1.6: Validity
-
- Last updated
- Save as PDF
So far we have discussed what arguments are and how to determine their structure, including how to reconstruct arguments in standard form. But we have not yet discussed what makes an argument good or bad. The central concept that you will learn in logic is the concept of validity. Validity relates to how well the premises support the conclusion, and it is the golden standard that every argument should aim for. A valid argument is an argument whose conclusion cannot possibly be false, assuming that the premises are true. Another way of putting this is as a conditional statement: A valid argument is an argument in which if the premises are true, the conclusion must be true. Here is an example of a valid argument:
1. Violet is a dog
2.  But, for the purposes of validity, it doesn’t matter whether premise 1 is actually true or false. All that matters for validity is whether the conclusion follows from the premise. And we can see that the conclusion, Violet is a mammal, does seem to follow from the premise, Violet is a dog. That is, given the truth of the premise, the conclusion has to be true. This argument is clearly valid since if we assume that “Violet is a dog” is true, then, since all dogs are mammals, it follows that “Violet is a mammal” must also be true. As we’ve just seen, whether or not an argument is valid has nothing to do with whether the premises of the argument are actually true or not. We can illustrate this with another example, where the premises are clearly false:
1. Everyone born in France can speak French
2. Barack Obama was born in France
3. Therefore, Barak Obama can speak French (from 1-2)
This is a valid argument. Why? Because when we assume the truth of the premises (everyone born in France can speak French, Barack Obama was born in France) the conclusion (Barack Obama can speak French) must be true. Notice that this is so even though none of these statements is actually true. Not everyone born in France can speak French (think about people who were born there but then moved somewhere else where they didn’t speak French and never learned it) and Obama was not born in France, but it is also false that Obama can speak French. So we have a valid argument even though neither the premises nor the conclusion is actually true. That may sound strange, but if you understand the concept of validity, it is not strange at all. Remember: validity describes the relationship between the premises and conclusion, and it means that the premises imply the conclusion, whether or not that conclusion is true. In order to better understand the concept of validity, let’s look at an
example of an invalid argument:
1. George was President of the United States
2. Therefore, George was elected President of the United States (from 1)
This argument is invalid because it is possible for the premise to be true and yet the conclusion false. Here is a counterexample to the argument. Gerald Ford was President of the United States but he was never elected president, since Ford Replaced Richard Nixon when Nixon resigned in the wake of the Watergate scandal. 2 So it doesn’t follow that just because someone is President of the United States that they were elected President of the United States. In other words, it is possible for the premise of the argument to be true and yet the conclusion false. And this means that the argument is invalid. If an argument is invalid it will always be possible to construct a counterexample to show that it is invalid (as I have done with the Gerald Ford scenario). A counterexample is simply a description of a scenario in which the premises of the argument are all true while the conclusion of the argument is false.
In order to determine whether an argument is valid or invalid we can use what I’ll call the informal test of validity . To apply the informal test of validity ask yourself whether you can imagine a world in which all the premises are true and yet the conclusion is false. If you can imagine such a world, then the argument is invalid. If you cannot imagine such a world, then the argument is valid. Notice: it is possible to imagine a world where the premises are true even if the premises aren’t, as a matter of actual fact, true. This is why it doesn’t matter for validity whether the premises (or conclusion) of the argument are actually true. It will help to better understand the concept of validity by applying the informal test of validity to some sample arguments.
1. Joan jumped out of an airplane without a parachute
2. Therefore, Joan fell to her death (from 1)
To apply the informal test of validity we have to ask whether it is possible to imagine a scenario in which the premise is true and yet the conclusion is false (if so, the argument is invalid). So, can we imagine a world in which someone jumped out of an airplane without a parachute and yet did not fall to her death? (Think about it carefully before reading on.) As we will see, applying the informal test of validity takes some creativity, but it seems clearly possible that Joan could jump out of an airplane without a parachute and not die—she could be perfectly fine, in fact. All we have to imagine is that the airplane was not operating and in fact was on the ground when Joan jumped out of it. If that were the case, it would be a) true that Joan jumped out of an airplane without a parachute and yet b) false that Joan fell to her death. Thus, since it is possible to imagine a scenario in which the premise is true and yet the conclusion is false, the argument is invalid. Let’s slightly change the argument, this time making it clear that the plane is flying:
1. Joan jumped out of an airplane travelling 300 mph at a height of 10,000 ft without a parachute
2. Joan fell to her death (from 1)
Is this argument valid? You might think so since you might think that anyone who did such a thing would surely die. But is it possible to not die in the scenario described by the premise? If you think about it, you’ll realize that there are lots of ways someone could survive. For example, maybe someone else who was wearing a parachute jumped out of the plane after them, caught them and attached the parachute-less person to them, and then pulled the ripcord and they both landed on the ground safe and sound. Or maybe Joan was performing a stunt and landed in a giant net that had been set up for that purpose. Or maybe she was just one of those people who, although they did fall to the ground, happened to survive (it has happened before). All of these scenarios are consistent with the information in the first premise being true and also consistent with the conclusion being false. Thus, again, any of these counterexamples show that this argument is invalid. Notice that it is also possible that the scenario described in the premises ends with Joan falling to her death. But that doesn’t matter because all we want to know is whether it is possible that she doesn’t. And if it is possible, what we have shown is that the conclusion does not logically follow from the premise alone. That is, the conclusion doesn’t have to be true, even if we grant that the premise is. And that means that the argument is not valid (i.e., it is invalid).
Let’s switch examples and consider a different argument.
1. A person can be President of the United States only if they were born
in the United States.
2. Obama is President of the United States.
3. Kenya is not in the United States.
4. Therefore, Obama was not born in Kenya (from 1-3)
In order to apply the informal test of validity, we have to ask whether we can imagine a scenario in which the premises are both true and yet the conclusion is false. So, we have to imagine a scenario in which premises 1, 2, and 3 are true and yet the conclusion (“Obama was not born in Kenya”) is false. Can you imagine such a scenario? You cannot. The reason is that if you are imagining that it is a) true that a person can be President of the United States only if they were born in the United States, b) true that Obama is president and c) true that
Kenya is not in the U.S., then it must be true that Obama was not born in Kenya. Thus we know that on the assumption of the truth of the premises, the conclusion must be true. And that means the argument is valid. In this example, however, premises 1, 2, and 3 are not only assumed to be true but are actually true. However, as we have already seen, the validity of an argument does not depend on its premises actually being true. Here is another example of a valid argument to illustrate that point.
1. A person can be President of the United States only if they were born in Kenya
2. Obama is President of the United States
3. Therefore, Obama was born in Kenya (from 1-2)
Clearly, the first premise of this argument is false. But if we were to imagine a scenario in which it is true and in which premise 2 is also true, then the conclusion (“Obama was born in Kenya”) must be true. And this means that the argument is valid. We cannot imagine a scenario in which the premises of the argument are true and yet the conclusion is false. The important point to recognize here—a point I’ve been trying to reiterate throughout this section—is that the validity of the argument does not depend on whether or not the premises (or conclusion) are actually true. Rather, validity depends only on the logical relationship between the premises and the conclusion. The actual truth of the premises is, of course, important to the quality of the argument, since if the premises of the argument are false, then the argument doesn’t provide any reason for accepting the conclusion. In the next section we will address this topic.
Exercise
Determine whether or not the following arguments are valid by using the informal test of validity. If the argument is invalid, provide a counterexample.
