The given sample of the randomly selected players from the teams as described is a stratified sample. Hence, the right answer is option A.
In a stratified sample, the population is divided into groups (or strata) based on some characteristic, and a random sample is selected from each group. In this case, the population is the football players, and the groups are the varsity and junior varsity teams. The coach randomly selects one of these teams and then asks all players from that team their opinion on a new logo.
This type of sampling is used when the population is divided into subgroups that are different in some way, and the researcher wants to ensure that these subgroups are represented in the sample. In this case, the coach wants to ensure that both varsity and junior varsity players are represented in the sample, as they may have different opinions on the new logo.
It's not a simple random sample because he selected the team first and then the players. Also, it's not a voluntary response sample because the coach is selecting the players.
It's not a cluster sample because the coach is not selecting the players based on location or geographic proximity, and it's not a systematic sample because he is not selecting the players based on the order in which they appear in a list or a database.
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using linear stability analysis, classify the fixed points of the gompertz model of tumor growth n an
The Gompertz model of tumor growth is a mathematical model that describes the growth of a tumor over time. It is characterized by two parameters, the intrinsic growth rate (r) and the carrying capacity (K), and is described by the following differential equation:
dn/dt = rn(1 - n/K).where n is the size of the tumor and t is time.
To classify the fixed points of the Gompertz model of tumor growth using linear stability analysis, we first need to find the fixed points by setting dn/dt = 0 and solving for n. The fixed points are the values of n that make the tumor size constant. In this case, the fixed point is n* = K.
Next, we need to linearize the system around the fixed point by using the Jacobian matrix. The Jacobian matrix for the Gompertz model is:
J = [dr/dn, d(rn(1-n/K))/dn]
[-rn(1-n/K)/K, rn(1-n/K)+(r*n/K^2)]
In the Gompertz model, the fixed point is n* = K, and the eigenvalues are -r and r/K, which are both negative. This means that the fixed point is stable, and the tumor size will converge to the carrying capacity K if perturbed.
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P= a+b+c
solve for b
Answer:
[tex]b = P - a - c[/tex]
Step-by-step explanation:
Notice that there are 3 terms on the right hand side. You want to isolate b in order to solve for it.
I find it less confusing to place term containing the variable you want on the left hand side. (As long as it is positive).
[tex]a + b + c = P[/tex]
To isolate b subtract a and c from both sides
[tex]b = P -a - c[/tex]
Which is the area, A
A
, of this triangle, using the formula A=12ab⋅sin(C)
A
=
1
2
a
b
·
sin
C
?
The area of triangle, using the formula A is 146.9 in^2
How to find a area of triangle using trigonometry?Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. It can be used to calculate the area of a triangle by using the length of its sides.
The most commonly used formula to calculate the area of a triangle is known as Heron's formula. This formula uses the lengths of the triangle's three sides, known as a, b, and c. Then use the formula A = 1/2 x[tex]\sqrt{(a + b+ c)(-a + b + c)(a - b + c)(a + b -c)}[/tex] to calculate the area of the triangle.
To calculate the area of a triangle using Heron's formula, first measure the length of each side of the triangle. Then use the lengths of the sides to calculate s using the formula above. Once you have calculated s, plug the values for a, b, and c into Heron's formula to calculate the area of the triangle.
A = 1/2ab⋅sin(C)
= 1/2(21 in. )(14 in.)⋅sin(88)
= 1/2(294 in.2 )⋅sin(88)
= 1/2(294 in.2 )⋅0.9945
A = 146.9 [tex]in^{2}[/tex]
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Show that each conditional statement in Exercise 11 is a tautology by applying a chain of logical identities as in Example 8. (Do not use truth tables.) a) (PA) P b) p (pv) c) p + ( pa) d) (p) - () e) (P+) - P f) (p)
a) (PA) P is a tautology because P is logically equivalent to P v F, and P v F is logically equivalent to P.
b) p (pv) is a tautology because p is logically equivalent to p v T, and p v T is logically equivalent to p.
c) p + ( pa) is a tautology because p is logically equivalent to p v F, and p v F is logically equivalent to p v (p v A).
d) (p) - () is a tautology because p is logically equivalent to p v T, and p v T is logically equivalent to p v F.
e) (P+) - P is a tautology because P+ is logically equivalent to P v T, and P v T is logically equivalent to P.
f) (p) is a tautology because p is logically equivalent to p v F, and p v F is logically equivalent to p.
