kalium channelrhodopsins are natural light-gated potassium channels that mediate optogenetic inhibition.T/F

Answers

Answer 1

Widely used for optical control of neurons, channelrhodopsins produce photoinduced proton, sodium, or chloride influx. Despite the fact that potassium (K+) is essential for neuron electrophysiology, no naturally occurring light-gated potassium channel has been discovered.

The kalium channelrhodopsins (KCRs) from Hyphochytrium catenoides are described here. The majority of previously identified gated potassium channels are voltage- or ligand-gated, and they all have a conserved K+-selectivity filter. KCRs are unique in that they have a different K+ selectivity mechanism and are light-gated. Following photoactivation, the KCRs are powerful, highly selective for K+ over Na+, and open in less than 1 ms.

H. catenoides KCR1 (HcKCR1) has been shown here in mouse cortical neurons to have a potent hyperpolarizing effect to decrease excitable cell firing upon illumination due to its 23 permeability ratio PK/PNa. In order to research and maybe treat potassium channelopathies such epilepsy, Parkinson's disease, long-QT syndrome, and other cardiac arrhythmias, HcKCR1 allows optogenetic modulation of K+ gradients.

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Related Questions

A elephant cell has 20 chromosomes. how many chromosomes will the cell have just before mitosis begins in the elephant cell?

Answers

The elephant cell will have 20 chromosomes.

Cells undergo interphase before getting to the mitotic phase. At the S phase of the interphase, the amount of DNA in the cell is double by replication. However, the number of chromosomes remains intact.

Thus, the cell gets to the mitotic phase with the same number of chromosomes that is usually present in normal vegetative cells of the animal.

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Correctly label the following anatomical features of a neuron. Axon Axon terminals Myelin sheath Soma Internode Nucleus Node of Ranvier Dendrites Nucleolus

Answers

A neuron is a specialized cell,  found in the brain, spinal cord and the peripheral nerves  known as the nerve cell. The structure of a neuron varies with their shape and size and it mainly depends upon their functions

what is the structure of neuron ?

Dendrites which is A branch-like structure that functions by receiving messages from other neurons and allow the transmission

Cell Body has a cell body with a nucleus, Golgi apparatus, endoplasmic reticulum, mitochondria and other components.

Axon is a tube-like structure that functions by carrying an electrical impulse from the cell body to the axon terminals

Synapse functions by permitting the entry of a neuron to move an electrical or chemical signal from one neuron to another neuron.

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What is the range for the following set of measurements? 27°C, 12°C, 31 °C, 19°C, 23°C, 11 °C, 17°C​

Answers

Explanation:

Range is the highest number minus the lowest number

Range = 21°C - 11°C = 10°C

Answer : 10°C

_____ is a binocular cue used to judge distance and depth based on the tension of the muscles that direct where the eyes are focusing.

Answers

Answer:

An important binocular depth cue is convergence, the inward turning of our eyes that is required to focus on objects that are less than about 50 feet away from us. The visual cortex uses the size of the convergence angle between the eyes to judge the object's distance.

Explanation:

although many cloning applications involve introducing recombinant dna into bacterial host cells, many other cell types are also used as hosts for recombinant dna . part a why are cell types other than bacteria also used as hosts for recombinant dna ? select the three correct answers. why are cell types other than bacteria also used as hosts for recombinant ?select the three correct answers. some studies are carried out to research a specific dna segment in a specific host environment. the mutation rate in bacteria is relatively high as compared to unicellular eukaryotes. bacteria possess an elaborate system of foreign dna deactivation. bacteria are not very easy to handle and grow in the lab. bacteria cannot carry out some posttranslational modifications as eukaryotes do. bacteria do not process transcripts as eukaryotes do.

Answers

The correct responses Bacteria, unlike eukaryotes, cannot perform some posttranslational modifications.

How can you tell if a cell was eukaryotic or not?

Organelles bound by the membrane such as the nuclei or mitochondria are found in eukaryotic cells but not in prokaryotic tissues. DNA is discovered inside the nucleus of eukaryotic cells, whereas DNA is found in the cytoplasm of prokaryotic cells. In general, eukaryotic cells are bigger as well as more complicated than prokaryotic cells.

Where can you find eukaryotic cells?

Overview. Eukaryotic cells are one of two types of cells. Plants, animals, fungi, or protists are examples of eukaryotes, which are organisms based in the eukaryotic cell. The only creatures that do not have a eukaryotic cell structure are those with a prokaryotic cells structure.

