two atoms are isotopes of the element. which of the following should be the same for these two atoms?

Answers

Answer 1

Answer:

An isotopes are atoms located in the same spot on the periodic table. They are considered the same element, but they differ in the number neutrons in their nuclei. They have the same location on the periodic table, atomic number, number of protons, and number of electrons.


Related Questions

Use the forked-line method to solve this problem (SHOW YOUR WORK): In cucumbers, there are 3 genetic traits, as follows: dull fruit is dominant to glossy fruit orange fruit color is dominant to cream fruit color bitter cotyledons are dominant to nonbitter cotyledons You cross a plant that is heterozygous for all 3 genes to another plant that is heterozygous for dull fruit but has cream fruit color and nonbitter cotyledons. Among the next generation, what proportion of the offspring will be a) dull, orange, bitter b) glossy, cream, nonbitter c) heterozygous for all 3 genes (HINT: it's not the same answer as a) above

Answers

Answer:

a) dull, orange, bitter ---->  3/16 D- Oo Bb

b) glossy, cream, nonbitter ---> 1/16 dd oo bb

c) heterozygous for all 3 genes ---> 2/16 Dd Oo Bb

Explanation:

Available data:

dull fruit (D-) is dominant to glossy fruit (dd)orange fruit color (O-) is dominant to cream fruit color (oo)bitter cotyledons (B-) are dominant to non-bitter cotyledons (bb)Cross: a plant heterozygous for all 3 genes with a plant that is heterozygous for dull fruit but has cream fruit color and non-bitter cotyledons.

Parentals) Dd Oo Bb     x    Dd oo bb

To get the proportions of the offspring using the forked-line method, we must analyze each gene separately.

D gene:

Parentals) Dd    x    Dd

Gametes ) D   d    D    d

Punnett square)      D      d

                        D   DD    Dd

                        d    dD     dd

F1) 1/4 DD

     2/4 Dd

     1/4 dd

O gene:

Parentals) Oo    x    oo

Gametes) O    o     o     o

Punnett square)     O      o

                        o    Oo     oo

                         o    Oo    oo

F1) 1/2 Oo

     1/2 oo

B gene:

Parentals) Bb    x    bb

Gametes) B   b      b    b

Punnett square)   B        b

                  b         Bb      bb

                  b         Bb      bb

F1) 1/2 Bb

     1/2 bb

What proportion of the offspring will be

a) dull, orange, bitter

   (1/4 DD + 2/4 Dd) x 1/2 Oo x 1/2 Bb = 3/4 D- x 1/2 Oo x 1/2 Bb

   3/16 D- Oo Bb

b) glossy, cream, nonbitter

   1/4 dd x 1/2 oo x 1/2 bb

   1/16 dd oo bb

c) heterozygous for all 3 genes

    2/4 Dd x 1/2 Oo x 1/2 Bb

    2/16 Dd Oo Bb

Give one function for this structure

Answers

We are very happy to let you know that one function of the structure labelled from the image given here is that:

It is used for se- x -ual intercourse

In addition to the function above, the structure is also used for urination. That is, it used to pass out urine from the body

The structure is s it the pe- nis ( the male reproductive organ )

What is reproduction?

Reproduction is one of the characteristics of living organisms which involves the giving birth to the young ones alive or reproduction of new offsprings

So therefore, we are very happy once again to let you know that one function of the structure labelled from the image given here is that:

It is used for se- x-ual intercourse

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mike is studying the phylogenetic tree for big cats. He made several statements about the tree. which statement is not true

Answers

Answer:

D. The leopard is more closely related to the tiger than to the snow leopard.

Explanation:

Leopards are more related to snow leopards than tigers.

Brainliest, please :)

How are coral reefs similar to tropical rainforests? Both are home to just a few types of rare animals. Both can easily be restored if they are destroyed. Both support a huge quantity and variety of organisms. Both are found in all types of climates around the world.

Answers

Answer:

c

Explanation:

Answer:

its C

Explanation:

i took the test on edge 2021

Maintaining blood glucose levels is an important homeostatic activity of the body, not specifically because every cell of the body must have glucose but primarily because the brain relies on glucose for its metabolism.

a. True
b. False

Answers

Answer:

a. True.

