The triangle ABC has sides of length a = 106.5, b = 126, and c = 162, and angles A = 83.3, B = 43, and C = 53.7. Additionally, we have A₁ = 32.7, A₂ = 32.7, and C₁ = 8.2.
To solve the triangle ABC, we can use the Law of Cosines and the Law of Sines.
First, we can use the Law of Cosines to find the length of side a, which is opposite angle A:
a² = b² + c² - 2bc cos(B)
a² = (126)² + (162)² - 2(126)(162) cos(43)
a = 106.5
Next, we can use the Law of Sines to find angle A:
sin(A) / a = sin(B) / b
sin(A) = (a sin(B)) / b
A = 83.3
To find angle C, we can use the fact that the angles of a triangle add up to 180:
C = 180 - A - B
C = 53.7
Next, we can use the given relationship between angles A₁ and A₂ to find their values:
A₂ = A₁ = 2C₁
A₁ + A₂ + C₁ = 180
A₁ + 2A₁ + A₁/2 = 180
5.5A1₁ = 180
A₁ = 32.7
A₂ = 32.7
C₁= 8.2
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Which equation represents the function?
The equation from the graph of the function is g(x) = |x - 1|
How to determine the equation from the graphFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the function
The function is an absolute value function
The parent function of an absolute value function is:
y = |x|
The function y = |x| is shifted right by 1 units
Using the above as a guide, we have the following:
g(x) = f(x - 1)
This represents a translation to the right by 1 unit
So, we have
g(x) = |x - 1|
Hence, the translation is g(x) = |x - 1|
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D. Erin has two dogs, a beagle and a Great Dane. Her Great Dane weighs twice as much as the beagle plus 2 more pounds. If the Great Dane weighs 72 pounds, how much does the beagle weigh?
The weight of the beagle D. Erin has weighs 35 pounds.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
From the given information, Let the weight of the beagle is 'x'.
So, the weight of a Great Dane is (2x + 2) pounds.
Therefore, 2x + 2 = 72.
2x = 70.
x = 35 pounds.
So, The beagle weighs 35 pounds.
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if a coin is tossed thrice successively, what is the probability of obtaining at least one head and at least one tail?'
The probability of obtaining at least one head and at least one tail when a coin is tossed thrice successively is 7/8.
In probability theory, the likelihood of a particular event occurring is measured in terms of probability. When it comes to tossing a coin, there are two possible outcomes: heads or tails.
To calculate the probability of obtaining at least one head and at least one tail when a coin is tossed thrice successively, we need to use the concept of complementary events. Complementary events are two events that make up the whole sample space
Let's first calculate the probability of not getting at least one head and at least one tail. The only way to not get at least one head and at least one tail is to get either three heads or three tails. The probability of getting three heads or three tails in a row is (1/2)³ or 1/8 since there are 8 possible outcomes when a coin is tossed thrice successively.
Now we can calculate the probability of obtaining at least one head and at least one tail by subtracting the probability of not getting at least one head and at least one tail from 1.
1 - 1/8 = 7/8
Therefore, the probability of obtaining at least one head and at least one tail when a coin is tossed thrice successively is 7/8.
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Suppose that $2000 is invested at a rate of 5.3%, compounded semiannually. Assuming that no withdrawals are made, find the total amount after 9 years.
Do not round any intermediate computations, and round your answer to the nearest cent.
Answer:
Rounding to the nearest cent, the total amount after 9 years is $3182.67.
Step-by-step explanation:
The formula for compound interest is given by:
A = P(1 + r/n)^(nt)
where:
A = final amount
P = principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case, P = 2000, r = 0.053, n = 2 (compounded semiannually), and t = 9.
Plugging in these values, we get:
A = 2000(1 + 0.053/2)^(2*9)
= 2000(1.0265)^18
≈ 3182.67
Rounding to the nearest cent, the total amount after 9 years is $3182.67.
