Fx Sat Y vs Lo for any L - Biology

Fx Sat Y vs Lo for any L

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Fx Sat Y vs Lo for any L - Biology

Set-Builder and Interval Notations

Set-Builder Notation

Set-builder notation is commonly used to compactly represent a set of numbers. We can use set-builder notation to express the domain or range of a function. For example, the set given by,

is in set-builder notation. This set is read as,

&ldquoThe set of all real numbers x, such that x is not equal to 0,&rdquo

(where the symbol | is read as such that). That is, this set contains all real numbers except zero.

Another example of set-builder notation is,

&ldquoThe set of all real numbers x, such that x is greater than &minus2 and less than or equal to 3.&rdquo

As stated above, we can use set-builder notation to express the domain of a function. For example, the function

has domain that consists of all real numbers greater than or equal to zero, because the square root of a negative number is not a real number. We can write the domain of f(x) in set builder notation as,

If the domain of a function is all real numbers (i.e. there are no restrictions on x), you can simply state the domain as, &lsquoall real numbers,&rsquo or use the symbol to represent all real numbers.

Interval Notation

We can also use interval notation to express the domain of a function. Interval notation uses the following symbols

Interval notation can be used to express a variety of different sets of numbers. Here are a few common examples.

A set including all real numbers except a single number.

The union symbol can be used for disjoint sets. For example, we can express the set,

using interval notation as,

We use the union symbol (&cup) between these two intervals because we are removing the point x = 0.

We can visualize the above union of intervals using a number line as,

Notice that on our number line, an open dot indicates exclusion of a point, a closed dot indicates inclusion of a point, and an arrow indicates extension to &minus&infin or &infin.

Open and closed intervals

Now let's look at another example. The set given by,

can be expressed in interval notation as,

We can visualize this interval using a number line as,

A set including all real numbers

If the domain of a function is all real numbers, you can represent this using interval notation as (&minus&infin,&infin).

The Biology Project > Biomath > Notation > Set-Builder and Interval Notations

Lung Tests

    : An X-ray is the most common first test for lung problems. It can identify air or fluid in the chest, fluid in the lung, pneumonia, masses, foreign bodies, and other problems.
  • Computed tomography (CT scan): A CT scan uses X-rays and a computer to make detailed pictures of the lungs and nearby structures. (PFTs): A series of tests to evaluate how well the lungs work. Lung capacity, the ability to exhale forcefully, and the ability to transfer air between the lungs and blood are usually tested. : Part of PFTs measures how fast and how much air you can breathe out. : Culturing mucus coughed up from the lungs can sometimes identify the organism responsible for a pneumonia or bronchitis. : Viewing sputum under a microscope for abnormal cells can help diagnose lung cancer and other conditions. : A small piece of tissue is taken from the lungs, either through bronchoscopy or surgery. Examining the biopsied tissue under a microscope can help diagnose lung conditions. : An endoscope (flexible tube with a lighted camera on its end) is passed through the nose or mouth into the airways (bronchi). A doctor can take biopsies or samples for culture during bronchoscopy. : A rigid metal tube is introduced through the mouth into the lungs' airways. Rigid bronchoscopy is often more effective than flexible bronchoscopy, but it requires general (total) anesthesia.
  • Magnetic resonance imaging (MRI scan): An MRI scanner uses radio waves in a magnetic field to create high-resolution images of structures inside the chest.


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Mozart's music does not make you smarter, study finds

For over 15 years, scientists have been discussing alleged performance-enhancing effects of hearing classical music. Now, University of Vienna researchers Jakob Pietschnig, Martin Voracek and Anton K. Formann present quite definite results on this so-called "Mozart effect" in the US journal Intelligence. These new findings suggest no evidence for specific cognitive enhancements by mere listening to Mozart's music.

In 1993, in the journal Nature, University of California at Irvine psychologist Frances H. Rauscher and her associates reported findings of enhanced spatial task performance among college students after exposure to Mozart's music. Mozart's 1781 sonata for two pianos in D major (KV 448) supposedly enhanced students' cognitive abilities through mere listening. Scientific articles only rarely attract such public attention and excitement as was the case for Rauscher's publication: the New York Times wrote that listening to Mozart would give college-bound students an edge in the SAT. What is more, other commentators hailed Mozart music as a magic bullet to boost children's intelligence.

