A sinusoidal function of the form y = a sin(x - c) + d is changed by increasing d by 2. The new graph will have moved right.
Define sine function.The sine function in trigonometry is the ratio of the hypotenuse's length to the opposite side's length in a right-angled triangle. To determine a right triangle's unknown angle or sides, utilize the sine function. The ratio of the perpendicular of a right-angled triangle to the hypotenuse is known as the sine of the angle. The following is the sin formula: sin = Perpendicular / Hypotenuse.
Given,
A sinusoidal function of the form y = a sin(x - c) + d is changed by increasing d by 2.
The new graph will have moved right.
For periodic functions, phase shift refers to a horizontal shift to the left or the right. The sine wave is moved to the left if c = 2. if, the sine wave is then three degrees to the right. Despite going in the opposite way from what you may anticipate, this follows the general transformational principles for all functions.
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Write an equation for a parabola with x-intercept (-3,0) and (2,0) which pae through the point (1,-20)
An equation for a parabola with x-intercept (-3,0) and (2,0) which pass through the point (1,-20) is "[tex]5x^2+5x-30[/tex]".
parabola is a major conic section that has wide applications in science and technology. know according to the condition by following intercepts we begin with an equation
[tex]y=a(x+3)(x-2)[/tex]
where a is any number that restricts the parabola to pass through (1,-20)
know we have to choose a for what the above equation got its require achievements. substitute (1,-20) in [tex]y=a(x+3)(x-2)[/tex] we get
[tex]-20=a(1+3)(1-2)\\\\-20=a(4)(-1)\\\\a=5[/tex]
substituting a back in the first equation we get the equation of the parabola. so, the parabola has an equation y= f(x)=[tex]5x^2+5x-30[/tex].
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At the local health food tore, macadamia nut are priced at 0. 45 per ounce. Taylor meaure out 1 3/4 of macadamian nut. How much will taylor pay for the macadamia nut
Taylor has to pay 0.7875 ounces for the macadamia nut.
What is the rule of multiplication?
If a, b, and c are three numbers given to us and any expression is expressed as [tex]a\frac{b}{c}[/tex] then it can be expressed as
[tex]a\frac{b}{c}[/tex] = [tex]\frac{a*c + b}{b}[/tex]
It is given that, Taylor measures out [tex]1\frac{3}{4}[/tex] of macadamia nut.
[tex]1\frac{3}{4} = \frac{1*4 + 3}{4}\\\\ 1\frac{3}{4} = \frac{7}{4}[/tex]
= 1.75 macadamia nut.
Per ounce is at 0.45
then 1.75 macadamia nuts will cost her = 1.75 * 0.45
= 0.7875 ounces.
Hence, Taylor has to pay 0.7875 ounces for the macadamia nut.
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The sum of √12 and 5√3 is?
Answer: 7*[tex]\sqrt{3}[/tex]
Step-by-step explanation:
what type of variable would necessitate using a hypothesis test of the population proportion rather than a test of the population mean?
Categorical data are the sort of variable that would need utilizing a population proportion hypothesis test rather than a population mean hypothesis test.
Categorical data – what is it?Data that cannot be easily gathered by counting is referred to as categorical data, which is another name for qualitative data. Hypothesis testing may be used with this type of data. Data are used in hypothesis testing to draw conclusions about population characteristics.
The findings are reached after first proposing a null hypothesis. Therefore, for qualitative or categorical data, a hypothesis test of the population is performed rather than a numerical test of the population mean.
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How do you solve a system of equations with X and Y?.
A system of linear equations is a collection of two or more linear equations that have two or more variables each. All of these equations are considered at once.
Finding a numerical value for each variable in the system that will simultaneously satisfy all of the system's equations is necessary to identify the one and only solution to a system of linear equations. There could be an unlimited number of solutions for some linear systems, whereas others might not have any. There must be at least as many equations as there are variables for a linear system to have a singular solution. However, this does not ensure an original answer. There is always one answer to a set of equations that makes sense. A consistent system, like the one we just examined, is said to be an independent system if it only has one solution. The two lines cross at one location in the plane and have different slopes. If the equations' slopes and y-intercepts match, the system is said to be consistent and considered a dependent system.