In an orthonormal coordinate system, what are the coordinates of all the points generated from (x, y, z) by repeatedly applying the following operations? (a) A mirror whose plane is perpendicular to the y-axis, and that passes through the origin. (b) A four-fold rotation whose axis is coincident with the x-axis, and that passes through the origin. (c) A 4 rotoinversion whose axis is coincident with the x-axis, and that passes through the origin. (d) A three-fold rotation whose axis passes through the origin and the point (1,1,1). (e) A 3 rotoinversion whose axis passes through the origin and the point (1, 1, 1).
The coordinates of all the points generated from (x, y, z) by repeatedly applying the operations in the order given are: (a) (x, -y, z); (b) (x, y, -z); (c) (-x, y, -z); (d) (-x, z, y); and (e) (x, -z, -y).
For (a), a mirror perpendicular to the y-axis and passing through the origin reflects the coordinates in the y-axis, so the new coordinates will be (x, -y, z).
For (b), a four-fold rotation whose axis is coincident with the x-axis and passing through the origin rotates the coordinates around the x-axis by 90 degrees, so the new coordinates will be (x, y, -z).
For (c), a 4 roto inversion whose axis is coincident with the x-axis and passing through the origin inverts the coordinates in the x-axis, so the new coordinates will be (-x, y, -z).
For (d), a three-fold rotation whose axis passes through the origin and the point (1,1,1) rotates the coordinates around the axis by 120 degrees, so the new coordinates will be (-y, -z, x).
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i need help with this
Mr. Utivich needs to buy an equal number of canvasses and paint sets for a community center art class. Each canvas costs $4 and each paint set costs $7.25. If he has $120 to spend on the art supplies, then the inequality 4x+7.25x≤120
can be used to find the number of each item he can buy. How much money will he have left after buying the greatest number of canvasses and paint sets?
Answer:
Step-by-step explanation:
23x
after a long series of calls to fib(k1), fib(k2),. . . fib(km), with k1, k2, . . . km being random values between 0 and maxmemo, what will be the big-o for the expected work performed by a call to fib(n) (where n < maxmemo)?
The big-o for the expected work performed by a call to fib(n) (where n < maxmemo) will be constant.
If the function is implemented with memoization, i.e., storing the results of previously calculated Fibonacci numbers to avoid redundant calculations, the expected work performed by a call to fib(n) would be O(1) for n < maxmemo, regardless of the number of previous calls made to fib.
This is because if the function has already calculated fib(n) earlier, it can simply look up the result in the memoized dictionary and return the stored value without performing any additional calculations. Otherwise, it would calculate fib(n) once and store the result in the memoized dictionary for future lookups.
Therefore, the expected work performed by a call to fib(n) is constant, O(1), as long as the previously calculated Fibonacci numbers are stored in memory using memoization. The number of previous calls made to fib has no impact on the expected work performed by a call to fib(n) as long as n is less than maxmemo.
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A die with six faces has the number 1 painted on three of its faces, the number 2 painted on two of its faces, and the number 3 painted on one face. Assume that each face is equally likely to come up.
(a) Find the sample space for this experiment.
(b) Find P(odd number).
(c) If the die were loaded so that the face with the 3 on it were twice as likely to come up as each of the other five faces:
(i) Find the probability of the single events.
(ii) Find P(even number).
Assuming that each face is equally likely to come up.
(a) The sample space for this experiment = {1, 2, 3}
(b) P(odd number) = 2/3
(c) If the die were loaded so that the face with the 3 on it was twice as likely to come up as each of the other five faces:
(i) The probability of the single events, P(3) = 2/7
(ii) P(even number) = 1/3
(a) The sample space for this experiment is the set of all possible outcomes, which are the numbers 1, 2, and 3 that can appear on the face of the die.
Sample space = {1, 2, 3}
(b) To find the probability of getting an odd number, we need to find the probability of getting a 1 or a 3. There are 3 faces with the number 1 and 1 face with the number 3, so there are 3 + 1 = 4 faces that result in an odd number. There are 6 faces total, so the probability of getting an odd number is 4/6 = 2/3.