1. Katie is a human being. Therefore, Katie is smarter than a chimpanzee.
2. Bob is a fireman. Therefore, Bob has put out fires.
3. Gerald is a mathematics professor. Therefore, Gerald knows how to teach mathematics.
4. Monica is a French teacher. Therefore, Monica knows how to teach French.
5. Bob is taller than Susan. Susan is taller than Frankie. Therefore, Bob is taller than Frankie.
6. Craig loves Linda. Linda loves Monique. Therefore, Craig loves Monique.
7. Orel Hershizer is a Christian. Therefore, Orel Hershizer communicates with God.
8. All Muslims pray to Allah. Muhammad is a Muslim. Therefore, Muhammad prays to Allah.
9. Some protozoa are predators. No protozoa are animals. Therefore, some predators are not animals.
10. Charlie only barks when he hears a burglar outside. Charlie is barking. Therefore, there must be a burglar outside.
2 As it happens, Ford wasn’t elected Vice President either since he was confirmed by the Senate, under the twenty fifth amendment, after Spiro Agnew resigned. So Ford wasn’t ever elected by the Electoral College—as either Vice President or President.


9.7: Information-Systems Users – Types of Users
-
- Last updated
- Save as PDF
- Ly-Huong T. Pham, Tejal Desai-Naik, Laurie Hammond, & Wael Abdeljabbar
- ASCCC Open Educational Resources Initiative (OERI)
Information-Systems Users – Types of Users
Besides the people who work to create, administer, and manage information systems, one more significant group of people: the users of information systems. This group represents a considerable percentage of the people involved. If the user cannot successfully learn and use an information system, the system is doomed to failure.
One tool used to understand how users will adopt a new technology comes from a 1962 study by Everett Rogers. In his book, Diffusion of Innovation, 1 Rogers explains how new ideas and technology spread via communication channels over time. Innovations are initially perceived as uncertain and even risky. To overcome this uncertainty, most people seek out others like themselves who have already adopted the new idea or technology. Thus, the diffusion process consists of successive groups of consumers adopting new technology( shown in blue in the graph below); the adoption rate will start slowly and then dramatically increase once adoption reaches a certain point - its market share(yellow curve) reaches saturation level and becomes self-sustaining.
Figure 9.4:
Technology adoption user types
Image by
Rogers Everett
, licensed under
Public domain, via Wikimedia Commons
Rogers identified five (sections of the blue curve) specific types of technology adopters:
- Innovators : Innovators are the first individuals to adopt new technology. Innovators are willing to take risks, are the youngest in age, have the highest social class, have great financial liquidity, are very social, and have the closest contact with scientific sources and interaction with other innovators. Risk tolerance has them adopting technologies that may ultimately fail. Financial resources help absorb these failures (Rogers 1962 5th ed, p. 282).
- Early adopters: The early adopters adopt an innovation after a technology has been introduced and proven. These individuals have the highest degree of opinion leadership among the other adopter categories, which means that they can influence the largest majority's opinions. They are typically younger in age, have higher social status, more financial liquidity, more advanced education, and are more socially aware than later adopters. These people are more discrete in adoption choices than innovators and realize the judicious choice of adoption will help them maintain a central communication position (Rogers 1962 5th ed, p. 283).
- Early majority : Individuals in this category adopt an innovation after a varying degree of time. This time of adoption is significantly longer than the innovators and early adopters. This group tends to be slower in the adoption process, has above average social status, has contact with early adopters, and seldom holds opinion leadership positions in a system (Rogers 1962 5th ed, p. 283).
- Late majority : The late majority will adopt an innovation after the average member of the society. These individuals approach an innovation with a high degree of skepticism, have below-average social status, very little financial liquidity, contact others in the late majority and the early majority, and show very little opinion leadership.
- Laggards : Individuals in this category are the last to adopt an innovation. Unlike those in the previous categories, individuals in this category show no opinion leadership. These individuals typically have an aversion to change agents and tend to be advanced in age. Laggards typically tend to be focused on “traditions,” are likely to have the lowest social status and the lowest financial liquidity, be the oldest of all other adopters, and be only in contact with family and close friends.
Knowledge of the diffusion theory and the five types of technology users help provide additional insight into how to implement new information systems within an organization. For example, when rolling out a new system, IT may want to identify the innovators and early adopters within the organization and work with them first, then leverage their adoption to drive the implementation.
This process of diffusion of new ideas and technology can usually take months or years. But there are exceptions: the use of the internet in the 1990s and mobile devices in recent years to communicate, interact socially, access news and entertainment have spread more rapidly than possibly any other innovation in humankind's history.
References
Rogers, E. M. (1962). Diffusion of innovations . New York: Free Press


5.2: Electric Current
By the end of this section, you will be able to:
- Describe an electrical current
- Define the unit of electrical current
- Explain the direction of current flow
Up to now, we have considered primarily static charges. When charges did move, they were accelerated in response to an electrical field created by a voltage difference. The charges lost potential energy and gained kinetic energy as they traveled through a potential difference where the electrical field did work on the charge.
Although charges do not require a material to flow through, the majority of this chapter deals with understanding the movement of charges through a material. The rate at which the charges flow past a location—that is, the amount of charge per unit time—is known as the electrical current . When charges flow through a medium, the current depends on the voltage applied, the material through which the charges flow, and the state of the material. Of particular interest is the motion of charges in a conducting wire. In previous chapters, charges were accelerated due to the force provided by an electrical field, losing potential energy and gaining kinetic energy. In this chapter, we discuss the situation of the force provided by an electrical field in a conductor, where charges lose kinetic energy to the material reaching a constant velocity, known as the “ drift velocity .” This is analogous to an object falling through the atmosphere and losing kinetic energy to the air, reaching a constant terminal velocity.
If you have ever taken a course in first aid or safety, you may have heard that in the event of electric shock, it is the current, not the voltage, which is the important factor on the severity of the shock and the amount of damage to the human body. Current is measured in units called amperes; you may have noticed that circuit breakers in your home and fuses in your car are rated in amps (or amperes). But what is the ampere and what does it measure?
Defining Current and the Ampere
Electrical current is defined to be the rate at which charge flows. When there is a large current present, such as that used to run a refrigerator, a large amount of charge moves through the wire in a small amount of time. If the current is small, such as that used to operate a handheld calculator, a small amount of charge moves through the circuit over a long period of time.
The average electrical current \(I\) is the rate at which charge flows,
\[I_{ave} = \dfrac{\Delta Q}{\Delta t}, \label{Iave}\]
where \(\Delta Q\) is the amount of net charge passing through a given cross-sectional area in time \(\Delta t\) (Figure \(\PageIndex{1}\)). The SI unit for current is the ampere (A), named for the French physicist André-Marie Ampère (1775–1836). Since \(I = \dfrac{\Delta Q}{\Delta t}\), we see that an ampere is defined as one coulomb of charge passing through a given area per second:
\[1 A \equiv 1 \dfrac{C}{s}.\]
The instantaneous electrical current, or simply the electrical current , is the time derivative of the charge that flows and is found by taking the limit of the average electrical current as \(\Delta t \rightarrow 0\).
\[I = \lim_{\Delta t \rightarrow 0} \dfrac{\Delta Q}{\Delta t} = \dfrac{dQ}{dt}.\]
Most electrical appliances are rated in amperes (or amps) required for proper operation, as are fuses and circuit breakers.
The main purpose of a battery in a car or truck is to run the electric starter motor , which starts the engine. The operation of starting the vehicle requires a large current to be supplied by the battery. Once the engine starts, a device called an alternator takes over supplying the electric power required for running the vehicle and for charging the battery.
- What is the average current involved when a truck battery sets in motion 720 C of charge in 4.00 s while starting an engine?
