suppose the starting pressure in the container p1 is below atmospheric pressure when the stopper is popped. draw the adiabatic and isochoric processes on a p-v diagram.
Answers
The diagram of adiabatic and isochoric process on a pv diagram is given below.
In the given question we have to suppose the starting pressure in the container p1 is below atmospheric pressure when the stopper is popped the draw the adiabatic and isochoric processes on a p-v diagram.
The Adiabatic Process
A thermodynamic process known as adiabatic means that no heat is transferred into or out of the system. For an ideal gas, an adiabatic process is a reversible process with constant entropy. The adiabatic process is mathematically represented by the expression ∆Q=0.
The Isochoric Process
A thermodynamic process known as an isochoric process, also known as a constant-volume process, isovolumetric process, or isometric process, occurs when the volume of the closed system undergoing the process remains constant.
The diagram of adiabatic and isochoric process on a pv diagram is given below:
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Related Questions
Omar is a quality control expert at a factory that paints car parts. He knew that 20% of parts were being painted with an error, so he made a change in the painting process. After the change, he wanted to test H, :p=0.2 versus H, p<0.2, where p is the proportion of parts that were being painted with an error Omar took a sample of 400 parts and found that 16% of them had an error. He used these results to calculate a test statistic of 2 = -2.00 and a P-value of approximately 0.023. Assume that the conditions for inference were met. Is there sufficient evidence at the a = 0.05 level to conclude that less than 20% of the parts are being painted with an error? Choose 1 answer Yes, because 0.023 <0.05. Yes, because 16% < 20%. No, because 0.05 0.023. No, because 0.16 0.05.
Answers
Yes, there is sufficient evidence at the α = 0.05 level to conclude that less than 20% of the parts are being painted with an error.
We have,
There is sufficient evidence at the α = 0.05 level to conclude that less than 20% of the parts are being painted with an error.
The calculated P-value of approximately 0.023, which is less than the significance level of 0.05.
The P-value indicates the probability of observing a test statistic as extreme as or more extreme than the observed value of -2.00 under the null hypothesis.
Since the P-value is smaller than the significance level, we reject the null hypothesis and conclude that the proportion of parts with an error is significantly less than 20%.
The fact that 16% is less than 20% also supports this conclusion.
Thus,
Yes, there is sufficient evidence at the α = 0.05 level to conclude that less than 20% of the parts are being painted with an error.
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maria rolls a pair of dice. what is the probability that she obtains a sum that is either a multiple of 3 or a multiple of 4?
Answers
When a pair of dice rolled, the probability that the sum is either a multiple of 3 or a multiple of 4 is 5/9.
If an event A and an event B is independent to each other, then the probability A or B is:
P(A or B) = P(A∪B) = P(A) + P(B)
In the given problem:
The possible outcomes or the sample space of rolling a pair of dice = 6 x 6 = 36.
The maximum sum is 6 + 6 = 12
Multiple 3 or multiple 4 that ≤ 12 is {3, 4, 6, 8, 9, 12}
Possible outcomes for Sum = 3 are 1 + 2 and 2 + 1
Hence,
P(3) = 2/36
Possible outcomes for Sum = 4 are 1 + 3, 3 + 1, 2 + 2
Hence,
P(4) = 3/36
For Sum = 8, 2 + 6, 6 + 2, 3 + 5, 5 + 3, 4 + 4
Hence,
P(8) = 5/36
Similarly,
P(6) = 5/36
P(9) = 4/36
P(12) = 1/36
Therefore,
P(Multiple 3 or multiple 4) = P(3, 4, 6, 8, 9, 12)
= 2/36+3/36+5/36+5/36+4/36+1/36
= 20/36
= 5/9
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the differential equation has as a solution. applying reduction order we set . then (using the prime notation for the derivatives) u'x^4 4ux^3 u''x^4 8u'x^3 12ux^2 so, plugging into the left side of the differential equation, and reducing, we get u''x^6 u'x^5 the reduced form has a common factor of which we can divide out of the equation so that we have . since this equation does not have any u terms in it we can make the substitution giving us the first order linear equation . this equation has integrating factor x for x > 0. if we use
Answers
The solution of the given differential equation u'x^4 4ux^3 u''x^4 8u'x^3 12ux^2 be,
u''x^6 u'x^5
Given, a differential equation
u'x^4 4ux^3 u''x^4 8u'x^3 12ux^2
we have to find the solution of the given differential equation
on integrating both the sides, we get
u''x^6 u'x^5
So, we get u''x^6 u'x^5 as a solution of the given differential equation on solving by the reduction method.