P(odd number) = 2/3
(c)
(i) If the die were loaded so that the face with the 3 on it was twice as likely to come up as each of the other five faces, then each of the other five faces would have a probability of 1/7 of coming up, and the face with the 3 on it would have a probability of 2/7 of coming up.
P(1) = P(2) = 1/7
P(3) = 2/7
(ii) To find the probability of getting an even number, we need to find the probability of getting a 2. There are 2 faces with the number 2, so there are 2 faces that result in an even number. There are 6 faces total, so the probability of getting an even number is 2/6 = 1/3.
P(even number) = 1/3
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if PQRS is a parallelogram find the value for x and y
3y
7x+5
x+29
8y-35
Diagonals of a parallelogram bisect each other.
[tex]x+29=7x+5 \implies x=4 \\ \\ 3y=8y-35 \implies y=7[/tex]
Draw the image of triangle △ABC under a dilation whose center is P and scale factor is 3
The Triangle ABC has been dilated through point p and scale factor 3 to produce this finished picture.
What exactly is a triangle?Having three sides, three angles, and three points, a triangle is indeed a closed, two-dimensional object. A hexagon also includes a triangular. Triangles can be found in a variety of everyday objects, such as sandwiches, traffic signals, clothes hooks, and billiards racks.
Assume point P as origin then.
P has coordinate (0,0).
And point A has coordinate (-4,0).
point B has coordinate (0,-3).
point C has coordinate (-4,-3).
P(0,0), A(-4,0) B(0,-3) C(-4,-3).
Since the triangle goes an dilation with center at P and scale factor 3.
Then k=scale factor =3.
Now the new coordinate of Triangle is given by A',B' and C', whose coordinate in (x, y) plane is calculated as.
[tex](\mathrm{x}, \mathrm{y}) \rightarrow(\mathrm{kx}, \mathrm{ky})[/tex]
Now calculating the Coordinates on dilated triangle
A'=3(-4,0)=(-12,0)
B'=3(0,-3)=(0,-9)
C'=3(-4,-3)=(-12,-9).
We will calculate the coordinates of dilated triangle assuming the point P as origin
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Find the quotient. 1/4 2 2/3
When finding the quotient of 5016 divided by 11, Issac first divides 50 by 11 as shown. What value does the digit 4 have in the quotient?
Answer:
I'm not sure, but the quotient is divided, so 5016/11
Step-by-step explanation:
5016/11, and then 50/11, and find out the answer.
C. What does this slope tell you about the relationship between lengths and width: of rectangles with perimeter 24?
Using linear function, the slope of -1 means that when one of the ratio of dimension is increased by 1, the other is decreased by 1.
What is a linear function?A linear function is modeled by:
y = mx + b
Here, m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
Also shown as b is the y-intercept, which is the value of y when x = 0.
Given that the lengths and the widths are interchangeable, that is, either can be considered as the input or as the output.
The slope of -1 means that when the input in increased by 1, the output is decreased by -1, that is;
= length/width
This is increased by 1, and the other is decreased by 1.
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National results for the SAT test show that for college-bound seniors the average combined SAT Writing, Math and Verbal score is 1500 with a standard deviation of 250. National results for the ACT test show that for college-bound seniors the average composite ACT score is 20.4 with a standard deviation of 4.8.
Sean took both the SAT and the ACT college entrance exams. His SAT score was 1700 and his ACT score was 24. He wants to know on which test he performed better.
Find the z-scores for his result on each exam.
Comparing the z-scores, we can see that Sean's SAT score is slightly higher relative to the mean and standard deviation of the SAT population than his ACT score is relative to the mean and standard deviation of the ACT population.
How to find Z-score value?To find the z-score for Sean's SAT score, we use the formula:
z = (x - μ) / σ
where x is Sean's SAT score, μ is the population mean (1500), and σ is the population standard deviation (250). Substituting the values, we get:
z = (1700 - 1500) / 250 = 0.8
Therefore, Sean's z-score on the SAT is 0.8.