Explanation:

Even though the cells in our body rely on glucose as a source of energy, they can replace glucose's energy with lipids or proteins' energy. In the brain's case, this is not possible since the blood-brain barrier, which is a highly selective barrier between the blood and the extracellular fluid in the central nervous system, allows the passage of glucose as the only source of energy. This is why maintaining the correct levels of glucose is crucial for the metabolism in the brain.

Decrease in a person's life span is an example of ____
A. Adverse health effects
B. Hazard
C. Incidents
D. Risk​

Answers

Answer: D. Occupational health and safety

MARK ME BRAINLIST

Read each question carefully, and answer yes or no to each one. At the end of each section, follow the directions to score your answers (pay close attention as the directions for scoring may change for each section). After you complete the entire assessment, total the points from all seven sections. This will give you a total health score. The higher the score, the more healthy your lifestyle. If you feel you have a low score, look back through the assessment and identify areas where you can change your unhealthy habits, and explain what changes you would make and why. Write your assessment in the essay box below.

Section 1: Physical Fitness

Section 2: Family History

Section 3: Hygiene and Medical Care

Section 4: Nutrition

Section 5: Drug Use

Section 6: Safety

Section 7: Emotional and Social Health

Total Health Score: ____

Answers

Answer:

Section 1: Physical Fitness

Do you exercise or play a sport for at least 30 minutes three or more times a week? Yes

Do you stretch before and after exercising? No

Do you warm up before exercising and cool down afterward? No

Do you think that you are at a healthy weight? Yes

Are you mostly happy with the way your body looks and feels? Yes

Do you think you have enough energy? Yes

Give yourself one point for each No response and two points for each Yes response. Section score: _10___

Section 2: Family History

Do you have a family member who:

has high blood pressure? Yes

has diabetes? Yes

has heart disease? No

has cancer? Yes

is extremely overweight? No

Give yourself one point for each Yes response and two points for each No response. Section score: ___7_

Section 3: Hygiene and Medical Care

Do you floss your teeth every day? Yes

Do you brush your teeth at least twice a day? Yes

Do you visit the dentist at least once a year? Yes

Do you use sunscreen? No

Do you know basic first aid? Yes

Are all your immunizations current? Yes

Do you get your vision and hearing checked each year? Yes

Do you see the doctor for a check-up once each year? Yes

Do you feel you get enough sleep at night? Yes

Do you know the warning signs for cancer? No

Give yourself one point for each No response and two points for each Yes response. Section score: _18___

Section 4: Nutrition

Do you eat a lot of red meat or eggs? No

Do you add salt to your food? Yes

Do you add sugar to your food? Yes

Do you eat a lot of high-fat or high-sugar foods? Yes

Do you add butter or cheese to your food? Yes

Do you choose fried foods more often than baked or broiled foods? Yes

Do you drink caffeinated drinks, such as coffee or sodas? Yes

Do you skip meals? No

Give yourself one point for each Yes response and two points for each No response. Section score: _10___

Section 5: Drug Use

Do you smoke or chew tobacco? No

Do you drink alcohol? No

Have you ever used marijuana or other illegal drugs? No

Have you ever abused a prescription drug? No

Give yourself zero points for each Yes response and two points for each No response. Section score: __8__

Section 6: Safety

Have you ever ridden with drivers who were under the influence of alcohol or drugs? No

Have you ever ridden with drivers who speed or disobey traffic laws?no

Do you ever forget to wear your seat belt? No

Do you ever forget to wear a helmet when riding a bike or skateboarding? No

Do you ever play with matches or hazardous materials? No

Is there a gun in your house? No

Give yourself zero points for each Yes response and two points for each No response. Section score: __12__

Section 7: Emotional and Social Health

Do you have hobbies or activities that you enjoy? Yes

Do you give your best effort when doing your work? Yes

Do you find it easy to laugh? Yes

Do you express anger in an appropriate way? Yes

Do you easily fall asleep at night? Yes

Do you share personal problems with someone you trust? Yes

Do you feel well-liked by others? Yes

Do you have someone you can turn to if you need help? Yes

Are your family members and close friends in good health? Yes

Are you generally happy? Yes

Give yourself one point for each No response and two points for each Yes response. Section score: _20___

Total Health Score: __85__

This is mine so it's not going to be accurate for you but please can I get a brainliest.