Hence, the solution of the given differential equation u'x^4 4ux^3 u''x^4 8u'x^3 12ux^2 be,
u''x^6 u'x^5
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Demi was given a riddle to solve: the sum of two consecutive positive integers is 71. find the two positive integers.
Answers
The required number of two positive consecutive integers are 35 and 36.
Consecutive integers are the whole numbers that follow each other without gaps. consecutive integers are even, and odd integers.
consecutive even integers that differ from previous integer by difference of 2 and each integer is divisible by 2.
consecutive odd integers that differ from previous integer by difference of 2 and each integer is an odd number.
let the first positive integer be x
Therefore the second positive integer be (x+1)
Given that the sum of two consecutive positive integer is 71:
x+(x+1)=71
open the bracket
x+x+1=71
Add the similar terms
2x+1=71
2x=71-1
2x=70
x=35
Finding the second integer Substituate the value of x=35 in (x+1):
x+1=35+1
x+1=36
The required number of two positive consecutive integers are 35 and 36.
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
The function has its graph to be represented by graph (a)
Table:
x -2 -1 0 1 2
y 16/9 4/3 1 3/4 9/16
How to plot the graph of the functionThe equation that represents the function is given as
f(x) = (3/4)ˣ
Next, we extract the x values from the given table
These x values are represented as
x = -2, -1, 0, 1 and 2
Solving further, we need to calculate the function at the x values
So, we have the following computations
f(-2) = (3/4)⁻² = 16/9
f(-1) = (3/4)⁻¹ = 4/3
f(0) = (3/4)⁰ = 1
f(1) = (3/4)¹ = 3/4
f(2) = (3/4)² = 9/16
When these values are presented on a table, we have:
x -2 -1 0 1 2
y 16/9 4/3 1 3/4 9/16
Some of the points on the table are
(0, 1), (1. 3/4) and (2. 9/16)
The graph that passes through these points is graph (a)
So, the
Hence, the graph of the function is graph (a)
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what is the maximum number of roads that can be closed while still making sure that for any two buildings in the city, there still exist roads that people can use to travel from one to the other?graph theory math stack math.stackexchange
Answers
Yes, you can still get from one city to another even if a road is closed for maintenance.
How is it feasible to get from one city to another if one road is closed for repairs?
It is sufficient to show that even with route AB closed, we can still get from point A to point B. In the connected component that contains vertex A, all the vertices would be even if this weren't the case.
When a connected component has exactly one odd vertex, the "A graph must have an even number of odd vertices" condition is violated.
Therefore, even if one of the roads is closed for maintenance, it is still possible to go from Point A to Point B by another road or city.
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The given question is improper. Proper question is given below;
in a certain country, 40 roads lead out of each city. when all roads are open, it is possible to travel from any city to any other. each road leads from one city to another; there are no dead end roads. if one road is closed for repairs, is it still necessarily possible to travel from any city to any other? prove your answer.
Pls help super hard question
Answers
he got the same answer i did
Step-by-step explanation:
Question 14 (5 points)
Solvex² - 2x=15 by applying the quadratic formula.
Ox= 1 + √14i, x = 1 - √√14i
Ox = -5, x = 3
Ox = 5, x = -3
Ox= -1 + √14i, x = -1 - √√14i
Answers
The required solution of the given expression is given as x = 5 and x = -3.
Given that,
To solve x² - 2x=15,
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
x² - 2x - 15 = 0
x² -5x + 3x - 15 = 0
x (x - 5) + 3 (x - 5) = 0
(x + 3)(x - 5) = 0
So,
x = -3 and x = 5
Thus, the required solution of the given expression is given as x = 5 and x = -3.