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Question 7 of 10
If f(x)=-2 and g(x)=2x²+x-3, find (f+g)(x).
OA. x²-6
OB. 2x²+2x+1
OC. 2x² -+1
OD. 2x²+x-5
SUI
The solution of the given functions (f+g)(x) is 2x²+x-5.
What is function?This connection is typically represented as y = f(x), or "f of x," where y and x are coupled so that for any value of x, there is a certain value of y. This means that f(x) can only have one value for a given x. In set theory jargon, a function connects an element x to an element f(x) in another set.
Here, the given functions are,
f(x) = x/2 - 2
g(x) = 2x ^ 2 + x - 3
(f+g) x = f(x) + g(x)
(f+g) x = x/2 - 2 + 2x ^ 2 + x - 3
(f+g) x = (3x)/2 - 5 + 2x ^ 2
(f+g) x = 2x ^ 2 + (3x)/2 - 5.
= 2x²+x-5
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Find the slope of the line described in the table. (Please help)
Answer:
-1/2
Step-by-step explanation:
use any difference in Y
divided by the difference in X.
ΔY = 3-2 = 1
ΔX=-4-(-2)=-2
1/(-2) = slope
please show solution.. thank you
196 millilitres of tomato paste for 16 litres of spaghetti sauce.
=======================================================
Explanation:
We're told that 12 litres of sauce goes with 147 millilitres of paste.
Divide the larger value over the smaller: 147/12 = 12.25 exactly.
Do the same thing to each of the answer choices A through D.
(A) 94/8 = 11.75(B) 108/9 = 12(C) 196/16 = 12.25(D) 169/14 = 12.071 approximatelyOptionally we could represent the results in a table like so
[tex]\begin{array}{|c|c|c|c|} \cline{1-4}\text{Choice} & \text{Paste} & \text{Sauce} & \text{Paste/Sauce}\\\cline{1-4}\text{A} & 94 & 8 & 11.75\\\cline{1-4}\text{B} & 108 & 9 & 12\\\cline{1-4}\text{C} & 196 & 16 & 12.25\\\cline{1-4}\text{D} & 169 & 14 & 12.071 \ \text{(approx)}\\\cline{1-4}\end{array}[/tex]
Spreadsheet software is handy if you go this route. You don't have to worry about the units in this case.
Choice C is the only option that yields the ratio 12.25, which means it's the only possible answer.
What is the five number summery for this set of numbers 34,35,37,38,42,45,49
The five number summary of the set of numbers is :
Minimum: 34First Quartile (Q1): 37Median: 38Third Quartile (Q3): 42Maximum: 49What is the five number summary ?A five number summary is a way to summarize a set of numerical data by providing five key values: the minimum, the first quartile (Q1), the median, the third quartile (Q3), and the maximum.
For the set of numbers 34, 35, 37, 38, 42, 45, and 49, the five number summary would be:
The minimum value is 34, the lowest value in the set.
The first quartile, also known as Q1, is the value that separates the lowest 25% of the data from the rest of the data, which is 37.
The median is the middle value, which is 38.
The third quartile, also known as Q3, is the value that separates the highest 25% of the data from the rest of the data, which is 42.
The maximum value is 49, the highest value in the set.
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An open box is made from a 40-cm by 89-cm piece of tin by cutting a square from each corner and folding up the edges. The area of the resulting base is 2100cm^. What is the length of the sides of the square
Answer:
√365 cm
Step-by-step explanation:
We can begin by using the formulas for the area of a rectangle and a square to set up an equation. Let x be the length of the sides of the square that is cut out of each corner of the rectangle.
The area of the original rectangle is 40cm * 89cm = 3560cm^2.
The area of the square that is cut out of each corner is x^2.
The area of the remaining base of the box is 2100cm^2.
So, we have:
3560cm^2 - 4x^2 = 2100cm^2
Solving for x, we get:
x = √(3560cm^2 - 2100cm^2)/4 = √(1460cm^2)/4 =√365cm
So the length of the sides of the square is √365 cm
if i helped you, can you mark my answer as best?
please help with math
Answer:-3
Step-by-step explanation:
The y-intercept is where the line crosses the y-axis so in this case it is -3.
Question 16 of 25
Simplify 67 +63
OA. 610
OB. 6-4
O C. 364
O D. 64
The simplification of the given expression after addition = 130.