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what is the formula used to find the degrees of freedom used to choose the correct t-distribution in a two sample test of means with unknown but equal population standard deviation?
Some calculations of degrees of freedom with multiple number of parameters or relationships use the formula
Df = N - P,
where P is the number of different parameters or relationships.
For example, in a 2-sample t-test, N - 2 is used because there are two parameters to estimate.
What Are Degrees of Freedom?
The maximum number of logically independent values—that is, values with the freedom to change—in the data sample is referred to as the degree of freedom. If there is a remaining requirement for the data sample, specific data sample items or parameters must be chosen after the degrees of freedom quantity has been chosen.The formula to determine degrees of freedom is:
Df = N − 1
where:
Df =degrees of freedom
N=sample size
The number of independent variables that can be calculated in a statistical study is known as the degrees of freedom. These variables' values are not constrained, but if the data set is to meet the estimate parameters, the values do impose limitations on other variables.To know more about degree of freedom check the below link:
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How is the tax base of an area calculated?.
The total market value of all the assets, properties, and income in a given region or jurisdiction is what is referred to as the tax base. The tax base must be multiplied by the tax rate to determine the overall tax obligation: Tax Base x Tax Rate equals Tax Liability.
Describe the tax base?
The whole amount of income, property, assets, consumption, transactions, or other economic activity that a tax authority is allowed to tax is known as the tax base.
What is tax base formula?
Multiplying the tax base by the tax rate yields the tax obligation. The tax liability divided by the tax rate would be the result. Tax Liability/Tax Rate in the Tax Base Formula.Learn more about tax base
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Find all of the zeros for f(x).
f(x)=x²-3x³-27x² - 13x +42
x=1, -29+√337/2 and -29-√337/2 are zeros of function f(x)=x²-3x³-27x² - 13x +42
What is Polynomial?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.
We need to find zeros of f(x)=x²-3x³-27x² - 13x +42
f(x)=-3x³-26x²-13x+42
Use division method
1 -3 -26 -13 42
0 -3 -29 -42
-3 -29 -42 0
-3x²-42x-42=0
x=1 is a zero
Now use the quadratic formula to find zeros
x=42±√(42)²-4(-3)(-42)/-6
x=-29+√337/2
and x=-29-√337/2
Hence, x=1, -29+√337/2 and -29-√337/2 are zeros of function f(x)=x²-3x³-27x² - 13x +42
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Answer:
-3,-2,1,7
Step-by-step explanation:
That's what Acellus said it was <3
The two polygons are similar, find the missing length. (the ?)
4 is the length of missing length of polygon.
What are Polygons?Polygon, in geometry, any closed curve consisting of a set of line segments (sides) connected such that no two segments cross. The simplest polygons are triangles (three sides), quadrilaterals (four sides), and pentagons (five sides)
Similar polygons are two polygons with the same shape, but not the same size. Similar polygons have corresponding angles that are congruent, and corresponding sides that are proportional.
16/2=8
15.4/2=7.7
16/2=8
8/2=4
Hence, 4 is the length of missing length.
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The pumped-storage hydroelectricity pumps water from the lower elevation reservoir to a higher elevation to store electricity. Suppose that the water is pumped out
from the upper elevation which is h meters above the top to the lower reservoir. The
lower reservoir has the shape of half ball with radius r meters. The lower reservoir is
full at the beginning. How much work should be done given the density of water is ρ
kg/m3? You do not need to replace the acceleration g as 9.8m/sec2. Just leave g in
the expression.
The work done by the water from the reservoir, traveling a distance, h, meters, can be found using the expression; (2/3)·π·r³×ρ×g×h
What is the relationship between work energy and power?Energy is the ability to do work, and power is the rate at which work is done.
The work done is the product of the force applied and the distance traveled in the direction of the force.
