in criminal cases where dna evidence was used to overturn a previous conviction because the evidence exonerated the accused (and potentially imprisoned) person, what was found to be the compelling factor in more than 70 percent of the original cases that led to the wrongful conviction?

Answers

Answer 1

These issues include basic human error and human bias, linking innocent people to crimes, privacy rights, and increasing racial disparities.

If a suspect is known, a sample of that persons DNA can be compared to biological evidence found at the crime scene. The results of this comparison can help establish whether the suspect was at the crime scene or whether he or she committed the crime. In general, an exoneration occurs when a person who has been convicted of a crime is officially acquitted after new evidence of innocence available. A judicial error occurs when there is a manifestly unfair result in a criminal or civil proceeding, such as the conviction and punishment of a person for a crime that he did not commit. Miscarriages are also known as wrongful convictions. Because extremely small DNA samples can be used as evidence, more attention needs to be paid to contamination issues when identifying, collecting, and preserving DNA evidence.

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Related Questions

why does a lack of proton gradient being produced, the atp synthesis would cease which causes metabolic problem

Answers

Without a proton gradient, protons will not flow through ATP synthase, hence no ATP will be produced.

What happens if ATP synthesis is blocked ?

The output of ATP from OXPHOS is compromised by ATP synthase inhibition, and the energy metabolism is reprogrammed to favour enhanced glycolysis.

The proton motive force drives the synthesis of ATP once there are enough protons present. Therefore, a gradient enables cells to accumulate protons as "loose change," and this difference is crucial in determining whether there is growth or not, and whether there is life or not.

Protons need more and more energy to be pushed across the gradient as it increases. When the energy needed to push protons reaches 69.5 kJ/mole, electron transport must stop. In fact, before the gradient reaches that level, the second law of thermodynamics requires that electron transport cease.

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define double fertilisation in breif with example ??​

Answers

Double fertilization refers to the situation in which a sperm is fused with the egg to form the embryo and another sperm combines with the polar nucleus to yield the endosperm.

The term double fertilization applies mostly to the angiosperms. The angiosperms are those flowering plants in which their seed is enclosed within a carpel.

Hence, the term double fertilization refers to the situation in which a sperm is fused with the egg to form the embryo and another sperm combines with the polar nucleus to yield the endosperm.

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Send a picture of how it would look​

Send a picture of how it would look

Answers

The complete diagram of the Calvin cycle is shown in the image attached.

What is the diagram of the Calvin cycle?

The Calvin Cycle, also known as the light-independent reactions or the dark reactions, is a series of biochemical reactions that occur in the chloroplasts of photosynthetic organisms such as plants, algae, and some bacteria.

The Calvin Cycle is responsible for the synthesis of organic molecules from carbon dioxide (CO2) using the energy stored in ATP and NADPH, which are produced during the light-dependent reactions of photosynthesis.

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Send a picture of how it would look

Which plant tissue is the part of the plant that is edible?
ground
dermal
meristematic
vascular

Answers

Answer:

ground

Explanation:

Correlation between Mendels factors observed from the garden peas experimentation.

Answers

Mendelian inheritance was discovered when Gregor Mendel cross two pure breeds of peas. One is a pure breed of a purple pea plant and the other is a pure breed of a white pea plant. The result of the experiment is a hybrid offspring with violet flowers. The hybrid offspring is cross with each other and produce violet and white flowers.

For Mendel, it gave him the idea that there are "factors" affecting the inheritance of traits. These "factors" are now known as the genes, which are pairs of alleles that can have three genotypes: AA (homozygous dominant), aa (homozygous recessive), and Aa (heterozygous).

ANSWER:

In Mendel's experiment, the pure purple pea plant is homozygous dominant (PP) and the pure white pea plant is a homozygous recessive (pp). When they are crossed, the offspring become heterozygous/hybrid (Pp). Since the purple flower is dominant over the white flower based on their genotypes, the offspring will manifest a purple flower instead of a white flower.