What is addition?Addition is defined as one of the arithmetic operations that is used for the combination of two of more values.
The given values from the question above;
67 + 63 = 130
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Find an equation for the line below.
Answer: - 4/5x + 1.8
Step-by-step explanation:
"-": because the slope is negative
"4/5": because its the slope
"x": because it is part of 'mx + b'
"1.8": because it's the y-intercept that fits this equation
Answer:
y = -4/5x + 1.8
Step-by-step explanation:
1st find the slope, m, using these 2 points: (-4,5) and (6,-3)
m = (-3-5) / (6--4) = -8/10 = -4/5
Now use the point (-4, 5) in the the point-slope form to find b:
y - 5 = -4/5(x - -4)
y - 5 = -4/5(x + 4)
y - 5 = -4/5x - 16/5
y = -4/5x -16/5 + 25/5 = -4/5x + 9/5
Now write the equation in slope-intercept form:
y = -4/5x + 1.8
The population of a small town increased from 25,056 people in 2002 36,720 in 2010 what is the percentage change in the population
well, we know in 2002 it was 25,056, then it ballooned to 36,720 in 2010, the difference is really 36720-25056 = 11664.
now, if we take 25,056(origin amount) to be the 100%, what's 11664 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 25056 & 100\\ 11664& x \end{array} \implies \cfrac{25056}{11664}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 58 }{ 27 } ~~=~~ \cfrac{ 100 }{ x }\implies 58x=2700\implies x=\cfrac{2700}{58} \implies x\approx \stackrel{\%}{46.55}[/tex]
Which of the following describe(s) petroleum formation? (Select all that apply.)
*
1 point
a. When dinosaurs became extinct 65 million years ago, their bodies decayed to become petroleum.
b. Petroleum is renewable over human lifetimes.
c. It takes hundreds of millions of years for petroleum to form.
d. Petroleum formed in cold places.
petroleum formation happens When dinosaurs became extinct 65 million years ago, their bodies decayed to become petroleum.
What is decomposition?Dead creatures are broken down into their basic chemicals through the process of decomposition by bacteria and fungus. The cycle can be completed by plants absorbing and using these substances once again. Because of how they decompose dead organic stuff, decomposing bacteria and fungus are referred to be saprophytic.
Oil and gas are created from organic material that has been decomposed and altered over millions of years, mostly as sediments on the seafloor.
Fuels known as petroleum products are created from crude oil and the hydrocarbons found in natural gas. Coal, natural gas, and biomass can also be used to make petroleum products.
Plant and animal remains are used to create petroleum. Animals and plants that pass away sink and land on the seafloor. These extinct animals and plants decayed millions of years ago and mingled with sand and silt.
Therefore, we can say Petroleum is produced. Dinosaurs became extinct 65 million years ago, and when their corpses decomposed, petroleum was created. Petroleum doesn't form until hundreds of millions of years. Oil was created in chilly climates.
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Please help
Select the correct choices that make the statement true.
Look at image
For the given image, the value of iota (i) is -i and 1.
What does the arithmetic term "iota" mean?
Thus, the development of complex numbers has given rise to imaginary roots. The sign I which stands for Iota, is used to represent -1. (Imaginary number). In essence, I refers to the imaginary component, often known as the iota. I's value is -1. A square root with a negative value represents an imaginary value. Imaginary numbers can be calculated using any of the standard arithmetic operators. An imaginary number has a negative value when squared.
Complex numbers are expressed using the imaginary unit number, where I is defined as imaginary or unit imaginary. Here, we'll go over the chart and principles for imaginary numbers that are employed in mathematical computations.
The value of iota (i²) = -1
The given expressions can be represented in the following way -
i³ = i² × i = -1 × i = -i
i⁸ = i² × i² × i² × i² = -1 × -1 × -1 × -1 = 1
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a destroyer simultaneously fires two shells with different initial speeds at two different enemy ships. the shells follow the parabolic trajectories shown.
1. At 4.142s the first shell will hit the first enemy ship.
2. At 3.536s the second shell will hit the second enemy ship.
3. The two shells will be 677.1 meters apart when they hit their respective targets.
To solve this problem, we can use the equations for the horizontal and vertical motion of a projectile.