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Linda can sell 12 magazine subscriptions per week and makes $\$ 4.00$ for each magazine subscription she sells. Obviously this means that Linda will make (12) $(\$ 4.00)=$ $\$ 48.00$ per week from magazine subscriptions. Explain this result mathematically, using mathematical notation and the chain rule.
Answers
The case mentioned above is resolved via multiplication.
Given information,
Linda can sell 12 magazine subscriptions per week and makes 4$ for each magazine subscription she sells. This means that Linda will make 48$ per week from magazine subscriptions.
To show it mathematically,
1 week ⇒ 12 magazines
Each of them costs $4;
⇒ 12 * 4$ = 48$ per week
By using multiplication we solve the above-given case.
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When the distance is half the gravitational force is?.
Answers
The gravitational force increases four times when the space between the items is cut in half.
What exactly does gravity mean?
Any two things with mass are drawn together by the gravitational force. Because it consistently attempts to pull masses together rather than pushing them apart, the gravitational force is known as attractive. In actuality, every thing in the cosmos, including you, is pulling on every other object.Who made the discovery of gravity?
It is said that after observing an apple fall and wondering why it fell straight down rather than sideways or even upward, Isaac Newton developed the theory of gravitation in 1665 or 1666.
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Rewrite 6a 18ab using a common factor. 6a(1 3b) 6a(0 3b) 6ab(0 3) 6ab(1 18ab)
Answers
Solution of the given expression 6a + 18ab after rewriting using a common factor is equal to :
A. 6a(1 + 3b).
As given in the question,
Given expression is equal to :
6a + 18ab
Find common factors of both the terms we get.
6 = 1, 2, 3, 6
18 = 1, 2, 3, 6, 9, 18
Highest common factor of 6 and 18 is equal to 6.
Now take 6a as a common factor from both the terms we get,
6a + 18ab
= ( 6a × 1 ) + ( 6a × 3b )
= 6a × ( 1 + 3b )
= 6a ( 1 + 3b )
Therefore, solution of the given expression 6a + 18ab after rewriting using a common factor is equal to :
A. 6a(1 + 3b).
The complete question is :
Rewrite 6a + 18ab using a common factor.
A.6a(1 + 3b)
B. 6a(0 + 3b)
C.6ab(0 + 3)
D. 6ab(1 + 18ab)
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Answer: 6a(1 + 3b)
Step-by-step explanation: I took the test
What are the rules for angles of a triangle?.
Answers
There are basically three to four rules for angles of a triangle.
sum of all interior angle of triangle is 180°.
.
Angle in triangle
Triangles are one of the most basic geometric shapes and have a variety of well-studied properties. Triangle: Largest interior angle and sides facing each other. The same rules apply for minimum angles and sides, medium angles and medium sides.
The largest interior angle is opposite the largest side The smallest interior angle is opposite the smallest side The medium interior angle is opposite the medium sideExterior angle ∠A is the measure of the far interior angle equal to the sum 180°To learn more about Angles of triangle , efer:
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URGENT
What is the slope of the line that passes through the points (-3, 3), and (1, -5)?
Answers
The slope of the line that passes through the points (-3, 3), and (1, -5) is -2.
Steps to finding slope:
In the first point, use the symbols x₁, and y1 to indicate the x and y coordinates, respectively.In the second point, write "x₂ " for the x coordinate and " y₂" for the y coordinate.Find the differences between y₂ and y₁ and x₂ and x1.To calculate the slope, divide the difference between the y- and x-coordinates (m). For example, m = (y₂ - y₁) / (x₂ - x₁,).The formula for finding slope from two points (x₁, y₁) and (x₂, y₂) on a line is m = (y₂ - y₁) / (x₂ - x₁). Here,
m = slope of the line
x₁ = the x-coordinate of the first point
y₁ = the y-coordinate of the first point
x₂ = the x-coordinate of the second point
y₂ = the x-coordinate of the second point
Here, the given points are (-3, 3), and (1, -5):
y₂ = -5, y₁ =3 , x₂ = 1, x₁ = -3
Substitute the values,
m = (y₂ - y₁) / (x₂ - x₁)
m = (-5 - 3) / (1 - (-3))
= -8 / (1+3)
= -8 / 4
m = -2
Hence, the slope of the line that passes through the points (-3, 3), and (1, -5) is -2.