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Hemophilia is an X-linked recessive genetic disorder. A baby girl is found to have inherited the trait from her parents. What are the phenotypes of the parents?

Answers

X-linked genes are inherited. The affected girl's father is hemophilic (X-Y), and the mother might be either hemophilic (X-X-) or carrier normal (X+X-).

What are the X-linked genes?

These are the genes located in the X séx chromosome and not in the somatic ones.

Traits coded by these genes are inherited. This is, X-linked genes are transmitted from parents to children through generations.

According to this, X-linked genetic disorder will be inherited as well.

Men have a high probability of being affected since they only have one copy of the X chromosome.  In women, the effect of the mutation might be musk in heter0zyg0us state.

Hemophilia is a X-linked recessive genetic disorder.

Let us represent the recessive allele with the symbol -, and the dominant allele with the symbol +.

X- is the chromosome carrying the recessive allele X+ is the chromosome carrying the dominant allele

For the affection to be expressed, the person must be either,

X-X-  ⇒   woman/girlX-Y  ⇒    man/boy

If the baby girl is found to have inherited the trait from her parents, then her genotype is X-X-. She must have received one X- chromosomes from each parent.

Her father provided the X chromosome, so he must be hemophilic (X-Y)Her mother provided the other X chromosome, but she can be either a carrier (heter0zyg0us, X+X-) or hemophilic (h0m0zyg0us recessive, X-X-).

Options,

Cross 1) affected father x carrier mother

Parentals)   X-Y    x    X+X-

Gametes)  X-      Y    X+     X-

Punnett square)       X-       Y

                       X+   X+X-    X+Y

                       X-    X-X-     X-Y  

F1) 1/2 = 50% of the progeny is expected to be healthy (25% X+X- girls + 25% X+Y boys)

    1/2 = 50% of the progeny is expected to be hemophilic (25% X-X- girls + 25% X-Y boys)

Cross 2) affected father x affected mother

Parentals)   X-Y    x    X-X-

Gametes)  X-      Y    X-     X-

Punnett square)       X-       Y

                       X-    X-X-    X-Y

                       X-    X-X-     X-Y  

F1) 100% of the progeny is expected to be hemophilic (50% X-X- girls + 50% X-Y boys)

the phenotype of the fatherhemophilic (X-Y)the phenotype of the mother ⇒ normal carrier (X+X-) or hemophilic (X-X-)

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explain how plants are involved in the carbon cycle

Answers

Through the process of photosynthesis, carbon dioxide is pulled from the air to produce food made from carbon for plant growth.
Plants are involved with the carbon cycle because they go through a process called photosynthesis. Photosynthesis is when the plant absorbs carbon dioxide(CO2) and releases oxygen, this is for the plant to grow and live. This is very good for our environment and keeping the air clean.

(a) based on the distribution of biomes in the united states, describe the ecological niche that is occupied by the dominant native plant community that inhabits region a.

Answers

A biome is a sizable region distinguished by its flora, fauna, soil, and climate. Aquatic, grassland, forest, desert, and tundra biomes

what are the types of major biome ?

A biome is a specific large area which is characterized by its vegetation, soil, climate, and wildlife.

There are five major types of biomes such as aquatic, grassland, forest, desert, and tundra and some of these biomes can be further classified into more specific categories, such as freshwater, marine, savanna, tropical rain forest, temperate rain forest, and taiga.

on the other hand Ecological niche can be defined as the position of a species within an ecosystem which describe both the range of conditions necessary for persistence of the species in an ecosystem.

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¿¿What substance promote cell growth??​

Answers

Answer:

A growth factor is a naturally occurring substance capable of stimulating cell proliferation, wound healing, and occasionally cellular differentiation. Usually it is a secreted protein or a steroid hormone. Growth factors are important for regulating a variety of cellular processes.Explanation:

Usually it is a secreted protein or a steroid hormone.

Examples of Models
of Elements
0₂
Oxygen
He
Helium
S₁
Sulfur
Examples of Models of Compounds
A. Only elements are gases.
H₂O
Water
CO₂
Carbon dioxide
What is the difference between an element and a compound?
B. Only elements have one kind of atom.
C. Only elements have an odd number of atoms.
D. Only elements form large molecular structures.
NH,
Ammonia

Examples of Modelsof Elements0OxygenHeHeliumSSulfurExamples of Models of CompoundsA. Only elements are

Answers

The correct option is (B) only elements have one kind of compound.

