The set of all differentiable real-valued functions defined on the real line. Proved that V is a vector space with the operations of addition and scalar multiplication defined as:
(f + g)(s) = f(s) + g(s)
(c f)(s) = c[f(s)].
Let V denote the set of all differentiable real-valued functions defined on the real line. Prove that V is a vector space with the operations of addition and scalar multiplication defined as:
(f + g)(s) = f(s) + g(s)
(c f)(s) = c[f(s)].
To prove vector space, we need to hold eight properties of vector space.
1) Closed
(f + g)(s) = f(s) + g(s) (given)
so, closed holds with respect to given defined operation.
2) Associative law
let defined three function, f,g,h in V,
(f+g)(s)+h(s)=f(s)+g(s)+h(s)
= f(s)+(g+h)(s)
hence associative law hold.
3) Existence of identity,
(f+o)(s)=f(s)
f(s)+o(s)=f(s)
Hence, O(s) is identity for this function,
4) Existences of Inverse,
(-f)(s) is inverse for f(s)
5) Commutative law,
(f+g)(s)=(g+h)(s)
6)( cf)(s)=c[f(s)]g
7) c(f+g)(s)=cf(s)+g(s)
8) c(fg)(s)=(cf(s))g(s)
Hence, the given function is defined Operations.
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if points p and q are contained in a plane, then pq is entirely contained in that plain
When P and Q are combined, they will be completely contained in the plane if P and Q are already inside the plane. PQ would therefore be totally in the aircraft.
What are two or more points if they lie on the same line?A plane may contain a number of points. A plane is carrying P and Q. A two-dimensional figure that never ends, the plane. It implies that there is no end. It has a level surface. If we draw a line to join the two points P and Q, the line will also be in the same plane. since the plane never comes to an end.
Collinear points are a group of points that all lie on the same line.The right response to this question is that a segment is a finite portion of a line connecting two locations, including its two ends.Coplanar points are groups of at least four points that all lie on the same plane. Keep in mind that given any two points, they are always coplanar, as are given any three points.
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Find the length of size x in simplest radical form with a rational denominator
Answer: Please provide me with more details regarding the issue, such as an expression or equation that x is a component of. Could you kindly provide me with additional background or details regarding the issue you're seeking to resolve?
Step-by-step explanation:
Give me more details about the answer and I will solve it for you.
Graph of the piecewise function
Answer:
See below
Step-by-step explanation:
As 0 is included in the first part, this means that there is a jump discontinuity at x=0 for the second part of the function as you can see in the graph.
what’s the domain of this function please help
1) f(x) = x(x − 4)³(x+4)²
x-intercepts:
Positive or Negative
Even or Odd
End Behavior:
The given function has
x-intercepts: x = 0, x = 4, x = -4, x = -4i and x = 4i.
Positive or Negative: The function f(x) = x(x − 4)³(x+4)² is positive for x > 0 and negative for x < 0.
Even or Odd: The function f(x) = x(x − 4)³(x+4)² is an even function.
End behavior: x approaches positive or negative infinity the value of f(x) approaches positive infinity.
What is a function?
A function is a mathematical relationship between a set of inputs (referred to as the domain) and a set of outputs (referred to as the range). In other words, a function assigns a unique output to each input value in the domain.
Given the function f(x) = x(x − 4)³(x+4)²
x-intercepts: The x-intercepts are the points at which the function crosses the x-axis, meaning the y value is equal to zero. To find the x-intercepts we need to set f(x) = 0 and solve for x.
x(x - 4)^3(x+4)^2 = 0
the x-intercepts of the function f(x) = x(x - 4)^3(x+4)^2 are x = 0, x = 4, x = -4, x = -4i and x = 4i.
Positive or Negative: The function f(x) = x(x − 4)³(x+4)² is positive for x > 0 and negative for x < 0.
Even or Odd: The function f(x) = x(x − 4)³(x+4)² is an even function.
End Behavior: The end behavior of this function is that as x approaches positive or negative infinity the value of f(x) approaches positive infinity.
Hence, the given function has
x-intercepts: x = 0, x = 4, x = -4, x = -4i and x = 4i.