The horizontal velocity of a projectile can be found using the equation: [tex]v_x = v_0 * cos\theta[/tex] where,
[tex]v_0[/tex] is the initial velocity[tex]v_x[/tex] is the horizontal velocity[tex]\theta[/tex] is the angle at which the projectile is fired.The vertical velocity of a projectile can be found using the equation:
[tex]v_y = v_0 * sin\theta[/tex]
The horizontal displacement of a projectile can be found using the equation:
[tex]x = v_0 * cos\theta * t[/tex]
The vertical displacement of a projectile can be found using the equation:
[tex]y = v_0 * sin\theta * t - (1/2)gt^2[/tex] where,
t is the time g is the acceleration due to gravity (approximately 9.8 m/s^2) x and y are the horizontal and vertical displacements.1. To find the time that the first shell will hit the first enemy ship, we can use the equation for the horizontal displacement:
[tex]t = x / (v_0 * cos\theta)[/tex]
t = 2000m / (800m/s * cos(45))
= 4.142s
2. To find the time that the second shell will hit the second enemy ship, we can use the equation for the horizontal displacement:
[tex]t = x / (v_0 * cos\theta)[/tex]
t = 2000m / (1000m/s * cos(60))
= 3.536s
3. To find the distance between the two shells when they hit their respective targets, we can use the equation for the horizontal displacement:
[tex]x_1 = v_0 * cos\theta * t \\x_2 = v_0 * cos\theta * t[/tex]
x1 = 800m/s * cos(45) * 4.142s
= 2858.9m
x2 = 1000m/s * cos(60) * 3.536s
= 3536m
x2 - x1 = 3536m - 2858.9m
= 677.1m
So the two shells will be 677.1 meters apart when they hit their respective targets.
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The complete question is:
A destroyer simultaneously fires two shells at two different enemy ships. The first shell has an initial speed of 800 m/s and is fired at an angle of 45 degrees. The second shell has an initial speed of 1000 m/s and is fired at an angle of 60 degrees. The distance between the two enemy ships is 2 km.
1. At what time will the first shell hit the first enemy ship?
2. At what time will the second shell hit the second enemy ship?
3. How far apart will the two shells be when they hit their respective targets?
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Briefly explain the three lines of evidence for the Earth's relative age. Write your answer in the essay box below.
WILL GIVE BRAINLIEST
Answer:
There are several lines of evidence that scientists use to determine the relative age of the Earth and its various features. These include:
Stratigraphy: This refers to the study of rock layers and the sequence in which they were formed. Scientists use stratigraphy to determine the relative ages of different rock layers and the fossils they contain. The principle of superposition states that in any undisturbed sequence of rocks, the oldest rock layers will be at the bottom and the youngest will be at the top.
Fossil record: Fossils are the remains of plants and animals that lived in the past. By studying the fossils in rock layers, scientists can determine the relative ages of different rock formations and the organisms that lived in them. Fossils of extinct species found in lower rock layers are older than those found in higher rock layers.
Radiometric dating: This is a method that uses the decay of radioactive isotopes in minerals to determine the absolute age of rocks and minerals. Scientists can use radiometric dating to determine the age of a rock or mineral, and by comparing the ages of different rocks and minerals, they can determine the relative ages of different rock formations and the Earth's surface features.
consider the expression 4(8x+5)
complete 2 descriptions of parts the expression
1. the entire expression is the product of ____.
2. on its own, (8x+5) is a sum with ___.
the choices are
2 factors
3 factors
2 terms
3 terms
The entire expression is the product of two terms and 8x+5 is the sum of two terms.
What is an Algebraic Expression?An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.
Given here: The expression 4(8x+5)
Evaluating the expression we get 4(8x+5)=32x+20
The entire expression is the product of two factors 4&(8x+5)
Also the expression (8x+5) has two terms and therefore its a binomial
Thus it is the sum of two terms.
Hence, The entire expression is the product of two terms and 8x+5 is the sum of two terms.
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Write y=1/2x +8 in standard form using integers
Work Shown:
y = (1/2)x+8
2y = 2*( (1/2)x+8 )
2y = x + 16
2y - 16= x
-16= x-2y
x-2y = -16
Side note: I multiplied both sides by 2 in the second step to clear out the fraction.
The answer x-2y = -16 is in standard form Ax+By = C
A = 1, B = -2, C = -16
A researcher reports that a sample of workers with high-stress careers slept significantly less than workers in the general
population, t(49)-2.5, p<.05.
• Compute eta-squared for this one-sample t test.
• Classification of effect.