- How long does it take 1.00 C of charge to flow from the battery?
Strategy
We can use the definition of the average current in Equation \ref{Iave} to find the average current in part (a), since charge and time are given. For part (b), once we know the average current, we use Equation \ref{Iave} to find the time required for 1.00 C of charge to flow from the battery.
Solution
a. Entering the given values for charge and time into the definition of current gives
\[ \begin{align*} I &= \dfrac{\Delta Q}{\Delta t} \\[5pt] &= \dfrac{720 \, C}{4.00 \, s} \\[5pt] &= 180 \, C/s \\[5pt] &= 180 \, A. \end{align*}\]
b. Solving the relationship \(I = \dfrac{\Delta Q}{\Delta t}\) for time \(\Delta t\) and entering the known values for charge and current gives
\[ \begin{align*} \Delta t &= \dfrac{\Delta Q}{I} \\[5pt] &= \dfrac{1.00 \, C}{180 \, C/s} \\[5pt] &= 5.56 \times 10^{-3}s \\[5pt] &= 5.56 \, ms. \end{align*}\]
Significance
- This large value for current illustrates the fact that a large charge is moved in a small amount of time. The currents in these “starter motors” are fairly large to overcome the inertia of the engine.
- A high current requires a short time to supply a large amount of charge. This large current is needed to supply the large amount of energy needed to start the engine.
Consider a charge moving through a cross-section of a wire where the charge is modeled as \(Q(t) = Q_M (1 - e^{-t/\tau})\). Here, \(Q_M\) is the charge after a long period of time, as time approaches infinity, with units of coulombs, and \(\tau\) is a time constant with units of seconds (Figure \(\PageIndex{2}\)). What is the current through the wire?
Strategy
The current through the cross-section can be found from \(I = \dfrac{dQ}{dt}\). Notice from the figure that the charge increases to \(Q_M\) and the derivative decreases, approaching zero, as time increases (Figure \(\PageIndex{2}\)).
Solution
The derivative can be found using \(\dfrac{d}{dx} e_u = e^u \dfrac{du}{dx}\).
\[ \begin{align*} I &= \dfrac{dQ}{dt} \\[5pt] &= \dfrac{d}{dt} \left[ Q_M \left( 1 - e^{-t/\tau}\right)\right] \\[5pt] &= \dfrac{Q_M}{\tau} e^{-t/\tau}.\end{align*}\]
Significance
The current through the wire in question decreases exponentially, as shown in Figure \(\PageIndex{3}\). In later chapters, it will be shown that a time-dependent current appears when a capacitor charges or discharges through a resistor. Recall that a capacitor is a device that stores charge. You will learn about the resistor in Model of Conduction in Metals .
Handheld calculators often use small solar cells to supply the energy required to complete the calculations needed to complete your next physics exam. The current needed to run your calculator can be as small as 0.30 mA. How long would it take for 1.00 C of charge to flow from the solar cells? Can solar cells be used, instead of batteries, to start traditional internal combustion engines presently used in most cars and trucks?
- Answer
-
The time for 1.00 C of charge to flow would be
\[\Delta t = \dfrac{\Delta Q}{I} = \dfrac{1.00 \, C}{0.300 \times 10^{-3} C/s} = 3.33 \times 10^3 \, s.\]
This is slightly less than an hour. This is quite different from the 5.55 ms for the truck battery. The calculator takes a very small amount of energy to operate, unlike the truck’s starter motor. There are several reasons that vehicles use batteries and not solar cells. Aside from the obvious fact that a light source to run the solar cells for a car or truck is not always available, the large amount of current needed to start the engine cannot easily be supplied by present-day solar cells. Solar cells can possibly be used to charge the batteries. Charging the battery requires a small amount of energy when compared to the energy required to run the engine and the other accessories such as the heater and air conditioner. Present day solar-powered cars are powered by solar panels, which may power an electric motor, instead of an internal combustion engine.
Circuit breakers in a home are rated in amperes, normally in a range from 10 amps to 30 amps, and are used to protect the residents from harm and their appliances from damage due to large currents. A single 15-amp circuit breaker may be used to protect several outlets in the living room, whereas a single 20-amp circuit breaker may be used to protect the refrigerator in the kitchen. What can you deduce from this about current used by the various appliances?
- Answer
-
The total current needed by all the appliances in the living room (a few lamps, a television, and your laptop) draw less current and require less power than the refrigerator.
Current in a Circuit
In the previous paragraphs, we defined the current as the charge that flows through a cross-sectional area per unit time. In order for charge to flow through an appliance, such as the headlight shown in Figure \(\PageIndex{4}\), there must be a complete path (or circuit ) from the positive terminal to the negative terminal. Consider a simple circuit of a car battery, a switch, a headlight lamp, and wires that provide a current path between the components. In order for the lamp to light, there must be a complete path for current flow. In other words, a charge must be able to leave the positive terminal of the battery, travel through the component, and back to the negative terminal of the battery. The switch is there to control the circuit. Part (a) of the figure shows the simple circuit of a car battery, a switch, a conducting path, and a headlight lamp. Also shown is the schematic of the circuit [part (b)]. A schematic is a graphical representation of a circuit and is very useful in visualizing the main features of a circuit. Schematics use standardized symbols to represent the components in a circuits and solid lines to represent the wires connecting the components. The battery is shown as a series of long and short lines, representing the historic voltaic pile. The lamp is shown as a circle with a loop inside, representing the filament of an incandescent bulb. The switch is shown as two points with a conducting bar to connect the two points and the wires connecting the components are shown as solid lines. The schematic in part (c) shows the direction of current flow when the switch is closed.
When the switch is closed in Figure \(\PageIndex{4c}\), there is a complete path for charges to flow, from the positive terminal of the battery, through the switch, then through the headlight and back to the negative terminal of the battery. Note that the direction of current flow is from positive to negative. The direction of conventional current is always represented in the direction that positive charge would flow, from the positive terminal to the negative terminal.
The conventional current flows from the positive terminal to the negative terminal, but depending on the actual situation, positive charges, negative charges, or both may move. In metal wires, for example, current is carried by electrons—that is, negative charges move. In ionic solutions, such as salt water, both positive and negative charges move. This is also true in nerve cells. A Van de Graaff generator, used for nuclear research, can produce a current of pure positive charges, such as protons. In the Tevatron Accelerator at Fermilab, before it was shut down in 2011, beams of protons and antiprotons traveling in opposite directions were collided. The protons are positive and therefore their current is in the same direction as they travel. The antiprotons are negativity charged and thus their current is in the opposite direction that the actual particles travel.
A closer look at the current flowing through a wire is shown in Figure \(\PageIndex{5}\). The figure illustrates the movement of charged particles that compose a current. The fact that conventional current is taken to be in the direction that positive charge would flow can be traced back to American scientist and statesman Benjamin Franklin in the 1700s. Having no knowledge of the particles that make up the atom (namely the proton, electron, and neutron), Franklin believed that electrical current flowed from a material that had more of an “electrical fluid” and to a material that had less of this “electrical fluid.” He coined the term positive for the material that had more of this electrical fluid and negative for the material that lacked the electrical fluid. He surmised that current would flow from the material with more electrical fluid—the positive material—to the negative material, which has less electrical fluid. Franklin called this direction of current a positive current flow. This was pretty advanced thinking for a man who knew nothing about the atom.
We now know that a material is positive if it has a greater number of protons than electrons, and it is negative if it has a greater number of electrons than protons. In a conducting metal, the current flow is due primarily to electrons flowing from the negative material to the positive material, but for historical reasons, we consider the positive current flow and the current is shown to flow from the positive terminal of the battery to the negative terminal.