Positive or Negative: The function f(x) = x(x − 4)³(x+4)² is positive for x > 0 and negative for x < 0.
Even or Odd: The function f(x) = x(x − 4)³(x+4)² is an even function.
End behavior: x approaches positive or negative infinity the value of f(x) approaches positive infinity.
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Find the value of k for which each equation has the following: a real double root two different double roots imagenary roots k^2x^2-8x 4
The value of k for which the equation has imaginary roots is k > ±2.
Function value of x intervalFor a quadratic equation of the form k²x²-8x+4 to have a real double root, the discriminant (b²-4ac) must be equal to zero. For this equation, the discriminant is (-8)² - 4 * k² * 4 = 64 - 16k².
For the discriminant to be equal to zero, 64 - 16k² = 0 and k² = 4. Therefore, the value of k for which the equation has a real double root is k = ±2.
For a quadratic equation of the form k²x²-8x+4 to have two different double roots, the discriminant (b²-4ac) must be greater than zero. For this equation, the discriminant is (-8)² - 4 * k² * 4 = 64 - 16k².
For the discriminant to be greater than zero, 64 - 16k² > 0 and k² < 4. Therefore, the value of k for which the equation has two different double roots is k < ±2.
For a quadratic equation of the form k²x²-8x+4 to have imaginary roots, the discriminant (b²-4ac) must be less than zero. For this equation, the discriminant is (-8)² - 4 * k^2 * 4 = 64 - 16k².
For the discriminant to be less than zero, 64 - 16k² < 0 and k² > 4. Therefore, the value of k for which the equation has imaginary roots is k > ±2.
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2. A person has a beginning balance of $660. She pays $90 on the ninth day, and she charges $320 on the 28th day. What amount of interest is due on her account if it has an APR of 26 percent?
The amount of interest due on the account is $8.36.
What is the simple interest?The interest on a loan or deposit can be calculated using simple interest. In order to calculate it, multiply the principal amount by the interest rate and then by the number of time periods (usually in years).
We must first determine the number of days for which the interest will accrue in order to calculate the amount of interest owed on the account. Since the charge was made on the 28th day after the payment was made on the 9th day, the interest will accrue for 19 days instead of the 28 since the payment was made.
We then use the formula for simple interest: Interest = Principal x Rate x Time
In this instance, the Principal is the initial balance of $660, the Rate is the annual percentage rate (APR), which needs to be converted to decimal form by dividing by 100, and the Time is the total number of days over which interest will accrue (19 days).
The Interest = $660 × 0.26 × (19/365) = $8.36
Thus, the total amount of interest due on the account is $8.36.
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The data set, {+3, -1, -2, +1} shows the moves a player made. Explain the meaning of zero in this situation.
The meaning of a zero in this situation shows that there was a time the player was in a steady position or without movement.
What is a data set?A data set is defined as the number of variables that makes up the data of an event, research or an experiment.
The data sets that was given are {+3, -1, -2, +1} which represent the number of moves that was made by a player.
But when a zero is included in that data set, this means that the player didn't make a move at the particular point in time.
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5/8 + 3/5 greater than 1
Answer: Yes
Step-by-step explanation:
First You need to find a common denominator between 5/8 and 3/5 so you can add them together.
The earliest common denominator between 8 and 5 is 40.
So you have to Multiply the numerator by whatever it takes the denomintor to reach 40.
So for 8 to reach 40 you have to multiply 8 by 5 so you must also multiple the numerator by 5 giving you 25 so your fraction becomes 25/40.
If you do the same for the other fraction you end with 24/40.
so 25/40 + 24/40 = 49/40 which is greater than 1
3. Model Real Life A beehive has 9,268 fewer drone
bees than worker bees. There are 651 drone bees
in the beehive. How many worker bees are in the
beehive?
If the number of drone bees in the beehive is 9,268 fewer than the number of worker bees, we can set up an equation to represent the relationship:
Drone bees = Worker bees - 9,268
We know that there are 651 drone bees in the beehive, so we can substitute that value into the equation:
651 = Worker bees - 9,268
To find the number of worker bees, we need to solve for Worker bees. To do this, we need to add 9,268 to both sides of the equation:
651 + 9,268 = Worker bees
Worker bees = 9,919
So, there are 9,919 worker bees in the beehive.
