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## A center lane with solid and broken yellow lines that is used by vehicles making left turns in both directions is called a:

Left turn lane

Left turn lanes are used when vehicles are turning left. It is mandatory for a vehicle to come inside the lane completely and then wait for the traffic to clear before making the turn. The vehicle is not allowed to be half inside the lane and half outside, blocking the traffic and producing dangerous driving conditions.

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## Which equation turns food into energy

Which equation turns food into energy

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## Trevor is pulling his younger brother in a wagon. He pulls the wagon 50 m to the corner with a force that is a parallel with the ground. He then turns the wagon around and pulls it 50 m back to the starting point with the same force at an angle of 30 degrees with respect to the ground. How does the amount of work Trevor performs going to the corner compare with the amount of work he performs coming back? A) they are the same because he uses the same amount of force B) they are the same because he travels the same distance C) he does less work coming back because the force moving the wagon is only 50cos30 D)he does more work coming back because the force moving the wagon is only 50cos60

Work has the greatest value when the force done is
parallel to the direction of motion. In this case, the work done in pulling the
wagon to the corner is greater than the amount of work done in pulling the
wagon back to the starting point. This is because an angle of 30 degrees is
applied when pulling it back. The formula for work when angle is applied is:

Wx = W cos θ

Where in this case, θ = 30

Therefore,
the answer to this is letter:

C) he does less work coming back because the force moving
the wagon is only 50cos30

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## John goes for a run. From his house, he jogs north for exactly 5.0 min at an average speed of 8.0 km/h. He continues north at a speed of 12.0 km/h for the next 30.0 min. He then turns around and jogs south at a speed of 15.0 km/h for 15.0 min. Then he jogs south for another 20.0 min at 8.0 km/h. He walks the rest of the way home. Which is the correct plot of total distance as a function of time for John’s jog?

John goes for a run. From his house, he jogs north for exactly 5.0 min at an average speed of 8.0 km/h. He continues north at a speed of 12.0 km/h for the next 30.0 min. He then turns around and jogs south at a speed of 15.0 km/h for 15.0 min. Then he jogs south for another 20.0 min at 8.0 km/h. He walks the rest of the way home. Which is the correct plot of total distance as a function of time for John’s jog?

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## Think about an igneous rock at the top of a mountain. If this rock went through the whole rock cycle, number the steps that would follow. 1. Step 1 Regolith is dumped into some type of reservoir, usually water, by deposition. 2. Step 2 Metamorphic rock begins to melt back into magma. 3. Step 3 Regolith is transported or eroded by rain or wind. 4. Step 4 Rock is broken down into regolith by weathering. 5. Step 5 Layers deposited begin to compact and cement together to form sedimentary rock. 6. Step 6 Sedimentary rock is buried deeper into the earth’s crust. The intense heat and pressure begins metamorphism and the rock turns into metamorphic rock. 7. Step 7 Magma is resurfaced from volcanic activity, cools, and becomes igneous rock.

The correct sequence according to the question is steps- 4→1→3→5→6→2→7.

Explanation:

The given steps show that how the rocks are recycled from one form to another form due to certain factors like weathering over geological time scale which was explained by James Hutton and he termed this concept as the rock cycle.

The steps of the rock cycle in sequence according to the question are:

1.  Breakdown of rock by weathering into regolith- step 4

2.  Dumping and deposition of regolith in a reservoir- step  1

3.  Erosion and transportation of regolith by rain or wind- step  3

4. Cementing of the deposited layer to form sedimentary rock- step  5

5. Conversion of sedimentary rock to a metamorphic rock due to intense heat and pressure- step 6

6. Conversion of  metamorphic rocks to magma due to the melting of metamorphic rocks-
step 2

7. Conversion of magma to igneous rocks due to volcanic activities and cooling of magma-  step 7

Therefore sequence according to the question is steps- 4→1→3→5→6→2→7 is correct.

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## The difference in emf between the primary coil of a transformer and the secondary coil is directly related to the relative number of turns in the coils. true or false

The difference in emf between the primary coil of a transformer and the secondary coil is directly related to the relative number of turns in the coils. true or false

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## How is energy converted in a hydroelectric plant? A) The kinetic energy of water is converted to electrical energy when water flows down the dam's channel and into the transformer. B) The potential energy of water is converted to electrical energy when water flows past a generator. C) The kinetic energy of water turns turbines; the mechanical energy of the turbines turns the generator, which produces electrical energy. D) The potential energy of water turns the generator's turbines, which results in the production of electrical energy.