It is important to realize that an electrical field is present in conductors and is responsible for producing the current (Figure \(\PageIndex{5}\)). In previous chapters, we considered the static electrical case, where charges in a conductor quickly redistribute themselves on the surface of the conductor in order to cancel out the external electrical field and restore equilibrium. In the case of an electrical circuit, the charges are prevented from ever reaching equilibrium by an external source of electric potential, such as a battery. The energy needed to move the charge is supplied by the electric potential from the battery.
Although the electrical field is responsible for the motion of the charges in the conductor, the work done on the charges by the electrical field does not increase the kinetic energy of the charges. We will show that the electrical field is responsible for keeping the electric charges moving at a “drift velocity.”


29.18B: Infertility
Infertility, in both males and females, refers to the inability to contribute to conception.
- Evaluate the factors involved in infertility
Key Points
- Several clinical and epidemiological guidelines exist to determine infertility, often based on regular sexual intercourse in the absence of contraception without conception.
- Infertility can result from genetic factors or more general factors such as endocrine disorders ( diabetes, thyroid disorders, etc.) and environmental factors.
- In the U.S., up to 20% of infertile couples have unexplained infertility. In these cases abnormalities are likely to be present but not detected by current methods.
- Medical treatment of infertility generally involves the use of fertility medication, medical device, surgery, or intrauterine insemination. If these treatments fail to achieve a full term pregnancy, in vitro fertilization or other assisted reproductive techniques (ART) can be used.
Key Terms
- contraception : The use of a device or procedure to prevent conception as a result of sexual activity.
- infertility : The inability to conceive children.
- conception : The fertilization of an ovum by a sperm to form a zygote.
Infertility primarily refers to the biological inability of a person to contribute to conception. Infertility may also refer to the state of a woman who is unable to carry a pregnancy to full term. There are many biological causes of infertility, some which may be bypassed with medical intervention.
Definitions of infertility differ, with demographers tending to define infertility as childlessness in a population of women of reproductive age, while the epidemiological definition is based on “trying for” or “time to” a pregnancy, generally in a population of women exposed to a probability of conception. Existing definitions of infertility lack uniformity, rendering comparisons in prevalence between countries or over time problematic, and therefore data estimating the prevalence of infertility cited by various sources differs significantly. A couple that has tried unsuccessfully to have a child after a certain period of time (often a short period, but definitions vary) is sometimes said to be subfertile, meaning less fertile than a typical couple. Both infertility and subfertility are defined as the inability to conceive after a certain period of time (the length of which vary), so often the two terms overlap. Couples with primary infertility have never been able to conceive, while, secondary infertility is difficulty conceiving after already having conceived (and either carried the pregnancy to term or had a miscarriage).
Causes
Factors that can cause male as well as female infertility are:
- Genetic factors
- Chromosomal defects
- Diabetes mellitus, thyroid disorders, adrenal disease
- Hypothalamic-pituitary factors
- Hyperprolactinemia
- Hypopituitarism
- Environmental factors
- Toxins such as glues, volatile organic solvents or silicones, physical agents, chemical dusts, and pesticides. Tobacco smokers are 60% more likely to be infertile than non-smokers.
For a woman to conceive, certain things have to happen: intercourse must take place around the time when an egg is released from her ovary; the systems that produce eggs and sperm have to be working at optimum levels; and her hormones must be balanced. Some women are infertile because their ovaries do not mature and release eggs. In this case synthetic FSH by injection or Clomid (Clomiphene citrate) via a pill can be given to stimulate follicles to mature in the ovaries. Other factors that can affect a woman’s chances of conceiving include being over- or underweight, or her age as female fertility declines sharply after the age of 35. Sometimes it can be a combination of factors, and sometimes a clear cause is never established.
The main cause of male infertility is low semen quality. Another possible cause is a low sperm count. In some cases, both the man and woman may be infertile or sub-fertile, and the couple’s infertility arises from the combination of these conditions. In other cases, the cause is suspected to be immunological or genetic; it may be that each partner is independently fertile but the couple cannot conceive together without assistance.
Unexplained Infertility
In the U.S., up to 20% of infertile couples have unexplained infertility. In these cases abnormalities are likely to be present but not detected by current methods. Possible problems could be that the egg is not released at the optimum time for fertilization, that it may not enter the fallopian tube, sperm may not be able to reach the egg, fertilization may fail to occur, transport of the zygote may be disturbed, or implantation fails. It is increasingly recognized that egg quality is of critical importance and women of advanced maternal age have eggs of reduced capacity for normal and successful fertilization. Also, polymorphisms in folate pathway genes could be one reason for fertility complications in some women with unexplained infertility.
Treatment
Medical treatment of infertility generally involves the use of fertility medication, medical device, surgery, or a combination of the following. If the sperm are of good quality and the mechanics of the woman’s reproductive structures are good (patent fallopian tubes, no adhesions or scarring), physicians may start by prescribing a course of ovarian stimulating medication. The physician may also suggest intrauterine insemination (IUI), in which the doctor introduces sperm into the uterus during ovulation, via a catheter. In these methods, fertilization occurs inside the body. If conservative medical treatments fail to achieve a full term pregnancy, the physician may suggest the patient undergo in vitro fertilization (IVF). IVF and related techniques are called assisted reproductive technology (ART) techniques.
ART techniques generally start with stimulating the ovaries to increase egg production. After stimulation, the physician surgically extracts one or more eggs from the ovary, and unites them with sperm in a laboratory setting, with the intent of producing one or more embryos. Fertilization takes place outside the body, and the fertilized egg is reinserted into the woman’s reproductive tract, in a procedure called embryo transfer.
Causes of Infertility : Numerous factors may contribute to infertility.
LICENSES AND ATTRIBUTIONS
CC LICENSED CONTENT, SHARED PREVIOUSLY
- Curation and Revision. Authored by : Boundless.com. Provided by : Boundless.com. License : CC BY-SA: Attribution-ShareAlike
CC LICENSED CONTENT, SPECIFIC ATTRIBUTION
- ectopic pregnancy. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/ectopic_pregnancy . License : CC BY-SA: Attribution-ShareAlike
- Ectopic pregnancy. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Ectopic_pregnancy . License : CC BY-SA: Attribution-ShareAlike
- heterotopic pregnancy. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/heterotopic%20pregnancy . License : CC BY-SA: Attribution-ShareAlike
- Ectopic. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/File:Ectopic.png . License : Public Domain: No Known Copyright
- Infertility causes. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/File:In...ity_causes.png . License : CC BY-SA: Attribution-ShareAlike
- infertility. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/infertility . License : CC BY-SA: Attribution-ShareAlike
- conception. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/conception . License : CC BY-SA: Attribution-ShareAlike
- contraception. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/contraception . License : CC BY-SA: Attribution-ShareAlike
- Ectopic. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/File:Ectopic.png . License : Public Domain: No Known Copyright
- Infertility causes. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/File:Infertility_causes.png . License : Public Domain: No Known Copyright


7.7.3: Lipid Biosynthesis
-
- Last updated
- Save as PDF
- Boundless
- Boundless
Learning Objectives
- Outline the characteristics and processes of lipid biosynthesis, including:; lipogenesis and fatty acid biosynthesis
Lipids constitute a broad group of naturally occurring molecules that include fats, waxes, sterols, fat-soluble vitamins (such as vitamins A, D, E, and K), monoglycerides, diglycerides, triglycerides, phospholipids, and others. The main biological functions of lipids include energy storage, as structural components of cell membranes, and as important signaling molecules.
