why the take-home pay is different than the gross pay.
Take-home pay is the amount an employee receives after deductions such as taxes, insurance premiums,and retirement contributions are subtracted from their gross pay.
What is Gross Pay?Gross pay is the total amount of wages earned byan employee before any deductions are made.
The difference between take-home pay and gross pay is due to various withholdings and deductions mandated by government regulations or chosen by the employee,which reduce the overall amount received in the paycheck.
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Is trolling for fish in a lake in the summer
A) fixed-Interval schedule
B) variable-interval schedule
C) fixed-ratio schedule
D) variable-ratio schedule
Variable-interval schedule Is trolling for fish in a lake in the summer . Possibly as soon as the line is cast, the first fish will be caught, but the second one won't be for several hours.
An interval that is variable is what?
Variable-interval schedule Is trolling for fish in a lake in the summer . Possibly as soon as the line is cast, the first fish will be caught, but the second one won't be for several hours.It is not constant how many fish are caught. Possibly as soon as the line is cast, the first fish will be caught, but the second one won't be for several hours. As you catch more fish, the habit will continue to be reinforced with each capture.Your Work is Being Checked by Your Employer: Does your manager visit you at work occasionally to see how things are going is, a schedule with varying intervals would look something like this. You never know when these check-ins might happen because they happen at erratic times.To learn more about Variable-interval schedule refer to:
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How do I solve this using long polynomial division?
answer and the explanation is on the picture.
hope it helps.
Please help asap
Walk forward, pushing the ball first with one foot then the other. • Use the inside of your foot to contact the ball. Gently push the ball; don’t kick it. • The ball should never be more than a foot or two away from your feet. Describes what soccer skill?
Dribbling
Kicking
Scoring
Trapping
Industrialist and businessperson Andrew Carnegie lived and prospered in a growing US at the
turn of the century. In 1889, the North American Review published his essay “The Gospel of
Wealth,” in which he argues that charity is a responsibility that the wealthy must provide
strategically to improve society for all. Read the excerpt from his essay and analyze how Carnegie
incorporates rhetorical strategies to build his argument.
Answer:
To help build the formidable American steel industry
Explanation:
A generous philanthropist, he slashed the wages of the workers who made him rich. One of the captains of the industry of 19th century America, Andrew Carnegie helped build the formidable American steel industry, a process that turned a poor young man into the richest man in the world.
A teacher has decided to take her Psychology classes on a trip to Fiji. She has recently come into a large sum of money after an unfortunate work-related injury involving three wheelie chairs and a huddle board. The teacher purchases a private jet and procures a pilot license for the occasion. Mid-flight, the teacher accidentally spills a mug of coffee on the cockpit controls to the chagrin of everyone on board, especially her co-pilot. This results in a crash landing on a seemingly uninhabited island in the South Pacific. Everyone was able to survive the crash, but now they are faced with the task of trying to survive on the island.
Directions: create a story or scenario to explain how the stranded group might struggle to achieve each level of needs on Maslow’s hierarchy, beginning at the bottom with physiological needs and working your way up. You must describe each level of needs by name and provide specific examples of how that need could be met on the island
AP physcology
Answer:
asdasdasd
Explanation:
Basic survival needs must be met before he or she can address more complex needs.
What is Maslow's hierarchy?Maslow's hierarchy of needs can be illustrated as a pyramid of necessities that build on the previous. This means that each category in the hierarchy is a prerequisite for the other.
At the very bottom, survival needs like having food, and a place to live is essential so the individual can then ascend in the stair of needs. Maslow identifies that at the bottom the physiological needs need to be fully satisfied then secondary needs and tertiary means will arise as a consequence.
Therefore, Basic survival needs must be met before he or she can address more complex needs.
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The radius of a cone is increasing at a constant rate of 8 feet per second. The volume remains a constant 56 cubic feet. At the instant when the radius of the cone is 3 feet, what is the rate of change of the height? The volume of a cone can be found with the equation V = farh. Round your answer to three decimal places.
Answer:
\(\Rightarrow \frac{dh}{dt}\approx -31.690 \)
Explanation:
The volume of a cone, V = 1/3πr^2h
Where r is the radius, and h is the height of the cone.
Given:
Volume is constant at 56 cubic feet.
Radius of cone increases at a constant rate of 8 feet per second.
The radius of the cone is 3 feet.