How many times larger is 9 × 109 than 3 × 10-4?
By taking a quotient, we will see that the first number is 3×10¹³ times larger than the second one.
How many times larger is 9 × 10⁹ than 3 × 10⁻⁴?Here we have two numbers written on scientific notation, and we want to see how many times is the first number larger than the second one.
To see that, we need to take the quotient between the two numbers, so we will get:
(9 × 10⁹)/(3 × 10⁻⁴) = (9/3)× (10⁹/ 10⁻⁴)
Remember that the in the quotient of powers with a same base we just need to take the difference between the exponents, then we will get:
(9/3)*(10⁹/ 10⁻⁴) = 3*10⁽⁹⁺⁴⁾ = 3×10¹³
The first number is 3×10¹³ larger than the second.
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What is the quotient of the expression (5.04 × 10¹2) (6.3 × 109) written in scientific notation?
O 0.8 x 10³
0 8 x 10³
0 8 x 10²
O 0.8 x 1021
The quotient of the expression is 8 × 10² and option C is the correct answer.
What are exponents?The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.
Adding exponents while maintaining the same base is the rule for multiplying like bases.
Exponents should be multiplied while bases are kept constant when bases are raised by a power of two or more.
Division Rule: When dividing like bases, maintain the base constant and deduct the exponent of the denominator from the exponent of the numerator.
Rewrite as fraction:
[tex]\frac{(5.04) (10^{12})}{(6.3)(10^9)}[/tex]
Simplify using exponent rule with same base [tex]\frac{a^n}{a^m} = a^{(n-m)}[/tex]:
[tex]\frac{(5.04) (10^{12-9})}{(6.3)}[/tex]
Calculate the sum or difference:
[tex]\frac{(5.04) (10^{3})}{(6.3)}[/tex]
Convert fraction into decimal: 0. 8 × 10³ = 8 × 10².
Hence, the quotient of the expression is 8 × 10² and option C is the correct answer.
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Encuentra dos ángulos que sean consecutivos y formen un ángulo de 120°, el mayor debe tener 20º menos que el triple del menor.
Los ángulos de mayor y menor medida son 85° y 35°, respectivamente.
¿Cómo determinar las medidas de dos ángulos consecutivos?
En esta pregunta tenemos dos ángulos, cuyas medidas deben ser determinadas a partir de las ecuaciones matemáticas derivadas del enunciado. Primero, escriba la relación de las sumas de las medidas de los ángulos:
x + y = 120°
Donde:
x - Medida del ángulo de mayor medida, en grados.y - Medida del ángulo de menor medida, en grados.Segundo, establezca la ecuación que relaciona las medidas de los ángulos:
x = 3 · y - 20°
Tercero, se resuelve el sistema de ecuaciones lineales:
(3 · y - 20°) + y = 120°
4 · y = 140°
y = 35°
x = 3 · 35° - 20°
x = 85°
ObservaciónNo existen preguntas verificadas en español sobre el tema, de modo que se añade una pregunta en inglés.
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A square has sides that measure 8x + 5 inches. A rectangle has two sides that measure 4x - 5 inches and two sides that measure 12x + 15 inches.
For what value of x will the perimeters of the square and rectangle be the same?
Answer:
The perimeter of the square is 32x + 20 inches, and the perimeter of the rectangle is (4x - 5) + (4x - 5) + (12x + 15) + (12x + 15) = 32x + 20 inches.
So, to find the value of x that makes the perimeters the same, we set 32x + 20 = 32x + 20 and solve for x.
x = 0
Step-by-step explanation:
Part A: Graph the piecewise function g(x) and determine the domain.
Part B: Determine the x-intercepts of g(x). Show all necessary calculations.
Part C: Describe the interval(s) in which the graph of g(x) is positive.
a) The graph of the piece-wise function is given by the image presented at the end of the answer.
b) The x-intercepts of the function are given as follows: x = -4, x = 0 and x = 19.
c) The graph of g(x) is positive on these following intervals: (-4,0) and (4,19).