How is energy converted in a hydroelectric plant? A) The kinetic energy of water is converted to electrical energy when water flows down the dam’s channel and into the transformer. B) The potential energy of water is converted to electrical energy when water flows past a generator. C) The kinetic energy of water turns turbines; the mechanical energy of the turbines turns the generator, which produces electrical energy. D) The potential energy of water turns the generator’s turbines, which results in the production of electrical energy.

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## Read the following excerpt taken from the US Supreme Court case Plessy v. Ferguson (1896). The case coming on for a hearing before the Supreme Court, that court was of opinion that the law under which the prosecution had was constitutional, and denied the relief prayed for by the petitioner. Ex parte Plessy, 45 La.Ann. 80. Whereupon petitioner prayed for a writ of error from this court, which was allowed by the Chief Justice of the Supreme Court of Louisiana. MR. JUSTICE BROWN, after stating the case, delivered the opinion of the court. This case turns upon the constitutionality of an act of the General Assembly of the State of Louisiana, passed in 1890, providing for separate railway carriages for the white and colored races. Acts 1890, No. 111, p. 152. The first section of the statute enacts “that all railway companies carrying passengers in their coaches in this State shall provide equal but separate accommodations for the white and colored races by providing two or more passenger coaches for each passenger train, or by dividing the passenger coaches by a partition so as to secure separate accommodations: Provided, That this section shall not be construed to apply to street railroads. No person or persons, shall be admitted to occupy seats in coaches other than the ones assigned to them on account of the race they belong to.” The Supreme Court’s ruling in Plessy v. Ferguson was problematic because

In the Plessy v. Ferguson case, the Supreme Court’s ruling of the “separate but equal” law being constitutional was problematic because the “separate but equal” law accepted segregation and the discrimination that were against blacks.

Hope this helps!

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## True or false: left turns are permitted at a traffic signal displaying a steady red light if the driver is turning onto a one-way street from a one-way street.

Well, I would say False. Its usually a seperate light for anyone thats going left especially for traffic or you would have to wait on a green light and then turn when there is no on coming traffic. I do know you usually can turn right on red not left. But I would go with False.

## Related questions

### Grandparents under 65 are more likely to display a _____ style.

Grandparents under 65 are more likely to display a fun-seeking style
They are relatively young grandparents, which means that they will be more modern, and understand their grandchildren more. This is why they will apply a fun-seeking style, as opposed to those grandparents above 65, who will be more formal.

ANSWERED AT 22/10/2019 – 12:23 PM

QUESTION POSTED AT 22/10/2019 – 12:23 PM

### A temporary license permits the holder to drive for up to ___ days while the application is reviewed

A temporary license permits the holder to drive for up to 60 days while the application is reviewed.
After you pass a driving test, the government of the state need some time to register all your data and produce your driver license. During this time, temporary license permits act as a legal substitute for the driver license

ANSWERED AT 22/10/2019 – 10:20 AM

QUESTION POSTED AT 22/10/2019 – 10:20 AM

### Which of the following is not a true statement about the life of Andrew Jackson

idk the answer but these are the options

A.) he taught himself enough law to practice on the frontier

B.) he was a prisoner of war during the Revolutionary war

C.) he was born into a wealthy new england family

D.) he was nicknamed “Old Hickory”

ANSWERED AT 22/10/2019 – 07:00 AM

QUESTION POSTED AT 22/10/2019 – 07:00 AM

### Select true or false: a military professional must utilize any means necessary to contribute to the common good.

The answer to this statement is false. It is because yes, it is the job of the military professional to do necessary things to contribute to common good or to promote common good. But using any means necessary is not appropriate to handle this situation even if it is for the good cause. It is best to follow measures and standards because using any means necessary is like being able to do anything you want even if it is bad just to produce something good.

ANSWERED AT 22/10/2019 – 05:53 AM

QUESTION POSTED AT 22/10/2019 – 05:53 AM

### Why do autistic children have difficulty passing the false belief task?

The reason why  autistic children have difficulty passing the false belief task is:  They lack a theory of mind.
Normal children brain have the capability to make a proper train of thought that help them in developing a concept. Autistic children on the other hand, tend to have disarray way of thinking that make it difficult for them to pass the false belief task

ANSWERED AT 22/10/2019 – 05:51 AM

QUESTION POSTED AT 22/10/2019 – 05:51 AM

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## Which process turns food into energy in any cell? A) photosynthesis Or B) cellular respiration

Correct answer: C). Genetically different haploid cells

Meiosis is a type of cell division in which four haploid cells are produced, which are genetically different from the parent. It reduces the chromosome number exactly half as contained in the parent. That is why it is called as a reductional division.

