 .
Calculate 101111 2 + 1100011 2 .
Subtraction in Bases Other Than Base 10
Subtraction in bases other than base 10 follow the same processes as base 10 subtraction, but, as with addition, using the addition table for the base.
Calculate 52 6 − 34 6 .
- Answer
-
Step 1: Let’s set up the subtraction using columns.
5 2 − 3 4 Step 2: Just as we might do in base 10, we borrow a 1 from the 5 for the ones digit.
12 − 3 4
Step 3: Referring to the base 6 addition table (Table 4.4), we see that 4 + 4 = 12, so 12 6 − 4 6 is 4 6 .
| 1 2 | ||
| − | 3 | 4 |
| 4 |
Step 4: Now we deal with the “tens” (really, sixes) digit, 4 6 − 3 6 , which equals 1 6 according to the base 6 addition table (Table 4.4).
| 4 | 1 2 | |
| − | 3 | 4 |
| 1 | 4 |
So, 52 6 − 34 6 = 14 6 .
Calculate 115 6 − 43 6 .
Calculate A17 12 − 4B3 12 .
- Answer
-
Step 1: Let’s set up the subtraction using columns.
A 1 7 − 4 B 3 Step 2: Even in base 12, 7 12 − 3 12 = 4 12 .
A 1 7 − 4 B 3 4
Step 3: Moving to the “tens” digit, we have 1 12 − B 12 . Since 1 is less than B in base 12, we need to borrow a 1 from the A, just as we would for subtraction in base 10.
| 9 | 11 | 7 | |
| − | 4 | B | 3 |
| 4 |
Step 4: According to the base 12 addition table in the solution for Example 4.31, B 12 + 2 12 = 11 12 , so 11 12 − B 12 = 2 12 .
| 9 | 1 1 | 7 | |
| − | 4 | B | 3 |
| 2 | 4 |
Step 5: Finally, we deal with the “hundreds” digit. According to the base 12 addition table in the solution for Example 4.31, 4 12 + 5 12 = 9 12 , so 9 12 − 4 12 = 5 12 .
| 9 | 11 | 7 | |
| − | 4 | B | 3 |
| 5 | 2 | 4 |
So, A17 12 − 4B3 12 = 524 12 .
Calculate 716 12 − 4AB 12 .
Errors When Adding and Subtracting in Bases Other Than Base 10
Errors when computing in bases other than 10 often involve applying base 10 rules or symbols to an arithmetic problem in a base other than base 10. The first type of error is using a symbol that is not in the symbol set for the base. For instance, if a 9 shows up when working in base 7, you know an error has happened because 9 is not a legal symbol in base 7.
Explain the error in the following calculation:
- Answer
-
Since the problem is in base 6, the symbol set available is 0, 1, 2, 3, 4 and 5. The 9 in the answer is clearly not a legal symbol for base 6. Looking back to the base 6 addition table (Table 4.4), we see that . Correcting the error, we see the sum is .
Explain the error in the following calculation and correct the problem:
\({133_4} + {112_4} = {245_4}\)
The second type of error is using a base 10 rule when the numbers are not in base 10. For instance, if you are working in base 13, then 9 13 + 9 13 is not 18 13 , even though 18 is the correct answer in base 10.
Explain the error in the following calculation, and correct the error:
- Answer
-
If this problem was a base 10 problem, this would be the correct answer. However, in base 12, 9 + 6 is not 15, but is instead 13. To correct this error, carefully use the addition table for base 12. If properly used, the correct answer would be , as seen below:
8 9 + 7 6 1 4 3
Explain the error in the following calculation, and correct the error:
\({149_{14}} + {19_{14}} = {168_{14}}\)
Check Your Understanding
- Determine the addition table for base 8.
- Compute 24 6 + 53 6 .
- Compute 35 8 − 26 8 .
- Compute 3B 14 + 45 14 .
- Compute A4 12 − 9B 12 .
- How do you know an error has occurred in a base 8 addition question if the answer obtained was 28 8 ?
- What is one common error made in calculating in base 14?