But when two hybrid offspring are crossed, the produced offspring will either be purple or white. Thus, the "factors" can either be dominant or recessive.

Mendel carefully sorted the progeny derived from the parent plants based on the characteristics and counted the number that inherit each character.

Mendel studied inheritance in peas (Pisum sativum). He chose peas because they had been used for similar studies, are easy to grow and are biennial plants, and can be sown each year. Pea flowers contain both male and female parts, called stamen and stigma, and usually self-pollinate.

Mendelian factors are simply genes. Mendel while experimenting on the inheritance of traits (characteristics), used the term factors for the units that code for these traits. Later, these factors were given the term genes.

The main reason for their success of Mendel was that he took one character at one time in his experiments on hybridization. So it was easy. Other scientists also performed cross-hybridization for many characters, this made the experiments complex and they could not accurately explain the results.

Mendel observed seven different characteristics in the pea plants, and each of these characteristics had two forms. The characteristics included height (tall or short), pod shape (inflated or constricted), seed shape (smooth or wrinkled), pea color (green or yellow), and so on.

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The data indicate the populations of mammals in the Florida Everglades in different years over the past two decades. The Burmese python, a non-native species, was introduced to Florida as an exotic pet. After Hurricane Andrew hit Florida in 1992, many pet owners lost track of their non-native snakes. The biodiversity of the Everglades has decreased since then. According to the data, what hypothesis is best supported with regard to Burmese pythons and Florida Everglade biodiversity?

Answers

Answer:

The correct hypothesis would be - C) Burmese pythons lack natural predators and can utilize a wide variety of food sources in the Everglades.

Explanation:

Burmese pythons are the invasive species in this new region as they originally found in South Africa, and also one of the largest snakes so they lack natural predators in this new setting or region.

These snakes depend on both types of food which means they are omnivorous and eat both herbivore and carnivores prey.

Thus, the correct answer is - Burmese pythons lack natural predators and can utilize a wide variety of food sources in the Everglades.

Answer:

C. Burmese pythons lack natural predators and can utilize a wide variety of food sources in the Everglades

6. Students who attend Space Camp in Huntsville, Alabama are given the opportunity to learn about space travel. While
there, they explore distances between objects in space. One camper was asked to compare the distances between objects
in space and Earth. Which statement below is correct?
O The distance from Earth to the Sun is measured in astronomical units (AU).
O The distance from Earth to the Moon and Mars are both measured in light years.
The distance from Earth to the edge of the solar system is measured in kilometers.
O The distance from Earth to the star, Alpha Centauri, is measured in astronomical units (AU).

Thank you so much!

6. Students who attend Space Camp in Huntsville, Alabama are given the opportunity to learn about space

Answers

The correct statement is: "The distance from Earth to the Sun is measured in astronomical units (AU)."

An astronomical unit (AU) is a unit of measurement commonly used in astronomy to represent distances within the solar system.

It is defined as the average distance from the Earth to the Sun, which is approximately 93 million miles or 150 million kilometers. Using AU as a unit allows for a more convenient way to express and compare distances between objects within our solar system.

The statement that the distance from Earth to the Moon and Mars are both measured in light years is incorrect.

A light year is a unit of distance used to measure vast distances in space and is defined as the distance that light travels in one year (approximately 5.88 trillion miles or 9.46 trillion kilometers).

The distances between Earth and the Moon, as well as Earth and Mars, are much smaller and are typically measured in terms of thousands or millions of miles or kilometers.

Similarly, the distance from Earth to the edge of the solar system is not measured in kilometers.

The outermost edge of the solar system is typically defined by heliopause, where the influence of the Sun's solar wind diminishes. This distance is often measured in astronomical units or other astronomical measurements.

The distance from Earth to the star Alpha Centauri, which is the closest star system to our solar system, is not measured in astronomical units (AU).