The process of creating an mRNA strand from one side of DNA is called:

A. Protein synthesis
B. Transcription
C. DNA replication
D. Translation

Answers

Answer:

It is TRANSCRIPTION option (b)

ANSWER:

B. transcription

1. a) Two nerve cells are shown below. In the drawing, label an axon, a dendrite, and a nucleus. Also
indicate where a
neurotransmitter would act. (4 points)

Answers

A nerve cell consists of a cell body or soma, a main fiber (axon) and many small branches (dendrites).

What is a neuron?A neuron or nerve cell forms the basic unit of brain and nervous system.These cells receive stimulus from the external world, relay the information to brain and help to generate a response.The neurons communicate with each other via special connections called synapses where they release neurotransmitter.A typical neuron consists of a cell body (soma), dendrites (brings information), and a single axon (send information away from neurons).The dendrites and axon branch out from the cell body.Cell body contains nucleus and specialized organelles.At the tip of axon are axon terminals where neurotransmitters are released to transmit signal across the synapse to other cell.

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If a koala bear has sixteen pairs of chromosomes, what are the possible
combinations of genes that will be represented?

Answers

Answer:

Explanation:

All vombatid species have 2n = 14 chromosomes; the koala has 2n = 16, which G-banding studies suggest is derivable from a wombat-like karyotype by means of a simple centric fission in the equivalent of the submetacentric wombat second autosomal element

15. What's the requirement of every single natural process on Earth?
O A. Oil
O B. Trees
O C. Sunlight
O D. Energy source
O Mark for review (Will be highlighted on the review page)
<< Previous Question
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Answers

15. What's the requirement of every single natural process on Earth?

answer: Energy source

The sum of all chemical reactions that occur in an organism is

Answers

Answer:

It is called metabolism.

You have a pea plant with a yellow pea phenotype but do not know if the genotype is homozygous (YY) or heterozygous (Yy). What type of cross would you do determine the genotype of this plant and what would be the predicted phenotypes of the offspring?

Answers

To determine the genotype of this plant, a test cross should be performed. The expected phenotypes of the descendants are yellow and green peas.

What does test-cross mean?

An F1 progeny is bred with a double (homozygous) recessive(green pea) mother generation to determine if an offspring is homozygous or heterozygous for a specific characteristic. A test cross is what this is called.

If the hybrid's mother is homozygous (YY) dominant, all of the hybrid's offspring will have the dominant (yellow) phenotype.

Mother yellow pea (YY)     x       green pea (yy)                 - P generation

                                  Y                            y                           - Gamete

                                   Yy (yellow) , Yy (yellow)                   -F1 generation

The ratio should be 1:1 if the mother is heterozygous dominant (Yy), in which case half of the kids will display the dominant phenotype, while the other half will display the recessive phenotype(yy).

Mother yellow pea (Yy)     x         green pea (yy)              -P generation

                                 Y, y                             y                       - Gamete

                                 Yy (yellow) , yy (green)                       -F1 generation

The conclusion drawn from the foregoing explanation is that in order to determine the genotype of the pea plant, a test cross should be conducted. The expected progenies are - yellow and green peas.

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In comparing the behavior of a 10,000 and 45,000 molecular weight protein using sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE) and gel filtration column chromatography, which of the following statements is most likely to be true. Assume other proteins are single polypeptide chains with no disulfide bonds.

a. The smaller protein will migrate (move) faster relative to the larger protein in SDS-PAGE but slower in gel filtration.
b. The smaller protein will migrate (move) slower relative to the larger protein in both SDS-PAGE and gel filtration
c. The smaller protein will migrate (move) faster relative to the larger protein in both SDS-PAGE and gel filtration
d. The smaller protein will migrate slower (move) relative to the larger protein in SDS-PAGE but faster in gel filtration

Answers

Answer:

a. The smaller protein will migrate (move) faster relative to the larger protein in SDS-PAGE but slower in gel filtration.

Explanation:

Gel filtration chromatography is a technique of chromatography in which particles facilitate separation based on molecular size. The larger protein come out of the column and form gel permeation chromatograph. The smaller proteins move faster to migrate from the column.

Every plant has structures that function to help the plants survive. How does phototropism help a plant to survive.