When radius is 3 feet
\(\Rightarrow h= \frac{3V}{\pi r^2}\)
\(\Rightarrow h= \frac{3\times 56}{\pi \times 3^2} \)
\(\Rightarrow h= \frac{3\times 56}{\pi \times 9} \)
\(\Rightarrow h= \frac{ 56}{3\pi} \)
Where h is in feets.
\(\frac{dV}{dt}=\frac{d (\frac{1}{3}\pi r^2h) }{dt} \)
\(\Rightarrow \frac{dV}{dt}=(\frac{1}{3}\pi \frac{dr^2}{dt}h)+(\frac{1}{3}\pi r^2 \frac{dh}{dt}) \)
\(\Rightarrow \frac{dV}{dt}=(\frac{1}{3}\pi \frac{dr^2}{dr}.\frac{dr}{dt}h)+(\frac{1}{3}\pi r^2 \frac{dh}{dt}) \)
\(\Rightarrow \frac{dV}{dt}=(\frac{1}{3} \pi 2r\frac{dr}{dt}h)+(\frac{1}{3}\pi r^2 \frac{dh}{dt}) \)
Since the volume is constant so \( \frac{dV}{dt}=0 \)
The rate of change of radius is \(\frac{dr}{dt}=8 \)
\(\Rightarrow 0=(\frac{1}{3} \pi (2\times 3)(8)(\frac{56}{3\pi}))+(\frac{1}{3}\pi (3^2) \frac{dh}{dt}) \)
\(\Rightarrow 0=(\frac{56\times 16}{3})+(\frac{1}{3}\pi (9) \frac{dh}{dt}) \)
\(\Rightarrow 0=(\frac{56\times 16}{3})+(3\pi \frac{dh}{dt}) \)
\(\Rightarrow 3\pi \frac{dh}{dt}=-\frac{56\times 16}{3} \)
\(\Rightarrow \frac{dh}{dt}=-\frac{56\times 16}{3\times 3 \times \pi} \)
\(\Rightarrow \frac{dh}{dt}=-\frac{56\times 16}{9\pi} \)
\(\Rightarrow \frac{dh}{dt}=-31.689518 \)
\(\Rightarrow \frac{dh}{dt}\approx -31.690 \)
The minus indicates that the rate of change of height is decreasing.
when using the outlining system for note-taking,key ideas are
Answer:
The outlining method is perhaps the most common form of note taking used by college students; an outline naturally organizes the information in a highly structured, logical manner, forming a skeleton of the textbook chapter or lecture subject that serves as an excellent study guide when preparing for tests.
For each of the following, describe its characteristics, explain its significance, or identify relevant causes and effects.
George Greenville
vice-admiralty courts
Patrick Henry
Stamp Act Congress
Sons of Liberty
Charles Townshend
Nonimportation agreement
Boston Massacre
Committes of Correspondence
Boston Tea Party
First Continental Congress
Loyalists and Patriots
Lexington and Concord
Second Continental Congress
George Washington
Olive Branch Petition
Common Sense
principles contained in the Declaration of Independence
Battle of Saratoga
Valley Forge
Gen. Cornwallis
Treaty of Paris
"Remember the Ladies"
Articles of Confederation
Northwest Ordinance of 1787
Shay's Rebellion
Virginia and New Jersey Plans
3/5ths Compromise
Necessary and Proper Clause
Federalist Papers
Anti-Federalists
Federalist Party
Democratic-Republican Party
Whiskey Rebellion
Jay's Treaty
Thomas Jefferson
Alexander Hamilton
loose vs. strict constructionism
Washington's Farewell Address
Naturalization Act
Alien and Sedition Acts
Virginia and Kentucky Resolutions
Virginia Statute for Religious Freedom
C). What has driven these trends
D). Which type of pesticide has seen the greatest increase in use overtime
E) Why might this be?
2. Why does glyphosate target plants specifically?
C) The trends of launching translation campaigns to spread tendentious remarks and misinformation can be driven by various factors.
D) The particular variety of pesticide that has experienced the most significant surge in usage over time could differ based on geographical location and unique context.
What is the glyphosateIn recent times, the controversial use of glyphosate, a commonly adopted pesticide, has attracted significant interest.
Glyphosate is distinguished as a broad-spectrum herbicide which makes it exclusively effective against plants. This prevents the functioning of EPSP synthase, an essential enzyme involved in the synthesis of specific amino acids needed for the development of plants. Glyphosate disrupts the plant's protein synthesis process by interfering with the enzyme responsible for it, ultimately causing the plant to die.