What is a piece-wise function?A piece-wise function is a function that has different definitions, depending on the input of the function.
The definitions for the function in this problem are given as follows:
Left of x = 4.Right of x = 4.The features of the function are given as follows:
x-intercept: values of x for which the graph crosses the x-axis.Positive: values of x for which the graph of the function is above the x-axis.More can be learned about piece-wise functions at brainly.com/question/19358926
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what is the answer ??
FILL IN THE BLANK Fill in the blank: You should distinguish elements of your data visualization by _____ the foreground and background and using contrasting colors and shapes. This makes the content more accessible.
You should distinguish elements of your data visualization by discriminating data the foreground and background and using contrasting colors and shapes. This makes the content more accessible.
The term shapes in math is known as the process of define the outline or the boundary of an object.
Here we have given that should distinguish elements of your data visualization and the content more accessible.
Here we have given that distinguishing elements of your data visualization by separating the foreground and background and using contrasting colors and shapes makes the content easier to see.
While we looking into this one than we have identified that this can help make data visualizations more accessible for audience members with low vision.
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Isosceles trapezoid SCEL has parallel sides SC and EL. If vertices S (1,4) and C (3,0), then what are a possible set of points for E and L?
My teacher provided the answers on our review packet, but didn't show any steps whatsoever and didn't explain in class. Thanks for any help!
A possible set of coordinate points for E and L are; E(2, 8) and L(6, 0)
How to find the slope between two coordinates?
We are given the coordinate of the vertices S and C as;
S (1,4) and C (3,0)
Now, when two lines are parallel, it means that their slopes are equal. Now, formula to find the slope between two coordinates is;
Slope = (y₂ - y₁)/(x₂ - x₁)
Slope of SC = (0 - 4)/(3 - 1)
Slope pf SC = -2
Now, for EL to be parallel to SC, it must have a slope of -2. Thus;
Potential coordinates could be gotten by multiplying Coordinates of SC by 2 to get;
(2, 8) and (6, 0)
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15% off of a total $41.10 what s discounted total price
Answer:
34.94
Step-by-step explanation:
Answer: 34.94
Step-by-step explanation:
Mr. Williams pays $40 a month for city
water, no matter how many gallons of water he uses in
a given month. Let x represent the number of gallons
of water used per month. Let y represent the monthly
cost of the city water in dollars. What is the equation
of the line that represents this information? What is
the slope of the line?
y = $40 is the equation of the line that represents the information. The line has no slope.
What is the equation and the slope?A linear equation can be used to represent the equation that represents Mr. Williams' total payment for city water. A linear equation is one that is composed of a single variable raised to the power of one.
A linear equation takes the following form:
y = ax + b
Where: a = slope = which measures the equation's rate of change
b = the intercept
y = $40 + (x × 0)
y = $40
A linear equation can have an upward, downward, or zero slope when plotted on a graph.
The equation of the line that represents the information is y = $40. There is no slope to the line.
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Part 1
The graph shown is that of a function, f. Determine (a) f(); (b) the domain; (c) all x-values such that f(x); and (d) the range.
Question content area bottom left
Part 1
a) f()
enter your response here
Part 2
b) Find the domain. Select the correct choice below and fill in the answer box to complete your choice.
A.
The domain is the set
.
(Use a comma to separate answers as needed.)
B.
The domain is the interval
enter your response here.
(Type your answer in interval notation.)
Part 3
c) Find all x-values such that f(x). Select the correct choice below and fill in the answer box to complete your choice.
A.
f(x) only for the specific value(s) x
enter your response here.
(Use a comma to separate answers as needed.)
B.
f(x) for all values of x in the interval
enter your response here.
(Type your answer in interval notation.)
Part 4
d) Find the range. Select the correct choice below and fill in the answer box to complete your choice.
A.
The range is the set
.
(Use a comma to separate answers as needed.)
B.
The range is the interval
enter your response here.
(Type your answer in interval notation.)
.
.
.