2.5: Failure is Not an Option
-
- Last updated
- Save as PDF
- Cheryl E. Ball & Drew M. Loewe ed.
- West Virginia University via Digital Publishing Institute and West Virginia University Libraries
Author: Allison Carr Director of Writing Across the Curriculum, Coe College
Failure, so goes the dominant cultural narrative, is a sign of weakness. Of laziness.  Failure will ruin your life. In action, suspense, and sports films, failure is not an option . In real life, failure only happens to bad people. Or, more to the point in this context, to bad writers. Failure in writing betrays dullness of mind, smallness of imagination. The failed writer—the one who cannot learn to write well (which is to say, according to accepted conventions of good writing)—is discounted as dim, unprepared, non-serious, wacky, or weird, distracted, behind.
Or, failure is acceptable if we learn from it. If we can recuperate it, if it brings us virtue and strength and morality because what doesn’t kill us makes us stronger. And if we never, ever do it again.
No. Stop with this. This is stupid, and the opposite is actually true: Failure should be welcomed, if not actively sought out, signaling as it does both the presence of creative, risky thinking and an opportunity to explore a new direction. To writing especially, failure is integral, and I will go so far as to assert that the best writing (and the best learning-to-write) happens when one approaches the activity from a mindset trained on failure. Failure represents a certain against-the-grain jettisoning of established ideas about what counts as good writing in favor of rogue, original, attention-capturing, and intentional art. To fail willingly in writing is to be empowered by the possibilities that emerge. It is to trust oneself and one’s ideas, a quality too rare in the age of hyper-achievement, in which the only progress that counts is progress that moves up.
A History of Failure
Broadly speaking, failure’s bad reputation is an inherited relic of another time. Though it would certainly be possible to trace its
origins back to many religious mythologies, I will in the interest of brevity go back only so far as the mid-19th century in America, when the economy shifted from one based in agriculture to one based in industry (closing, in theory, the opportunity gap between rich and poor). From this backdrop grew the recognition that literacy, the ability to read and write (and generally comprehend information), would be the bedrock of a thriving community. Thus, literacy took on the status of social necessity for the masses, not simply a luxury for the ruling class. By the middle of the 19th century, a system of common schools had been codified, and central to its curriculum was grammar instruction and conventions of speech and writing.
According to literacy scholar John Trimbur, from whom I have been piecing together this history, reading and writing instruction functioned “as both a means to regulate popular literacy and a social marker to divide the literate from the illiterate, the worthy poor from the unworthy, ‘us’ from ‘them.’” Given the then-corresponding (perhaps correlative) rates of illiteracy among incarcerated populations, success and failure in this realm came to be perceived not simply as an indication of intelligence or economic advantage, but as a matter of moral fiber. To fail in reading or writing meant a failure of moral fortitude.
But cultural attitudes toward failure remain as sinister as ever, perhaps more so in the wake of standardized testing, No Child Left Behind, and Race to the Top. Failure continues to represent not just ill preparedness, but weakness in spirit and mind, stupidity, inadequacy, and a lifetime of toiling. And there is something about failure in writing that amplifies these judgments, suggesting that the subject somehow deserves to be judged and disadvantaged in these ways.
An Alternative View
What we have failed to grasp—why the idea that failure is bad needs to die—is the integral connection between failure and risk, creativity, and innovation, not to mention emotional and cognitive resilience. This relationship is well documented, making its tenacious hold on cultural ideology especially confounding. For example, many of us use and benefit daily from innovations discovered by accident: penicillin, Corn Flakes, Post-it Notes, Corningware, WD-40, oral contraception, and potato chips. All of these were discovered when the discoverer was working on a different puzzle. And discoveries like these are the norm, not the exception. This is the primary activity of lab research, after all: A researcher may run hundreds, thousands of trials and experiments, each a failure in its own unique way (and some leading to accidental discoveries) before landing on, say, the polio vaccine or the secret to the expanding universe. Likewise, in the tech industry, we need only look as far as Silicon Valley and the dozens of stories of failed startups to understand how integral failure is to the culture of innovation there (even when it is difficult to stomach). In fact, failure is so common and so prominent in tech, they’ve developed an entire annual conference around it, FailCon.
And though writing is not obviously about discovery of life-altering products, it is about discovery of a different sort and thus, the virtue of failure should be similarly celebrated. In fact, knowing what I know about learning to write (as a writer and a writing teacher myself), I would argue that it is impossible for one to develop anything approaching a good writing ability without years—decades, probably—of repeated failure. We aren’t born pen in hand, fully primed to write sonnets or political treatises as soon as we get a grip on those fine motor skills. Writing is learned slowly, over a long period of time, and with much difficulty, and anybody who says otherwise is lying or delusional or both.
Consider the testimony of renowned journalist and public intellectual Ta-Nehisi Coates who, in an interview for The Atlantic ’s “Creative Breakthroughs” series, describes writing as a process of repeated failures that, with persistence, accumulate to create breakthroughs. “I always consider the entire process about failure,” he says, “and I think that’s the reason why more people don’t write.” Similarly, novelist Stephen King speaks publicly (and repeatedly) about his impressively large stack of rejection slips before Carrie was finally picked up by Doubleday, thereby launching his illustrious career (powered by persistence, no doubt, in the face of his continued fear “of failing at whatever story I’m writing”). Pulitzer Prize winning novelist Junot Díaz writes memorably of his difficulty in writing his second novel, a years-long exercise in failure; it famously took Jane Austen fourteen years to write Sense and Sensibility ; and Joyce Carol Oates, in her “Notes on Failure,” reminds us that Faulkner considered himself a failed poet and that Henry James only became a novelist after a failed turn at playwriting.
There is much disagreement, or shall I say healthy debate, in the community of writing scholars about the best and most effective ways to teach writing. The specifics in this case are immaterial, because these scholars do agree on (at least) one foundational
idea: that writing is a process , which is a coded way of avoiding the harsher truth: Writing—and learning to write—involves a great deal of failure. We start a draft; we get frustrated or stuck or sidetracked, or we discover halfway through that we’re actually interested in something else. We move to a clean sheet of paper or a fresh document and start again. And the process continues until we’ve made something cohesive, something that works. We scholars know this not only because we’ve researched it, but because we are writers ourselves, and we spend a great deal of time with people struggling to improve their writing.
Writing scholars don’t use the word “failure” very often (or at all), but we should. There is something bold there, something that a dogged denial of failure closes off: permission to make a mess, to throw something away, to try thirty different ideas instead of toiling away on one. It’s a reset button for the brain. That didn’t work! Let’s salvage what we can and try again! Scholars and teachers don’t use this word, but we should—it is the most honest thing we have to say about writing.
Making Failure an Option
What should be clear is that failure is a significant part of the entire scene of learning, an assertion that, again, is borne out by widely respected research. Malcolm Gladwell isn’t wrong when he insists upon the 10,000-hour rule, which, in suggesting that it takes 10,000 hours to truly master anything (shooting free-throws, playing an instrument), implicitly builds in a generous rate of failure. It’s true that writing is not stable in the way that chess is stable, but the broad message of Gladwell’s limited theory—that to excel at anything takes a tremendous amount of practice and persistence— easily aligns with prevailing thought on what is central to development in writing: Writing is difficult and complex, and development is not linear. More recently, Carol Dweck’s concept of growth mindset suggests that people learn better when their efforts are assessed and praised as opposed to their autonomous being: “You seem to be working really hard” instead of “You’re smart.” Drawing on this learning paradigm, cognitive researcher Manu Kapur tells us that our brains are actually wired for failure.
Failure is integral to learning and development, more so than external markers of achievement or success. An avoidance of failure in learning, or in writing, or in industry or parenting or any other human/community endeavor, represents an absence of creativity and an abundance of predictability, little to no risk, and perhaps even harmful or counter-productive thinking. This is not a mindset anyone should encourage or reinforce. Instead, teachers, scholars, mentors, and anybody involved in the conversation about writing development should be taking concrete steps toward normalizing failure. This means rethinking the frame of the entire scene of writing, including what it means to learn how to do it and what it means to teach it. As my invocation of Gladwell above demonstrates, it is foolish to imagine writing as a discrete and stable skill that can be mastered, a mindset that unfortunately dominates much writing instruction (especially in this era of testing); instead, it is crucial that the project of developing as a writer is understood as an always ongoing process of learning and discovery and that writing classrooms should be thought of as laboratories where experimentation and question-asking prevails over rule-memorization and formulaic discipline. Writing is not a list of dos and don’ts, nor is success in writing a universally acknowledged ideal. Writing is about risk and wonder and a compulsion to make something known. Failure—and a willingness to fail often in large, obvious ways—should always be an option.
Further Reading
To learn more about the correlation between organized writing instruction and the rise of industrial capitalism, see John Trimbur’s essay titled “Literacy and the Discourse of Crisis” in the collection The Politics of Writing Instruction: Postsecondary (Boynton/Cook), edited by Trimbur and Richard Bullock.
Cultural attitudes about education, learning, and literacy have been challenged in recent years, most successfully by advocates for a “growth mindset,” which strives to distinguish learners’ natural ability from learned and determined effort, ultimately empowering students in the face of struggle and failure. To learn more about this research, see Ingfei Chen’s “New Research: Students Benefit from Learning that Intelligence is not Fixed” ( Mind/Shift ), Manu Kapur’s “Productive Failure in Learning Math” ( Cognitive Science ), and Katrina Schwartz’s “Growth Mindset: How to Normalize Mistake Making and Struggle in Class” ( Mind/Shift ).
Stephen King may be the most well-known writer to address failure, as evident in Lucas Reilly’s article “How Stephen King’s Wife Saved Carrie and Launched His Career” ( Mental Floss) as well as Andy Greene’s interview with him ( Rolling Stone) . Outside the world of writing, the culture of failure thrives most prominently in technological innovation. For more, consider Rory Carroll’s “Silicon Valley’s Culture of Failure... And the ‘Walking Dead’ it Leaves Behind” ( The Guardian ), Kevin Maney’s “In Silicon Valley, Failing is Succeeding” ( Newsweek ), Bo Yaghmaie’s “A Case of Startup Failure” ( Techcrunch.com ), and “146 Startup Failure PostMortems,” compiled by the editor at CBInsights.com.
Keywords
basic writers, failure, growth mindset, productive failure, struggle, writing process
Author Bio
Allison Carr is an assistant professor of rhetoric and Director of Writing Across the Curriculum at Coe College.  She tweets about food, politics, writing, and baseball @hors_doeuvre.


7.12: Modify Graphics
Learning Objectives
- Modify graphics
Once a graphic has been inserted into a worksheet, text or data will need to be entered and edited. The graphic can also be modified to fit the scale and style desired for a worksheet. The following actions can be taken for any graphic selected in Excel:
- Adding/editing text
- Resizing graphic
- Changing design style
- Moving graphics
- Rotating graphics
Adding/Editing Text
Type text into the graphic by either selecting the [Text] area in the graphic, or by selecting [Text] in the Type your text here dialog box to the left. If there is no text dialog box on the left, click on the graphic and the box will open. If there is data or text from within a worksheet such as labels, values, etc. you wish to add to the graphic, select the desired text and copy and paste into the graphic. Editing text in a graphic is the same process as adding a graphic’s text.
Practice Question
Resizing Graphic
Select a point on the outer edge of a graphic, hold down the left mouse button (or cursor) and drag the graphic to fit the size desired.
Changing Design Style
Roll the cursor over the layout or SmartArt style sections to see the various options that are available for the selected graphic. Select the style best suiting the purpose of the graphic.
Moving Graphics
To place a graphic next to an Excel table or other desired spot, hold down the cursor until the four-way arrow appears, while continuing to hold, drag the graphic within the worksheet to the desired location.
Rotating Graphics
To rotate a graphic in an Excel worksheet, place the cursor on the circular arrow and drag to rotate the graphic.
Practice Question
Contributors and Attributions
- Modify Graphics. Authored by : Sherri Pendleton. Provided by : Lumen Learning. License : CC BY: Attribution