A. The plant grows toward the sun so that its leaves can better make food.

B. It helps the plant leaves to eat the roots

C. It helps the plant drink nutrients

D. It helps the roots grow down to the dirt.

Answers

Answer:

A

Explanation:

more light energy means more photosynthesis = more food for the plant

What is it called when pairs of homologous chromosomes fail to SEPARATE normally
during MEIOSIS.

Answers

Answer: Nondisjunction occurs when homologous chromosomes or sister chromatids fail to separate during meiosis, resulting in an abnormal chromosome number. Nondisjunction may occur during meiosis I or meiosis II.

Explanation:

2 cells will have the normal haploid number of chromosomes. Additionally, one cell will have an extra chromosome and one will be missing a chromosome

function of mitochondria???​

Answers

Answer:

Powerhouse of the cell, creates ATP (energy for the cell).

Explanation:

You have successfully engineered E. coli to make human insulin by adding a transgene that has an E. coli promoter and the coding sequence of human insulin. You try to generate a new strain that would make a lot more insulin by making one with 10 copies of the transgene. Although your genetic engineering is successful, your new strain doesn't make much more insulin. What do you think could have gone wrong

Answers

Answer:are you asking a question?

Explanation:

Which combinations of DNA could be present in a transgenic organism?
1. invertebrate animal DNA in mammal DNA
2. prokaryotic DNA in plant DNA
3. plant DNA in animal DNA
A) 2 only
B) 1 and 2 only
C) 1 and 3 only
D) 2 and 3 only
E) 1, 2 and 3

Answers

The correct option is D) 2 and 3 only

2. prokaryotic DNA in plant DNA

3. plant DNA in animal DNA

What is a transgenic organism?

Transgenic refers to an organism or cell whose genome has lived changed by the introduction of one or more additional foreign DNA series from another species by synthetic means. Transgenic organisms are generated in the laboratory for analysis purposes.

Transgenic has been used in genetic investigations for an extended time. They were used to indicate that DNA is the molecule that carries the genetic code and that oncogenes can induce cancer. Transgenic animals have been generated to comprehend normal physiological processes such as metabolism and blood cell presentation. Transgenic animals have lived operated to model human diseases and to create new treatments. Transgenic crops include been produced that stand resistant to communicable diseases and grow faster.

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Carrying capacity is the
population size of
the species that the environment
can sustain indefinitely, given
environmental necessities.
A. minimum
B. median
C. mean
D. maximum

Answers

Answer:

C. Mean

Explanation:

sir / ma your question isn't clear. That aside.

to know how population size of species affect the sustainability we find the mean carrying size(just a guess)

What are examples of carbohydrates rich foods

Answers

Answer:

Which Foods Have Carbs?

Dairy. Milk, yogurt, and ice cream.

Fruit. Whole fruit and fruit juice.

Grains. Bread, rice, crackers, and cereal.

Legumes. Beans and other plant-based proteins.

Starchy Vegetables. Potatoes and corn.

Sugary Sweets. Limit these! Soda, candy, cookies, and other desserts.

Examples of carbohydrate-rich foods include bread, pasta, rice, potatoes, fruits, sugary snacks, and sweets.

What are carbohydrates rich foods?

Carbohydrates are one of the three main macronutrients found in food and are a primary source of energy for the body. Carbohydrates can be found in many different foods, including:

Grains: bread, pasta, rice, cereal, oatmeal, etc.Starchy vegetables: potatoes, sweet potatoes, corn, etc.Fruits: apples, bananas, grapes, oranges, etc.Sugary snacks and sweets: candy, cakes, cookies, soda, etc.

It is important to note that not all carbohydrates are created equal. Simple carbohydrates, such as those found in sugary snacks and sweets, can cause spikes in blood sugar levels and can lead to weight gain if consumed in excess. On the other hand, complex carbohydrates, such as those found in whole grains and starchy vegetables, are a more slowly digested form of energy and are a healthier option for providing energy for the body.

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What process has increased pollutants and carbon dioxide in the atmosphere? geothermal heat
production hydroelectric
power production
using biomass fuels
burning fossil fuels

Answers

Burning fossil fuels has increased pollutants and carbon dioxide in the atmosphere.

What consequences do fossil fuel burning have on the environment?

Carbon dioxide, water, and energy are produced when fossil fuels are burned; this process is referred to as "combustion".