Question content area right
Part 1
-12
-10
-8
-6
-4
-2
2
4
6
8
10
12
-12
-10
-8
-6
-4
-2
2
4
6
8
10
12
x
y
A coordinate system has a horizontal x-axis labeled from negative 12 to 12 in increments of 1 and a vertical y-axis labeled from negative 12 to 12 in increments of 1. From left to right, a curve starts at a closed dot at (negative 5, negative 7), rises at a decreasing rate, flattens out to pass through (negative 2, 2), and rises at an increasing rate until it ends at a closed dot at (2, 10). The curve also passes through the points left parenthesis negative 4 comma negative 2 right parenthesis and left parenthesis negative 3 comma 1 right parenthesis.
Answer:
Step-by-step explanation:
Part one is when you need to do area/perimiter.
DO
A Sulfa drug is to be given to a 130-pound patient at the rate of 2.5 mg per pound of body weight.
How many mL are necessary if the concentration of the drug is 200 mg per mL?
Answer:
1.625 mL
Step-by-step explanation:
2.5 mg per lb
For 130 lb, 130 × 2.5 mg = 325 mg are needed.
1 mL has 200 mg
1 mL is to 200 mg as x ml is to 325 mg
1/200 = x/325
200x = 325
x = 1.625
Answer 1.625 mL
sue is buying a new kitchen table. the table measure 6 feet by 4 feet how much space will be taken up by the table? draw a math sketch and write a number expression. explain your answer.
The space taken up by the table is 24 feet².
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
Kitchen table = 6 feet by 4 feet
This means,
The table is a rectangle.
The area of the table.
= 6 x 4
= 24 feet²
Thus,
The area of the rectangle is 24 feet².
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solve this system of equations by using the elimination method.
2x+6y=2 2x+2y=2
Answer: The elimination method is a method for solving a system of equations by eliminating one of the variables. One way to do this is to multiply one equation by a constant and then add or subtract it from the other equation to cancel out one of the variables.
We will start by multiplying the first equation by 3:
2x + 6y = 2 ----> 6x + 18y = 6
Now we will subtract the second equation from the modified first equation:
6x + 18y = 6
(2x + 2y = 2)
4x + 16y = 4
Now we can solve for one of the variables, we will solve for x:
4x = 4
x = 1
Now that we know x = 1, we can substitute this back into one of the original equations, for example the first one:
2x + 6y = 2
2(1) + 6y = 2
6y = 0
y = 0
So the solution to the system of equations is x = 1 and y = 0
Therefore, the solution is (1,0)
Step-by-step explanation:
integer numstudents and doubles firststudent and laststudent are read from input. first, declare a vector of doubles named swimminglogs with a size of numstudents. then, initialize the first and last element in swimminglogs to firststudent and laststudent, respectively. ex: if the input is 10 10.88 92.42, then the output is: 10.88 0 0 0 0 0 0 0 0 92.42
Declare a vector of doubles named swimming logs with size of num students. Initialize first element to first student and last element to last student. Fill the middle elements with zeros.
Firstly, declare a vector of doubles named swimming logs with a size of num students. This is done by writing "vector swimming logs(num students);". This creates a vector with the size specified by num students, which can be read from input.
Next, initialize the first element of the vector to first student. This is done by writing "swimming logs[0] = first student;". This sets the first element of the vector to the value of first student, which can be read from input.
Then, initialize the last element of the vector to last student. This is done by writing "swimming logs[num students - 1] = last student;". This sets the last element of the vector to the value of last student, which can be read from input.
Finally, fill the middle elements of the vector with zeros. This is done by writing "for (int i = 1; i < num students - 1; i++) { swimming logs[i] = 0; }". This loop iterates from the second element to the second last element of the vector, setting each element to 0. This completes the initialization of swimming logs with the specified values.