In the first round of meiosis I homologous pairs of chromosome separate and the sister chromatids separate during meiosis II.

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## He stops at the ocean’s edge, smiles almost shyly, as if he fears disturbing her, and stretches out a colossal hand. His blue eyes are like lasers in the night. The beams bounce off his fingernails, five hard blue shields. They scan the beach, illuminating shells and sleeping gulls, then focus on her. The porch turns blue, ultraviolet. Her hands, too, are blue. Celia squints through the light, which dulls her eyesight and blurs the palms on the shore. Which of the following is an example of a hyperbole? “smiles almost shyly, as if he fears disturbing her” “and stretches out a colossal hand” “His blue eyes are like lasers in the night.” “The porch turns blue, ultraviolet.”

He stops at the ocean’s edge, smiles almost shyly, as if he fears disturbing her, and stretches out a colossal hand. His blue eyes are like lasers in the night. The beams bounce off his fingernails, five hard blue shields. They scan the beach, illuminating shells and sleeping gulls, then focus on her. The porch turns blue, ultraviolet. Her hands, too, are blue. Celia squints through the light, which dulls her eyesight and blurs the palms on the shore. Which of the following is an example of a hyperbole? “smiles almost shyly, as if he fears disturbing her” “and stretches out a colossal hand” “His blue eyes are like lasers in the night.” “The porch turns blue, ultraviolet.”

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## During winters freezing temperatures, some plants can remove water from their cells to reduce the amount of water that will freeze inside them. Why would plants need to do this? A. The frozen water constricts organelles and causes plant cells to shrink. B. As the water contracts during freezing, the cells would pull away from each other, causing damage. C. Less water in the cells means the cells are smaller and need to do less work. D. The expansion of excess water as it turns to ice inside the cells would break the cells apart.

Correct answer: C). Genetically different haploid cells

Meiosis is a type of cell division in which four haploid cells are produced, which are genetically different from the parent. It reduces the chromosome number exactly half as contained in the parent. That is why it is called as a reductional division.

In the first round of meiosis I homologous pairs of chromosome separate and the sister chromatids separate during meiosis II.

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## Your baby is driving you crazy because he turns the light switch on and off for hours. what would piaget say about this behavior?

The answer is C. In order to carefully control conditions and confirm or disconfirm a hypothesis about the causes of behavior, one must perform an experiment.

Explanation:

Experimental research allows the researcher to control all the variables in order to create the conditions that can confirm or disconfirm a hypothesis. This method aimes to establish a relation of causality between two variables, which means that one variable is generated and determined by the other; this is posible because all of the other variables that can influence it have been controlled.

When a researcher conducts a survey or engages in naturalistic observation, he can’t control the variables, therefore, he can only establish a correlation between two variables, but not of causality.

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## The primary coil of an ideal transformer has 100 turns and its secondary coil has 400 turns. if the ac voltage applied to the primary coil is 120 v, what voltage is present in its secondary coil?

The primary coil of an ideal transformer has 100 turns and its secondary coil has 400 turns. if the ac voltage applied to the primary coil is 120 v, what voltage is present in its secondary coil?

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## A chef places sugar crystals in a cooking pan. He turns on the burner under the pan. In a few minutes, the sugar begins to melt. Which process is most directly responsible for transferring heat from the burner into the sugar? radiation convection conduction resonance

A chef places sugar crystals in a cooking pan. He turns on the burner under the pan. In a few minutes, the sugar begins to melt. Which process is most directly responsible for transferring heat from the burner into the sugar? radiation convection conduction resonance

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## When a young child begins to learn how to take turns in conversation, stay on topic, and give appropriate responses such as “please” and “thank you,” the child is demonstrating knowledge of?

Explanation:  Animals, however well preserved and bred in conditions that are not in nature, that is, not in their natural habitat, animals still retain the animal instinct. Thus, young animals in the wild can be met daily, except for members of their species, and members of all other species, including predators, as well as humans. This means that in the natural environment, young animals can find themselves in a variety of dangers on a daily basis, but not only that. In this way young animals develop their ability to survive, escape from predators, manage, and develop their hunting skills, etc. All this is essential for socialization because according to all these developed skills and abilities their socialization depends. To deny any of the conditions prevailing in the wild means to deny the development of any skill or instinct, to deny proper socialization.