12.2H: Fluorescent Antibodies
- Describe how fluorescent antibody conjugates can be used in immunoassays for protein detection
Fluorescent labeling is another method of demonstrating the complexity of antigens and antibodies. Fluorescent molecules are used as substitutes for radioisotope or enzyme labels. The fluorescent antibody technique consists of labeling antibody with dyes such as fluorescein isothiocyanate (FITC). These compounds have high affinity for proteins with which they conjugate.
Fluorescent techniques are very specific and sensitive, so fluorescent antibody-based techniques require a fluorescent microscope. A fluorescent substance absorbs light of one wavelength and emits light of a longer wavelength. Fluorescein fluoresces an intense apple-green color when excited under fluorescent microscopy. The chemical manipulation in labeling antibodies with fluorescent dyes to permit detection by direct microscopy examination does not impair antibody activity.
After the labeling of a specific antibody with a fluorescent molecule, it can still be reacted with its antigen and identified microscopically. Fluorescent antibody conjugates are commonly used in immunoassays. The basic methods utilizing fluorescent antibodies include direct, inhibition, and indirect immunofluorescent assay.
In the direct technique, a fluorescent antibody is used to detect antigen-antibody reactions at a microscopic level. The inhibition immunofluorescent assay is a blocking test in which an antigen is first exposed to an unlabeled antibody, then to a fluorescent antibody, and is finally washed and examined. Indirect immunofluorescence assay is based on the ability of antibodies to react with antigens as well as act as antigens and react with anti-antibody (anti-immunoglobulin). This technique is used extensively for the detection of autoantibodies and antibodies to tissue and cellular antigens. The methods described are mostly performed on glass slides with patient serum or tissue sections. Immunofluorescence can also be performed to identify specific antigens on live cells in suspension. This method is known as flow cytometry and requires a flow cell sorter rather than a fluorescent microscope.
Key Points
- Fluorescent labeling of antibodies is used in place of radioisotopes and enzymes to enhance the sensitivity and specificity of immunological tests.
- Fluorescent antibodies can be used to stain proteins from patient serum or tissue sections fixed on a slide or live cells in suspension.
- Fluorescent antibodies can be detected with a fluorescent microscope or a flow cell sorter.
Key Terms
- radioisotope : A radioactive isotope of an element.


5: Sequences, Summations, and Logic
In this chapter, we will explore the mathematics behind situations such as these. We will take an in-depth look at annuities. We will also look at the branch of mathematics that would allow us to calculate the number of ways to choose lottery numbers and the probability of winning.
-
- 5.0: Introduction to Sequences, Probability and Counting Theory
- A lottery winner has some big decisions to make regarding what to do with the winnings. Buy a villa in Saint Barthélemy? A luxury convertible? A cruise around the world? The likelihood of winning the lottery is slim, but we all love to fantasize about what we could buy with the winnings. One of the first things a lottery winner has to decide is whether to take the winnings in the form of a lump sum or as a series of regular payments, called an annuity, over the next 30 years or so.
-
- 5.1: Sequences and Their Notations
- This section introduces sequences, defining them as ordered lists of terms generated by a specific rule. It covers notations for sequences, including explicit and recursive formulas, and explains how to find terms in a sequence. The section also introduces factorial notation and explores patterns in sequences.
-
- 5.2: Arithmetic Sequences
- This section explains arithmetic sequences, where the difference between consecutive terms is constant. It covers explicit and recursive formulas, how to find terms in a sequence, and calculating the sum of an arithmetic sequence. Examples show how to identify and apply these sequences in different contexts.
-
- 5.4: Series and Their Notations
- This section explains series as the sum of terms in a sequence and introduces sigma notation for representing series. It covers the distinction between finite and infinite series, including arithmetic and geometric series. Examples show how to calculate sums and apply series in real-world contexts.
-
- 5.5: Mathematical Induction
- This section introduces mathematical induction, a proof technique used to establish statements for all natural numbers. It explains the process in two steps: proving a base case and showing that if the statement holds for one integer, it also holds for the next. Examples illustrate how to apply induction to verify formulas and inequalities, providing a foundation for proving mathematical statements systematically.
-
- 5.6: Binomial Theorem
- A polynomial with two terms is called a binomial. We have already learned to multiply binomials and to raise binomials to powers, but raising a binomial to a high power can be tedious and time-consuming. In this section, we will discuss a shortcut that will allow us to find \((x+y)^n\) without multiplying the binomial by itself \(n\) times.
-
- 5.7: Chapter Review
- Probability is always a number between 0 and 1, where 0 means an event is impossible and 1 means an event is certain. The probabilities in a probability model must sum to 1. See Example. When the outcomes of an experiment are all equally likely, we can find the probability of an event by dividing the number of outcomes in the event by the total number of outcomes in the sample space for the experiment.
-
- 5.8: Exercises
- Probability is always a number between 0 and 1, where 0 means an event is impossible and 1 means an event is certain. The probabilities in a probability model must sum to 1. See Example. When the outcomes of an experiment are all equally likely, we can find the probability of an event by dividing the number of outcomes in the event by the total number of outcomes in the sample space for the experiment.


5.17: Discussion- Parenting Styles
Contributors and Attributions
CC licensed content, Shared previously
Public domain content
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DISCUSSION : In this discussion, reflect upon and discuss the following question:
STEP 1 : First, write a response with at least EIGHT substantial sentences, integrating concepts you learned from the reading and other materials (include links with necessary). Show that you can think critically on the topic by integrating your own thoughts, analysis, or experiences.
STEP 2 : Return to the discussion to comment on at least TWO classmates’ posts (in at least FIVE sentences). Expand on a classmate’s comments in a value-adding, topic-related way. Promote a collaborative, supportive community, and advance the dialogue through follow-up questions. Reply posts cannot be one-liners, off-topic posts, vague statements, unsupported opinions, inadequate explanations or simply say, “I agree” or “good job.”


16: Gene Expression
Whereas each cell shares the same genome and DNA sequence, each cell does not turn on, or express, the same set of genes. Each cell type needs a different set of proteins to perform its function. Therefore, only a small subset of proteins is expressed in a cell. For the proteins to be expressed, the DNA must be transcribed into RNA and the RNA must be translated into protein. In a given cell type, not all genes encoded in the DNA are transcribed into RNA or translated into protein because specific cells in our body have specific functions. Specialized proteins that make up the eye (iris, lens, and cornea) are only expressed in the eye, whereas the specialized proteins in the heart (pacemaker cells, heart muscle, and valves) are only expressed in the heart. At any given time, only a subset of all of the genes encoded by our DNA are expressed and translated into proteins. The expression of specific genes is a highly regulated process with many levels and stages of control. This complexity ensures the proper expression in the proper cell at the proper time.
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- 16.0: Prelude to Gene Expression
- Each somatic cell in the body generally contains the same DNA. A few exceptions include red blood cells, which contain no DNA in their mature state, and some immune system cells that rearrange their DNA while producing antibodies. In general, however, the genes that determine whether you have green eyes, brown hair, and how fast you metabolize food are the same in the cells in your eyes and your liver, even though these organs function quite differently.
-
- 16.1: Regulation of Gene Expression
- The regulation of gene expression conserves energy and space. It would require a significant amount of energy for an organism to express every gene at all times, so it is more energy efficient to turn on the genes only when they are required. In addition, only expressing a subset of genes in each cell saves space because DNA must be unwound from its tightly coiled structure to transcribe and translate the DNA.
-
- 16.2: Prokaryotic Gene Regulation
- The DNA of prokaryotes is organized into a circular chromosome supercoiled in the nucleoid region of the cell cytoplasm. Proteins that are needed for a specific function, or that are involved in the same biochemical pathway, are encoded together in blocks called operons. For example, all of the genes needed to use lactose as an energy source are coded next to each other in the lactose (or lac) operon.
-
- 16.3: Eukaryotic Epigenetic Gene Regulation
- Eukaryotic gene expression is more complex than prokaryotic gene expression because the processes of transcription and translation are physically separated. Unlike prokaryotic cells, eukaryotic cells can regulate gene expression at many different levels. Eukaryotic gene expression begins with control of access to the DNA. This form of regulation, called epigenetic regulation, occurs even before transcription is initiated.
-
- 16.4: Eukaryotic Transcription Gene Regulation
- Like prokaryotic cells, the transcription of genes in eukaryotes requires the actions of an RNA polymerase to bind to a sequence upstream of a gene to initiate transcription. However, unlike prokaryotic cells, the eukaryotic RNA polymerase requires other proteins, or transcription factors, to facilitate transcription initiation. Transcription factors are proteins that bind to the promoter sequence and other regulatory sequences to control the transcription of the target gene.
-
- 16.5: Eukaryotic Post-transcriptional Gene Regulation
- RNA is transcribed, but must be processed into a mature form before translation can begin. This processing after an RNA molecule has been transcribed, but before it is translated into a protein, is called post-transcriptional modification. As with the epigenetic and transcriptional stages of processing, this post-transcriptional step can also be regulated to control gene expression in the cell. If the RNA is not processed, shuttled, or translated, then no protein will be synthesized.
-
- 16.6: Eukaryotic Translational and Post-translational Gene Regulation
- After the RNA has been transported to the cytoplasm, it is translated into protein. Control of this process is largely dependent on the RNA molecule. As previously discussed, the stability of the RNA will have a large impact on its translation into a protein. As the stability changes, the amount of time that it is available for translation also changes.
-
- 16.7: Cancer and Gene Regulation
- Cancer is not a single disease but includes many different diseases. In cancer cells, mutations modify cell-cycle control and cells don’t stop growing as they normally would. Mutations can also alter the growth rate or the progression of the cell through the cell cycle. One example of a gene modification that alters the growth rate is increased phosphorylation of cyclin B, a protein that controls the progression of a cell through the cell cycle and serves as a cell-cycle checkpoint protein.
Thumbnail: Nucleosomes spaced far apart so that the DNA is exposed. Transcription factors can bind, allowing gene expression to occur. (CC BY 4.0 / modified from original; OpenStax ).