Burning fossil fuels like coal and oil has increased the amount of carbon dioxide in the atmosphere during the past century (CO2). This rise is brought on by the burning of coal or oil, which produces CO2 when airborne carbon and oxygen mix. When fossil fuels are burned, nitrogen oxides are released into the atmosphere and help to create smog and acid rain. Nitrogen oxides are the collective name for the most prevalent nitrogen-related substances released into the atmosphere as a result of human activity.

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Which of the following is associated with schizophrenia?

Reduced fluid-filled sacs
Less gray matter
More brain tissue
"Normal" brain chemistry

Answers

Less gray matter is associated with schizophrenia and is denoted as option B.

What is Grey matter?

These are usually darker tissues which are found in the brain and spinal cord. They contain a rich network of neurons present.

This is therefore the reason why schizophrenia is associated with mental health.

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Answer:

B. Less gray matter.

Explanation:

Took the test and got it right.

Have a nice day!

Using the strand mRNA below along with either of the codon charts, place the amino acids in the correct order.

Strand mRNA & codón chart: photo 2&3


1?
2?
3?
4?
5?
6?
7?
8?
9?
10?

Answers

Codons are triplets of nucleotides found on mRNA which code for particular amino acids .

What are codons?

Codons are triplets of nucleotides found on mRNA which code for particular amino acids.

In an mRNA, strands, the first three codons, AUG code for the amino acid methionine.

Similarly, the codons GCA codes for alanine, CCA codes for proline.

In conclusion, given an mRNA strand, the amino acids coded by the codons can be deduced.

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compares and contrasts transformation, transduction, and conjugation

Answers

Answer:

In transformation, a bacterium takes up a piece of DNA floating in its environment. In transduction, DNA is accidentally moved from one bacterium to another by a virus. In conjugation, DNA is transferred between bacteria through a tube between cells.

Explanation:

How do DNA and mRNA vaccines produce spike proteins ? Drag each item into the correct category.


1. mRNA

______________________

2. DNA

_______________________

3. Both

_____________________



A. Has an artificial membrane to allow it into the human cell

B.completes the translation process to create spike proteins that mimic SARS-CoV-2 spike proteins

C.Is brought into a cell through an inactivated adenovirus

D.completes transcription prior to translation

Answers

DNA and mRNA vaccines produce spike proteins by completing the translation process to create spike one or more long mRNA will enter the muscle cells to create spike protein

mRNA uses muscles cells to produce spike proteinsThe DNA is recognized by the host's cell which produces the proteins Both uses cells to produce proteins

What are proteins?

Proteins simply refers to those class of

any of a class of nitrogenous organic compounds which have large molecules composed of chains of amino acids

So therefore, DNA and mRNA vaccines produce spike proteins by completing the translation process to create spike one or more long mRNA will enter the muscle cells to create spike protein

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2. How is modeling useful to scientists?

Answers

Answer:

scientific modeling, the generation of a physical, conceptual, or mathematical representation of a real phenomenon that is difficult to observe directly. Scientific models are used to explain and predict the behaviour of real objects or systems and are used in a variety of scientific disciplines, ranging from physics and chemistry to ecology and the Earth sciences. 

What is the role of the EPA in water purification?
It provides guidelines to implement cleaning projects.
It forms laws and rules.
It deploys personnel for water purification.
It finds sources of freshwater.

Answers

B, it forms laws and rules for clean water and regulations

In some bunnies, the gene for fur color is controlled by condominance. The allele for gray color is G and the allele white color is W. The heterozygous phenotype results in a gray and white bunny/ What is the genotype for gray bunnies? what is the genotype for white bunnies? what is the genotype for gray and white bunnies?

Answers

Answer:

Genotype gray bunnies: GG

Genotype white bunnies: WW

Genotype gray and white bunnies: GW

Explanation:

In diploid species (2n), organisms receive one gene copy (allele) from each parent. Codominance is a relationship that occurs when both alleles of the same gene show dominance. In consequence, the expression of both alleles in heterozygous individuals results in a new phenotype. In this example, the expression of G and W alleles results in a gray and white phenotype. Examples of codominance include individuals with type AB blood group in humans or the roan coat color in horses.

Answer:

Genotype gray bunnies: GG

Genotype white bunnies: WW

Genotype gray and white bunnies: GW

Explanation:

In diploid species (2n), organisms receive one gene copy (allele) from each parent. Codominance is a relationship that occurs when both alleles of the same gene show dominance. In consequence, the expression of both alleles in heterozygous individuals results in a new phenotype. In this example, the expression of G and W alleles results in a gray and white phenotype. Examples of codominance include individuals with type AB blood group in humans or the roan coat color in horses.