It is typically measured in terms of light years, as the distance is extremely vast (approximately 4.37 light years away from Earth). Therefore, the correct statement is: "The distance from Earth to the Sun is measured in astronomical units (AU)."

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Which of the following types of organisms use ATGC bases in their DNA?
A)Bacteria
B)Plants
C)Animals
D)All of the above

Answers

Answer:

B) Plants is the answer correct me if I'm wrong

thermometer is used for​

Answers

Measuring the temperature of something.

Carbonate reefs (max 10 pts) a. Why are reefs generally attractive exploration targets? b. hat determines generally the depth of the hydrocarbon-water contact in reefs (use sketches)?
Que

Answers

a) Carbonate reefs are attractive exploration targets due to their unique characteristics and fossilized rocks, and they are known to host significant hydrocarbon accumulations. b)depth of these rocks is determined by the depth of the reef crest.

The exploration of these reefs involves a great deal of investment and high risks. In general, they are considered to be some of the most difficult areas to explore. As a result, companies may benefit greatly from their discoveries as the findings may result in major oil deposits.  Reefs are located in marine waters and are formed from the remains of carbonate shells that have accumulated over time.

They also contain other sedimentary rocks such as sandstones and shales. The reefs' ability to preserve fossils makes them a valuable target for exploration. Carbonate reefs are unique geological structures that can contain large amounts of hydrocarbons. It is important to note that reef reservoirs are incredibly complex, and the variations in the properties of these structures can be challenging to understand.  The depth of the hydrocarbon-water contact in reefs is determined by the depth of the reef crest, which is the highest point of the reef. In general, the depth of the hydrocarbon-water contact increases with the depth of the reef crest.

The crest height of the reef determines the water depth that the hydrocarbon-bearing rocks are exposed to. If the reef crest is located at a shallow depth, then the hydrocarbon-bearing rocks will be located at a shallow depth, and the hydrocarbon-water contact will be shallow as well. Conversely, if the reef crest is located at a deep depth, then the hydrocarbon-bearing rocks will be located at a deep depth, and the hydrocarbon-water contact will be deeper as well.

In general, the hydrocarbon-bearing rocks are located below the reef crest, and the depth of these rocks is determined by the depth of the reef crest.

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Targe
1.
The independent variable is
and the dependent variable is
in an experiment.
changed, observed
d 07/01
ce
kept the same, observed
d 07/01
observed, changed
07/01
hypothesized, changed
ursday

Answers

Independent variable: part of an experiment that is changed in a controlled manner.
Dependent variable: the effect that depends on the independent variable.

For example, an experiment measures how light (independent variable) affects plant growth (dependent variable). Every other component of plant growth is kept the same to isolate the effect the independent variable has on the dependent variable.

So, the independent variable is CHANGED while the dependent variable is OBSERVED

22) in a sewage treatment facility, an optimal environment is maintained for the survival of naturally occurring species of microorganisms. these organisms can then break the sewage down into relatively harmless wastewater. for these microorganisms, the wastewater facility serves as question 40select one: a. a food chain b. its carrying capacity c. an energy pyramid d. an ecosystem

Answers

For these microorganisms, the wastewater facility serves as an ecosystem. (Option d)

In a sewage treatment facility, a complex ecosystem of microorganisms is established to effectively break down the sewage into harmless wastewater. This ecosystem consists of various species of microorganisms that work together in a coordinated manner to degrade and process the organic matter present in the sewage.

An ecosystem refers to a community of living organisms (microorganisms in this case) interacting with their physical environment. In the sewage treatment facility, the microorganisms play specific roles in the degradation process, with some breaking down complex organic compounds into simpler forms, while others utilize the byproducts produced by the first group. This interdependent relationship between different microorganisms forms the basis of an ecosystem.

The sewage treatment facility provides an optimal environment, including the necessary nutrients, oxygen levels, and temperature conditions, to support the survival and growth of these microorganisms. As a result, they are able to efficiently break down the sewage and convert it into relatively harmless wastewater, contributing to the overall functioning of the ecosystem within the facility.