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Evaluate the line integral by the two following methods.
Image for Evaluate the line integral by the two following methods. Integrate xy dx + x2y3 dy C is counterclockwise aroun
xy dx + x2y3 dy
C is counterclockwise around the triangle with vertices (0, 0), (1, 0), and (1, 4)
(a) directly
(b) using Green's Theorem
Answers
The line integral in both cases is 52/3
Given,
a) The line integral; L = ∫c xy dx + x² y³ dy
Where C is counterclockwise around the triangle with vertices (0, 0),
(1, 0) and (1, 4)
Our first line integral is
L₁ = ₁∫₍₀, ₀₎ ⁽¹ ⁰⁾ xy dx + x² y³ dy
The equation of this line is y = 0, x varies from 0 to 1.
L₁ = 0
Our second line integral is
L₂ = ₁∫₍₁, ₀₎ ⁽¹ ⁴⁾ xy dx + x² y³ dy
The equation of this line is x = 0 and y varies from 1 to 4.
L₂ = 64/3
The third line integral is
L₃ = ∫₁⁰ xy dx + x² y³ dy
The equation of this line is y = 4x and x varies from 0 to 1.
L₃ = -4
The value of the line integral is
L = L₁ + L₂ + L₃ = 0 + 64/3 + (-4) = 52/3
b) The second part requires the use of Green's Theorem to evaluate:
This is given by:
∫c Pdx + Qdy = ∫ ∫ R Qy - Px dA
∫c xy dx + x² y³ dy = ∫ ∫R 3x² y² - ydA
We choose our region of integration parallel to the y-axis.
∫c xy dx + x² y³ dy
= ∫¹₀ ∫⁴ˣ₀ 3x² y² - y dy dx
= ∫¹₀ x² y³ - 1/4 |y²|²ˣ₀ dx
= ∫¹₀ 64x⁵ - 4x² dx = 52/3
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How many prime multiples of 8 are there?.
Answers
The prime multiples of 8 are number 2 and 4
The multiples of 8 are 1, 2, 4, 8.
The prime numbers are the numbers who can be divided only by 1 and itselves.
First we need the multiplies of 8
And then find their factors, if the number of factors is exactly two( that is 1 and the number itself) then it is prime.
The factors of 1 is 1
The factors of 2 are 1 and 2
The factors of 4 are 1, 2and 4
The factors of 8 are 1, 2, 4 and 8
The numbers which have only two factors are prime.
2 and 4 are prime multiples of 8
Therefore, the number 2 and 4 can be said as the prime multiples of 8
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a cook has 10 red peppers and 5 green peppers. if the cook selects 6 peppers at random, what is the probability that he selects at least 4 green peppers? express your answer as a common fraction.
Answers
The probability that he selects at least 4 green peppers is 0.0024
A cook has 10 red peppers and 5 green peppers
If the cook selects 6 peppers at random, what is the probability that he selects at least 4 green peppers
Event of getting green peppers be X
We need to find the probability that he selects at least 4 green peppers. This can be when the cook selects either 4 green peppers or 5 green peppers.
This can be found by binomial probabilty distribution.
P(X ≥ 4) = P(X = 4) + P(X = 5)
6C4(5/15)⁴(10/15)¹¹ + 6C5(5/15)⁵(10/15)¹⁰
15 x (1/3) ⁴ x (2/3) ¹¹ + 6 (1/3⁵) (2/3)¹⁰
= 0.002 + 0.0004
= 0.0024
Therefore, the probability that the cook selects at least 4 green peppers out 6 peppers he picked from 10 pred peppers and 5 green peppers is is 0.0024
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how many 4-digit positive integers (that is, integers between 1000 and 9999, inclusive) having only even digits are divisible by 5?