What are elements?An element is a pure substance made up of only one kind of atom, each of whose nuclei contains the same amount of protons.An element is a group of atoms that all have the same number of protons in their atomic nuclei. An element's atoms always contain the same amount of protons, however, the mass can differ depending on the number of neutrons present.Atoms of the same element that contain different numbers of neutrons are known as isotopes. There are currently 118 elements, the first 94 of which are naturally occurring, and the last 24 of which are synthetic.Currently, an element, which is a complete chemical compound, corresponds to a single entry in the periodic table. They can only exist as molecules or atoms and cannot be broken down into smaller parts.

Compounds:

Chemical substances known as compounds are composed of two or more elements that are chemically bonded together in a certain proportion.

Therefore, the correct option is (B) only elements have one kind of compound.

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Describe the internal and external costs of one of the technologies mentioned in the ecological footprint questionnaire (energy)

Answers

Answer:

internal measure human demand on natural capital

external  costs are costs that are NOT included in what the business bases its price on. These include: the cost of disposing of the product at the end of its useful life the environmental degradation caused by the emissions,

Explanation:

I'm trying to look for answer to im not sure if it helpful

classify each of the following as an element, compound, homogeneous mixture, or heterogeneous mixture. 1.water
2.Caesar Salad
3.milk and cereal
4.Iron filings
5.blood
6.sugar
7.sand
8.sea water
9.salt
10.carbon dioxide​

Answers

Caesar Salad, milk and cereal, Blood, Sand  are heterogeneous mixture while water, sugar and salt are compounds and Iron filings is a element and Sea water is a homogeneous mixture

A pure substance with only one kind of atom makes up an element. The elements oxygen, hydrogen, and iron are examples.

A compound is a substance that is composed of two or more distinct elements that have been chemically bonded together in a specific proportion. Examples include sodium chloride, carbon dioxide, and water.

A combination of two or more substances that are evenly distributed at the molecular level is referred to as a homogeneous mixture. The mixture's composition is constant throughout. Examples include air, sugar water solutions, and saltwater.

A combination of two or more substances that are not distributed equally is referred to as a heterogeneous mixture. Visual differentiation between the various elements is possible and with time, they may settle or separate. A salad with various ingredients, soil and vinegar dressing are some examples.

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Which answer below accurately explains a scientific theory.

A. A specific happening given specific circumstances

B. An inference based on past experience

C. A well-substantiated explanation accepted as true

D. An agreeable testable explanation that eventually becomes a law

Answers

Answer:

I think it is c since "A scientific theory is an explanation of an aspect of the natural world that can be repeatedly tested and verified in accordance with the scientific method, using accepted protocols of observation, measurement, and evaluation of results. Where possible, theories are tested under controlled conditions in an experiment. "

Imagine you are standing in a meadow of sunflowers. Compare your view of sunflowers from the perspective of typological thinking and from that of population thinking.

Answers

Typological thinking is that classifies things only in terms of the types to which they belong, and ignore variations among individuals.

Ernst  coined the term 'typo-logical thinking' for the collection of misguided  metaphysical  ideas and evolutionary. The typo-logical thinking is real and the variation an illusion, while for popularization the type is an abstraction and variation is real only.

The idealized species into an individual that represented character of that differentiated from all other individuals. Population thinking rejects idea of each species in natural type and instead sees every species as a varying population of interbreeding individuals.

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HELP!!!! 48PTS!!!!

What happens to water when it warms above 4 °C? (4 points)
It contracts.
It forms ice.
Its density decreases.
Its composition changes.

Answers

Answer:

Its Density decreases.

Explanation:

trusted source used.

Answer: It’s density decreases.

As the temperature of warm water decreases, the water molecules slow down and the density decreases. At 4 °C, the clusters start forming. The molecules are slowing down and coming closer together.

When you palpate the spine, the dorsal most point is the _____ .

Answers

When palpating the spine, the dorsal most point is the spinous process.

The spinous process refers to the bony prominence that can be felt along the midline of the back when palpating the spine. It is the most prominent and easily identifiable part of each vertebra. The spinous processes extend backward from the vertebral bodies and serve as attachment points for muscles and ligaments.

When palpating the spine, a person can run their fingers along the midline of the back to feel the series of spinous processes. Each spinous process corresponds to a specific vertebra, and their alignment and spacing can provide valuable information about the spinal anatomy and any potential abnormalities or misalignments.