Lipids may be broadly defined as hydrophobic or amphiphilic small molecules. The amphiphilic nature of some lipids allows them to form structures such as vesicles, liposomes, or membranes in an aqueous environment. Biological lipids originate entirely or in part from two distinct types of biochemical subunits or “building-blocks”: ketoacyl and isoprene groups. Using this approach, lipids may be divided into eight categories: fatty acids, glycerolipids, glycerophospholipids, sphingolipids, saccharolipids, and polyketides (derived from condensation of ketoacyl subunits); and sterol lipids and prenol lipids (derived from condensation of isoprene subunits).
Although humans and other mammals use various biosynthetic pathways to both break down and synthesize lipids, some essential lipids cannot be made this way and must be obtained from the diet.
In animals, when there is an oversupply of dietary carbohydrate, the excess carbohydrate is converted to triglycerides. This involves the synthesis of fatty acids from acetyl-CoA and the esterification of fatty acids in the production of triglycerides, a process called lipogenesis. Fatty acids are made by fatty acid synthases that polymerize and then reduce acetyl-CoA units. The acyl chains in the fatty acids are extended by a cycle of reactions that add the acetyl group, reduce it to an alcohol, dehydrate it to an alkene group and then reduce it again to an alkane group.
The enzymes of fatty acid biosynthesis are divided into two groups, in animals and fungi all these fatty acid synthase reactions are carried out by a single multifunctional protein, while in plant plastids and bacteria separate enzymes perform each step in the pathway. The fatty acids may be subsequently converted to triglycerides that are packaged in lipoproteins and secreted from the liver.
One important reaction that uses these activated isoprene donors is steroid biosynthesis. Here, the isoprene units are joined together to make squalene and then folded up and formed into a set of rings to make lanosterol. Lanosterol can then be converted into other steroids such as cholesterol and ergosterol.
Key Points
- Lipid A is a lipid component of an endotoxin held responsible for toxicity of Gram-negative bacteria.
- The synthesis of unsaturated fatty acids involves a desaturation reaction, whereby a double bond is introduced into the fatty acyl chain.
- In archaea, the mevalonate pathway produces reactive precursors isopentenyl pyrophosphate and dimethylallyl pyrophosphate from acetyl-CoA, while in plants and bacteria the non-mevalonate pathway uses pyruvate and glyceraldehyde 3-phosphate as substrates.
Key Terms
- lipid A : Lipid A is a lipid component of an endotoxin held responsible for toxicity of Gram-negative bacteria. It is the innermost of the three regions of the lipopolysaccharide (LPS, also called endotoxin) molecule, and its hydrophobic nature allows it to anchor the LPS to the outer membrane.
- endotoxin : Any toxin secreted by a microorganism and released into the surrounding environment only when it dies.
- lipogenesis : The biochemical production of fat, especially the conversion of carbohydrate into fat so that it may be stored as a long-term source of energy when food is scarce.


13.10: ¹³C NMR Spectroscopy - Signal Averaging and FT-NMR
-
- Last updated
- Save as PDF
Objectives
After completing this section, you should be able to
- Understand why the nuclei C NMR looks at is 13 C and not 12 C.
- Know why more scans are needed in 13 C NMR than 1 H NMR.
Most of what we have learned about 1 H-NMR spectroscopy also applies to 13 C-NMR, although there are several important differences.
Signal strength in 13 C-NMR spectroscopy
The 12 C isotope of carbon - which accounts for more than 98% of the carbons in organic molecules - does not have a nuclear magnetic moment, and thus is NMR-inactive. Fortunately for organic chemists, however, the 13 C isotope, which accounts for 1.1% of the remaining carbon atoms in nature, has a magnetic moment just like protons.
The magnetic moment of a 13 C nucleus is much weaker than that of a proton, meaning that NMR signals from 13 C nuclei are inherently much weaker than proton signals. This, combined with the low natural abundance of 13 C, means that it is much more difficult to observe carbon signals and there is a much lower signal-to-noise ratio than in 1 H NMR. Therefore, more concentrated samples are required to generate a useful spectrum, and often the data from hundreds of scans must be averaged in order to bring the signal-to-noise ratio down to acceptable levels. This type of signal averaging works since background noise in a spectrum is typically random while the signal caused by the 13 C nuclei is not. Therefore if the spectra from multiple scans is averaged, the noise gets closer to 0 while the signal stays the same, increasing the signal-to-noise ratio.
Fourier Transform (FT) NMR
Earlier versions of NMR instruments used variable magnetic fields which required recording of each signal in the spectrum sequentially which is called continuous wave (CW) NMR. The Fourier Transform allows recording of all signals simultaneously by introducing a short pulse of all RF frequencies that cause resonance for a given nucleus. This complex signal is then manipulated through complex mathematical processing that creates an NMR spectrum that looks similar to a CW spectrum, but in much less time.


Skip to main content
Table of Contents
menu
search
Search
build_circle
Toolbar
fact_check
Homework
cancel
Exit Reader Mode
school
Campus Bookshelves
menu_book
Bookshelves
perm_media
Learning Objects
login
Login
how_to_reg
Request Instructor Account
hub
Instructor Commons
Search
Search this book
Submit Search
x
Text Color
Reset
Bright
Blues
Gray
Inverted
Text Size
Reset
+
-
Margin Size
Reset
+
-
Font Type
Enable Dyslexic Font
Downloads
expand_more
Download Page (PDF)
Download Full Book (PDF)
Resources
expand_more
Periodic Table
Physics Constants
Scientific Calculator
Reference
expand_more
Reference & Cite
Tools
expand_more
Help
expand_more
Get Help
Feedback
Readability
x
selected template will load here
Error
This action is not available.
chrome_reader_mode
Enter Reader Mode
HGTC BIO 225: Microbiology Lab Manual
Horry-Georgetown Technical College
{ }
{ }
{ }
Wed, 21 Feb 2024 19:02:12 GMT
10: Biochemical Characterization Part II
131063
131063
Madison Rost
{ }
Anonymous
Anonymous
2
false
false
[ "article:topic-guide", "showtoc:no", "license:ccby", "licenseversion:40" ]
[ "article:topic-guide", "showtoc:no", "license:ccby", "licenseversion:40" ]
https://bio.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fbio.libretexts.org%2FCourses%2FHorry-Georgetown_Technical_College%2FHGTC_BIO_225%253A_Microbiology_Lab_Manual%2F10%253A_Biochemical_Characterization_Part_II
Search site
Search
Search
Go back to previous article
Username
Password
Sign in
Sign in
Sign in
Forgot password
Expand/collapse global hierarchy
Home
Campus Bookshelves
Horry-Georgetown Technical College
HGTC BIO 225: Microbiology Lab Manual
10: Biochemical Characterization Part II
Expand/collapse global location
10: Biochemical Characterization Part II
Last updated
Save as PDF
Page ID
131063


4.5: Assessment
True/False
Indicate whether the statement is true or false.
____ 1. NIST developed the Cybersecurity Framework as a mandatory set of standards to manage risks to critical infrastructure.
____ 2. Risk tolerance is the acceptable level of risk a company is willing to take.
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 3. Which of the following is not considered a basic security service?
| a. Confidentiality | c. Integrity |
| b. Authentication | d. Network Security |
____ 4. All of the following are standards defined in the NERC CIP standards, except:
| a. Personnel and Training | c. Authentication and Access Controls |
| b. Sabotage Reporting | d. Recovery Plans for Critical Cyber Assets |
____ 5. Continuous Monitoring activities occur under which Framework Core activity?
| a. Identify | c. Respond |
| b. Detect | d. Protect |
____ 6. An impact analysis is a part of which step in the risk management process?
| a. Risk control | c. Risk identification |
| b. Risk assessment | d. Risk mitigation |
____ 7. Which risk handling method reduces the likelihood of the risk occurring to as low as zero?
| a. Mitigation | c. Transference |
| b. Avoidance | d. Acceptance |
Multiple Response
Select all the choices that apply.