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A telephone survey of 1000 adults was taken shortly after the united states began bombing iraq. if 832 voiced their support for this action, what is the confidence interval that can it be asserted that 83.2% + 3% of the adult u.s. population supported the decision to go to war?
The confidence interval for the proportion of the adult U.S. population supporting the decisionto go to war is approximately 80.48% to 85.92% (or 80.5% to 85.9%) with a 95% confidence level.
How is this so ?Calculate the sample proportion
p = 832 / 1000 = 0.832
Calculate the standard error
SE = √((p * (1 - p)) /n)
SE =√((0.832 * (1 - 0.832)) / 1000)
SE ≈ 0.0139
Calculate the margin of error
ME = z * SE
Since the confidence level is not specified, we'll assume a 95% confidence level,corresponding to a z-value of approximately 1.96.
ME = 1.96 * 0.0139
ME ≈ 0.0272
Calculate the lower and upper bounds of the confidence interval:
Lower bound = p - ME
Lower bound = 0.832 - 0.0272
Lower bound ≈ 0.8048
Upper bound = p + ME
Upper bound = 0.832 + 0.0272
Upper bound ≈ 0.8592
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Please post detailed answers to the following questions. Please use complete sentences.
Spreadsheets can be intimidating when you first look at them, so knowing how to use spreadsheet tools can make large chunks of data easier to navigate. What are two tools that you can use to help you better use or understand large amounts of data in a spreadsheet? Your discussion should include the tool, how it functions, and how it makes the data easier to use and understand.
When working with large amounts of data in a spreadsheet, two tools that can greatly aid in understanding and manipulating the data are filters and pivot tables.
How to explain the informationFilters allow you to selectively display specific data based on criteria you define. When applied to a column or multiple columns in a spreadsheet, filters hide rows that do not meet the specified conditions, making it easier to focus on the data that is relevant to your analysis.
Filtering by a single criterion
You can apply filters to individual columns and specify conditions such as equal to, not equal to, greater than, less than, etc.
Filtering by multiple criteria: You can also apply filters to multiple columns simultaneously, allowing you to create more complex conditions.
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Problem 1. 2, here's a table from the previous screen describe any patterns you notice on the table
Here is the table given in the previous screen. x y 1 4 2 7 3 10 4 13 5 16 6 19 7 22 8 25 9 28 10 31The data set in the table above is known as a linear function.
A linear function is one in which the data points lie on a straight line. If you examine the data set, you'll notice that the slope is equal to 3, which means that for every increase of 1 in the x value, the y value increases by 3. The graph of this equation would be a straight line that goes upward. As the value of x increases, the value of y increases as well, and the two variables are proportional.
The relationship between x and y is thus linear. Therefore, in the given table, we notice a pattern that shows how the value of y is related to the value of x. As x increases, y also increases in a linear fashion, and we can calculate y by using the equation y=3x +1.
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Explain how supply change and affect price
Answer:
The law of supply and demand is an economic theory that explains how supply and demand are related to each other and how that relationship affects the price of goods and services. It's a fundamental economic principle that when supply exceeds demand for a good or service, prices fall. When demand exceeds supply, prices tend to rise
Explanation:
What type of signal word is used in the sentence?
a. generalization
b. description
c. thought
d. feeling
'Energy' and 'power' are often confused, but aren't the same. Why do we say 'power plants' instead of energy plants'?
Answer:Both are important capabilities of a generator to keep the lights on.
Explanation:Power plants do provide both energy and power. Both are important capabilities of a generator to keep the lights on. And, in fact, power plants are rated, not by how much energy they produce, but by how much power they can produce, because if the grid does not have enough power generation capacity, it won’t work. It is arguably the more important parameter to specify in an electrical generation facility.
So, you could probably call them either power or energy plants. I do not know the history of why we chose to use power.
how can an dagerous situation be fun?
Answer: adrenaline rush
Explanation:
an adrenaline rush can make dangerous situations fun, think of riding a roller-coaster
1. A student weighing 460.0 N climbs a vertical stairway that is 4.5 m high in 32.5 seconds. What is his power output?
2. A worker pushes horizontally on a large crate with a force of 215.0 N and the crate moved 2.6 m. How much work was done?
3. While rearranging a dorm room, a student does 318.0 J of work in moving a desk 2.4 m. What was the magnitude of the applied horizon
Answer:
1. Power = 63.69 Watts.
2. Workdone = 559 Joules.
3. Force = 132.5 Newton.
Explanation:
Given the following data;
1. Force = 460N
Distance = 4.5m
Time = 32.5 seconds.