4.4: Precautions Used to Prevent the Spread of Infection
Health care agencies use several methods to prevent the spread of infection: standard precautions and transmission-based precautions.
Standard Precautions
Standard precautions are used by health care workers during client care when contact or potential contact with blood or body fluids may occur. Standard precautions should also be used when assisting a client with activities of daily living (ADLs) and using water, soap, or lotion. Standard precautions are based on the principle that all blood, body fluids (except sweat), nonintact skin, and mucous membranes may contain transmissible infectious agents. These precautions reduce the risk of exposure for the health care worker and protect patients from potential transmission of infectious organisms. [1]
According to the Centers for Disease Control and Prevention (CDC), standard precautions include the following [2] :
- Using proper hand hygiene at the appropriate times
- Using personal protective equipment (e.g., gloves, gowns, masks, eyewear) whenever exposure to infectious agents may occur
- Implementing respiratory hygiene for staff, patients, and visitors
- Proper cleaning and sanitizing of the environment, equipment, and devices
- Handling laundry safely
- Using transmission-based precautions when indicated
Hand Hygiene
The easiest and most effective way to break the chain of infection is by using proper hand hygiene at appropriate times during patient care. Knowing when to wash your hands, how to properly wash your hands, and when to use soap and water or hand sanitizer are vital for reducing the spread of infection and keeping yourself healthy. Hand hygiene is the process of removing, killing, or destroying microorganisms or visible contaminants from the hands. There are two hand-hygiene techniques: handwashing with soap and water and the use of alcohol-based hand rub (ABHR), also referred to as hand hygiene gel or hand sanitizer. [3]
Health care providers’ hands are the most common mode of transmission of microorganisms. As a nursing assistant, your hands will touch many people and objects when providing care. When you touch a client, their personal items, medical equipment, or their surrounding environment, you can indirectly transmit microorganisms to the client, another client, yourself, equipment, or a new environment. Microorganisms can easily be transferred from your hands to others or objects in the health care setting if proper hand hygiene practices are not followed. Consistent and effective hand hygiene is vital for breaking the chain of transmission. [4]
It is essential for all health care workers to use proper hand hygiene during specific moments of patient care [5] :
- Immediately before touching a patient
- Before performing an aseptic task, such as emptying urine from a Foley catheter bag
- Before moving from a soiled body site to a clean body site
- After touching a patient or their immediate environment
- After contact with blood, body fluids, or contaminated surfaces (with or without gloves)
- Immediately after glove removal
See Figure 4.4 [6] for an illustration of the five moments of hand hygiene.
Hand hygiene also includes health care workers keeping their nails short with tips less than 0.5 inches and no nail polish. Nails should be natural, and artificial nails or tips should not be worn. Artificial nails and chipped nail polish have been associated with a higher level of pathogens carried on the hands of health care workers despite using proper hand hygiene. [7]
Review the Moments of Hand Hygiene by clicking on the interactive activity below.
Query \(\PageIndex{1}\)
This work is a derivative of Your 4 Moments for Hand Hygiene by Michelle Hughes and is licensed under CC BY 4.0.
Proper hand hygiene includes handwashing with soap and water or the use of alcohol-based hand rub. Both procedures are described in the following sections.
Handwashing With Soap and Water
Handwashing involves the use of soap and water to physically remove microorganisms from one’s hands. Certain health care situations require handwashing with soap and water instead of using alcohol-based hand rub (ABHR). For example, hands must be washed with soap and water if they are visibly soiled, have been exposed to blood or body fluids, or have been exposed to norovirus , C. difficile , or Bacillus anthracis . The mechanical action of lathering and scrubbing with soap for a minimum of 20 seconds is vital for removing these types of microorganisms. [8]
Soap is required during handwashing to dissolve fatty materials and facilitate their subsequent flushing and rinsing with water. Soap must be rubbed on all surfaces of both hands followed by thorough rinsing and drying. Water alone is not suitable for cleaning soiled hands. The entire procedure should last 40 to 60 seconds, and soap approved by the health agency should be used. [9]
When washing with soap and water, the Centers for Disease Control and Prevention (CDC) recommends the following steps [10] :
- Wet hands with warm or cold running water and apply facility-approved soap.
- Lather hands by rubbing them together with the soap. Use the same technique as the hand rub process to clean the palms and fingers, between the fingers, the backs of the hands and fingers, the fingertips, and the thumbs.
- Scrub thoroughly for at least 20 seconds.
- Rinse hands well under clean, running water.
- Dry the hands, using a clean towel or disposable toweling, from fingers to wrists.