To find the z-score for Sean's ACT score, we use the formula:
z = (x - μ) / σ
where x is Sean's ACT score, μ is the population mean (20.4), and σ is the population standard deviation (4.8). Substituting the values, we get:
z = (24 - 20.4) / 4.8 = 0.75
Therefore, Sean's z-score on the ACT is 0.75.
Comparing the z-scores, we can see that Sean's SAT score is slightly higher relative to the mean and standard deviation of the SAT population than his ACT score is relative to the mean and standard deviation of the ACT population.
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given: cn perpendicular to ab; h is the geomtric mean between d and e. prove abc is a right triangle
Pythagorean theorem and its converse to prove that triangle ABC is a right triangle.
The converse of Pythagorean theorem states that if the sum of the squares of two sides of a triangle is equal to the square of the third side, then the triangle is a right triangle.
Let's begin by visualizing the given triangle ABC and the line CN that is perpendicular to side AB. Since CN is perpendicular to AB, we can say that triangle ACN and triangle BCN are right triangles (as the angle at C is 90 degrees).
Now, let's focus on the point H that is the geometric mean of points D and E. This means that DH multiplied by HE is equal to CH squared (as per the definition of geometric mean).
We can represent this relationship using the Pythagorean theorem as well. Since triangle CDH and triangle CEH are right triangles (as angle C is 90 degrees), we can say that:
CD² + DH² = CH² (using Pythagorean theorem for triangle CDH)
CE² + EH² = CH² (using Pythagorean theorem for triangle CEH)
From the given relationship of geometric mean, we can substitute CH² in the above equations and get:
CD² + DH² = HE*DH
CE² + EH² = HE*EH
Adding these two equations, we get:
CD² + CE² + DH² + EH² = HE*(DH + EH)
AB² = 4HE² (using the fact that DH + EH = DE = 2HE)
This equation gives us an important insight about the triangle ABC. It tells us that the sum of the squares of the sides (AB²) is equal to four times the square of the length HE (4HE²).
Now, we can use the converse of Pythagorean theorem to prove that triangle ABC is a right triangle.
In our case, we have AB² = 4HE², which satisfies the converse of Pythagorean theorem. Therefore, we can conclude that triangle ABC is a right triangle.
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can someone please help me? ill give brainlist
The true statement is: The difference in height between the whale and the plane is 11,835 feet.
How to find the true statementWe can calculate this difference by subtracting the height of the whale from the height of the plane:
= Height of plane - Height of whale
= 10,300 feet - (-1,535 feet)
= 11,765 feet
Therefore, the difference in height between the whale and the plane is 11,765 feet.
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What is the most important thing to know when working with circle
theorems?
a) identifying the theorem by looking at the information provided
b) identify the angles
c) identifying arcs
d) B and C Only
Identifying the theorem is the most important step while working with circle theorems.
What is a circle?Circle is a round plane figure whose boundary (circumference) consists of points equidistant from a fixed point (centre). The general equation of the circle is -x² + y² = r²
Given are the points about circle theorems.
While working with circle theorems, identifying the theorem by looking at the information provided is the most important step.
Therefore, identifying the theorem is the most important step while working with circle theorems.
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samantha mixes some amount of 25% sugar syrup with x grams of 10% sugar syrup. the result is120 grams 15% sugar syrup. how many grams of 25% sugar syrup did samantha use?
Answer:
Final mixture is 120 gm
x = 10% then (120-x) = 25%
.25(120-x) + .1 (x) = .15 (120) solve for x= 10% amount
then 25% amount = 120-x
Step-by-step explanation:
Reflect (9, 3) across the y-axis.
Then reflect the result across the x-axis.
What are the coordinates of the final point?
Evaluate xy + 2x if x = 7 and y =5
Answer:
Step-by-step explanation:
35 + 2x
Answer:
xy+2x
x=7
y=5
input the value of x and y in the equation.
7×5+(2×7)
=35+14
=49
What is the surface area of this cylinder? Use ≈ 3.14 and round your answer to the nearest hundredth. 9.4 yd 18.6 yd square yards
The surface area of the cylinder has a radius of 9.4cm and a height of 18.6 cm is 1098.56 square centimeters.