It is important to note that palpation of the spine should be done with caution and by trained professionals to ensure accuracy and prevent any potential discomfort or injury to the person being examined.

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The dorsal most point of the spine, when palpated from the back, is located at the top of the cervical spine, near the base of the skull.

When palpating the spine, it is important to understand the anatomical terms used to describe its different regions. The spine is divided into several sections, including the cervical (neck), thoracic (chest), lumbar (lower back), sacral (pelvic), and coccygeal (tailbone) regions.

The dorsal most point refers to the highest point on the spine when palpated from the back. This point is typically located at the top of the cervical spine, near the base of the skull. Palpating the spine can help identify any abnormalities or changes in the alignment of the vertebrae.

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Remembering the function of chloroplasts, in which part(s) of the leaf is photosynthesis taking place​

Answers

\(the \: primary \: cellular \: structures \: that \: ensures \: photosynthesis \ \\ takes \: place \: are \: chloroplasts \\ thylakoids \: and \: chlorophyll. \\ photosynthesis \: takes \: place \: inside \: the \: chloroplasts \\ that \: sit \: in \: the \: mesophyll \: of \: the \: leaves. \\ the \: thylakoids \: sit \: inside \: the \: chloroplast \: and \: they \: contain \\ chlorophyll \: which \: absorbs \: the \: different \: colours \\ of \: the \: light \: spectrum \: to \: create \: energy. \\ \\ hopefully \:it \: helps \\ have \: a \: nice \: day \: ahead\)

The photosynthesis occurs in the palisade layer of the leaf.

What is photosynthesis?

Photosynthesis refers to a series of metabolic reactions by which plants generate simple carbohydrates (sugars) by using the energy from the sun and carbon dioxide.

Photosynthesis has two main types of reactions: light-dependent and light-independent reactions.

Photosynthesis occurs in a specialized plant organelle known as chloroplast, which is able to absorb solar energy to convert it into ATP

In conclusion, photosynthesis occurs in the palisade layer of the leaf.

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what is one primary variation in the human genome that can be used to distinguish different individuals?

Answers

One primary variation in the human genome that can be used to distinguish different individuals is single nucleotide polymorphisms (SNPs). SNPs are variations in a single DNA base pair that occur in at least 1% of the population.

These variations can result in different forms of genes, called alleles, which can affect an individual's traits or susceptibility to certain diseases. The human genome contains over 10 million SNPs, and they are spread throughout the entire genome.

SNPs can be used in genetic testing and forensics to identify individuals. By comparing the SNP patterns between two individuals, it is possible to determine if they are related or if they are completely unrelated. This technique is commonly used in paternity testing, ancestry testing, and criminal investigations.

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Have you ever considered air pollution when thinking about someplace you'd like to live, or live currently?

If the air pollution here in Killeen was as bad as in other cities, what would you do? Why do you think the people in those cities don't leave?

Answers

Answer:

I would come up with a plan to help decrease pollution and be like: "Ey if you want to live in (insert city) Then we can make this city like that."

Explanation:

what medical technology have some chinese chosen to pursue in order to increase the possibility of multiple children in a single pregnancy

Answers

The use of fertility drugs is the technology used by some Chinese that can increase the possibility of multiple children in a single pregnancy.

Fertility drugs are the medications that serve various functions like production of eggs or sperms, or their quality.  Some drugs can speed up the growth and maturity of egg cells, resulting in the release of more than one egg cell at the same time. This is how multiple children are born from a single pregnancy.

Pregnancy is the stage when the fusion of the male and female gamete happens and the fetus develops inside the body of the mother. For humans, this time period is of 9 months.

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What is the difference in the structure of the cell walls of gram-positive and grarn-negative
bacteria?

Answers

Answer:

The major difference between Gram-positive and Gram-negative peptidoglycan involves the thickness of the layers surrounding the plasma membrane. Whereas Gram-negative peptidoglycan is only a few nanometers thick, representing one to a few layers, Gram-positive peptidoglycan is 30–100 nm thick and contains many layers.

Explanation:

During meiosis, genetic diversity results from which of the following processes?

recombination via crossing over
independent assortment of chromosomes
replication of the cell's DNA

Answers

Answer:recombination via crossing over

independent assortment of chromosomes

Explanation:Because You Know I am right !

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During meiosis, genetic diversity results from which of the following processes? recombination via crossing

Genetic variety is produced during meiosis by two processes: autonomous chromosomal sorting and recombination by crossing over.