Radius of the reservoir = r
Density of the water = ρ
Height of the upper elevation = h
Gravitational acceleration = g
The force is the weight of the water pumped
Weight = Mass × Gravity
Mass = Density × Volume
Therefore;
Volume of the water = (2/3)·π·r³
Mass of the water = (2/3)·π·r³ × ρ
Weight of the water = (2/3)·π·r³ × ρ × g
The work done by the water is therefore;
The work that should be done is, W = (2/3)·π·r³ × ρ × g × h
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How do you know what is ABC on a triangle?.
The three angles of the triangle ABC are ∠ABC, ∠BCA, and ∠CAB. These angles are also called ∠B, ∠C, and ∠A, respectively.
What does ABC mean in a triangle?
In triangle ABC, the sides are AB, BC, and CA. The angle formed by any two sides of a triangle is the angle of the triangle, denoted by the symbol ∠. A triangle has three angles. The three angles of the triangle ABC are ∠ABC, ∠BCA, and ∠CAB. These angles are also called ∠B, ∠C, and ∠A, respectively.
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What is the formula of obtuse angle triangle?.
The Formula of Area of Obtuse Triangle is equal to ½ × b× h .
and by using Heron's formula,
A = √(S(S-a)(S-b)(S-c)) ; S = (a+b+c)/2
A closed two-dimensional figure with three sides of equal or unequal length and three corners of equal or unequal angles is called a triangle.
Obtuse triangle: A type of triangle with the following properties:
One of the angles of the triangle is greater than the other two angles (>90 degrees). One of the angles is obtuse, this triangle is known as obtuse triangleThe sum of interior angles of a triangle is always 180 degrees. Therefore, the other two angles of an obtuse triangle are acute.The sum of the squares of the shortest sides of an obtuse triangle is equal to the square of the largest side of the triangle.Area formula of obtuse triangle :
Area of obtuse triangle = ½ × b × h
where b --> base of triangle
h ---> height of triangle.
The area of a triangle can also be found using Heron's formula.
A = √(S(S-a)(S-b)(S-c)),
where s is half the perimeter of the triangle and a, b, c are the three sides of the triangle.
the perimeter of the triangle = a + b + c cm then
S = (a + b + c)/2
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Determine which of the lines, if any, are parallel or perpendicular. Explain. Line a: y=6x−2 Line b: 6y=−x Line c: y+6x=1
Line y=6x−2 and line 6y=−x are perpendicular.
What is slope ?Slope is a notation that shows that a surface of which one end or side is at a higher level than another surface.
In the equation of line y=mx+c, m represents the slope of the line.
The given lines are
a: y=6x−2 (1)
b: 6y= -x (2)
and c: y+6x=1 (3)
To determine lines are parallel or perpendicular,
Find the slope of the lines, use the standard equation of line is y=mx+c,
Compare the given equations with standard equation of line,
Slope of line (1) m₁= 6
Slope of line (2) m₂ = -1/6
Slope of line (3) m₃ = -6
By multiplying slope of line (1) and (2), gives -1
Implies that line (1) and (2) are perpendicular to each other.
Therefore, Line y=6x−2 and line 6y=−x are perpendicular.
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Given the number of rows and the number of columns, write nested loops to print a rectangle.
Answer:
You need to use a nested for loop. Use the range() builtin to produce an iterable sequence. The outer for loop should iterate over the number of rows.
Step-by-step explanation:
Use the range() builtin to produce an iterable sequence. The outer for loop should iterate over the number of rows overtime.
What is a shape that is not a quadrilateral?
Answer:
triangle
Step-by-step explanation:
a quadrilateral is a four-sided figure, but a triangle is three-sided, so a triangle isn't a quadrilateral.
2 of 8
The angle marked a = 109⁰.
Work out the angle marked x.
Answer:
x = 71 degrees
Step-by-step explanation:
Answer:
Step-by-step explanation:
180-109
x=71
Vic's favorite cookie recipe uses 250 grams of flour for every 170 grams of butter. Imani made cookies using 750 grams of flour for every 630 grams of butter.