____ 8. Which of the following are a part of the Framework Processes?
| a. Framework Profile | c. Framework Implementation Tiers |
| b. Framework Drivers | d. Framework Core Functions |
Completion
Complete each sentence.
9. The Framework ________________ provide background on how an organization views cybersecurty risk and the processes that are in place to manage that risk.
10. ____________________ is defined as the process of identifying vulnerabilities and taking carefully reasoned steps to ensure the confidentiality, integrity, and availabiliity of the information system.
For the answers to these questions, email your name, the name of your college or other institution, and your position there to<EMAIL_ADDRESS>. CyberWatch West will email you a copy of the answer key.


2.3: The Process of Human Resources Planning
- Describe the process of human resource planning
On a functional level, human resource management is responsible for developing human capital strategies that align with the organization’s mission, goals and objectives. Human capital planning—often characterized as a roadmap—generally has a 3–5 year timeframe. Human Resource strategy sets the direction for all the key areas of HR, including hiring, performance management, compensation and training and development.
The U.S Office of Personnel Management describes human capital strategic planning as the method by which human resource management “designs a coherent framework of human capital policies, programs, and practices to achieve a shared vision integrated with the [organization’s] strategic plan.” [1]
Personnel Management’s planning guide identifies the following essential elements:
- A clearly understood strategic direction
- Customer and stakeholder human capital management outcomes/goals
- Strategies/objectives for accomplishing the goals
- An implementation plan
- A communication/change management plan, if needed
- An accountability system
Developing a strategic direction requires a detailed understanding of the organization’s strategic plan and objectives, budgetary constraints, current workforce characteristics, key senior management and stakeholder perceptions regarding human resource challenges and requirements and internal and external factors driving human capital needs. The conceptual objective is to develop a vision of the future workforce. The implementation plan is a roadmap as well as a framework for transforming culture and operations. The accountability system establishes how success will be measured and tracked, information that is essential for measuring and evaluating performance and for monitoring progress towards objectives.
The guide recommends that data collection support the identification of key themes associated with any gaps between the current and desired workforce and related human capital functions. These themes become the broad human capital goals and are the building blocks of the plan. For example, talent, performance management and leadership might be themes that will be translated into goals. Goals would be developed to address the gap and specific objectives would be identified to support achievement of the goal. Implementation plans are developed with varying levels of detail but at an operational level, should identify the specific actions required, who is responsible, what resources are required and the completion timeframe.
For perspective, here’s an excerpt from the U.S. Government Accountability Office’s (GAO) 2013–2015 Human Capital Plan: [2]
Performance Goal: Strengthen recruiting and hiring initiatives to attract a diverse workforce.
Human Capital Initiatives:
- Improve recruitment program by expanding efforts to maintain relationships with colleges, universities, and pipeline and professional organizations through participating in virtual outreach efforts, hosting representatives from partner institutions, and inviting candidates to visit GAO.
- Build annual recruitment plans based on analysis of data from prior years, with consideration to GAO’s workforce diversity plan, budget, and workforce planning needs.
- Monitor hiring process data and compare this data to established goals.
- Offer incentives where needed for positions that are hard to fill to help recruit and retain staff with critical skills.
Quantitative Measures (Accountability)
- Meet or exceed established benchmarks to maintain a diverse workforce.
- Meet the 80-day goal (+/− 1 percent) for the hiring process.
- Meet the new hire target established in GAO’s performance and accountability report
- " Human Resources Management in Agencies; Final Rule. " Office of Personnel Management. April 28, 2008. Accessed July 30, 2019. ↵
- " GAO's Human Capital Strategic Plan 2013-2015. " United States Government Accountability Office. 2013. Accessed July 30, 2019. ↵
- Untitled. Authored by : You X Ventures. Provided by : Unsplash. Located at : https://unsplash.com/photos/vbxyFxlgpjM . License : CC0: No Rights Reserved . License Terms : Unsplash License


7.5: Operating Budget
Operating budgets include separate budgets for each of three key line items on the income statement.
- Sales budget
-
Cost of goods sold budget *
* To prepare the cost of goods sold budget, a manufacturer first prepares the following five supporting budgets:
a. production budget
Requires sales budget result
b. direct materials purchases budget
Requires production budget result
c. direct materials cost budget
Requires materials purchases budget result
d. direct labor cost budget
Requires production budget result
e. factory overhead budget
Independent of previous budgets
-
Selling and administrative budget
The results of all the individual operating budgets are combined to present a budgeted income statement, which culminates with the anticipated amount of net income.
To illustrate, two distinct master budgets for 2019 for two different manufacturing companies will be presented side by side.
The first company makes only one product, a 42” art deco replica of the Statue of Liberty, which it sells to wholesalers and souvenir shops. Only one direct material, metal, is used in producing these statues.
The second company makes protective headgear and produces two products: bicycle helmets and ski helmets. Each type of headgear requires two direct materials: plastic and foam lining.
The best approach is to first review the budgets for the statue souvenirs in the left column of the side-by-side budgets. It is the simpler of the two since it covers only one product that uses one direct material. It illustrates the basic concepts. The budgets for the helmets are similar to those for the statues, but they are a bit more complex since two products and two direct materials are involved. The manufacture of the helmets occurs in two departments: forming and assembly.
The following information will be used to prepare a sales budget, production budget, direct materials purchases budget, direct materials cost budget, direct labor cost budget, factory overhead budget, selling and administrative budget, and budgeted income statement. The data in the left column is for the statue souvenirs; the information in the right column is for the helmets.