What happens in the case of homologous chromosomes ?

When homologous chromosomes exchange genetic material during the first meiotic prophase, recombination by crossing over takes place.

By mixing up the alleles on homologous chromosomes, this mechanism produces genetic variety by giving the daughter cells unique allele combinations. When homologous chromosomes randomly align at the metaphase plate during the second meiotic prophase, a process known as independent assortment of chromosomes takes place.

By randomly segregating the alleles of the homologous chromosomes into the daughter cells, this process generates genetic variety. The S-phase of the cell cycle, which is not a part of meiosis, is when the process of the cell's DNA replication takes place. Consequently, imitation of the same. During meiosis, the DNA of the cell does not contribute to genetic diversity.

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Where can gliding and condyloid joints be found?

Answers

Gliding and condyloid joints are the two main types of synovial joints in the human body. Gliding joints are located in between flat bones, such as those found in the ankles, wrists, vertebrae and jawbone.

These small joints enable a smooth gliding motion when motion is applied. Condyloid joints consist of an oval-shaped end of a bone fitting into another oval-shaped concave surface on another bone; this type of joint has wide range movements, enabling flexing and extending motions to occur. They can be found at the wrist and elbow joints, where the radius or ulna meets proximal carpals or humerus respectively.

In addition, they can be found where structures such as the medial cuneiform meet with cuboid and navicular bones.

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Question 9 of 10
How does an atom become a positive ion?
A. It loses an electron,
B. It loses a neutron,
C. It gains an electron
D. It gains a neutron,
SUSAN

Answers

The answer is A it loses and election
Ionization or ionisation is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged atom or molecule is called an ion. Ionization can result from the loss of an electron after collisions with subatomic particles, collisions with other atoms, molecules and ions, or through the interaction with electromagnetic radiation. Heterolytic bond cleavage and heterolytic substitution reactions can result in the formation of ion pairs. Ionization can occur through radioactive decay by the internal conversion process, in which an excited nucleus transfers its energy to one of the inner-shell electrons causing it to be ejected. So it is A

DNA Bases - A code for the ______ in your cells

Answers

DNA bases code for the proteins in your cells

Which of the following best predicts and justifies how the proportion of the Tibetan population with big blood vessels living in the mountains will change over the next 1,000 years (assuming conditions remain stable)?

Question 2 options:

I predict that the proportion of individuals with big blood vessels living in the mountains will decrease because there is a variation in blood vessel size and those with the smaller blood vessels can store more red blood cells than larger vessels, so more oxygen can be moved to the body cells. Therefore, they have a better chance of surviving and passing this trait on to their offspring.


I predict that the proportion of individuals with big blood vessels living in the mountains will stay the same because there is a variation in blood vessel size and that variation will remain in a population. The is what is so cool about humans, we are all so unique.


I predict that the proportion of individuals with big blood vessels living in the mountains will increase because there is a variation in blood vessel size and those with the bigger blood vessels can deliver more oxygen to the body cells and therefore have a better chance of surviving and passing this trait on to their offspring.


I predict that over 1,000 years, the proportion of individuals with big blood vessels living in the mountains will not change because a change can’t happen to an individual, an individual can only increase the amount of red blood cells it makes, not its blood vessels.

Which of the following best predicts and justifies how the proportion of the Tibetan population with

Answers

Answer:

Over 1,000 years, the proportion of individuals with big blood vessels living in the mountains will not change because a change can’t happen to an individual, an individual can only increase the number of red blood cells it makes, not its blood vessels.

Explanation:

Evolution is the change in the characteristics of a species over several generations and relies on the process of natural selection

What is blood vessels?

The blood vessels are the components of the circulatory system that transport blood throughout the human body.

I predict that over 1,000 years, the proportion of individuals with big blood vessels living in the mountains will not change because a change can’t happen to an individual, an individual can only increase the amount of red blood cells it makes, not its blood vessels.

Hence, option D is correct.

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The main role of calcium ions at chemical synapses is to
Select one:
a. depolarize the axon terminal of the presynaptic cell.
b. bind to neurotransmitter receptors on the postsynaptic cell
c. cause fusion of synaptic vesicles with the plasma membrane of the axon terminal.
d. interfere with IPSPs in the postsynaptic cell.
e. diffuse across the synaptic space and enter the postsynaptic cell.