Answers
There are 100, 4-digit positive integers that are divisible by 5 between 1000 and 9999.
Define the term divisibility by 5?A integer is divisible by 5 if it ends with 0 or 5. 35, 790, and 55, for instance, are also all divisible by 5.
There are [0, 2, 4, 6, and 8] things in all.Only one digit should be present because it is the only one that makes the integer divisible by five.There still are 1 methods for filling a position, making a total of 1.A location can be filled in five different ways, hence there are five different methods to fill it.Since all of the numbers in the specified sets can be used to fill the hundreds position, all integers can be used there.There are five different approaches to fill this hundreds place as a result.A set number of even numbers can be used to fill thousands of spots with four different numbers.The very next step is to apply the idea of factorial to determine how many even integers that really are divisible by five may be combined to create a 4-digit number.We then multiply all the computed ways to fill in the corresponding spaces (4 x 5 x 5 x 1 = 100).
Therefore, there are 100 potential 4-digit positive integers.
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Hannah has a rectangular prism with a length of 7 cm, a width of 2 cm, and a height of 6 cm.
Answers
The surface area of the given rectangular prism with a length 7cm , width 2cm and height 6cm is equal to 136cm².
As given in the question,
Dimensions for a given rectangular prism are:
Length = 7cm
Width = 2cm
Height = 6cm
Surface area of the given rectangular prism is equal to
= 2 ( length × width + width × height + height × length )
Substitute the value in the formula we get,
= 2 ( 7 × 2 + 2 × 6 + 6 × 7 )
= 2 ( 14 + 12 + 42 )
= 2 ( 68 )
= 136 cm²
Therefore, the surface area of the rectangular prism is equal to 136cm².
The complete question is :
Hannah has a rectangular prism with a length of 7 cm, a width of 2 cm,
and a height of 6 cm.
What is the surface area of Hannah's rectangular prism?
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a solution that is now widely used to allow two parties to secretly exchange keys is (fill the blank) protocol
Answers
By using the concept of cryptography, it can be concluded that
A solution that is now widely used to allow two parties to secretly exchange keys is Deffie - Hellman protocol
What is cryptography?
Cryptography refers to secure information and communication techniques derived from mathematical concepts and a set of rule-based calculations called algorithms, to transform messages in ways that are hard to decipher.
This is a concept of Cryptography
Diffie–Hellman key exchange establishes a shared secret between two parties which will be used for secret communication for exchanging data over a public network.
A solution that is now widely used to allow two parties to secretly exchange keys is Diffie - Hellman protocol
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when running-up an engine and testing a newly installed hydromatic propeller, it is necessary to exercise the propeller by moving the governor control through its entire travel several times to
Answers
When testing a newly installed hydromatic propeller, the propeller is exercised by moving the governor control through its entire travel several times to free the dome of any entrapped air.
A hydromatic propeller uses a double-acting governor control utilizing oil pressure on both sides of the propeller piston. It was introduced in the 1930s as a substantial advancement over the counterweight, controllable pitch propeller. The application of oil pressure to both sides of the actuating piston provided improved capacity and the potential of feathering or unfeathering by a single control knob. It was designed for larger blades, faster rate of pitch change, and wider range of pitch control. A hydromatic propeller should be checked before, during, and after the operation of the engine. A newly installed hydromatic propeller should be checked by moving the governor along its travel numerous times to ensure that no air is entrapped in the dome.
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An artist used 666 tubes of red paint, 222 tubes of yellow paint, 131313 tubes of white paint, and 999 tubes of blue paint for a mural. What is the ratio of tubes of blue paint to all of the tubes of paint used?.
Answers
The ratio of tubes of blue paint to all of the tubes of paint used was 75/10000 = 0.0075.
What is ratio?A ratio is a comparison of two or more numbers that indicates their sizes in relation to each other.
A ratio compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent.