Vic's recipe:
170 g of butter = 250 g of flour
1 g of butter = 250 ÷ 170
= 25 / 17 g of flour
Imani's recipe:
630 g of butter = 750 g of flour
1 g of butter = 750 ÷ 630 = 25 / 21 g of flour
Compare:
25 / 21 < 25 / 17
⇒ Imani uses less flour in her cookies than Vic
Imani's cookies are more dense.
Therefore, we get that Imani uses less flour in her cookies than Vic.
Imani uses less flour in her cookies than Vic because vic uses 25 / 17 g of flour while Imani uses 25 / 21 g of flour.
What is density and example?How much "stuff" is contained in a specific quantity of space is determined by its density. For instance, a block of the harder, lighter element gold (Au) will be denser than a block of the heavier element lead (Pb) (Au). Styrofoam blocks are less dense than bricks. Mass per unit volume serves as its definition.
Does density mean heavier?A substance's density is a measurement of how heavy it is in relation to its size. When placed in water, an object will float if its density is lower than that of the water, whereas it will sink if its density is higher.
if we see Vic's recipe:
170 g of butter = 250 g of flour
1 g of butter = 250 ÷ 170
= 25 / 17 g of flour
and Imani's recipe:
630 g of butter = 750 g of flour
1 g of butter = 750 ÷ 630 = 25 / 21 g of flour
Compare:
25 / 21 < 25 / 17
so Imani uses less flour in her cookies than Vic
moreover imani's cookies are more dense.
Therefore, we get that Vic uses more flour than imani.
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What i 1 and 3 over 4 time 2 and 2 over 3? 2 and 1 over 2 3 and 5 over 12 4 and 2 over 3 4 and 6 over 7
a)If if 1 and 3 over 4 time 2 and 2 over 3 then our answer is 14/3 and
b) If 2 and 1 over 2 3 and 5 over 12 4 and 2 over 3 4 and 6 over 7,then our answer is 647/42
a)We have 1 and 3 over 4 or in other word if we convert this in improper fraction it is 7/4
Similarly, we have 2 and 2 over 3,in improper fraction it is 8/3
Now ,we multiply both the number to find the required answer =(7/4)×(8/3)=14/3
B) In b part we need to follow the same procedure which we followed in part a.
We have,2 and 1 over 2 3 and 5 over 12 4 and 2 over 3 4 and 6 over 7
On Converting all the mixed fraction into improper fraction
5/2, 41/12, 14/3 , 34/7
Take LCM of 2,12,3,7
LCM = 84
Convert all the fraction into proper fraction
(5×42)/(2×42)=210/84--------(eq1)
(41 × 7)/(12×7) =287/84----------(eq2)
(14 × 28)/(3×28)= 292/84--------(eq3)
(34 ×12 )(7×12) =408/84----------(eq4)
Now add all equations
(210+287+ 392+408)/84
= 1294/84=647/42
Hence, our answers are a)14/3 and b)647/42
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How do you state congruent triangles?.
If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.
Given,
We have to state that the triangles are congruent;
Here,
Congruent state;-
In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
Conditions for congruent triangles;-
If two triangles satisfy one of the following conditions, they are congruent:
The three corresponding side pairings are all equal. The comparable angles between two pairs of corresponding sides are equal. The corresponding sides between two pairs of corresponding angles are equal.That is,
If each of the three corresponding sides and each of the three corresponding angles in two triangles equals one another, then the two triangles are said to be congruent.
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are the following statements true or false? ? 1. if the columns of an matrix are orthonormal, then is the orthogonal projection of onto the column space of ? 2. for each and each subspace , the vector is orthogonal to . ? 3. if is orthogonal to and and if , then must be in . ? 4. the orthogonal projection of onto a subspace can sometimes depend on the orthogonal basis for used to compute ? 5. if is in a subspace , then the orthogonal projection of onto is itself.
The given statements are true or false as following:
TrueTrueTrueFalse TrueWe have given some statements about matrix and subspace and we have to check whether the statements are true or false .