Answers

The main role of calcium ions at chemical synapses is to cause fusion of synaptic vesicles with the plasma membrane of the axon terminal. This process allows for the release of neurotransmitters into the synaptic cleft, which can then bind to neurotransmitter receptors on the postsynaptic cell and depolarize it.

Without the influx of calcium ions, the release of neurotransmitters and subsequent communication between neurons would not be possible.

Chemical synapses are biological connections that allow impulses to travel from neurons to non-neuronal cells, like those in muscles or glands, as well as between neurons. In the central nervous system, circuit formation is made possible via chemical synapses between neurons. They are essential to the biological calculations underlying vision and thinking. They make it possible for the nervous system to communicate with and regulate many bodily processes.

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how to control diarrhoea​

Answers

Answer:

Diarrhea should go away in a few days without treatment. until you feel better, rest, drink enough fluids, and watch what you eat.

What did u eat that made u have it?

1. I am a cloud. I look like a big cotton ball. I am gray and black. What kind of cloud am I.
A. cumulus
B. stratus
C. cumulonimbus
D. cirrus

Answers

Answer:

Cumulus

Explanation:

what kind of hormone stores glucose if its in excesse​

Answers

Answer:

A hormone that tells cells in your liver and muscles to convert glycogen into glucose and release it into your blood so your cells can use it for energy.

Other Questions
Claire was born with a Recombination activating gene (RAG) mutationresulting in complete loss-of-function in RAG1/2. Describe whyClaire is more susceptible to infection. Any organizational department or unit under the supervision of a single person who is responsible for itsactivity is called a(n)a.independent center.b.responsibility center.c.analysis center.d.control center.e.budgeting center Select the correct answer.Does the VERB agree with the SUBJECT in this sentence?Your group was surrounded by the enemy.A.YesB.NoHelp asap When a company such as Toyota or Hyundai opens a design or production facility in the United States, we see it as Pls help its for science The original source of new alleles, upon which selection operates, is mutation, a random event that occurs without regard to selectional value in the organism. Although many model organisms have been used to study mutational events in populations, some investigators have developed abiotic molecular models. Soll et al. (2006. Genetics 175: 267-275) examined one such model to study the relationship between both deleterious and advantageous mutations and population size in a ligase molecule composed of RNA (a ribozyme). Soll found that the smaller the population of molecules, the more likely it was that not only deleterious mutations but also advantageous mutations would disappear. Why would population size influence the survival of both types of mutations (deleterious and advantageous) in populations The world's oldest example of _____________ is written in Sumerian cuneiform. It is known as _______________. What high-tech device is going to be used to help solve the King Tut mystery? Who won the Election for 2021 2. How did early Americans consume apples? When and why did that change? How werenotions of the apple's healthfulness popularized? Reduce the ratio into its lowest term.2kg : 750gGive me in step-by-step Question is in the jpg ples help meh. ;( The combination of continual addition of new bone tissue (bone ____________) and removal of old bone tissue (bone ________________) is called bone ___________. This ongoing process occurs at both the ______________ (outer) and ___________ (inner) surfaces of a bone. Bone replacement is accomplished by the coordination of osteocytes and osteoclasts in a __________________________________The relative activities of these cells are influenced by two primary factors:hormones and ___________ to the bone. Why did many people move to the city around the 1890s to 1910s? Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options.18x - 15 = 7250x - 25 = 7218x - 9 = 723(6x - 3) = 72x = 4.5 Complete the proof.Given: 1/5x+3=2 x-24 Prove: x=15 Proof: PLEASE ANSWER THIS ASAP. PLEASE INCLUDE STEP BY STEP EXPLANATION!!!Last night, troy spent 1 2/5 hours doing his math homework, then 45 minutes on his science homework. what was the total time spent on doing homework? at edgars bakery one customer buys 4 donuts and 10 muffins for $32. Another customer buys 12 donuts and 5 muffins and pays $21. x=price of donut y=price of muffin1. Write an equation to represent the first customer2.write an equation to represent the 2nd customer3.solve system of equations Expand and simplifya) x(x + 2)(x + 3) Below is a statement from a historical document. How does the modern political system in the United States uphold the principles expressed in this statement?"A Prince whose character is thus marked by every act which may define a Tyrant, is unfit to be the ruler of a free people."answer choicesA. by allowing the U.S. House of Representatives to impeach the presidentB. by allowing federal judges to impeach members of CongressC. by allowing the president to impeach members of Congress