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the spreading out of molecules in air from a center of concentration is caused by

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The spreading out of molecules in the air from a center of concentration is caused by diffusion. Diffusion is the movement of molecules from a region of high concentration to a region of low concentration.

This process occurs due to the random motion of particles, and it is driven by the natural tendency of particles to move from an area of high concentration to an area of low concentration.

Diffusion plays a vital role in many natural processes, including gas exchange in the lungs, transport of nutrients and waste products across cell membranes, and the release of odor molecules into the air.

In each of these processes, the molecules move from a region of high concentration to a region of low concentration due to the natural tendency of particles to spread out and become evenly distributed over time.

The rate of diffusion is influenced by several factors, including the concentration gradient, the temperature of the environment, and the size and shape of the molecules involved.

Diffusion can be a slow process, particularly over long distances or in areas where the concentration gradient is small, but it is a fundamental mechanism that underlies many of the processes that allow living organisms to function and survive.

Overall, the spreading out of molecules in the air from a center of concentration is an essential process that is driven by the natural tendency of particles to diffuse and become evenly distributed over time.

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wich soil
dries faster after rainfall​

Answers

Answer:

There are 3 types of soil

Explanation:

-Sandy soil

-Clay soil

-Loam or something i forgot lol

1.basically Sandy soil absorbs and doesn't retents water (water retention) so it evaporates quizker than most soils

2.While clay say doesn't absord much water

3.And loamy soil (Mostly used in gardening) absorbs water but doesn't retain it so it evaporate or either used up by plants.

A student has obtained a sample of pond water for study. Using the high-power lens, he observes several cells with nuclei. He can conclude that the cells are NOT bacteria.

Answers

True, Using the high-power lens,  observes several cells with nuclei and can conclude that the cells are not bacteria.

Prokaryotic creatures include bacteria. Because they are prokaryotes, bacteria lack nuclei in their cells. The cytoplasm itself contains their genetic material, or DNA. Therefore, if the observed cells include a nucleus and other membrane-bound organelles, this indicates that those cells were not the bacterial cells. Additionally, bacterial cells lack additional membrane-bound organelles like mitochondria and endoplasmic reticulum.

The cell structure of bacteria is more straightforward than that of many other microorganisms. A single loop of DNA serves as their command center and houses all of their genetic information. Instead of a nucleus, some bacteria have a plasmid—an additional circular structure containing genetic material. Genes that offer the bacterium an edge over rival germs are frequently found in plasmids. By way of illustration, it might have a gene that renders the bacterium resistant to a specific drug.

Cocci, rod-shaped bacilli, spiral-shaped spirilla, comma-shaped vibrios, and corkscrew-shaped bacteria are divided into five groups based on their basic forms (spirochaetes). They can exist individually, in pairs, chains, or clusters.

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8) Several scientific laboratories across the globe are involved in research concerning the origin of life on Earth. Which of these questions is currently the most problematic and would have the greatest impact on our understanding if we were able to answer it?A) How can amino acids, simple sugars, and nucleotides be synthesized abiotically?B) How can RNA molecules catalyze reactions? C) How did RNA sequences come to carry the code for amino acid sequences?D) How could polymers involving lipids and/or proteins form membranes in aqueous environments?E) How can RNA molecules act as templates for the synthesis of complementary RNA molecules?

Answers

The most problematic question that would have the greatest impact on our understanding if we were able to answer about the origin of life on Earth is "How did RNA sequences come to carry the code for amino acid sequences?" (C)

RNА or Ribonucleic аcid plаys а vitаl role in protein synthesis. It аcts аs а messenger thаt trаnsfers genetic informаtion from DNА to ribosomes, where protein synthesis occurs. RNА cаrries out this function using the genetic code, а three-nucleotide sequence cаlled codon. This codon represents one of the 20 аmino аcids thаt mаke up proteins.