Newton's 2nd Law is F= ma. Write a problem that gives the mass and the acceleration of an object and asks us to find the force.

Answers

Answer:

An object having a mass of 20kg is pushed by John and it then accelerates down the inclined plane at a rate of 0.5m/s². Find the force applied on the object.

Explanation:

Newton's Second Law of Motion states that the acceleration of a physical object is directly proportional to the net force acting on the physical object and inversely proportional to its mass.

For example, an object having a mass of 20kg is pushed by John and it then accelerates down the inclined plane at a rate of 0.5m/s². Find the force applied on the object.

Given the following data;

Mass = 20kg

Acceleration = 0.5m/s²

To find the force;

Force = mass * acceleration

Substituting into the equation, we have;

Force = 20 * 0.5

Force = 10 Newton.

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The entity that is responsible for establishing the allocation and cost of capital is answered ut of 1.00Select one: uestion O O 0 a. the corporation b. the economy c. investors d, customers what is the solubility of lead chloride in pure water? (how many moles of pbcl2 could be completely dissolved in one liter Find the volume of the cylinder. Round your answer to the nearest tenth.The volume is about cubic feet. What type of prolog clause, does the following clause define? fruit(apple) = a. Fact b. Query c. Rule an object of height 1.20 cm is placed 35.0 cm from a convex spherical mirror of focal length of magnitude 12.5 cm a) Find the location of the image b) Indicate whether the image is upright or inverted. c) Determine the height of the image Choose 100 Newtons of applied force for the top spring. (100N is the amount of force equal to the weight of a 10.2kg mass. This is also 22.5 pounds.)a. What is the direction of the applied force?b. What is the direction of the spring force i.e. the force the spring exerts on the pincers? What is the magnitude of the spring force?c. Adjust the spring constant until you get a displacement of 0.100m to the right. What is the spring constant?d. Is the displacement the same as the length of the spring? The makers of Brand Z paper towel claim that their brand is twice as strong as Brand X and they use this graph to support their claim. Paper Towel Strength A bar graph titled Paper Towel Strength has Brand on the x-axis, and strength (pounds per inches squared) on the y-axis, from 90 to 100 in increments of 5. Brand X, 100; brand Y, 105; brand z, 110. Do you agree with this claim? Why or why not? a. Yes, because the bar for Brand Z is twice as tall as the bar for Brand X. B. Yes, because the strength of Brand Z is twice that of Brand X. C. No, because paper towel brands are all alike. D. No, because the vertical scale exaggerates the differences between brands. calculate the area of the surface of the cap cut from the paraboloidz = 12 - 2x^2 - 2y^2 by the cone z = x2 + y2 calculate the following limit. limx[infinity] ln x 3x A Carnot engine operating between hot and cold reservoirs at 250 K and 450 K produces a power output of 900 W. Find the rate of heat input, the rate of heat output, and the thermal efficiency? e6x = 5(a) find the exact solution of the exponential equation in terms of logarithms.x = (b) use a calculator to find an approximation to the solution rounded to six decimal places.x = What is number of maximum number of virtual processors for each of thefollowing Hyper-V client?Answer by a number such as 16.1. Windows 72. Windows 83. Open SUSE 12.1 Select the nuclide that completes the following nuclear reaction. 123 A) 12:Sb B) 1a,Te C) insb D) 111 E) none of the above the number of markets with which a firm and a competitor are jointly involved and the degree of importance of the individual markets to each is referred to as: One approximate solution to the equation cos x = 0.60 for the domain 0o x 360o is? T/F people like to be together to reduce uncertainties about themselves. suppose f is a real-valued continuous function on r and f(a)f(b) < 0 for some a, b r. prove there exists x between a and b such that f(x) = 0. Greek physician Galen was one of the first physicians to believe that mental illness could be caused by a. possessionb. head traumac. psychological stress d. excess bile How does the historical content of Daniel differ from that of other prophetic books? Use complete sentences. 70pts volumes suppose you drill a circular hole with radius through the center of a sphere with radius . you remove exactly half the volume of the sphere. the ratio of your radii is