To find the power;
First of all, we would determine the work done by the student using the formula;
Workdone = force * distance
Workdone = 460 * 4.5
Workdone = 2070 Joules.
Now, we can calculate the power;
Power = workdone/time
Power = 2070/32.5
Power = 63.69 Watts.
2. Force = 215N
Distance = 2.6 m
To find the work done by the worker;
Workdone = 215 * 2.6
Workdone = 559 Joules.
3. Workdone = 318 Joules
Distance = 2.4m
To find the magnitude of force applied;
Force = workdone/distance
Force = 318/2.4
Force = 132.5 Newton.
Based on your knowledge of Greek roots, which of the following words most
likely means "cultural heritage"?
A. Dehydration
B. Graffiti
OC. Ethnicity
OD. Epidermis
SUBMIT
Answer: I believe your answer would be C. Ethnicity.
Explanation: A is wrong because dehydration basically means a lack of fluids (water) which causes you to become dehydrated. B is wrong as well because graffiti is art, which isn't what we're looking for. D is wrong because Epidermis is the surface epithelium of the skin, in other words, not "cultural heritage". Ethnicity is about as close as you can get when it comes to "cultural heritage."
Have a great day! :)
Some of the most interesting psychological research are the studies done by milgram (obedience), asch (conformity), and zimbardo (assuming roles). select a study by one of these researchers. then use a real life example to discuss their ideas and illustrate their findings.
you can read more about this research topic at the zimbardo experiment site. how could the findings of his experiment be applied to what happened when prisoners were tortured at abu ghraib prison?
Philip Zimbardo, an American psychologist, worked on social experiments that involved the assumption of the role and conducted a prison experiment.
What was Zimbardo's experiment?Zimbardo was doing his research and conducted the experiment based on assuming roles. In real life, the workplace is the best example where a person accepts a role like a team leader and works according to it.
The prisoners in the Abu Ghraib prison showed a behavioral change and a strong psychological impact. The findings of the experiments can be used to show the changes in the prisoners as they underwent a lot of torture and abuse that affected them mentally and physically.
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Write political,social,economic, technological and other configurations that support cross border trade(multinational firms) in ethiopia
Answer:
Political configurations that support cross-border trade in Ethiopia:
Bilateral and regional trade agreements: Ethiopia can establish political agreements with other countries and regional organizations to facilitate cross-border trade. These agreements can include provisions for reduced trade barriers, streamlined customs procedures, and mutual recognition of standards.Stable political environment: A stable political environment with clear and consistent policies encourages multinational firms to engage in cross-border trade. Political stability reduces the risk of sudden policy changes or disruptions that could negatively impact trade.Social configurations that support cross-border trade in Ethiopia:
Skilled workforce: A well-educated and skilled workforce enhances Ethiopia's attractiveness as a destination for multinational firms. Skilled workers can contribute to the development of competitive industries and facilitate cross-border trade.Cultural diversity and openness: Ethiopia's cultural diversity and openness to different cultures can create an environment conducive to international trade. Understanding and appreciating different cultures can help foster relationships with multinational firms and promote cross-border trade.Economic configurations that support cross-border trade in Ethiopia:
Infrastructure development: Investing in transportation infrastructure, such as roads, railways, and ports, improves connectivity within Ethiopia and with neighboring countries. Efficient infrastructure facilitates the movement of goods and reduces trade costs, encouraging cross-border trade.Economic liberalization: Implementing economic policies that promote free trade, reduce trade barriers, and encourage foreign direct investment can attract multinational firms to Ethiopia. These policies can create a favorable business environment for cross-border trade.Technological configurations that support cross-border trade in Ethiopia:
Information and communication technology (ICT) advancements: Developing and improving ICT infrastructure and digital connectivity enhances communication, data exchange, and transactional efficiency. Advanced technology facilitates cross-border trade by enabling seamless communication and online transactions.E-commerce platforms: Embracing e-commerce platforms and digital marketplaces can open up new avenues for cross-border trade. Online platforms provide multinational firms with access to a wider customer base and enable easier international transactions.Other configurations that support cross-border trade in Ethiopia:
Access to finance: Availability of financing options and access to capital for businesses, including multinational firms, can support cross-border trade by providing necessary funds for expansion, investment, and operational needs.Business-friendly regulations: Implementing transparent and business-friendly regulations that promote fair competition, protect intellectual property rights, and ensure contract enforcement can attract multinational firms and foster cross-border trade.It's important to note that these configurations are general considerations and may require specific policy actions and implementation strategies tailored to the Ethiopian context to effectively support cross-border trade and attract multinational firms.