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## A barrel shaped like a cylinder is laid on its side and rolled up a ramp that is 92m long. The barrel has a circular base that turns 46 times in being rolled up the ramp. What is the diameter of the circular base?

Option C – BD=76 cm

Step-by-step explanation:

Given : You are designing a diamond-shaped kite. you know that AD = 44.8 cm, DC = 72 cm, and AC = 84.8 cm.

To find : How long BD should it be?

Solution :

First we draw a rough diagram.

The given sides were AD = 44.8 cm, DC = 72 cm and AC = 84.8 cm.

According to properties of kite

Two disjoint pairs of consecutive sides are congruent.

DC=BC=72 cm

The diagonals are perpendicular.

So, AC ⊥ BD

Let O be the point where diagonal intersect let let the partition be x and y.

AC= AO+OC

AC=   …….[1]

Perpendicular bisect the diagonal BD into equal parts let it be z.

BD=BO+OD

BD=z+z

Applying Pythagorean theorem in ΔAOD

where H=AD=44.8 ,P= AO=x , B=OD=z

………[2]

Applying Pythagorean theorem in ΔCOD

where H=DC=72 ,P= OC=y , B=OD=z

…………[3]

Subtract [2] and [3]

……….[4]

Add equation [1] and [4], to get values of x and y

Substitute x in [1]

Substitute value of x in equation [2], to get z

We know, BD=z+z

BD= 38.06+38.06

BD= 76.12

Nearest to whole number BD=76 cm

Therefore, Option c – BD=76 cm is correct.

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## Arrange the events from Book 13 in the correct order. 1. Ulysses finishes recounting his adventures of his journey home to the Phaeacians. 2. Neptune turns the Phaeacians’ ship into stone. 3.Minerva meets Ulysses in the guise of a young shepherd. 4. King Alcinous makes arrangements for Ulysses’s safe journey home to Ithaca. 5. Minerva disguises Ulysses as an old beggar. 6.Ulysses falls asleep after boarding the Phaeacian ship. 7.Minerva and Ulysses plot revenge against Penelope’s suitors.

Read this analysis of the Odyssey, Book XIII in order to better understand how to solve this problem.

Once Ulysses is done telling the Phaeacian court about what happened at sea, King Alcinous orders some of his men with the hero to ensure Ulysses’s safe return to Ithaca. While on the ship ride, Ulysses falls asleep. Once the boat reaches Ithaca, the men of King Alcinous do not wake him. Instead, they let him stay asleep, but they move his body from the boat onto shore and they return to their own journey. Minerva, a goddess, then places a ‘grey mist’ over Ulysses to protect him while he’s asleep. When Ulysses does finally wake up, he has some trouble remembering his land. Somehow, Ulysses deep sleep erased his memory of home. Basically this deep sleep allowed Ulysses to the last of his twenty years.

The fact that the Phaeacians followed Joves instructions and brought Ulysses back home anger Neptune. When the Phaeacians discover the fury of Neptune, they then try to satisfy him by making a sacrifice. Although the sacrifices they end up making don’t please Neptune. Neptune ends up sinking the Phaeacians ship by turning it into stone. Even though Jove sees an opportunity to stop Neptune, he does not. His simply also Neptune to destroy their ship.

Minerva ends up disguising herself as a shepherd when she talks to Ulysses. She does so to protect her identity and to test Ulysses. Ulysses passed Minerva’s test by not telling disguised Minerva who he really is. Pleased with this, Minerva then reveals her true identity to him. After that Minerva tells Ulysses about the suitors that are at his palace that are trying to marry his wife and take over Ithaca. Once she has went over the plan, they then plot revenge against them. Once there plan is ready Minerva disguises Ulysses as a beggar to go undercover and see which men are truly loyal.

There is a bit more, but I’ll end it there since that’s about how much information we’ll need.

Now, put the tiles in order according to the analysis.

• Ulysses finishes recounting his adventures of his journey home to the Phaeacians.

• King Alcinous makes arrangements for Ulysses’s safe journey home to Ithaca.

• Ulysses falls asleep after boarding the Phaeacian ship.

• Neptune turns the Phaeacians’ ship into stone.

• Minerva meets Ulysses in the guise of a young shepherd.

• Minerva and Ulysses plot revenge against Penelope’s suitors.

• Minerva disguises Ulysses as an old beggar.