What is the surface area of this cylinder?The surface area of this cylinder is defined as the product of the radius of the base and the height of the cylinder.
The surface area of this cylinder = (2π x r)h
We have given a radius of the base is 9.4 cm and the height of the cylinder is 18.6 cm.
The surface area of this cylinder = (2π x r)h
= (2π x 9.4)18.6
= (59.06)18.6
= 1098.56
Thus, The surface area of the cylinder has a radius of 9.4cm and a height of 18.6 cm is 1098.56 square centimeters.
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Are the two triangles similar? How do you know?
A.)no
B.)yes; by AA
C.)yes; by SAS
D.)yes; by SSS
Answer:
No
Step-by-step explanation:
At least two sides will have to be the same.
In Exercises 21 and 22 , determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system. 21. [ 2 4 3 6 h 7]
22. [ 1 5 −3 h −2 −7]
The original matrix [ 1 5 −3 h −2 −7] and [ 2 4 3 6 h 7] is the augmented matrix of a consistent linear system, regardless of the value of h.
The augmented matrix of a consistent linear system, we need to perform row operations and transform it into an echelon form or a reduced row echelon form. In this form, we can easily read the system of linear equations and determine its consistency.
Let's apply some row operations to the given matrix. We can start by dividing the first row by 2 to obtain a leading 1 in the first column:
[ 1 2 3/2 3 h/2 7/2]
Next, we can subtract twice the first row from the second row to get a zero in the first column of the second row:
[ 1 2 3/2 3 h/2 7/2]
[ 0 1 -3/2 0 h/2 -5/2]
Now, we can subtract 3/2 times the second row from the third row to get a zero in the first column of the third row:
[ 1 2 3/2 3 h/2 7/2]
[ 0 1 -3/2 0 h/2 -5/2]
[ 0 0 9/2 3 -3h/4 13/4]
At this point, the matrix is in echelon form, and we can read the system of linear equations:
x + 2y + (3/2)z = 3
y - (3/2)z + (h/2)w = -5/2
(9/2)z + 3w - (3h/4)v = 13/4
Therefore, the original matrix [ 2 4 3 6 h 7] is the augmented matrix of a consistent linear system, regardless of the value of h.
Exercise 22 follows a similar procedure. The matrix is [ 1 5 −3 h −2 −7], and we can apply row operations to transform it into echelon form:
[ 1 5 -3 h -2 -7]
[ 0 1 -1/5 h/5 4/5 -3/5]
[ 0 0 -6/5 (h²)/5 -38/25 22/25]
The resulting system of linear equations is:
x + 5y - 3z + hw - 2v = -7
y - (1/5)z + (h/5)w + (4/5)v = -3/5
(-6/5)z + (h²)/5w - (38/25)v = 22/25
We see that the last row has no zeros, except for the rightmost column, so the system is consistent for any value of h
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. Order the following numbers from least to greatest: 3√2 , √3 − 1, √19 + 1, 6,
2√10 ÷ 5 and √14.
pls someone help me
The required order from least to greatest is √3 − 1, 2√10 ÷ 5, √14, 3√2, √19 + 1 and 6
What is ascending order?An arrangement of numbers in which the numbers are arranged from smallest to greatest numbers is called ascending order.
Given that, some numbers, 3√2, √3 − 1, √19 + 1, 6, 2√10 ÷ 5 and √14.
We need to order them from least to greatest,
3√2 = 4.24
√3 − 1 = 0.73
√19 + 1 = 5.35
6
2√10 ÷ 5 = 1.26
√14 = 3.74
The order from least to greatest is :-
0.73, 1.26, 3.74, 4.24, 5.35 and 6
i.e.
√3 − 1, 2√10 ÷ 5, √14, 3√2, √19 + 1 and 6
Hence, the required order from least to greatest is √3 − 1, 2√10 ÷ 5, √14, 3√2, √19 + 1 and 6
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You moved 5 units north, 3 units west, and ended at point D.