See Figure 4.5 [11] for an illustration of handwashing with soap and water.
See the “ Skills Checklist: Hand Hygiene With Soap and Water ” section later in this chapter for a checklist of steps and an associated demonstration video of this procedure. Common safety considerations and errors when washing hands are described in the following box.
Safety Considerations [12]
- Always wash hands with soap and water if hands are visibly soiled.
- When working with clients where C. difficile , norovirus , or Bacillus anthracis is suspected or confirmed, soap and water must be used. It is more effective in physically removing the C. difficile spores compared to ABHR, which is not as effective at penetrating the spores.
- Friction and rubbing are required to remove transient bacteria, oil, and debris from hands.
- Always use soap and water if hands are exposed to blood, body fluids, or other body substances.
- Multistep rubbing techniques using soap and water are required to promote coverage of all surfaces on hands.
Common Errors When Washing Hands With Soap and Water [13]
- Not using enough soap to cover all surfaces of the hands and wrists.
- Not using friction when washing hands.
- Not washing hands long enough. The mechanical action of lathering and scrubbing should be a minimum of 20 seconds, and the entire procedure should last 40 to 60 seconds.
- Missing areas such as the fingernails, wrists, backs of hands, and thumbs.
- Not removing all soap from hands and wrists.
- Shaking water off hands.
- Not thoroughly drying the hands.
- Drying hands from wrists to fingers or in both directions.
Practice your knowledge by clicking on this interactive learning activity.
Query \(\PageIndex{2}\)
This work is a derivative of the YouTube Hand Washing Video by Michelle Hughes and is licensed under CC BY-NC 4.0.
Alcohol-Based Hand Rub
When performing hand hygiene using the alcohol-based hand rub (ABHR) technique, a liquid, gel, or foam alcohol-based solution is used. ABHR is the preferred method for hand hygiene when soap and water handwashing is not required. It reduces the number of transient microorganisms on hands and is more effective for preventing healthcare-acquired infections (HAIs) caused by Methicillin-resistant Staphylococcus aureus (MRSA) and Vancomycin-resistant enterococcus (VRE). Hand hygiene with ABHR should be performed in front of the client prior to the beginning of care and at the end of the interaction. ABHR provided by the agency should be used with a 70–90% alcohol concentration. [14]
The benefits of ABHR include the following [15] :
- It kills the majority of microorganisms (including viruses) from hands.
- It requires less time than soap and water handwashing.
- It provides better skin tolerability and reduces skin irritation because it contains emollients.
- It is easy to use and available at the point of care (i.e., where three elements of the client, the health care provider, and care involving the client occur together).
Read safety considerations and common errors when using ABHR in the following box. See the “ Skills Checklist: Hand Hygiene With Alcohol-Based Hand Sanitizer ” section later in this chapter for a checklist of steps and an associated demonstration video of this procedure.
Safety Considerations [16]
- Do not use ABHR in combination with soap and water because it may increase skin irritation.
- Use ABHR that contains emollients (oils) to help reduce skin irritation and overdrying.
- Allow hands to dry completely before initiating tasks (e.g., touching the client or the environment or applying clean gloves).
- Use ABHR for all moments of hand hygiene if soap and water are not required.
- DO NOT use ABHR if hands are visibly soiled, have been exposed to blood or body fluids, or the client is suspected to have C. difficile , norovirus , or Bacillus anthracis .
- Only use ABHR supplied by the facility.
Common Errors When Performing an ABHR [17]
- Not letting hands air dry (for example, rubbing one’s hands on pants to dry it off).
- Shaking hands to dry.
- Applying too much alcohol-based solution.
- Not applying enough alcohol-based solution.
- Not rubbing hands long enough (a minimum of 20 seconds) and until hands are dry.
- Missing areas such as the fingernails, wrists, backs of the hands, and thumbs.
Practice your knowledge by clicking on this interactive learning activity.
Query \(\PageIndex{3}\)
Query \(\PageIndex{4}\)
This work is a derivative of Performing an Alcohol-Based Hand Rub by Michelle Hughes and is licensed under CC BY-NC 4.0.
Respiratory Hygiene and Other Hygienic Practices
Respiratory hygiene should be used by any person with signs of illness, including cough, congestion, or increased production of respiratory secretions to prevent the spread of infection. Respiratory hygiene refers to coughing or sneezing into the inside of one’s elbow or covering one’s mouth/nose with a tissue when coughing and promptly disposing of used tissues. Hand hygiene should be immediately performed after contact with one’s respiratory secretions. A coughing person should also wear a surgical mask to contain secretions. [18]
Additional hygiene measures are also used to prevent the spread of infection. For example, regularly changing bed linens, towels, and hospital gowns eliminates potential reservoirs of bacteria. Gripper socks should be removed before patients get into bed to prevent pathogens from the floor from being transferred to the patient’s bed linens.
Mobile devices should be cleaned regularly. Research has shown that cell phones and mobile devices carry many pathogens and are dirtier than a toilet seat or the bottom of a shoe. Patients, staff, and visitors routinely bring mobile devices into health care facilities that can cause the spread of infection. Mobile devices should be frequently wiped with disinfectant.
Disinfection and Sterilization
Disinfection and sterilization are procedures used to remove harmful pathogens from equipment and the environment to decrease the risk of spreading infection. Disinfection is the removal of microorganisms, but it does not destroy all spores and viruses. Sterilization destroys all pathogens on equipment or in the environment, including spores and viruses, and includes methods such as steam, boiling water, dry heat, radiation, and chemicals. Because of the harshness of sterilization methods, skin can only be disinfected and not sterilized. [19]
Asepsis refers to the absence of infectious material or infection. Surgical asepsis is the absence of all microorganisms during any type of invasive procedure, such as during surgery or heart catheterizations. Sterilization is performed on equipment used during invasive procedures. As a nursing assistant, you may assist a registered nurse during a procedure requiring sterile technique; however, performing sterile procedures independently is not in the scope of practice for nursing assistants.
In long-term care and other health care settings other than surgery, medical asepsis is used. Medical asepsis refers to techniques used to prevent the transfer of microorganisms from one person or object to another but do not eliminate all microorganisms. Nursing assistants implement medical asepsis in the following ways:
- Performing hand hygiene at the appropriate moments of patient care. (See previous Figure 4.4.)
- Using a barrier when placing clean linens, wash basins, and other items on a shared surface such as the countertop in a resident’s room.
- Pulling the privacy curtain when one resident has a droplet-transmitted infection to protect transmission to the other resident in a shared room.
- Cleaning equipment (such as blood pressure cuffs) between use on residents.
- Starting with “cleaner” areas of the body when assisting with care and then moving to areas with higher levels of microorganisms. For example, when bathing a client, the face is washed first, followed by the upper body and then finishing with perineal care. ( Perineal care involves washing the genital and rectal areas of the body.)
Laundry
When handling dirty linens, textiles, and patients’ clothing, follow agency policy regarding transport to prevent the potential spread of infection. The Centers for Disease Control and Prevention (CDC) states that contaminated textiles and fabrics should be handled with minimal agitation to avoid contamination of air, surfaces, and other individuals. They should be bagged at the point of use, and leak-resistant bags should be used for textiles and fabrics contaminated with blood or body substances. [20]
Transmission-Based Precautions