Statue Souvenirs (1 product and 1 direct material) Estimated sales volume
3,000 units
Selling price per unit
$200
Estimated inventory of completed units on Jan. 1
2,600 units
Desired inventory of completed units on Dec. 31
600 units
Number of pounds of metal per completed unit
8.6 pounds
Price per pound of metal
$6
Estimated inventory of metal on Jan. 1
1,800 pounds, $10,800
Desired inventory of metal on Dec. 31
300 pounds, 1,800
Time spent for direct labor per completed unit
5 hours
Direct labor rate per hour
$10
Estimated factory overhead costs for the year:
\(\ \quad \quad\)Supervisor salary
$7,600
\(\ \quad \quad\)Utilities
1,900
\(\ \quad \quad\)Indirect materials
1,700
\(\ \quad \quad\)Depreciation
800
Estimated work in process on Jan. 1
$25,100
Desired work in process on Dec. 31
3,100
Estimated finished goods on Jan. 1
$36,700
Desired finished goods on Dec. 31
9,400
Estimated selling costs for the year:
\(\ \quad \quad\)Advertising expense
$16,300
\(\ \quad \quad\)Sales commissions expense
14,100
\(\ \quad \quad\)Utilities expense
12,000
Estimated administrative costs for the year:
\(\ \quad \quad\)Salaries expense
$87,700
\(\ \quad \quad\)Utilities expense
11,400
\(\ \quad \quad\)Office supplies expense
5,600
Estimated tax rate
20%
Bicycle and Ski Helmets (2 products and 2 direct materials) Estimated sales volume
\(\ \quad \quad\)Bicycle helmets
2,600 units
\(\ \quad \quad\)Ski helmets
4,800 units
Selling price per unit
\(\ \quad \quad\)Bicycle helmets
$50 per unit
\(\ \quad \quad\)Ski helmets
$130 per unit
Estimated inventory of completed units on Jan. 1
\(\ \quad \quad\)Bicycle helmets (@ $24 per unit)
110 units
\(\ \quad \quad\)Ski helmets (@ $95 per unit)
320 units
Desired inventory of completed units on Dec. 31
\(\ \quad \quad\)Bicycle helmets (@ $25 per unit)
150 units
\(\ \quad \quad\)Ski helmets (@ $93 per unit)
280 units
Number of pounds of plastic per completed unit
\(\ \quad \quad\)Bicycle helmets
0.8 pounds
\(\ \quad \quad\)Ski helmets
1.6 pounds
Number of pounds of foam lining per completed unit
\(\ \quad \quad\)Bicycle helmets
0.3 pounds
\(\ \quad \quad\)Ski helmets
0.6 pounds
Price per pound of plastic
$4
Price per pound of lining
$2
Estimated inventory of plastic on Jan. 1
120 pounds
Desired inventory of plastic on Dec. 31
90 pounds
Estimated inventory of foam lining on Jan. 1
100 pounds
Desired inventory of foam lining on Dec. 31
140 pounds
Estimated bicycle work in process on Jan. 1 (@$15)
450 units
Estimated bicycle work in process on Dec. 31 (@$10)
610 units
Estimated ski work in process on Jan. 1 (@$70)
520 units
Estimated ski work in process on Dec. 31 (@$40)
500 units
Number of direct labor hours of forming per completed unit
\(\ \quad \quad\)Bicycle helmets
0.2 hours
\(\ \quad \quad\)Ski helmets
0.4 hours
Number of direct labor hours of assembly per completed unit
\(\ \quad \quad\)Bicycle helmets
0.6 hours
\(\ \quad \quad\)Ski helmets
1.2 hours
Direct labor rate per hour for forming
$15
Direct labor rate per hour for assembly
$12
Estimated factory overhead costs for the year:
\(\ \quad \quad\)Indirect factory wages
$59,900
\(\ \quad \quad\)Depreciation plant and equipment
8,700
\(\ \quad \quad\)Utilities
2,800
\(\ \quad \quad\)Insurance and property tax
1,600
Estimated selling costs for the year:
\(\ \quad \quad\)Sales salaries expense
$129,200
\(\ \quad \quad\)Advertising expense
60,800
\(\ \quad \quad\)Telephone expense – selling
4,100
\(\ \quad \quad\)Travel expense – selling
6,300
Estimated administrative costs for the year:
\(\ \quad \quad\)Office salaries expense
$22,700
\(\ \quad \quad\)Depreciation expense – office
2,600
\(\ \quad \quad\)Telephone expense – office
900
\(\ \quad \quad\)Office supplies expense
800
\(\ \quad \quad\)Miscellaneous office expense
700
Estimated tax rate
25%


16.1: Control Panel
For administrators there is an additional choice of Control Panel at the top of the right hand menu when they login to the Conductor
The Control Panel provides LibreTexts and Campus administrators tools to manage their Conductor instances.
Master Tools Panel
The first three tools in the Master Tools panel access databases populated from forms accessible in the conductor,
- Account Requests View Account Requests submitted to the Conductor platform described here
- Adoption Reports View Adoption Reports submitted to the Conductor platform described here
- Harvesting Requests View and manage OER Integration Requests submitted to the Conductor Platform described here
The last two tools are controlled through the Master Tools Panel
- Organizations Manager View and manage Organizations on the Conductor platform
- Homework Manager View and manage Homework resources listed on the LibreCommons
The Organization Manager has the branding information entries for every LibreNET member organization.
The Homework Manager is the database which populates the Homework dropdown in the Commons Blue Bar. It is synched daily at 12:30 AM PST to entries in the ADAPT Homework System.
Campus Admin Tools
The Books Manager is the database which populates the Commons Catalog . It is synched daily at 6:30 AM PST to the Libraries
Collections Manager is the database that manages Collections displayed through the Collections tab on the Commons Blue Bar . Administrators have the option to manage collections, adding or removing LibreTexts.
Campus administrators can use the Peer Review Rubric tab on the Campus Admin Tool Panel to specify/create a campus peer review rubric that will be used for all Campus Books.
The Campus Settings is the database that manages organizational details for LibreNET members which have their own branded Campus Commons. To access this Campus Admins need to first select their Campus Commons in the LibreTexts Commons before logging in to the Conductor.
User Manager is a database of all Conductor users which provides information about the projects they are working on.


11.5: Exercises
LAB 11 EXERCISES \(\PageIndex{1}\)
|
Label the (visible) lobes of the cerebrum
|
|
|
Label the following
|
LAB 11 EXERCISES \(\PageIndex{2}\)
Lobes and Limbic System
|
Label the following
|
|
Label the following
|
LAB 11 EXERCISES \(\PageIndex{3}\)
Diencephalon and Brain Stem
Midbrain, Lateral ventricle, 3rd ventricle, Cerebral Aqueduct, 4th ventricle,
Central canal
|
Label the following
|
LAB 11 EXERCISES \(\PageIndex{4}\)
Ventricular System
|
Label the following
|
LAB 11 EXERCISES \(\PageIndex{6}\)
Cortex and CSF Circulation
|
1) Label the ventricles, aqueduct and canal.
2)
Draw
two choroid plexuses (in red, if you have a
|
|
Label CSF-related areas:
|
LAB 11 EXERCISES \(\PageIndex{7}\)
Cerebral Cortex
|
Label the following regions of the cortex
|
Match the following symptoms to the brain
|
LAB 11 EXERCISES \(\PageIndex{8}\)
CNS
|
Label the following
|
|
Label the following
|
|
Identify the following regions:
|
LAB 11 EXERCISES \(\PageIndex{9}\)
Coronal View and Miscellaneous
|
Identify the following regions:
|


5.6: Binomial Theorem
In this section, you will:
- Apply the 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 without multiplying the binomial by itself times.
Finding the Number of Permutations of n Distinct Objects Using a Formula
For some permutation problems, it is inconvenient to use the Multiplication Principle because there are so many numbers to multiply. Fortunately, we can solve these problems using a formula. Before we learn the formula, let’s look at two common notations for permutations. If we have a set of objects and we want to choose objects from the set in order, we write Another way to write this is a notation commonly seen on computers and calculators. To calculate we begin by finding the number of ways to line up all objects. We then divide by to cancel out the items that we do not wish to line up.
Let’s see how this works with a simple example. Imagine a club of six people. They need to elect a president, a vice president, and a treasurer. Six people can be elected president, any one of the five remaining people can be elected vice president, and any of the remaining four people could be elected treasurer. The number of ways this may be done is Using factorials, we get the same result.
There are 120 ways to select 3 officers in order from a club with 6 members. We refer to this as a permutation of 6 taken 3 at a time. The general formula is as follows.
Note that the formula stills works if we are choosing all objects and placing them in order. In that case we would be dividing by or which we said earlier is equal to 1. So the number of permutations of objects taken at a time is or just
Formula for Permutations of n Distinct Objects
Given distinct objects, the number of ways to select objects from the set in order is
How To
Given a word problem, evaluate the possible permutations.
- Identify from the given information.
- Identify from the given information.
- Replace and in the formula with the given values.
- Evaluate.
Example 4
Finding the Number of Permutations Using the Formula
A professor is creating an exam of 9 questions from a test bank of 12 questions. How many ways can she select and arrange the questions?
- Answer
-
Substitute and into the permutation formula and simplify.