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hich of the following expressions is never a prime number when p is a prime number? (a. p2 16, b. p2 24, c. p2 26, d. p2 46, e. p2 96)
From the given expressions of prime numbers, the following are never a prime number:
Option b. p²+ 24
Option c. p²+ 26
Prime number is represented by 'p'
The expressions which can never be a prime number is given by :
Let us consider value of p = 1
a. p²+ 16
⇒1² + 16
⇒17 a prime number
b. p²+ 24
⇒1² + 24
⇒25 is not a prime number.
c. p²+ 26
⇒1² + 26
⇒27 is not a prime number.
d. p²+ 46
⇒1² + 46
⇒47 a prime number.
e. p²+ 96
⇒1² + 96
⇒97 a prime number.
Therefore, the expression represented by option b. p²+ 24 and option c. p²+ 26 can never be a prime number.
The above question is incomplete , the complete question is :
Which of the following expressions is never a prime number when p is a prime number?
a. p²+ 16 b. p²+ 24 c. p²+ 26 d. p²+ 46 e. p²+ 96
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The number of hours people spent jogging last week is shown in the histogram below.
Hours Spent Jogging
Number of People
12
10
8
S SP
2-
0 1 2 3 4 5
Number of Hours
Which of the following statements is true for the data?
A. The majority of people jogged between 1 hour and 4 hours.
CB. The majority of people jogged between 1 hour and 2 hours.
C. The majority of people jogged between 2 hours and 3 hours.
The majority of people jogged between 3 hours and 5 hours.
Copyright
The majority of people jogged between 1 hour and 4 hours , 1 hour and 2 hours , 2 hour and 3 hours , 3 hour and 5 hours is 8,8,8,6 respectively.
What is bar chart ?
Bar chart can be defined as the graph which represents the data of any given information.
Given ,
The number of hours people spent jogging last week is shown in the histogram from the given question ,
The majority of people jogged between 1 hour and 4 hours
4,8,6,2 is 8.
The majority of people jogged between 1 hour and 2 hours
4,8, is 8.
The majority of people jogged between 2 hour and 3 hours
8,6 is 8.
The majority of people jogged between 3 hour and 5 hours
6,2,4 is 6.
Hence, The majority of people jogged between 1 hour and 4 hours , 1 hour and 2 hours , 2 hour and 3 hours , 3 hour and 5 hours is 8,8,8,6 respectively.
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Which of the following describes the growth rate of the exponential function in the graph below?
For each x increase of 1, the y increases by a common difference of 3.
For each x increase of 1, the y increases by a common factor of 3.
For each x increase of 1, the y increases by 4 more than the previous increase.
For each x increase of 1, the y increases by doubling and then adding 1.
The correct option regarding the growth rate of the exponential function is given as follows:
For each x increase of 1, the y increases by a common factor of 3.
How to classify the functions?A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.
A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.
As the function in this problem is exponential, the increase of the output y must be a common factor, purely.
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six hundred six and two thousand, three hundred seventy-one ten-thousandths in numerical form
Answer:606.02371
Step-by-step explanation:
The numerical representation of "six hundred six and two thousand, three hundred seventy-one ten-thousandths" is 606.02371.
which of the following is true of a scientific theory? view available hint(s)for part a which of the following is true of a scientific theory? it generates testable hypotheses, is supported by a large body of evidence, and is broad in scope. it is only accepted after the person who formulated it has died. it is formulated by many scientists over drinks at a convention. it is a method or device that applies scientific knowledge for some specific purpose. it must demonstrate the effect of one variable by testing control groups and experimental groups.
Out of the following, the statement is It generates testable hypotheses, is supported by a large body of evidence, and is broad in scope is true of a scientific theory.
A scientific theory is a well-substantiated explanation of some aspect of the natural world that is acquired through the scientific method and repeatedly tested and confirmed through observation and experimentation. A scientific theory is not just an idea or speculation. It is a systematic way of organizing and interpreting observations that are based on facts and evidence. It is also open to being tested and disproved if new evidence arises.
A scientific theory must be supported by a large body of evidence from multiple sources to be considered valid. Furthermore, a scientific theory must be broad in scope and explain a wide range of phenomena. It must also generate testable hypotheses that can be tested and verified through experimentation and observation.
A scientific theory is not accepted until it is thoroughly tested and confirmed through numerous experiments and observations. Therefore, it is not accepted after the person who formulated it has died.
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