When providing care for individuals with known or suspected infections, additional precautions are used in addition to the previously discussed standard precautions. Certain types of pathogens and communicable diseases are easily transmitted to others and require additional precautions to interrupt the spread of infectious agents to health care workers and other clients. For example, Coronavirus disease (COVID-19), C. difficile (C-diff), Methicillin-resistant Staphylococcus aureus ( MRSA), Vancomycin-resistant enterococci (VRE), Respiratory Syncytial Virus (RSV), measles, and tuberculosis (TB) require transmission-based precautions.
Transmission-based precautions (commonly referred to as isolation precautions) use specific types of personal protective equipment (PPE) and practices based on the pathogen’s mode of transmission. It is vital for nursing assistants to understand what PPE should be used in specific client care situations, which is determined by the pathogen’s mode of transmission and their possible risk of exposure. [21] Transmission-based precautions include three categories: contact, droplet, and airborne precautions. Read more about each type of transmission-based precaution in Table 4.1.
Table 4.1 Categories of Transmission-Based Precautions [22] , [23] , [24]
| Transmission-Based Precaution | PPE Required | Special Considerations |
|---|---|---|
| Contact | Gloves and gown, possibly face shield | Used for clients with known or suspected infections such as C-difficile (C-diff), methicillin-resistant staphylococcus aureus (MRSA), vancomycin resistant enterococcus (VRE), or norovirus transmitted by touch (e.g., drainage from wounds or fecal incontinence). Contact precautions should be used when there is expected contact with the source of the pathogen or any surfaces within the resident’s room. For example, MRSA in a client’s wound transmits with direct contact with the wound, so wearing gloves and a gown when entering the room with a meal tray is typically sufficient. However, MRSA in a client’s urine could be accidentally splashed onto one’s mucous membrane when emptying the bag of an indwelling urinary catheter, so a face shield is also necessary for this task, in addition to wearing gloves and a gown. |
| Droplet | Gloves and a mask | Used for clients with a diagnosed or suspected pathogen that is spread in small droplets from sneezing or other oral and nasal secretions, such as influenza or pertussis. Droplets can travel six feet, so using barriers such as privacy curtains and closing doors can also prevent the spread of infection to others. |
| Airborne | Gloves and respirator | Used for clients with diagnosed or suspected pathogens spread by very small airborne particles from nasal and oral secretions that can float long distances through the air, such as measles and tuberculosis.  Clients must be placed in a room with specialized air handling equipment found in doctors’ offices and hospitals. Residents in long-term care settings suspected of having an airborne illness should be transferred immediately to prevent the spread of infection to other residents. |
Signage for Transmission-Based Precautions
When a resident has an infectious illness requiring transmission-based precautions, a sign is placed on their door and a cart of PPE supplies is placed nearby. Signs vary by facility but look similar to the image in Figure 4.6. [25] Due to HIPAA regulations, the type of the pathogen and the source cannot be displayed publicly, so the sign instructs anyone wishing to enter the room to ask the nurse first. Additional information regarding the type and source of the infection can be found in the client’s nursing care plan. After you become aware of the pathogen, the source, and the required PPE, you can safely enter the room. If you are unsure about any aspect of PPE required or your risk of exposure, talk to the nurse before entering the room or providing care.
View the following YouTube video from the University of Iowa about isolation precautions in a health care setting: Standard and Isolation Precautions.
- Centers for Disease Control and Prevention. (2016, January 26). Standard precautions for all patient care. https://www.cdc.gov/infectioncontrol/basics/standard-precautions.html ↵
- Centers for Disease Control and Prevention. (2016, January 26). Standard precautions for all patient care. https://www.cdc.gov/infectioncontrol/basics/standard-precautions.html ↵
- This work is a derivative of Introduction to Infection Prevention and Control Practices for the Interprofessional Learner by Hughes, Kenmir, St-Amant, Cosgrove, & Sharpe and is licensed under CC BY-NC 4.0 ↵
- This work is a derivative of Introduction to Infection Prevention and Control Practices for the Interprofessional Learner by Hughes, Kenmir, St-Amant, Cosgrove, & Sharpe and is licensed under CC BY-NC 4.0 ↵
- Centers for Disease Control and Prevention. (2019, April 29). Hand hygiene in healthcare settings. https://www.cdc.gov/handhygiene/ ↵
- “5Moments_Image.gif” by World Health Organization is licensed under CC BY-NC-SA 3.0 IGO . Access for free at https://www.who.int/infection-prevention/campaigns/clean-hands/5moments/en/ ↵
- Blackburn, L., Acree, K., Bartley, J., DiGiannantoni, E., Renner, E., & Sinnott, L. T. (2020). Microbial growth on the nails of direct patient care nurses wearing nail polish. Oncology Nursing Forum, 47 (2), 155-164. https://doi.org/10.1188/20.onf.155-164 ↵
- This work is a derivative of Introduction to Infection Prevention and Control Practices for the Interprofessional Learner by Hughes, Kenmir, St-Amant, Cosgrove, & Sharpe and is licensed under CC BY-NC 4.0 ↵
- This work is a derivative of Introduction to Infection Prevention and Control Practices for the Interprofessional Learner by Hughes, Kenmir, St-Amant, Cosgrove, & Sharpe and is licensed under CC BY-NC 4.0 ↵
- Centers for Disease Control and Prevention. (2016, January 26). Standard precautions for all patient care. https://www.cdc.gov/infectioncontrol/basics/standard-precautions.html ↵
- “ How_To_HandWash_Poster.pdf ” by World Health Organization is licensed under CC BY-NC-SA 3.0 IGO . Access for free at https://www.who.int/infection-prevention/campaigns/clean-hands/5moments/en/ ↵
- This work is a derivative of Introduction to Infection Prevention and Control Practices for the Interprofessional Learner by Hughes, Kenmir, St-Amant, Cosgrove, & Sharpe and is licensed under CC BY-NC 4.0 ↵
- This work is a derivative of Introduction to Infection Prevention and Control Practices for the Interprofessional Learner by Hughes, Kenmir, St-Amant, Cosgrove, & Sharpe and is licensed under CC BY-NC 4.0 ↵
- Centers for Disease Control and Prevention. (2016, January 26). Standard precautions for all patient care. https://www.cdc.gov/infectioncontrol/basics/standard-precautions.html ↵
- Centers for Disease Control and Prevention. (2016, January 26). Standard precautions for all patient care. https://www.cdc.gov/infectioncontrol/basics/standard-precautions.html ↵
- Centers for Disease Control and Prevention. (2016, January 26). Standard precautions for all patient care. https://www.cdc.gov/infectioncontrol/basics/standard-precautions.html ↵
- Centers for Disease Control and Prevention. (2016, January 26). Standard precautions for all patient care. https://www.cdc.gov/infectioncontrol/basics/standard-precautions.html ↵
- Centers for Disease Control and Prevention. (2016, January 26). Standard precautions for all patient care. https://www.cdc.gov/infectioncontrol/basics/standard-precautions.html ↵
- This work is a derivative of Nursing Fundamentals by Chippewa Valley Technical College and is licensed under CC BY 4.0 ↵
- Centers for Disease Control and Prevention. (2020, April 29). Infection control. https://www.cdc.gov/infectioncontrol/index.html ↵
- This work is a derivative of Introduction to Infection Prevention and Control Practices for the Interprofessional Learner by Hughes, Kenmir, St-Amant, Cosgrove, & Sharpe and is licensed under CC BY-NC 4.0 ↵
- Office of Infectious Disease and HIV/AIDS Policy. (n.d.). Health care-associated infections. U.S. Department of Health & Human Services. https://www.hhs.gov/oidp/topics/health-care-associated-infections/index.html ↵
- This work is a derivative of Introduction to Infection Prevention and Control Practices for the Interprofessional Learner by Hughes, Kenmir, St-Amant, Cosgrove, & Sharpe and is licensed under CC BY-NC 4.0 ↵
- Siegel, J. D., Rhinehart, E., Jackson, M., Chiarello, L., & Healthcare Infection Control Practices Advisory Committee. (2019, July 22). 2007 guideline for isolation precautions: Preventing transmission of infectious agents in healthcare settings. Centers for Disease Control and Prevention . https://www.cdc.gov/infectioncontrol/guidelines/isolation/index.html ↵
- “contact-precautions-sign-P.pdf” by U.S. Department of Health and Human Services and Centers for Disease Control and Prevention is licensed in the Public Domain . Access for free at https://www.cdc.gov/infectioncontrol/basics/transmission-based-precautions.html#anchor_1564058318 ↵