There are 79,833,600 possible permutations of exam questions!
Analysis
We can also use a calculator to find permutations. For this problem, we would enter 12, press the function, enter 9, and then press the equal sign. The function may be located under the MATH menu with probability commands.
Q&A
Could we have solved Example 4 using the Multiplication Principle?
Yes. We could have multiplied to find the same answer .
A play has a cast of 7 actors preparing to make their curtain call. Use the permutation formula to find the following.
Try It #6
How many ways can the 7 actors line up?
Try It #7
How many ways can 5 of the 7 actors be chosen to line up?
Find the Number of Combinations Using the Formula
So far, we have looked at problems asking us to put objects in order. There are many problems in which we want to select a few objects from a group of objects, but we do not care about the order. When we are selecting objects and the order does not matter, we are dealing with combinations . A selection of objects from a set of objects where the order does not matter can be written as Just as with permutations, can also be written as In this case, the general formula is as follows.
An earlier problem considered choosing 3 of 4 possible paintings to hang on a wall. We found that there were 24 ways to select 3 of the 4 paintings in order. But what if we did not care about the order? We would expect a smaller number because selecting paintings 1, 2, 3 would be the same as selecting paintings 2, 3, 1. To find the number of ways to select 3 of the 4 paintings, disregarding the order of the paintings, divide the number of permutations by the number of ways to order 3 paintings. There are ways to order 3 paintings. There are or 4 ways to select 3 of the 4 paintings. This number makes sense because every time we are selecting 3 paintings, we are not selecting 1 painting. There are 4 paintings we could choose not to select, so there are 4 ways to select 3 of the 4 paintings.
Formula for Combinations of n Distinct Objects
Given distinct objects, the number of ways to select objects from the set is
How To
Given a number of options, determine the possible number of combinations.
- Identify from the given information.
- Identify from the given information.
- Replace and in the formula with the given values.
- Evaluate.
Example 5
Finding the Number of Combinations Using the Formula
A fast food restaurant offers five side dish options. Your meal comes with two side dishes.
- ⓐ How many ways can you select your side dishes?
- ⓑ How many ways can you select 3 side dishes?
- Answer
-
-
ⓐ
We want to choose 2 side dishes from 5 options.
-
ⓑ
We want to choose 3 side dishes from 5 options.
-
ⓐ
We want to choose 2 side dishes from 5 options.
Analysis
We can also use a graphing calculator to find combinations. Enter 5, then press enter 3, and then press the equal sign. The function may be located under the MATH menu with probability commands.
Q&A
Is it a coincidence that parts (a) and (b) in Example 5 have the same answers?
No. When we choose r objects from n objects, we are not choosing objects. Therefore,
Try It #8
An ice cream shop offers 10 flavors of ice cream. How many ways are there to choose 3 flavors for a banana split?
Identifying Binomial Coefficients
In Counting Principles , we studied combinations . In the shortcut to finding we will need to use combinations to find the coefficients that will appear in the expansion of the binomial. In this case, we use the notation instead of but it can be calculated in the same way. So
The combination is called a binomial coefficient . An example of a binomial coefficient is
Binomial Coefficients
If and are integers greater than or equal to 0 with then the binomial coefficient is
Q&A
Is a binomial coefficient always a whole number?
Yes. Just as the number of combinations must always be a whole number, a binomial coefficient will always be a whole number.
Example 1
Finding Binomial Coefficients
Find each binomial coefficient.
- ⓐ
- ⓑ
- ⓒ
- Answer
-
Use the formula to calculate each binomial coefficient. You can also use the function on your calculator.
- ⓐ
- ⓑ
- ⓒ
Analysis
Notice that we obtained the same result for parts (b) and (c). If you look closely at the solution for these two parts, you will see that you end up with the same two factorials in the denominator, but the order is reversed, just as with combinations.
Try It #1
Find each binomial coefficient.
- ⓐ
- ⓑ
Using the Binomial Theorem
When we expand by multiplying, the result is called a binomial expansion , and it includes binomial coefficients. If we wanted to expand we might multiply by itself fifty-two times. This could take hours! If we examine some simple binomial expansions, we can find patterns that will lead us to a shortcut for finding more complicated binomial expansions.
First, let’s examine the exponents. With each successive term, the exponent for decreases and the exponent for increases. The sum of the two exponents is for each term.
Next, let’s examine the coefficients. Notice that the coefficients increase and then decrease in a symmetrical pattern. The coefficients follow a pattern:
These patterns lead us to the Binomial Theorem , which can be used to expand any binomial.
Another way to see the coefficients is to examine the expansion of a binomial in general form, to successive powers 1, 2, 3, and 4.
Can you guess the next expansion for the binomial
See Figure 1 , which illustrates the following:
- There are terms in the expansion of
- The degree (or sum of the exponents) for each term is
- The powers on begin with and decrease to 0.
- The powers on begin with 0 and increase to
- The coefficients are symmetric.
To determine the expansion on we see thus, there will be 5+1 = 6 terms. Each term has a combined degree of 5. In descending order for powers of the pattern is as follows:
- Introduce and then for each successive term reduce the exponent on by 1 until is reached.
-
Introduce
and then increase the exponent on
by 1 until
is reached.
The next expansion would be
But where do those coefficients come from? The binomial coefficients are symmetric. We can see these coefficients in an array known as Pascal's Triangle , shown in Figure 2 .
To generate Pascal’s Triangle, we start by writing a 1. In the row below, row 2, we write two 1’s. In the 3 rd row, flank the ends of the rows with 1’s, and add to find the middle number, 2. In the row, flank the ends of the row with 1’s. Each element in the triangle is the sum of the two elements immediately above it.
To see the connection between Pascal’s Triangle and binomial coefficients, let us revisit the expansion of the binomials in general form.
The Binomial Theorem
The Binomial Theorem is a formula that can be used to expand any binomial.
How To
Given a binomial, write it in expanded form.
- Determine the value of according to the exponent.
- Evaluate the through using the Binomial Theorem formula.
- Simplify.
Example 2
Expanding a Binomial
Write in expanded form.
- ⓐ
- ⓑ
- Answer
-
-
ⓐ
Substitute
into the formula. Evaluate the
through
terms. Simplify.
-
ⓑ
Substitute
into the formula. Evaluate the
through
terms. Notice that
is in the place that was occupied by
and that
is in the place that was occupied by
So we substitute them. Simplify.
-
ⓐ
Substitute
into the formula. Evaluate the
through
terms. Simplify.
Analysis
Notice the alternating signs in part b. This happens because raised to odd powers is negative, but raised to even powers is positive. This will occur whenever the binomial contains a subtraction sign.
Try It #2
Write in expanded form.
- ⓐ
- ⓑ
Using the Binomial Theorem to Find a Single Term
Expanding a binomial with a high exponent such as can be a lengthy process.
Sometimes we are interested only in a certain term of a binomial expansion. We do not need to fully expand a binomial to find a single specific term.
Note the pattern of coefficients in the expansion of
The second term is The third term is We can generalize this result.
The (r+1)th Term of a Binomial Expansion
The term of the binomial expansion of is:
How To
Given a binomial, write a specific term without fully expanding.
- Determine the value of according to the exponent.
- Determine
- Determine
- Replace in the formula for the term of the binomial expansion.
Example 3
Writing a Given Term of a Binomial Expansion
Find the tenth term of without fully expanding the binomial.
- Answer
-
Because we are looking for the tenth term, we will use in our calculations.
Try It #3
Find the sixth term of without fully expanding the binomial.
Media
Access these online resources for additional instruction and practice with binomial expansion.