(Privitera, 2019, p. 233, Learning check 3, #4, modified)
Eta-squared is a small effect size that means the difference between the sample of workers with high-stress careers and the general population is statistically significant, but not clinically meaningful.
What is eta-squared?Eta-squared is a proportion of variation explained by a statistical model or an experimental design. It is used in ANOVA and other types of regression analysis to determine how much of a dependent variable's variation may be attributable to the independent variable (s).
In the given question, Eta-squared is computed by taking the square of the t-value (2.5 in this example) and dividing it by the sum of the t-value and degrees of freedom squares (49 in this case). The result is an eta-squared value of 0.050.
This eta-squared value corresponds to a modest impact size. This suggests that the gap between the sample of high-stress employees and the overall population is minor but statistically significant. In other words, high-stress professionals may sleep less than the general population, but the difference is not significant enough to be clinically significant.
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Which property would you use to simplify this monomial division problem?
a
O Quotient of a Power Property
O Power of a Quotient Property
Power of a Product Property
O Product of a Power Property
There are three terms in the polynomial so each term of the polynomial numerator is separately divided by the same monomial denominator.
What is a monomial ?
Monomial is polynomial in which it has only one term.
Given ,
To find Which property would you use to simplify this monomial division problem.
For example :
4a^3 - 10a^2 + 5a / 2a
Now the polynomials ( 4a^3 - 10a^2 + 5a) is written as numerator and the monomial (2a) is written as denominator
Therefore,
we get 4a^3 - 10a^2 + 5a / 2a .
Now we observe that there are three terms in the polynomial so each term of the polynomial numerator is separately divided by the same monomial denominator.
4a^3 / 2a - 10a^2 / 2a + 5a/2a
Therefore, there are three terms in the polynomial so each term of the polynomial numerator is separately divided by the same monomial denominator.
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The point (-7, 0) is on the graph of the function y = f(x). Which point cannot be on the graph of y=f(x) ?
a. (0,0)
b. (0, -7)
c. (-7, -7)
d. (7, 0)
In the end, the following is an illustration of a point that cannot appear on the graph of y = f(x): (-7, 1).
what is function ?Substances and their modifications, equations and surrounding structures, objects and their placements, and locations where they can be found are all included in the study of mathematics. The relationship between a group of inputs, each of which produces related output, is referred to as a "function." A function is a relationship between both inputs and outputs where each input produces a single, unique result. Every function has a domain and a codomain, often known as a scope. F is typically used to denote functions (x). An x is the input. Based on the following criteria, there are four primary categories of functions that are available: on functions, yet another functions, many-to-one functions, within functions, and on functions.
given
The task's purpose makes it clear that the point on the graph of y = f(x) that cannot be found.
The definition of a function, f(x), states that it is a relation that assigns just one value of y to each value of x.
As a result, the statement above suggests that the x-value -7 can only be given one y-value, which is 0, if the point (-7, 0) is on the graph of the function y = f(x).
In the end, the following is an illustration of a point that cannot appear on the graph of y = f(x): (-7, 1).
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Answer:
(-7, -7) you cannot have the same x
example:
The point (6,0) is on the graph of the function y=f(x) . Which point cannot be on the graph of y=f(x)?
(6, 3)
(4,6)
(3,8)
(4,8)
you cannot choose (6, 3)
Help with both of them please! Thank you!
The numbers to 3 significant figures are as follows:
0.0230 ≈ 0.0230
0.035 ≈ 0.0350
0.804 ≈ 0.804
3.150 ≈ 3.15
140 ≈ 140
509 ≈ 509
The eroding rate of the beach in millimetres per day is 0.109 mm per day.
How to represent decimal in three significant figures?Significant figures are the number of digits in a value. In other words, significant figures are the digits of a number that are important in terms of accuracy and precision.
Therefore, let's find the 3 significant figures of the numbers.
0.0230 ≈ 0.0230
0.035 ≈ 0.0350
0.804 ≈ 0.804
3.150 ≈ 3.15
140 ≈ 140
509 ≈ 509
A particular beach is eroding at a rate of 4cm per year. Let's convert to millimetres per day.
Therefore,
4 cm = 40 mm
365 days = 40 mm
1 day = ?