The most problemаtic question thаt would hаve the greаtest impаct on our understаnding if we were аble to аnswer it is "How did RNА sequences come to cаrry the code for аmino аcid sequences?". This question is the most chаllenging one becаuse it would explаin the origin of the genetic code, which is the foundаtion of life on Eаrth. Understаnding this question would help in comprehending how life emerged on Eаrth.

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which of the following cells and their function are correctly matched? dendritic cells – activate the immune system

Answers

The cells that are matched correctly are;

dendritic cells – activate the immune system

What is the immune system?

Immune cells known as dendritic cells are essential for triggering and controlling immune responses. They are in charge of engulfing antigens (foreign substances) and delivering them to different immune cells, like T cells and B cells.

Dendritic cells stimulate and activate the immune system by delivering antigens, aiding in the beginning of an immunological response against diseases or foreign invaders.

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which of the following cells and their function are correctly matched? dendritic cells activate the immune

The initial population of a bacteria colony is observed to be 500 bacteria. The population shows a growth rate of 50% per day, and the carrying capacity of the surrounding is estimated to be 2,000,000 bacteria. To the nearest whole number, find the population of bacteria after 15 days. A 165,822 bacteria B 622,707 bacteria C) 903,430 bacteria 2,000,000 bacteria

Answers

The population, to the nearest whole number, of bacteria after 15 days is approximately 4,769 bacteria, The correct option is E, None of the above.

To find the population of bacteria after 15 days, we can use the formula for exponential growth:

N = N₀ * \((1 + r)^t\)

Where: N = Final population after time t N₀ = Initial population r = Growth rate per time period t = Time period

Given: N₀ = 500 bacteria r = 50% per day (or 0.5) t = 15 days

Plugging in the values, we have:

N = 500 * \((1 + 0.5)^{15\)

Calculating this expression:

N = 500 * \((1.5)^{15\) N

= 500 * 9.537 N

= 4,768.5

Thus, the correct option is E, None of the above.

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The question is inappropriate; the correct question is:

The initial population of a bacterial colony is observed to be 500 bacteria. The population shows a growth rate of 50% per day, and the carrying capacity of the surrounding area is estimated to be 2,000,000 bacteria. To the nearest whole number, find the population of bacteria after 15 days.

A.  165,822 bacteria

B.  622,707 bacteria

C.  903,430 bacteria

D.  2,000,000 bacteria

E.  None of the above

How does nondisjunction affect the production of gametes?

Answers

Answer:

Nondisjunction Produces Abnormal Gametes. If nondisjunction occurs during anaphase I of meiosis I, this means that at least one pair of homologous chromosomes did not separate. The end result is two cells that have an extra copy of one chromosome and two cells that are missing that chromosome. Click to see full answer.

Explanation:

which best describes the nucleus of an atom?
A. it is the most massive part of an atom
B. It contains no mass.
C. Its made of neutrons and electrons.
D. it is negatively charged part of the atom.

Answers

The nucleus of an atom describes option A. It is the most massive part of an atom.

The nucleus is the central part of an atom and is composed of protons and neutrons. Protons have a positive charge, while neutrons have no charge (they are neutral). Electrons, on the other hand, are negatively charged particles that orbit the nucleus in electron shells. The nucleus is incredibly small compared to the overall size of the atom, but it contains most of the atom's mass.

The protons and neutrons within the nucleus contribute to the mass of the atom, while the electrons have a negligible mass in comparison. The mass of an atom is determined by the total number of protons and neutrons in the nucleus. Protons and neutrons have roughly the same mass, and their combined mass gives the atom its atomic mass.

Electrons, though they have mass, contribute very little to the overall mass of the atom. The nucleus also plays a critical role in determining the chemical properties and behavior of an atom. The number of protons in the nucleus determines the atomic number, which defines the element and its unique properties. Therefore, the correct answer is option A.