Given,
red paint= 666 tubes
yellow paint = 222 tubes
white paint = 131313 tubes
blue paint= 999 tubes
Total paint tubes = 666+222+131313+999 = 133200
The ratio of blue paint tubes to all of the paint tubes = 999/133200
= 75/10000.
The ratio of tubes of blue paint to all of the tubes of paint used = 75/10000 = 0.0075.
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Write the equation of the line in fully simplified slope-intercept form. pls help i’m failing this class
Answers
y=-3/4x+3
Explanation:
y-intercept is (0,3) on the graph
Determine slope by rise/run —> -3/4
So y=-3/4x+3
Answer:
y=-3/4x+3
Step-by-step explanation:
(See picture)
Please explain why the first option is correct.
Answers
Answer:
The ratio (center to focus)/(semi-major axis) is the greatest
Step-by-step explanation:
Given various foci coordinates and major axis lengths, you are asked to identify the ellipse with the highest eccentricity.
Ellipse EccentricityThe eccentricity of an ellipse can be defined as the ratio of distance between foci to the length of the major axis. A high value of eccentricity corresponds to a longer, narrower ellipse.
The attached graph plots the locations of the given foci. They are color coded to correspond with the color of the resulting ellipse. (We have used the given r-value as the semi-major axis, not the major axis.)
The blue focal points (A, A') of the blue ellipse give the "flattest" of the bunch, so corresponds to the highest eccentricity. Its parameters are those of the first answer choice.
ValuesIf we assume the given r-value is the semi-major axis, the eccentricity represented by each of the answer choices is ...
(15√2)/22 ≈ 0.964 . . . . highest(10√2)/20 ≈ 0.707(5√13)/22 ≈ 0.819(5√2)/12 ≈ 0.589The numerator in each case is the distance from the center (0, 0) to one focus.
lashonda swam 5 kilometers against the current in the same amount of time it took her to swim 15 kilometers with the current. the rate of the current was 2 kilometers per hour. how fast would lashonda swim if there were no current?
Answers
The correct answer is 4 km per hour Lashonda would swim if there were no current.
Here, we'll suppose that Lashonda is moving at x km/hr. in the absence of any current.
Speed of the current is 2 km/hr.
Distance swim against current is 5km
Time taken to swim against current is 5 ÷ (x - 2)
Distance swim with current is 15km
Time is taken to swim with current is 15 ÷ (x + 2)
Now,
Given that if the time taken in both instances are the same, So, the equation will be 5 ÷ (x - 2) = 15 ÷ (x + 2)
After solving for x we will be solving;
⇒ 5 ÷ (x + 2) = 15 ÷ (x - 2)
⇒ 5x + 10 = 15x - 30
⇒ 10 + 30 = 15x - 5x
⇒ 40 = 10x
⇒ x= 40 ÷ 10 = 4 km per hour
Hence, 4 km per hour Lashonda would swim if there were no current.
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How would you describe a chromatid and a sister chromatid?.
Answers
One of the two identical halves of a chromosome that has been replicated in preparation for cell division is referred to as a chromatid. The two "sister" chromatids are united at the centromere, a restricted portion.
A chromatid is an individual of two together alike halves of a deoxyribonucleic acid that has been copied imminent for the formation of cells by dividing. The two “twin” chromatids are linked at an inhibited domain of the chromosome named the centromere. The establishment of chromatids is a main become involved in cellular division guaranteeing that each new girl cell has the correct complement of DNA at the end of the formation of cells by dividing.
Cell division is the process by which a person's container divides into two woman cells. Cell division frequently happens as few the best container phase at which point the cell evolves and replicates allure deoxyribonucleic acid before separating.
There are two types of cell division: the formation of cells by dividing and the formation of cells by dividing. Most of the time when nations are concerned with “cellular division,” they mean the formation of cells by dividing, the process of making new carcass containers.
Sister chromatids differ from chromatids in that sister chromatids are two copies of a single chromosome and are products of the S phase of the cell cycle. The centromere links sister chromatids together.
During the early stages of cell division, chromatids are produced. Non-sister chromatids appear during metaphase I of meiosis, whereas sister chromatids replicate from the same chromosome.