3.0: Prelude to Descriptive Statistics
Skills to Develop
By the end of this chapter, the student should be able to:
- Recognize, describe, and calculate the measures of the center of data: mean, median, and mode.
- Recognize, describe, and calculate the measures of the spread of data: variance, standard deviation, and range.
- Recognize, describe, and calculate the measures of location of data: quartiles, percentiles, and deciles.
- Use quartiles to create a boxplot.
Once you have collected data, what will you do with it? Data can be described and presented in many different formats. For example, suppose you are interested in buying a house in a particular area. You may have no clue about the house prices, so you might ask your real estate agent to give you a sample data set of prices. Looking at all the prices in the sample often is overwhelming. A better way might be to look at the median price and the variation of prices. The median and variation are just two ways that you will learn to describe data. Your agent might also provide you with a graph of the data.
Measures of center, spread and location are additional ways you can describe data. We will explore important measures and another graph called a box plot.
This book contains instructions for constructing a histogram and a box plot for the TI-83+ and TI-84 calculators. The Texas Instruments (TI) website provides additional instructions for using these calculators.
Contributors and Attributions
-
Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>.


17.2A: Heart Circulation
- Describe circulation of blood in the heart
Atherosclerotic plaques in a coronary artery will slowly occlude (block) the vessel. As the vessel diameter narrows, less blood and oxygen will pass through and a region of the myocardium will consequently not receive an adequate supply of oxygen. This could result in angina and ultimately a myocardial infarction.
Coronary circulation is the circulation of blood in the blood vessels of the heart muscle. The vessels that deliver oxygen-rich blood to the myocardium are known as coronary arteries. The vessels that remove the deoxygenated blood from the heart muscle are known as cardiac veins. The blood supply to the heart is greater than that of other body tissues since the heart has a constant metabolic demand that must be satisfied to keep the heart pumping at all times.
Coronary Circulation : Coronary arteries labeled in red text and other landmarks in blue text.
Coronary Artery Structure
The coronary arteries originate from the left side of the heart descending from the aorta. There are multiple coronary arteries derived from the larger right and left coronary arteries. For example, important coronary arteries that branch off from the larger arteries include the left anterior descending (LAD) coronary and the right posterior coronary.
Coronary arteries run both along the surface of the heart and deep within the myocardium, which has the greatest metabolic demands of all the heart tissues due to its muscle content. Epicardial coronary arteries, which run along on the surface of the heart, are capable of autoregulating vasodilation and vasoconstriction to maintain coronary blood flow at appropriate levels to fit the metabolic demands of the heart muscle. These vessels are relatively narrow and thus vulnerable to blockage, which may cause a myocardial infarction. Subendocardial coronary arteries run deep within the myocardium to provide oxygen throughout the muscle tissue of the cardiac wall.
Systole and Diastole
In systole, the ventricular myocardium contracts, generating high intraventricular pressure and compressing the subendocardial coronary vessels while allowing the epicardial coronary vessels to remain fully open. With the subendocardial coronary vessels compressed, blood flow essentially stops below the surface of the myocardium.
In diastole, the ventricular myocardium contracts, lowering the intraventricular pressure and allowing the subendocardial vessels to become open again. Due to the high pressures generated in the ventricular myocardium during systole, most myocardial tissue perfusion occurs during diastole. Additionally, catecholamines such as norephinephrine, which normally cause vasoconstriction will instead cause vasodilation within the coronary arteries. This mechanism is due to beta-adrenergic receptors in the coronary arteries and helps enable the increased cardiac output associated with fight-or-flight responses.
Myocardial Infarctions
A myocardial infarction (heart attack) may be caused by prolonged ischemia (oxygen deprivation) in the heart, which occurs due to blockage of any of the coronary arteries. Since there is very little unnecessary blood supply to the myocardium, blockage of these vessels can cause serious damage. When these vessels become blocked, the myocardium becomes oxygen-deprived, a condition called ischemia. Brief periods of ischemia in the heart are associated with intense chest pain called angina, which may either be transient if the clot breaks up on its own or stable if it does not. As the time period of ischemia increases, the hypoxic conditions cause muscle tissue to die, causing a myocardial infarction (heart attack).
Myocardial infarction is one of the most common causes of death worldwide. The clots that cause the infarction are usually the result of ruptured atherosclerotic plaques that break off and occlude the coronary arteries, but arterial thrombosis from injury or pooled blood may also cause a heart attack. The tissues of the heart do not regenerate, so those that survive a myocardial infarction will generally have scar tissue in their myocardium and may be more susceptible to other heart problems in the future.
Key Points
- The vessels that supply blood to the myocardium are called coronary arteries and coronary veins.
- The left and right coronary arteries branch off into smaller arteries, such as the important left anterior descending (LAD) coronary artery.
- The vessels that deliver oxygen-rich blood to the myocardium are known as coronary arteries. The vessels that remove the deoxygenated blood from the heart muscle are known as cardiac veins.
- Most tissue perfusion in the heart occurs when the coronary arteries open during diastole.
- Failure of the coronary arteries to provide sufficient blood supply to the heart can lead to ischemia, angina, and myocardial infarction.
- Norepinephrine will cause vasodilation in the coronary arteries but vasoconstriction in the other arteries of the body.
- Myocardial infarctions are the result of ruptured artherosclerotic plaques or arterial thrombosis, which cause the death of heart tissue from prolonged ischemia.
Key Terms
- myocardial infarction : Necrosis of heart muscle caused by an interruption to the supply of blood to the heart, often as a result of prolonged ischemia.
- ischemia : Oxygen deprivation in tissues due to mechanical obstruction of the blood supply, such as by a narrowed or blocked artery or clot.
- angina : Chest pain that indicates ischemia in the heart. It may be either transient (unstable) or stable, and stable anginas typically lead to infarction.


7.3: Post-test
- True or False: Physical disabilities may not only be due to developmental causes, and can occur at any time in a person’s life.
-
Which of the following are
possible
causes of physical disabilities?
Select
all
that
apply
.
- Diabetes
- Motor vehicle accident
- Cerebrovascular accident (stroke)
- War-related injury
- Sports-related injury
- Traumatic Brain Injury
- Arthritis
- Work-related injury
- True or False: Temporary disabilities are those a person only has for a short period of time until healing occurs, while permanent disabilities are those the person has throughout their entire lives.
- True or False: Having a strong support system can help a person with a physical disability positively cope with stressors they face and adaptations they need to make in order to be as independent as possible.
- True or False: People with physical disabilities experience a variety of emotions, including happiness, joy, anger, depression, and frustration.
-
Which of the following are adaptive equipment that a person with a physical
disability
can use to be as independent as possible?
Select
all
that
apply
.
- Glasses
- Hearing aids
- Canes
- Walkers
- Wheelchairs
- Special shoes or boots
- Special writing and eating utensils
- True or False: It is very important to remember that adults with disabilities, even those who require complete care are not children, and should be treated as an adult.
- The HHA/PCA should keep in mind that disability does not define a person. All people should be treated as unique individuals with strengths and talents.
- Answer
-
1. True
2. All are possible causes
3. True
4. True
5. True
6. All are adaptive equipment
7. True
8. True


6.4: Synthesis of Your Own Ideas
- What was the author really trying to say?
- What parts of them do you agree with?
- What parts of them do you disagree with?
- Did they leave anything out?
- What does an author’s work lead you to say?
It’s wise to not only analyze—take apart for study—the sources, but also to try to combine your own ideas with those presented in class and in the resources. Professors frequently expect you to interpret, make inferences, and otherwise synthesize—bring ideas together to make something new or find a new way of looking at something old. It might help to think of synthesis as the opposite of analysis.
Getting Better at Synthesis
To get an A on essays and papers in many courses, such as literature and history, when you write in reaction to others’ work you should use synthesis to create new meaning or show a deeper understanding of what you learned. To do so, it helps to look for connections and patterns. One way to synthesize when writing an argument essay, paper, or other project is to look for themes among your sources. So try categorizing ideas by topic rather than by resource—making associations across sources. Synthesis can seem difficult, particularly if you are used to analyzing others’ points but are not used to making your own. Like most things, however, it gets easier as you get more experienced at it. So don’t be hard on yourself if it seems difficult at first.
Imagine that you have to write an argument essay about Woody Allen’s 2011 movie Midnight in Paris . Your topic is “nostalgia,” and the movie is the only resource you can use. In the movie, a successful young screenwriter named Gil is visiting Paris with his girlfriend and her parents, who are more politically conservative than he is. Inexplicably, every midnight he time-travels back to the 1920’s Paris, a time period he’s always found fascinating, especially because of the writers and painters—Hemingway, Fitzgerald, Picasso—that he’s now on a first-name basis with. Gil is enchanted and always wants to stay. But every morning, he’s back in real-time—feeling out of sync with his girlfriend and her parents.
You’ve tried to come up with a narrower topic, but so far nothing seems right. Suddenly, you start paying more attention to the girlfriend’s parents’ dialogue about politics, which amount to such phrases as “we have to go back to…,” “it was a better time,” “Americans used to be able to…” and “the way it used to be.” And then it clicks with you that the girlfriend’s parents are like Gil—longing for a different time, whether real or imagined. That kind of idea generation is synthesis.
You decide to write your essay to answer the research question: How is the motivation of Gil’s girlfriend’s parents similar to Gil’s? Your thesis becomes “Despite seeming to be not very much alike, Gil and the parents are similarly motivated, and Woody Allen meant Midnight in Paris ‘s message about nostalgia to be applied to all of them.” Of course, you’ll have to try to convince your readers that your thesis is valid and you may or not be successful—but that’s true with all theses. And your professor will be glad to see the synthesis.
There is a lot more you can learn about creating synthesis in scholarly writing. One place synthesis is usually required is in literature reviews for honors’ theses, master’s theses, and Ph.D. dissertations. In all those cases, literature reviews are intended to contribute more than annotated bibliographies do and to be arguments for the research conducted for the theses or dissertations. If you are writing an honors thesis, master’s thesis, or Ph.D. dissertation, check out Susan Imel’s Writing a Literature Review for more advice.