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hurry help me! the first person to answer gets brainest :)

hurry help me! the first person to answer gets brainest :)

Answers

Answer:

A: Golgi apparatus

B: vacuole

C: mitochondrion

D: nucleus

E: cell membrane

What interactions are occurring that allow the water to move against gravity in capillary action? Select three options.

Answers

Answer:

Adhesion and surface tension

Explanation:

Capillary action is the tendency of a liquid to rise or fall in a narrow tube. Two main terms are required to explain capillary action; adhesion and cohesion.

Cohesion is the force of attraction between molecules of the same kind while adhesion is the force of attraction between molecules of different kinds.

Forces of adhesion causes water to move up in a capillary tube. The water is held as it rises by surface tension forces acting on the circumference of the meniscus. The water keeps rising in the tube until the weight of the water drawn up in the tube balances the surface tension acting at the top column of the water.

A person has a gene that determines the nail and patellar defect syndrome (D is a dominant trait), as well as the gene that determines the blood group according to the ABO system, are located on the same chromosome at a distance of 10 morganides. List all possible types of gametes in a person with IV blood group and heterozygous for the gene for the defect of nails and kneecap. Describe your response widely, please.

Answers

The rhesus D (RhD) antigen is what determines whether a person is RhD positive or RhD negative. It's a chemical that's present on the outside of red blood cells. RhD positive individuals are those who have the RhD antigen, while RhD negative individuals do not.

What blood type has dominant and recessive traits?

The autosomal codominant inheritance pattern for the ABO blood type. The O allele is recessive, whereas the A and B alleles are codominant.

Even when combined with a Rh-negative gene, the Rh-positive gene prevails because it is dominant (stronger). The blood's Rh factor will be positive if a person possesses the + + gene combination.

The numerous blood types are created by various combinations of these three alleles.

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What is the phenotype of a person whith the genotype I^Ai?

What is the phenotype of a person whith the genotype I^Ai?

Answers

Answer:

Type A

Explanation:

Mode of inheritance for blood is tricky, but type A and B are codominant, while type A and type B are dominant over O. So in this situtation

I^Ai is A because type a is dominant over o


Jose designs an experiment to determine how music affects a plants' growth. He plans to carry
out his experiment by using six different flowering plants. Each plant will be placed in one liter
of potting soil, and given the same amount of water and sunlight each day. Each plant will be
exposed to six types of music for the duration of the experiment. He presents his plan to his
teacher for approval, but was told there is an error in the design of his experiment. What error
did Jose make?
A. Jose's plan does not have a hypothesis.
B. Jose's plan has too many control variables.
C. Jose's plan has more than one test variable (independent variable).
D. Jose's plan does not have an outcome variable (dependent variable).

Answers

Answer:

a

Explanation:

what are the first two fuel sources that the body uses during fasting?

Answers

In order to learn about what happens in the body while we’re fasting, it’s important to understand how the body fuels itself. The body uses two main sources of energy: glucose. Fat.

The human body uses different sources of energy to function, and the primary source of energy during fasting is stored glucose and fat. Here is a detailed explanation of the first two fuel sources the body uses during fasting:

Glucose: Glucose is the primary source of energy for the body, especially the brain. It is stored in the liver and muscles as glycogen and can be rapidly converted to glucose as needed. During fasting, the body will first use up stored glucose as its primary energy source. This glucose is released into the bloodstream, where it can be used by the cells to produce energy.

Fat: Once the stored glucose has been depleted, the body will start to break down stored fat as its primary source of energy. Fat is stored in adipose tissue throughout the body and can be broken down into fatty acids and glycerol, which can be used as fuel for the cells. The breakdown of fat is a slower process than the breakdown of glucose, but it provides a more sustained source of energy.

In summary, during fasting, the body first uses up stored glucose as its primary energy source and then switches to breaking down stored fat as its primary source of energy.

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Alternate versions of a gene that account for variations in inherited characteristics are called:.

Answers

Alternate versions of a gene that account for variations in inherited characteristics are called alleles.