1. True
The columns of U are linearly independent and thus form an orthonormal basis for Col U. So, projcolU y = UU^T*y for all y in R^n.
2. True
The statement is true because y can be written uniquely in the form y = projw y+z where y − projw y is in W and Z is in W⊥ and it follows that Z = projw y
3. True
since z is orthogonal to u1 and to u2 it is orthogonal to every vector in W = Span{u1, u2}, a set that spans W.
4. False
The uniqueness property of the orthogonal decomposition y = y^ + z indicates that, no matter the basis used to find it, it will always be the same.
5. True
For an orthogonal basis of W, B = u1, ..., uP y and projw y can be written as linear combinations of vectors in B with equal weights.
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For what value of a does 9 = (startfraction 1 over 27 endfraction) superscript a + 3?.
When the start fraction is 1 and the end fraction is 27, the value is a=-11/3.
What is meant by a fraction?A fraction is a part of a whole or, more broadly, any number of equal parts. In ordinary English, a fraction describes the number of components of a specific size and consists of a numerator displayed above a line (or before a slash like 12) and a non-zero denominator displayed below (or after) that line.
In addition to common fractions, numerators and denominators are used in rare fractions such as compound fractions, complex fractions, and mixed numerals.
Positive common fractions have natural integers as their numerator and denominator.
Here we need to find the value of n for which 9=(1/27)ᵃ⁺³
Now, we have to rewrite with a base of 3 we get,
3²=3⁻³.3ᵃ⁺³
2=-3(a+3)
2=-3a-9
=2+9=-3a
11=-3a
a=-11/3
Therefore, the values is a=-11/3
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during a recent soccer season, the starting forward made 10 out of 27 shots on goal. at this rate, how many goals would the forward make next season if 35 shots on goal were taken? explain how you determined your answer.
Step-by-step explanation:
10 goals out of 27 attempts gives a ratio of
10/27 = 0.37037037... goals per shot.
now, for 35 shots we expect
35 × 10/27 = 350/27 = 12.96296296... ≈ 13 goals
uniform thin rod of length 0.500 m and mass 4.00 kg can rotate in a horizontal plane about a vertical axis through its centre. The rod is at rest when a 3.00 g bullet travelling in the rotation plane is fired into one end of the rod. In the view from above, the bullet's path makes angle θ=60.0o with the rod. If the bullet lodges in the rod and the angular velocity of the rod is 10 rad/s immediately after the collision, what is the bullet's speed just before impact?
The speed of bullet just before the impact would be 1.28 x 10^3 meter per second.
Let the speed of the bullet before impact be 'V₀.'
According to the question, we are given the mass of the rod 'M' = 4 kg. Length of the rod 'l' = 0.5 meter. The angle of the bullet's path 'Θ' = 60 degree and the angular velocity 'ω' = 10 rad/s.
For bullet, the mass 'M' = 3 g = 3 x 10^3 kg. and the velocity is V₀.
According to the law of conservation of momentum, we get
L(bullet) = l (bullet + rod)
mV₀ (l/2 sinΘ) = Iω
mV₀ x (l/2 sinΘ) = [ ml²/ 12 + m (l/2) ²] x ω
By cancelling the like terms, we get the equation as,
V₀ = (m +3m) x l/6m sin Θ
By calculating the above equation, we get,
V₀ = 1.28 x 10^3 meter per second.
Therefore, the speed of bullet before the impact is 1.28 x 10^3 meter per second.
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Let f be a twice-differentiable function on R such that f′′ is continuous. Prove that f(x)f′′(x)<0 cannot hold for all x. I have been able to think of specific examples of f(x) in which f(x)f′′(x)<0 does not hold, but I have not been able to come up with specific values of x for which f(x)f′′(x)<0 does not hold. Any help is greatly appreciated!
Must assume positive values
f is above this line outside [a, b]
So, f(x)f′′(x)<0 cannot hold for all x.
Given,
In the question:
Let f be a twice-differentiable function on R such that f′′ is continuous. Prove that f(x)f′′(x)<0 cannot hold for all x.