– Marlon Nunez

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## Blake is driving home from the water park. He drives for 60 miles and stops to rest before driving 20 more miles. Unfortunately, Blake remembers he was supposed to pick up a present for his friend on the way home, so he turns around and drives 36 miles back towards the water park. Once he picks up the present, he drives the rest of the way home, which is 70 miles away. What is the distance from the water park to Blake’s home?

I think you need to use the SoHCaHToA method here.

S means sin
C means cos
T means tan
O means opposite
H means hypotenuse

The hypotenuse is the longest side in a right angled triangle.

The adjacent is the side between the angle and the right angle.

The opposite is the side that is left.

If you have the value of the opposite cross all of the o’s out. The same with the other sides. If only one type of letter is crossed out, cross out the type of letter that stands for the length you want to find. The part of the word with two crosses tells you what function to use (sin, cos or tan)

In this example, the function used will be sin.

sinx°=o÷h
cosx°=a÷h
tanx°=o÷a

since we are using sin, the formula we will use is :

sinx°=o÷h

Then you plug in what you know.

sin30°=30÷h
h=30÷sin30°
h=60ft

If there was a case when you needed to work out an angle, inverse sin, or cos, or tan would be used.

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## Which of the following statements does not represent a benefit of peer relationships? A. Jason and Sean argued over whose turn it was to play the video game but decided they would each get two turns in row. B. Josie listened attentively as Sonya told her what it was like to spend the summer at the beach. C. Erin teased her friend Jared constantly about his haircut even though Jared tried to explain why he liked it. D. Sondra and Alex often exchanged their favorite toys to play with every Saturday.

Which of the following statements does not represent a benefit of peer relationships? A. Jason and Sean argued over whose turn it was to play the video game but decided they would each get two turns in row. B. Josie listened attentively as Sonya told her what it was like to spend the summer at the beach. C. Erin teased her friend Jared constantly about his haircut even though Jared tried to explain why he liked it. D. Sondra and Alex often exchanged their favorite toys to play with every Saturday.

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## An​ assembly-line machine turns out washers with the following thicknesses​ (in millimeters). Find the mean and standard deviation of the thicknesses. 1.42, 1.83, 1.43, 1.87, 1.22, 1.44, 1.72, 1.91, 1.42, 1.87, 1.42, 1.99, 1.27, 1.94, 1.67, 1.22

When the profit is 0; then P(t)=0
You have this equation:
t⁴-5t²+4=0

Then, you have to do the following change:
t²=z

you have this other equation:
z²-5t+4=0

Now, you can solve this square equation:
z=[5⁺₋√(25-16)]/2=(5⁺₋√9)/2=
you have two solutions for z.
z₁=(5-3)/2=1
z₂=(5+3)/2=4

Now; if z=1; then
t²=z
t²=1
t=⁺₋√1

We have two solutions:
t=-1 this is not a valid solution:
t=1;

Then in 2001  (2000+t=2000+1=2001) the profit was 0.

If z=4, then:
t²=z
t²=1
t=⁺₋√4

We have two solutions:
t=-2 this is not a valid solution:
t=2;

Then in 2002  (2000+t=2000+2=2002) the profit was 0.

Answer: the yeares in which the profict was 0, were 2001 and 2002.

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## PLZZ HELP FASSSSST 1. Which of the following eyects would you expect if red blood cells were shaped like neurons? (1 point) They would not be able to move as easily through capillaries. They would more easily carry out gas exchange in the alveoli. They would not need to be transported through the body. They would become more eyective at picking up urea discarded by body cells. 2. Which of the following is not a function of the skeletal system? (1 point) supports the body works with other body systems to allow movement manufactures new blood cells sends signals to the brain 3. Which of the following body systems are involved in the first line of defense of the immune system against infection? (1 point) integumentary, digestive, respiratory nervous, circulatory, skeletal muscular, endocrine, urinary urinary, skeletal, integumentary 4. Which of the following sets of structures would be involved in ridding the body of unwanted urea? (1 point) sensory neuron, interneuron, spinal cord alveoli, atrium, cilia capillary, nephron, ureter brain, esophagus, small intestine 5. An infectious disease is a disease that (1 point) is caught because the weather turns cold. is caused by pathogens. can be spread only by bacteria. cannot be cured. 6. Which of the following statements is true regarding infectious agents? (1 point) Infectious agents are all too small to be seen without a microscope, and none can be classified as living. All infectious agents are living because they are all classified as microorganisms. Of all the infectious agents, only viruses are considered living because they actively inject their DNA or RNA into host cells. Viruses cannot be treated with antibiotics because they are not living organisms. 7. Which discovery in the 1800s led to the development of germ theory? (1 point) Vaccines could prevent a disease. Antibiotics exist that can be given to counteract an infection. Infection rates decline when health care professionals wash their hands in between seeing patients. Some diseases, such as cancer, are caused by chemical factors. 8. Follow a carbon atom in a piece of bread eaten by a boy. Which of the following describes a path that this atom could take? (1 point) mouth esophagus stomach large intestine blood body cell mouth esophagus stomach small intestine blood body cell mouth large intestine esophagus stomach blood body cell mouth esophagus small intestine stomach blood body cell 9. Which of the following sets of structures is innervated by the somatic nervous system? (1 point) esophagus, stomach, small intestine atrium, ventricle, arteries biceps, triceps, quadriceps diaphragm, bladder, large intestine 10. Which of the following cell types would you expect to increase in number azer a person becomes infected with a pathogen? (1 point) sensory neurons white blood cells epidermal cells red blood cells