Alleles are different versions of the same gene that are found at the same location on a chromosome. They can have different sequences of DNA and can produce different proteins, which can result in different traits or characteristics in individuals.

For example, the gene for eye color has different alleles that produce different amounts of pigment, resulting in variations in eye color.

Alleles can be inherited from parents in different combinations, which can further increase genetic diversity. If an individual inherits two different alleles for a particular gene, they are said to be heterozygous for that gene. If they inherit two identical alleles, they are said to be homozygous for that gene.

Understanding the concept of alleles is important in genetics and can help explain the inheritance patterns of traits in populations. By studying the different alleles present in a population, scientists can gain insight into the genetic diversity of a species and how it has evolved over time.

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What do scientists call an explanation that organizes observations and predicts future behaviors or events?.

Answers

An explanation that organizes observations and predicts future behaviors or events is called theory.

A theory is a logical abstraction regarding a phenomena or the conclusions of such an abstraction. Contemplative and logical thought are frequently linked to procedures like observational study or research.

Theories are developed to explain, predicts, and comprehend occurrences as well as, frequently, to question and advance current knowledge while staying within the bounds of crucial limiting assumptions. The structure that may retain or support a research study's hypothesis is known as the theoretical framework.

Theory enables us to make sense of what we observe and choose how to effect change. Theory is a tool that helps us to recognise issues and create plans for solutions.

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Find the solution of the given initial value problem: (a) y

−y=2xe
2x
,y(0)=1 (b) y

+(cotx)y=2cscx,y(π/2)=1

Answers

(A) The answer to the initial value problem is given by \(\(y = (x^2 + 1)e^x\)\), where \(\(y' - y = 2xe^{2x}\)\) and \(\(y(0) = 1\)\).

(B) The resolution to the initial value problem can be expressed as \(\(y = \frac{2x - (\pi - 1)}{\sin(x)}\)\), where \(\(y' + \cot(x)y = 2\csc(x)\)\) and \(\(y\left(\frac{\pi}{2}\right) = 1\)\).

(A) To solve the initial value problem:

\(\[y' - y = 2xe^{2x}, \quad y(0) = 1\]\)

We can use an integrating factor method. To begin, let us express the equation in its standard form:

\(\[y' - y - 2xe^{2x} = 0\]\)

The integrating factor \(\(I(x)\)\) is given by \(\(I(x) = e^{\int -1 \, dx} = e^{-x}\)\).

To obtain the solution, apply the integrating factor to both sides of the equation and perform the multiplication.

\(\[e^{-x}(y' - y) - 2xe^{2x}e^{-x} = 0\]\)

This simplifies to:

\(\[e^{-x}y' - e^{-x}y - 2x = 0\]\)

Now, observe that the expression on the left-hand side represents the derivative of \(\((e^{-x}y)\)\) with respect to \(\(x\)\).

Using this observation, we can rewrite the equation as:

\(\[\frac{d}{dx}(e^{-x}y) - 2x = 0\]\)

Integrating both sides with respect to \(\(x\)\), we get:

\(\[e^{-x}y - \int 2x \, dx = C\]\)

where \(\(C\)\) is the constant of integration.

Integrating \(\(\int 2x \, dx\)\), we have:

\(\[e^{-x}y - x^2 + C = 0\]\)

To find the constant \(\(C\)\), we use the initial condition \(\(y(0) = 1\)\).