Now, According to the question:
Assume that :
f"(0) > 0
Then, f(0) < 0 and as neither factor can change sign.
f"(x) > 0 > f(x) for all x ∈ R and f is strictly convex.
Pick a < b with f(a) ≠ f(b).
Then the line through (a f(b)) and (b f(b)) intersect the x - axis.
By convexity, f is above this line outside [a, b],
Hence, Must assume positive values
f is above this line outside [a, b],
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The triangles below are similar.
What does y equal to?
The value of y after solving the pair of similar triangle is 15.
What is similar triangle?Similar shapes are enlargements of each other using a scale factor.
To find the value of y from the similar triangle below, we use the formula below.
Note: The ratio of the corresponding sides of two similar triangle are equal
Formula:
22/10 = 33/ymake y the subject of the equation above
y = 33×10/22y = 15Hence, the value of y is 15
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What if the base of an exponent is a 1?.
Answer:
The answer will always be 1
Step-by-step explanation:
The exponent is how many times the base number is multiplied by itself
For example 2^4 means 2 multiplied by itself 4 times or 2*2*2*2
But it doesn't matter how many times you multiply 1 by itself and it will always be 1
For example 1^5 is 1*1*1*1*1 which is equal to 1. you can even have 1^16 which is 1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1 but the answer is still 1 so the answer will always be 1
Each possible outcome of the number cube has the same theoretical probability. what is that probability?
It is possible to determine the theoretical probability of an occurrence without doing the event itself. A number cube has 6 alternative outcomes, giving each one a theoretical probability of 1 out of 6.
For example, the likelihood of drawing an ace at random is 4 out of 52 since there are 4 aces in a deck of cards. The probability of hitting a double bullseye on a regular dartboard is roughly 78 out of 100,000 because the area of the double bullseye in the center is 0.078% of the dartboard's overall area.
The likelihoods of potential possibilities are instead calculated using the frequencies of past outcomes in empirical probability. They are merely projections. The empirical chance of rolling a 4 or a 5 on the following roll is 58 out of 96 since you rolled 4s and 5s more often than any other number when you rolled the number cube.
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Answer: 1/6 is the probability
How do you prove that SAS is congruent?.
By defining the SAS theorem of congruency, we have proved that SAS is congruent.
Congruency;-
Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.
Here,
We have to prove that SAS is congruent.
For that, lets consider the SAS theorem of congruence,
According to the side-angle-side (SAS) theorem of congruence, two triangles are congruent if their corresponding two sides and their included angles are precisely equivalent to those of the first triangle.
That is,
We proved by the definition SAS is congruent
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How do you find the equation of a line passing through the point and parallel to the y-axis?.
The equation of a line passing through the point (a,0) and parallel to the y-axis is x = a
The equation of line parallel to y axis is of the form x = a, and it cuts the x-axis at the point (a, 0). Here all the points on this line parallel to the y-axis will have the same x coordinate of a. Further the equation of line parallel to y-axis and cutting the x-axis at point (a, 0) is at a perpendicular distance of 'a' units from the y-axis
The equation of line parallel to the y axis and cutting the positive x-axis passes through the first and the fourth quadrant. And the equation of line parallel to the y axis and cutting the negative x-axis passes through the second and the third quadrant of the coordinate axes.
To find the equation of line passing through the point and parallel to y-axis:
Let Line cut the x-axis at point a .
So , the equation of line will be x = a
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generate a scatterplot of the variables. describe the relationship between gre scores and the chance of admission.
"Scatterplot is a quality controle tool",which shows us the increase or decrease of the function.Obviously it called the "Scatter Diagram".
It's totaly depand upon XY corelation.
In scatterplot the two variables are very important that are :
1. Indipendent
2. Dependent
To depict the values for two different numerical variables, dots are used in a scatter plot (also known as a scatter chart or scatter graph). Values for each data point are shown by the location of each dot on the horizontal and vertical axes. The relationships between variables are visualized using scatter plots.
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