Alex is in a serious car accident where he was not wearing his seatbelt. He suffered brain damage. Describe specifically how his behaviors/actions could be impacted if the following areas of the brain suffered damage: (a) medulla (b) cerebellum (c) reticular formation (d) pons. After two months, he miraculously improves. The doctors order a series of tests to determine what exactly the cause of his improvement is. What were they planning to see by ordering the following tests? (a) EEG (b) fMRI (c) PET
answer in a few paragraphs and number each answer
1. If the medulla suffered damage, Alex's behaviors/actions could be impacted in several ways. The medulla is responsible for vital functions such as heart rate, blood pressure, and breathing. Damage to the medulla could lead to irregularities in these functions, potentially causing changes in Alex's heart rate, blood pressure regulation, and breathing patterns. He may experience difficulties in maintaining a stable heart rate and blood pressure, leading to symptoms like dizziness, lightheadedness, or shortness of breath. In severe cases, it could even result in life-threatening complications.
2. Damage to the cerebellum could affect Alex's coordination and balance. The cerebellum plays a crucial role in motor control and coordination. If injured, Alex may experience difficulties with fine motor skills, muscle coordination, and balance. He may have trouble with precise movements, such as reaching for objects or walking steadily. Additionally, damage to the cerebellum can lead to problems with posture, muscle tone, and overall motor control.
3. The reticular formation is responsible for regulating arousal, attention, and sleep-wake cycles. Damage to this area could result in changes in Alex's level of consciousness and overall arousal. He may experience difficulties in maintaining attention and focus, leading to reduced alertness and increased drowsiness. It could also impact his sleep patterns, causing disruptions in the sleep-wake cycle and potentially leading to excessive sleepiness or insomnia.
4. The pons plays a critical role in relaying information between different regions of the brain and coordinating motor movements. Damage to the pons could affect Alex's ability to control voluntary movements and could lead to muscle weakness or paralysis in certain areas of the body. It may also impact his ability to communicate effectively, as the pons is involved in speech production.
After two months, the doctors ordered a series of tests to determine the cause of Alex's improvement:
(a) EEG (electroencephalogram): The doctors likely ordered an EEG to assess the electrical activity in Alex's brain. It can help identify any abnormal brain wave patterns or signs of seizure activity. By comparing the EEG results to previous recordings, they can determine if there are any changes in brain activity that may explain Alex's improvement.
(b) fMRI (functional magnetic resonance imaging): An fMRI provides detailed images of brain activity by measuring changes in blood flow. The doctors may have ordered an fMRI to identify any specific brain regions that show increased activity, suggesting neural recovery or compensation. It can help identify if certain areas of the brain are functioning better than before and provide insights into the neurological basis of Alex's improvement.
(c) PET (positron emission tomography): PET scans involve injecting a radioactive tracer into the body to measure metabolic activity in different organs, including the brain. By ordering a PET scan, the doctors can assess the overall metabolic activity and blood flow in Alex's brain. It can help determine if there are any areas of increased or improved brain activity that may be contributing to his recovery.
These tests allow the doctors to gather objective data and assess the physiological changes in Alex's brain, helping them better understand the underlying mechanisms behind his improvement.
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Write a thesis statement that explains the causes of Alphonse’s death: ASAP
Answer:
The straw was an underlying cause of Alphonse's death. It was Alphonse's back problem which sparked his death. Driving everything which happened to Alphonse was Frank's bitterness towards camels. The actions of the other camel owners provoked Frank into killing Alphonse.
Explanation:
why do followers need to be willing
Explanation:
because they want to.
....
When gas X is released from a mass spectrometer, two different ions are formed (+1 and +2) and pass through a magnetic field. Three isotopes are detected,3°X, 'X and 2X. When the photographic film is displayed, the results for the beams (1-6) are displayed in the rectangular box. (a) Which beam of ions (A or B) represents the X*2 jon? Explain. (b) Which beams (1-6) represent the X-32 isotope? Explain.
From the mass spectrometer results;
Beam B corresponds to the X+2 ionBeam 4 represents the X-32 isotope because Beam 4 corresponds to an ion with a mass-to-charge ratio of (A-2)/1 the same as the X+2 ion. What is a mass spectrometer?A mass spectrometer is an instrument that measures the mass-to-charge ratio (m/z) of one or more molecules present in a sample.