Where did you begin?
A) Point E
B) Point A
C) Point B
D) Point D
The required point of the beginning is given as Point A. Option B is correct.
What is coordinate?Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.
When you move 5 units north, you increase the y-coordinate by 5. When you move 3 units west, you decrease the x-coordinate by 3. So, if you start at an unknown point and move 5 units north and 3 units west, your final position would be at a point with the coordinates (x - 3, y + 5).
Since you ended at point D, and the final coordinates are not given, we cannot determine the starting point without more information.
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Can use anyones help asap
Answer: 2
Step-by-step explanation:
The following table gives the probability distribution of a discrete random variable X. Use the table to find
the following probabilities. Round solutions to three decimal places, if necessary.
The probability of the different discrete random variable X are;
a) P(x = 3) = 0.12
b) (P x ≤ 2) = 0.239
c) P(x ≥ 1) = 0.947
d) P(1 ≤ x ≤ 4) = 0.493
How to solve Probability distribution of a Discrete Random Variable?a) The probability expressed as P(x = 3) from the table is;
P(x = 3) = 0.12
b) The probability expressed as (P x ≤ 2) is;
(P x ≤ 2) = P(x = 2) + P(x = 1) + P(x = 0)
= 0.093 + 0.093 + 0.053
= 0.239
c) The probability expressed as P(x ≥ 1) is;
P(x ≥ 1) = P(x = 6) + P(x = 5) + P(x = 4) + P(x = 3) + P(x = 2) + P(x = 1)
P(x ≥ 1) = 0.267 + 0.187 + 0.187 + 0.12 + 0.093 + 0.093
P(x ≥ 1) = 0.947
d) The probability expressed as P(1 ≤ x ≤ 4) is;
P(1 ≤ x ≤ 4) = P(x = 4) + P(x = 3) + P(x = 2) + P(x = 1)
= 0.187 + 0.12 + 0.093 + 0.093
= 0.493
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If interest is compounded once every 12 months, how often is it compounded?
A) Monthly
B) Annually
C) Semiannually
D) Quarterly
Answer:
B) Annually
Step-by-step explanation:
If interest is compounded once every 12 months, it is compounded annually.
Answer:
B) Annually
Step-by-step explanation:
What does compounded mean?Compounded means to calculate interest on the borrowed amount and on previous interest.
What does monthly mean?Monthly means to be done one every month.
What does annually mean?Annually means to be done yearly or every year.
What does semiannually mean?Let's break this down. Semi means half or a partial of something. Annually, as we already discussed, means yearly or every year. Now, when we put it together, it creates half a year. So, semiannually means half a year.
What does quarterly mean?We know a quarter, as in, the coin, is 25 cent. if we multiply 25 cents by four, we get a dollar. So a quarter coin is one fourth, or, a quarter of a dollar. Now, applying that to years, since a year is twelve months and a quarter is one fourth, we can divide twelve by four to get three. Three months is one quarter of a year.
With this in mind, twelve months is equal to a year. So, the interest is compounded every year.
A is incorrect because it says monthly. We have already figured out that the interest is compounded yearly, so it is incorrect.
B is correct because the definition of Annually is yearly or every twelve months.
C is incorrect because semiannually means half or part of a year, not a full year.
D is incorrect because quarterly means one fourth of a year, or, three months.
Which of the following python methods can be used to perform simple...
Which of the following python methods can be used to perform simple linear regression on a data set? Select all that apply.
Question 3 options:
A. linregress method from scipy module
B. simplelinearregression from scipy module
C. ols method from statsmodels module
The python methods that can be used to perform simple linear regression on a data set are -
A. linregress method from scipy module
C. ols method from statsmodels module
The linregress method from the module is the most simplest and effortless method for performing simple linear on the data set. It consists of two arrays one represents the independent variables and the second represents the dependent variables.
The relationship between two variables can be modeled using simple linear regression, where the first variable is treated as the independent variable and the other as the dependent variable. Finding the line of best fit that lowers the squared sum of the residuals is the goal.
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