Hence,
eroding rate = 40 / 365 = 0.10958904109 per day
eroding rate = 0.109 mm per day
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Y=-2x-4 y=1/2x +6 what is the solution of the system of equation
Answer:
Step-by-step explanation:
write the abbreviation for each of the following: match the words in the left column to the appropriate blanks in the sentences on the right. make certain each sentence is complete before submitting your answer.
1. The abbreviation for femtogram is - fg.
2. The abbreviation for decimeters is - dm.
3. The abbreviation for microliter is - μL or ul.
4. The abbreviation for femtosecond is - fs.
1. Femtogram (fg): A unit of mass measurement in the International System of Units (SI). It is equal to [tex]10^{-15}[/tex] grams and is commonly used to measure the mass of small particles or atoms.
2. Decimeter (dm): A unit of length measurement in the International System of Units (SI). It is equal to 0.1 meters and is commonly used to measure small distances.
3. Microliter (μL or ul): A unit of volume measurement in the International System of Units (SI). It is equal to [tex]10^{-6}[/tex] liters and is commonly used to measure very small volumes of liquids.
4. Femtosecond (fs): A unit of time measurement in the International System of Units (SI). It is equal to [tex]10^{-15}[/tex] seconds and is commonly used to measure very short periods of time, such as in atomic and molecular physics, chemistry, and photonics.
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The complete question is -
write the abbreviation for each of the following: match the words in the left column to the appropriate blanks in the sentences on the right. make certain each sentence is complete before submitting your answer.
1. The abbreviation for femtogram is -
2. The abbreviation for decimeter is -
3. The abbreviation for microliter is -
4. The abbreviation for femtosecond is -
solve this system of equations by using the elimination method.
2x+4y=8 2x+3y=4
Hey there!
Solution:Point Form: [tex](-4,4)[/tex]Equation Form: [tex]x=-4,y=4[/tex]
Hope this helps!
Jai: IITs are producing great engineers, who ultimately end up benefiting science and technology in India, but more important is the fact that they are greatly improving the image of India in the west Vijay: No, you're mistaken. Producing great engineers who benefit science and technology in India is the most important function of IITs. Without IITs, most of our software industry wouldn't have existed.
No, what they said is not fact.
The statement "producing great engineers who benefit science and technology in India is the most important function of IITs" and "IITs are greatly improving the image of India in the West" are both important functions of IITs, and the priority of these functions may depend on individual perspectives and goals.
Some people might argue that producing engineers is more crucial for the development of India's technology and economy, while others might argue that improving the image of India in the West is equally important for increasing its global recognition and competitiveness. Both functions play important roles and it is a matter of perspective which one is considered more important.
Correct Question :
Jai: IITs are producing great engineers, who ultimately end up benefiting science and technology in India, but more important is the fact that they are greatly improving the image of India in the west
Vijay: No, you're mistaken. Producing great engineers who benefit science and technology in India is the most important function of IITs. Without IITs, most of our software industry wouldn't have existed.
What they said is fact or not? Explain.
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select the proper inverse operation to check the answer to 14+17=31
Answer:
31-17=14
Step-by-step explanation:
When you reverse it it equals the same answer
Answer:
31-14=17
Step-by-step explanation:
When We Reverse It,Will Be it Self.
write a real word multiplication problem involving whole numbers and decimals in which you would use estimation to solve then estimate to solve the problem show that your answer is reasonable
Answer:
.023
.75 X .33=.2475/11=.0225 rounded to .023
Step-by-step explanation:
Sam Is Building A Table for her gaming setup.The Length of the table is .75x.33 if she doubles the length of it then divides it by 11 then what will be the length of the table?Round to the nearest thousandths to solve your problem.
P.S:Mark Me Branlisist
integrate both sides of the differential equation you found for dp to obtain an equation for p . your equation should then include a constant that depends on initial conditions. determine the value of this constant by assuming that the pressure at some reference height y0 is p0 .
The value of this constant, by assuming that the pressure at some reference height y₀ is p₀, is p - p₀ = p.g(y₀ - y).
dp = -pg dy
At height y = y₀ and p = p₀
∫dp = ∫-pg dy
⇒p = -pgy + C Eqn(1)
Where c is the constant of integration
We know that y = y₀ and p = p₀
⇒p₀ = -pgy₀ + C
⇒C = p₀ + pgy₀
Put the value of C in Eqn(1)
⇒p = -pgy + p₀ + pgy₀
⇒p - p₀ = -pgy + pgy₀
⇒p - p₀ = pg(y₀ - y)
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