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a) find the coordinates of the point where y-4x=1 crosses on the axis
b) The diagram shows the graph of y=2x+c. where c is constant find the value of K
Answers
The coordinates of the point where y-4x=1 crosses on the axis is (0, 1).
The value of K is 6.5
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
a) The graph will cross the y-axis at the y-intercept. We can find the value by putting the given equation into slope-intercept form (y = mx + b).
y - 4x = 1
y = 4x + 1
The y-intercept is (0,1).
b) We need to find c, or the y-intercept. This is given to us on the graph, where the line crosses the y-axis at (0,-3).
Therefore, our line is;
y = 2x - 3.
Then, we can plug in 10 for y from the point (k,10) and solve for k as;
10 = 2x - 3
13 = 2x
x = 6.5
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In the following exercises, find the average value of the function over the given rectaf (x,y) = arctan (xy), R = [0,1] x [0,1]
Answers
The average value of the function over the given rectaf (x,y) = arctan (xy), R = [0,1] x [0,1] is 1/4( π - log4) - π²/48.
Define function.A function is a relationship between a number of inputs where each input has exactly one output, according to one definition. f is typically used to represent a function (x).
Given,
Function,
Region = [0,1] × [0,1]
Lˣ = 1/area of region ∫¹₀ ∫₀¹ f(xy) dx dy
Differentiating,
Lˣ
= 1/1 ∫₀¹ tan⁻¹ xy dxdy
= ∫¹₀ [ ∫¹₀ tan⁻¹(xy) dx ] dy
= ∫₀¹ [{x tan⁻¹ (xy) ¹₀ - 1/2 ∫ 2(x+y)/ 1 + xy₂ dx] dy
= ∫¹₀ tan⁻¹ y dy - ¹₀ log(y² + 1) 2y dy
= [ytan⁻¹ y - 1/2 log( y² + 1) ∫¹₀ - [1/4 log (y² +1) log y² +1/4log(y²+1)
= π/4 - 1/2 log 2 -π²/48
L = 1/4( π - log4) - π²/48
The average value of the function over the given rectaf (x,y) = arctan (xy), R = [0,1] x [0,1] is 1/4( π - log4) - π²/48.
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In a survey, 2.25 times
as many students
preferred pizza to hot
dogs. If 44 students
preferred hot dogs, how
many preferred pizza?
Answers
There are 99 students preferred pizza.
The students preferred pizza can be calculated as follows.
First, let’s make the equation.
Students preferred pizza is symbolized as P
Students preferred hotdogs is symbolized as H
P = 2.25H
Second, let’s put the number of student preferred hotdogs.
P= 2.25 x 44
= 99
Hence, there are 99 students preferred pizza.
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Convert the given polar equation to a Cartesian equation. (Use the following as necessary: x and y.)
r = 4 / sin(θ) + 5 cos(θ)
Answers
The Cartesian equation will be;
⇒ x² + y² - 4x - 5y = 0
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The polar equation will be;
⇒ r = 4 sin(θ) + 5 cos(θ)
Now,
Substitute r = √x² + y² , r sin θ = x, r cos θ = y in above equation, we get;
The polar equation will be;
⇒ r = 4 sin(θ) + 5 cos(θ)
⇒ r² = 4 r sin(θ) + 5 r cos(θ)
⇒ x² + y² = 4x + 5y
⇒ x² + y² - 4x - 5y = 0
Thus, The Cartesian equation will be;
⇒ x² + y² - 4x - 5y = 0
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three less than eight times a number is at
least 15
Answers
Answer:
x >= 2.25
x is greater than or equal to 2.25
Step-by-step explanation:
8x - 3 >= 15
add 3 to both sides
8x >= 18
divide 8 from both sides
x >= 2.25
Answer:
x≥6
Step-by-step explanation:
8x
3 less goes to 8x-3
then there is at least 15 which changes to
8x-3≥15
Then solve for x:
add 3 to the sides--> 3x≥15+3
3x≥18
Divide both of the sides by 3
x≥6
Hope this helped!