In the course of this hype, then Georgia governor Zell Miller even issued a bill in 1998, ensuring that every mother of a newborn would receive a complimentary classical music CD. In the same year, Florida's state government passed a law, requiring state-funded day-care centers to play at least one hour of classical music a day.

Debunking the myth

In the scientific community, however, Rauscher's finding was met with scepticism, as researchers around the world found it surprisingly hard to replicate. University of Vienna psychologists Jakob Pietschnig, Martin Voracek, and Anton K. Formann now report the findings of their meta-analysis of the "Mozart effect" in the US journal Intelligence.

Their comprehensive study of studies synthesizes the entirety of the scientific record on the topic. Retrieved for this systematic investigation were about 40 independent studies, published ones as well as a number of unpublished academic theses from the US and elsewhere, totalling more than 3000 participants.

The University of Vienna researchers' key finding is clear-cut: based on the cumulated evidence, there remains no support for gains in spatial ability specifically due to listening to Mozart music.

"I recommend listening to Mozart to everyone, but it will not meet expectations of boosting cognitive abilities," says Jakob Pietschnig, lead author of the study. A specific "Mozart effect," as suggested by Rauscher's 1993 publication in Nature, could not be confirmed. The meta-analysis from the University of Vienna exposes the "Mozart effect" as a legend, thus concurring with Emory University psychologist Scott E. Lilienfeld, who in his recent book "50 Great Myths of Popular Psychology" already ranked the "Mozart effect" number six.

Story Source:

Materials provided by University of Vienna. Note: Content may be edited for style and length.

LIFO method

Going by the LIFO method, Ted needs to go by his most recent inventory costs first and work backwards from there.

450 units x 900 = $405,000
300 units x 875 = $262,500
200 units x 850 = $170,000
150 units x $825 = $125,750

Ted’s cost of goods sold is $961,250.

You can see how for Ted, the LIFO method may be more attractive than FIFO. This is because the LIFO number reflects a higher inventory cost, meaning less profit and less taxes to pay at tax time.

The LIFO reserve in this example is $31,250. The LIFO reserve is the amount by which a company’s taxable income has been deferred, as compared to the FIFO method.

The remaining unsold 350 televisions will be accounted for in “inventory”.

COVID-19 Vaccinations Available for Ages 12 and Up

As our community strives to achieve herd immunity, vaccinating children ages 12 and up is a critical step towards achieving that goal and will help to keep our schools healthy places to learn. We encourage everyone 12 years of age and older to get the COVID-19 vaccine as soon as possible. Many locations offer same-day appointments, and some even have walk in availability. Children under the age of 18 must be accompanied by a parent or another adult at all community vaccination sites.

What the heck is leverage?

You are probably wondering how a small investor like yourself can trade such large amounts of money.

Think of your broker as a bank who basically fronts you $100,000 to buy currencies.

All the bank asks from you is that you give it $1,000 as a good faith deposit, which it will hold for you but not necessarily keep.

Sounds too good to be true? This is how forex trading using leverage works.

The amount of leverage you use will depend on your broker and what you feel comfortable with.

Typically the broker will require a deposit, also known as “margin“.

Once you have deposited your money, you will then be able to trade. The broker will also specify how much margin is required per position (lot) traded.

No problem as your broker would set aside $1,000 as a deposit and let you “borrow” the rest.

Of course, any losses or gains will be deducted or added to the remaining cash balance in your account.

The minimum security (margin) for each lot will vary from broker to broker.

In the example above, the broker required a 1% margin. This means that for every $100,000 traded, the broker wants $1,000 as a deposit on the position.

Let’s say you want to buy 1 standard lot (100,000) of USD/JPY. If your account is allowed 100:1 leverage, you will have to put up $1,000 as margin.

The $1,000 is NOT a fee, it’s a deposit.

You get it back when you close your trade.

The reason the broker requires the deposit is that while the trade is open, there’s the risk that you could lose money on the position!

Assuming that this USD/JPY trade is the only position you have open in your account, you would have to maintain your account’s equity (absolute value of your trading account) of at least $1,000 at all times in order to be allowed to keep the trade open.

If USD/JPY plummets and your trading losses cause your account equity to fall below $1,000, the broker’s system would automatically close out your trade to prevent further losses.

This is a safety mechanism to prevent your account balance from going negative.

Understanding how margin trading works is so important that we have dedicated a whole section to it later in the School.