There are four variables which govern changes in population size.
births
deaths
immigration
emigration

A population gains individuals by birth and immigration and loses individuals by death and emigration.

Biotic Potential
Populations vary in their capacity to grow. The maximum rate at which a
population can increase when resources are unlimited and environmental
conditions are ideal is termed the population’s biotic potential. Each
species will have a different biotic potential due to variations in
the species’ reproductive span (how long an individual is capable of reproducing)
the frequency of reproduction (how often an individual can reproduce)
“litter size” (how many offspring are born each time)
survival rate (how many offspring survive to reproductive age)

There are always limits to population growth in nature. Populations
cannot grow exponentially indefinitely. Exploding populations always
reach a size limit imposed by the shortage of one or more factors such
as water, space, and nutrients or by adverse conditions such as disease,
drought and temperature extremes. The factors which act jointly to
limit a population’s growth are termed the environmental resistance. The interplay of biotic potential and density-dependent environmental resistance keeps a population in balance.
Carrying Capacity
For a given region, carrying capacity is the maximum number of
individuals of a given species that an area’s resources can sustain
indefinitely without significantly depleting or degrading those
resources. Determining the carrying capacities for most organisms is
fairly straightforward. For humans carrying capacity is much more
complicated. The definition is expanded to include not degrading our
cultural and social environments and not harming the physical
environment in ways that would adversely affect future generations.

For populations which grow exponentially, growth starts out slowly,
enters a rapid growth phase and then levels off when the carrying
capacity for that species has been reached. The size of the population
then fluctuates slightly above or below the carrying capacity.
Reproductive lag time may cause the population to overshoot the carrying
capacity temporarily. Reproductive lag time is the time required for
the birth rate to decline and the death rate to increase in response to
resource limits. In this scenario, the population will suffer a crash
or dieback to a lower level near the carrying capacity unless a large
number of individuals can emigrate to an area with more favorable
conditions. An area’s carrying capacity is not static. The carrying
capacity may be lowered by resource destruction and degradation during
an overshoot period or extended through technological and social
changes.

An example of dieback occurred in Ireland after a fungus infection
destroyed the potato crop in 1845. During this potato famine
approximately 1 million people died and 3 million people emigrated to
other countries. Increased food production due to improved agricultural
practices, control of many diseases by modern medicine and the use of
energy to make historically uninhabitable areas of Earth inhabitable are
examples of things which can extend carrying capacity. The question is
how long will we be able to keep increasing our population on a planet
with finite size and resources?

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## Yi and Sue play a game. They start with the number 42000. Yi divides by a prime number, then passes the quotient to Sue. Then Sue divides this quotient by a prime number and passes the result back to Yi, and they continue taking turns in this way. For example, Yi could start by dividing 42000 by 3. In this case, he would pass Sue the number 14000. Then Sue could divide by 7 and pass Yi the number 2000, and so on. The players are not allowed to produce a quotient that isn’t an integer. Eventually, someone is forced to produce a quotient of 1, and that player loses. For example, if a player receives the number 3, then the only prime number (s)he can possibly divide by is 3, and this forces that player to lose. Who must win this game

Naturally, any integer larger than 127 will return , and of course , so we restrict the possible solutions to .

Now,

is the same as saying there exists some integer such that

We have

which means that any that satisfies the modular equivalence must be a divisor of 120, of which there are 16: .

In the cases where the modulus is smaller than the remainder 7, we can see that the equivalence still holds. For instance,

(If we’re allowing , then I see no reason we shouldn’t also allow 2, 3, 4, 5, 6.)