Substituting \(\(x = 0\)\) and \(\(y = 1\)\) into the equation, we get:

\(\[e^{0} \cdot 1 - 0^2 + C = 0\]\)

\(\[1 + C = 0\]\)

\(\[C = -1\]\)

Substituting \(\(C = -1\)\) back into the equation, we have:

\(\[e^{-x}y - x^2 - 1 = 0\]\)

Finally, we can solve for \(\(y\)\) by isolating it:

\(\[e^{-x}y = x^2 + 1\]\)

\(\[y = (x^2 + 1)e^x\]\)

(B) To solve the initial value problem:

\(\[y' + \cot(x)y = 2\csc(x), \quad y\left(\frac{\pi}{2}\right) = 1\]\)

We can use an integrating factor method. To begin, we will rewrite the equation in standard form:

\(\[y' + \cot(x)y - 2\csc(x) = 0\]\)

The integrating factor \(\(I(x)\)\) is given by:

\(\(I(x) = e^{\int \cot(x) \, dx} = e^{\ln(\sin(x))} = \sin(x)\).\)

Apply the integrating factor to both sides of the equation and perform the multiplication.

\(\[\sin(x)(y' + \cot(x)y) - 2\csc(x)\sin(x) = 0\]\)

This simplifies to:

\(\[\sin(x)y' + \cos(x)y - 2 = 0\]\)

Now, observe that the expression on the left-hand side represents the derivative of \(\((\sin(x)y)\)\) with respect to \(\(x\)\). Using this observation, we can rewrite the equation as:

\(\[\frac{d}{dx}(\sin(x)y) - 2 = 0\]\)

Integrating both sides with respect to \(\(x\)\), we get:

\(\[\sin(x)y -\)\(\int 2 \, dx = C\]\)

where \(\(C\)\) is the constant of integration. Integrating \(\(\int 2 \, dx\)\), we have:

\(\[\sin(x)y - 2x + C = 0\]\)

To find the constant \(\(C\)\), we use the initial condition \(\(y\left(\frac{\pi}{2}\right) = 1\).\)

Substituting \(\(x = \frac{\pi}{2}\)\) and \(\(y = 1\)\) into the equation, we get:

\(\[\sin\left(\frac{\pi}{2}\right) \cdot 1 - 2\left(\frac{\pi}{2}\right) + C = 0\]\)

\(\[1 - \pi + C = 0\]\)

\(\[C = \pi - 1\]\)

Substituting \(\(C = \pi - 1\)\) back into the equation, we have:

\(\[\sin(x)y - 2x + (\pi - 1) = 0\]\)

Finally, we can solve for \(\(y\)\) by isolating it:

\(\[\sin(x)y = 2x - (\pi - 1)\]\)

\(\[y = \frac{2x - (\pi - 1)}{\sin(x)}\]\)

\(\(y = \frac{2x - (\pi - 1)}{\sin(x)}\).\)

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The complete question is:

Find The Solution Of The Given Initial Value Problem:

(A) \(\(y' - y = 2xe^{2x}\)\), and \(\(y(0) = 1\)\)

(B) \(\(y' + \cot(x)y = 2\csc(x)\)\), and \(\(y\left(\frac{\pi}{2}\right) = 1\)\)

Which of the following are branches of the autonomic nervous system and innervate the gastrointestinal tract

Answers

Both the sympathetic and parasympathetic branches of the autonomic nervous system provide innervation to the gastrointestinal tract, but they exert opposing effects on its function. The balance between these two branches helps regulate and maintain the optimal functioning of the digestive system.

The branches of the autonomic nervous system that innervate the gastrointestinal tract are: Sympathetic Nervous System: The sympathetic division of the autonomic nervous system typically inhibits gastrointestinal activity. It is responsible for the "fight or flight" response and prepares the body for physical exertion or stressful situations. Sympathetic fibers innervate the gastrointestinal tract and can decrease digestive functions such as peristalsis and secretion. Parasympathetic Nervous System: The parasympathetic division of the autonomic nervous system promotes gastrointestinal activity. It is responsible for the "rest and digest" response, conserving energy and promoting digestion. Parasympathetic fibers innervate the gastrointestinal tract and can stimulate digestive functions such as peristalsis, secretion, and vasodilation. Both the sympathetic and parasympathetic branches of the autonomic nervous system provide innervation to the gastrointestinal tract, but they exert opposing effects on its function. The balance between these two branches helps regulate and maintain the optimal functioning of the digestive system.

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