7.1.5: Using Equations to Solve for Unknown Angles
Lesson
Let's figure out missing angles using equations.
Exercise \(\PageIndex{1}\): Is this Enough?
Tyler thinks that this figure has enough information to figure out the values of \(a\) and \(b\).
Do you agree? Explain your reasoning.
Exercise \(\PageIndex{2}\): What Does It Look Like?
Elena and Diego each wrote equations to represent these diagrams. For each diagram, decide which equation you agree with, and solve it. You can assume that angles that look like right angles are indeed right angles.
1. Elena: \(x=35\)
Diego: \(x+35=180\)
2. Elena: \(35+w+41=180\)
Diego: \(w+35=180\)
3. Elena: \(w+35=90\)
Diego: \(2w+35=90\)
4. Elena: \(2w+35=90\)
Diego: \(w+35=90\)
5. Elena: \(w+148=180\)
Diego: \(x+90=148\)
Exercise \(\PageIndex{3}\): Calculate the Measure
Find the unknown angle measures. Show your thinking. Organize it so it can be followed by others.
Lines \(l\) and \(m\) are perpendicular.
Are you ready for more?
The diagram contains three squares. Three additional segments have been drawn that connect corners of the squares. We want to find the exact value of \(a+b+c\).
- Use a protractor to measure the three angles. Use your measurements to conjecture about the value of \(a+b+c\).
- Find the exact value of \(a+b+c\) by reasoning about the diagram.
Summary
To find an unknown angle measure, sometimes it is helpful to write and solve an equation that represents the situation. For example, suppose we want to know the value of \(x\) in this diagram.
Using what we know about vertical angles, we can write the equation \(3x+90=144\) to represent this situation. Then we can solve the equation.
\(\begin{aligned} 3x+90&=144 \\ 3x+90-90&=144-90 \\ 3x&=54 \\ 3x\cdot\frac{1}{3}&=54\cdot\frac{1}{3} \\ x&=18\end{aligned}\)
Glossary Entries
Definition: Adjacent Angles
Adjacent angles share a side and a vertex.
In this diagram, angle \(ABC\) is adjacent to angle \(DBC\).
Definition: Complementary
Complementary angles have measures that add up to 90 degrees.
For example, a \(15^{\circ}\) angle and a \(75^{\circ}\) angle are complementary.
Definition: Right Angle
A right angle is half of a straight angle. It measures 90 degrees.
Definition: Straight Angle
A straight angle is an angle that forms a straight line. It measures 180 degrees.
Definition: Supplementary
Supplementary angles have measures that add up to 180 degrees.
For example, a \(15^{\circ}\) angle and a \(165^{\circ}\) angle are supplementary.
Definition: Vertical Angles
Vertical angles are opposite angles that share the same vertex. They are formed by a pair of intersecting lines. Their angle measures are equal.
For example, angles \(AEC\) and \(DEB\) are vertical angles. If angle \(AEC\) measures \(120^{\circ}\), then angle \(DEB\) must also measure \(120^{\circ}\).
Angles \(AED\) and \(BEC\) are another pair of vertical angles.
Practice
Exercise \(\PageIndex{4}\)
Segments \(AB\), \(DC\), and \(EC\) intersect at point \(C\). Angle \(DCE\) measures \(148^{\circ}\). Find the value of \(x\).
Exercise \(\PageIndex{5}\)
Line \(l\) is perpendicular to line \(m\). Find the value of \(x\) and \(w\).
Exercise \(\PageIndex{6}\)
If you knew that two angles were complementary and were given the measure of one of those angles, would you be able to find the measure of the other angle? Explain your reasoning.
Exercise \(\PageIndex{7}\)
For each inequality, decide whether the solution is represented by \(x<4.5\) or \(x>4.5\).
- \(-24>-6(x-0.5)\)
- \(-8x+6>-30\)
- \(-2(x+3.2)<-15.4\)
(From Unit 6.3.3)
Exercise \(\PageIndex{8}\)
A runner ran \(\frac{2}{3}\) of a 5 kilometer race in 21 minutes. They ran the entire race at a constant speed.
- How long did it take to run the entire race?
- How many minutes did it take to run 1 kilometer?
(From Unit 4.1.2)
Exercise \(\PageIndex{9}\)
Jada, Elena, and Lin walked a total of 37 miles last week. Jada walked 4 more miles than Elena, and Lin walked 2 more miles than Jada. The diagram represents this situation:
Find the number of miles that they each walked. Explain or show your reasoning.
(From Unit 6.2.6)
Exercise \(\PageIndex{10}\)
Select all the expressions that are equivalent to \(-36x+54y-90\).
- \(-9(4x-6y-10)\)
- \(-18(2x-3y+5)\)
- \(-6(6x+9y-15)\)
- \(18(-2x+3y-5)\)
- \(-2(18x-27y+45)\)
- \(2(-18x+54y-90)\)
(From Unit 6.4.2)


5.3: Early Telescopes
Jan (or Han) Lipperhey of Holland, a spectacle maker, is given credit for inventing the first telescope in 1608 — a refracting telescope . He called his telescope Kijker , meaning “looker” in Dutch. Lipperhey’s telescope was a refracting or lens-type telescope – as were all early telescopes; this used a convex lens to focus incoming light. Lipperhey thought the telescope’s best use was military .
Lipperhey unsuccessfully tried to patent the telescope, as well as telescope binoculars. Since Lipperhey was denied a patent – probably meaning he did not invent the telescope – who did invent the telescope? Rumor has it Lipperhey’s son actually discovered the correct lens combination – he put together two lenses and “spied” a local church steeple . Some historians argue that Lipperhey stole the idea from Hans and Zacharias Janssen , other spectacle makers, who supposedly built a telescope in 1595. However, historical references are not as clear on the Janssens and their telescope.
The first to use the telescope astronomically was Galileo Galilei . Galileo made his first telescope in 1609, based on what he had heard about the Lipperhey telescope. However Galileo’s telescope was of much-better quality than Lipperhey’s telescope.
“…[But] perhaps his [Galeleo] most famous invention was the telescope. Galileo made his first telescope in 1609, modeled after telescopes produced in other parts of Europe that could magnify objects three times. He created a telescope later that same year that could magnify objects twenty times. With this telescope, he was able to look at the moon, discover the four satellites of Jupiter, observe a supernova, verify the phases of Venue, and discover sunsports. His discoveries proved the Copernican system which sates that the earth and other planets revolve around the sun. Prior to the Copernican system, it was held that the universe was geocentric, meaning the sun revolved around the earth”
— The Galileo Project (1564-1642)


7.1: Introduction to Employee Development and Performance Evaluations
What you’ll learn to do: describe employee development and performance evaluations
Good managers know that employees are the company’s most valuable assets. Employee development is the process by which employees become even more valuable by building their skills and expanding their capabilities. The better their skills and abilities, the more likely it is that employees will succeed in their jobs and progress in their careers.
Performance evaluations are a tool for determining how quickly and well an employee is developing. They are also an opportunity to discover employees’ untapped strengths and interests, and to fill gaps in employee training that can lead to mistakes or lower productivity.
Contributors and Attributions
- Introduction to Employee Development and Performance Evaluations. Authored by : Lisa Jo Rudy and Lumen Learning. License : CC BY: Attribution


4.20: Introduction to Models of the Buying Process
What you’ll learn to do: Identify the various models of buying processes
In the sections titled Consumer Decision-Making Process and The Steps of the Buying Process , we introduced processes or steps consumers engage in as they prepare to make a purchase. In particular, we described three models: AIDA, path-to-purchase, and the consumer buying process.
We also identified the specific steps:
- Recognition of an Issue or Need
- Information Gathering
- Evaluation of Options or Alternatives
- Selection
- Purchase
- After-Purchase Evaluation
In the coming sections, we’ll go a bit deeper to describe three ways to evaluate consumers’ buying decisions. That is, is their motivation explained by: largely quantitative economic models, largely qualitative psychological models or a blend of the two, consumer behavior models?
Contributors and Attributions
- Introduction to Models of the Buying Process. Authored by : Patrick Williams. Provided by : Lumen Learning. License : CC BY: Attribution


15.0: Prelude to Thermodynamics
Heat transfer is energy in transit, and it can be used to do work. It can also be converted to any other form of energy. A car engine, for example, burns fuel for heat transfer into a gas. Work is done by the gas as it exerts a force through a distance, converting its energy into a variety of other forms—into the car’s kinetic or gravitational potential energy; into electrical energy to run the spark plugs, radio, and lights; and back into stored energy in the car’s battery. But most of the heat transfer produced from burning fuel in the engine does not do work on the gas. Rather, the energy is released into the environment, implying that the engine is quite inefficient.
It is often said that modern gasoline engines cannot be made to be significantly more efficient. We hear the same about heat transfer to electrical energy in large power stations, whether they are coal, oil, natural gas, or nuclear powered. Why is that the case? Is the inefficiency caused by design problems that could be solved with better engineering and superior materials? Is it part of some money-making conspiracy by those who sell energy? Actually, the truth is more interesting, and reveals much about the nature of heat transfer.
Basic physical laws govern how heat transfer for doing work takes place and place insurmountable limits onto its efficiency. This chapter will explore these laws as well as many applications and concepts associated with them. These topics are part of thermodynamics —the study of heat transfer and its relationship to doing work.