It is a must-read if you don’t want to blow up your account!

Calculus - Power Rule, Sum Rule, Difference Rule

In these lessons, we learn the Power Rule, the Constant Multiple Rule, the Sum Rule and the Difference Rule.

The following diagram gives the basic derivative rules that you may find useful: Constant Rule, Constant Multiple Rule, Power Rule, Sum Rule, Difference Rule, Product Rule, Quotient Rule, and Chain Rule. Scroll down the page for more examples and solutions.

It is not always necessary to compute derivatives directly from the definition. Instead, several rules have been developed for finding derivatives without having to use the definition directly. These formulas greatly simplify the task of differentiation.

Definition of the Power Rule

The Power Rule of Derivatives gives the following:
For any real number n,

the derivative of f(x) = x n is f ’(x) = nx n-1

which can also be written as

Differentiate the following:
a) f(x) = x 5
b) y = x 100
c) y = t 6

a) f’’(x) = 5x 4
b) y’ = 100x 99
c) y’ = 6t 5

We have included a Derivative or Differentiation calculator at the end of this page. It can show the steps involved including the power rule, sum rule and difference rule.

Derivative of the function f(x) = x

Using the power rule formula, we find that the derivative of the function f(x) = x would be one.

The derivative of f(x) = x is f ’(x) = 1

which can also be written as

Differentiate f(x) = x

f ’(x) = f ’(x 1 ) = 1x 0 = 1

Derivative of a Constant Function

Using the power rule formula, we find that the derivative of a function that is a constant would be zero.

For any constant c,
The derivative of f(x) = c is f ’(x) = 0

which can also be written as

Differentiate the following:
a) f(3)
b) f(157)

a) f ‘(3) = f ‘(3x 0 ) = 0(3 x-1 ) = 0
b) f ‘(157) = 0

The Constant Multiple Rule

The constant multiple rule says that the derivative of a constant value times a function is the constant times the derivative of the function.

If c is a constant and f is a differentiable function, then

Differentiate the following:
a) y = 2x 4
b) y = –x

The Sum Rule

The Sum Rule tells us that the derivative of a sum of functions is the sum of the derivatives.

If f and g are both differentiable, then

The Sum Rule can be extended to the sum of any number of functions.

For example (f + g + h)’ = f’ + g’ + h’

Differentiate 5x 2 + 4x + 7

The Difference Rule

The Difference Rule tells us that the derivative of a difference of functions is the difference of the derivatives.

If f and g are both differentiable, then

Differentiate x 8 – 5x 2 + 6x

Proof of the Power Rule for Derivatives

An explanation and some examples.

How to find derivatives using rules?

Differentiation Techniques: Constant Rule, Power Rule, Constant Multiple Rule, Sum and Difference Rule

Basic Derivative Rules - The Shortcut Using the Power Rule

In this video, we look at finding the derivative of some very simple functions by using the power rule.

Power Rule and Derivatives, A Basic Example

This video uses the power rule to find the derivative of a function.

Power Rule and Derivatives, Example #2

This video uses the power rule to find the derivative of a function.

Power Rule and Derivatives, Example #3

This video uses the power rule to find the derivative of a function.

How to determine the derivatives of simple polynomials?

How to differentiate using the extended power rule?

The extended power rule involves using the chain rule with the power rule.

Examples of using the extended power rule

Derivative Calculator

The following derivative calculator can show you the steps and rules used to get the derivative of the given function. Use it to check your answers.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.


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Q. What exactly is Autism? Why do one is Autistic and the other one isn't? there are levels of autism as far as i know .. How do i know in what level to categorize someone ?

A. it seems you have a lot of questions about Autism. if you seek info about it i suggest the following link. it'll give you a general idea and will direct you to the best sites about Autism.

Q. What exactly is Autism? Why do one is Autistic and the other one isn't? there are levels of autism as far i know . i would like to know how does the scale look like . and how do you categorize someone with a unique type of autism ?

A. Autism, part of a spectrum of diseases called “pervasive developmental disorders” is characterized by problems with communication, social interaction and behavior. In addition, more than two thirds of children with autistic disorder have mental retardation, although it is not required for the diagnosis.

Why does it occur? No one knows, although it’s thought to be due to a constellation of genetic predisposition and environmental conditions.

Watch the video: #Carnica and #Buckfast: are there any differences? Part 1 (January 2022).