It is frequently possible to determine the precise molecular weight of the sample's constituent parts using these measures.
Only after converting a molecule into an electrically charged gas-phase ion and translating the resulting flow of electrically charged ions into a proportionate electrical current that can then be read by a data system using a mass spectrometer can a molecule be mass measured.
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WILL GIVE BRAINLIEST
Which of the following best reflects how conditions described in this passage affected developing countries such as India?
A. The Indian government taking ownership of private industries to protect the country’s economy
B. People moving from India to more developed countries such as Great Britain in search of work
C. Industrial production centers closing in India, as those kinds of jobs moved back to Europe
D. India’s economy modernizing to catch up with the developed world
Answer:
B
Explanation:
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I need this to graduate!!
PLEASE HELP ASAP!!!
Viewing guide. We are going to watch the 1995 movie of Othello looking for the references to the scarf, listening for references to monsters, demons, and hell, and paying close attention to Iagos’s words to see how each of these was used to develop the theme of the danger of jealousy in the play.
Essential Question: How does Shakespeare develop a theme of the danger of jealousy in the play Othello?
Iago’s words
How do they connect to the theme of jealousy?
Example:
Explain:
Example:
Explain:
Example:
Explain:
Example:
Explain:
Scarf: What does it symbolize? How is it used to develop the theme of jealousy?
Example:
Explain:
Example:
Explain:
Example:
Explain:
Hell, demon, and monsters: References to hell, demon, and monsters are repeated as a motif. How do they connect to the theme of jealousy?
Example:
Explain:
Example:
Explain:
Example:
Explain:
Answer:
Explanation:
Ted might eat the cake.
11. Which of the following items appear on your credit report?
Answer:
The information that appears on your credit report includes: Personal information: Your name, including any aliases or misspellings reported by creditors, birth date, Social Security number, current and past home addresses, phone numbers, and current and past employers.
Explanation:
i hope this help
A gymnast must perform a floor routine in a large auditorium, while other gymnasts perform on the vault and uneven bars nearby. her ability to focus on her music and her routine best demonstrates (5 points)
a. her perceptual set
b. subliminal perception
c. weber's law
d. selective attention
e. distractibility
Selective Attention is the ability to focus on her music and her routine best demonstrates this. Therefore option D is correct.
What is Selective Attention?Having a conversation with someone in a busy public area is an example of selective attention. One decides to pay attention to what the friend is saying rather than to every background noise. The cocktail party effect is a phenomenon that describes this capacity.
Selective attention is the process of concentrating on a certain object in the environment for a set amount of time if we need to describe it. Our focus is constrained. Therefore, in order to make the most use of this finite resource, we require selective attention, which enables us to disregard irrelevant details.
Hence, Selective Attention is the ability to focus on her music and her routine best demonstrates this.
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17. Find the equation of the line that is tangent to the graph of F(x) and parallel to the given
line. Function: F(x) = 2x^2 Line: 4x + y + 3 = 0
Answer:
The equation of the line is \(y = -4\cdot x -2\).
Explanation:
Let the function be \(f(x) = 2\cdot x^{2}\) and the line be \(4\cdot x + y +3 = 0\). First, we transform the equation of the line into explicit form:
\(y = -4\cdot x + 3\) (1)
By Differential Calculus, the slope at any point of the function is represented by its first derivative, that is:
\(f'(x) = 4\cdot x\) (2)
If the line tangent to the function must be parallel to \(y = -4\cdot x + 3\), then \(f'(x) = -4\). In consequence, we clear \(x\) in (2):
\(4\cdot x = -4\)
\(x = -1\)
Then, we evaluate the function at the result found above to determine the associated value of \(y = f(x)\):
\(f(-1) = 2\cdot (-1)^{2}\)
\(y = f(-1) = 2\)
By Analytical Geometry we know that an equation of the line can be formed by knowing both slope (\(m\)) and y-intercept (\(b\)). If we know that \(x = -1\), \(y = 2\) and \(m = -4\), then the y-intercept of the equation of the line is:
\(b = y -m\cdot x\)
\(b = 2-(-4)\cdot (-1)\)
\(b = 2 -4\)
\(b = -2\)
Based on information found previously and the equation of the line, we have the equation of the line that is tanget to the graph of \(f(x)\), so that it is parallel to \(4\cdot x + y +3 = 0\) is:
\(y = -4\cdot x -2\)
The equation of the line is \(y = -4\cdot x -2\).