The mean number of cars sold by each salesman at Kovak Motors is 10 cars per month, with a standard deviation of 3 cars (distribution is symmetric). Ben Polamalu only sold 6 cars last month. The statement which true is B) Ben's sales were not unusual last month.
ABOUT MEAN IN MATHThe mean is one of the important formulas in mathematics. Another term for the mean is the average. The mean is a calculation that is studied further in statistics.
Calculating the mean is a basic math skill. The mean is a calculation that can be calculated using a simple formula. Usually, the mean is a formula that is used in conjunction with other statistical formulas such as the mode and median.
In everyday life, the mean is a calculation that is often used. An example of using the mean is to find out the average income of employees in an office.
Your question is incomplete but most probably your full question was:
The mean number of cars sold by each salesman at Kovak Motors is 10 cars per month, with a standard deviation of 3 cars (distribution is symmetric). Ben Polamalu only sold 6 cars last month. which statement is true?
A) Ben's sales were unusual last month.
B) Ben's sales were not unusual last month.
C) Ben's sales were not unusual this month.
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question 8 options: the caller times at a customer service center has an exponential distribution with an average of 22 seconds. find the probability that a randomly selected call time will be less than 30 seconds? (round to 4 decimal places.) answer:
The probability that a randomly selected call time will be less than 30 seconds is approximately 0.7445.
The problem involves exponential distribution which is a standard continuous distribution. The probability density function of this distribution is given by -
f(x) = θe^(-θx) ; where θ is a parameter and characteristic of the distribution, x is the random variable.
Also, the mean for an exponential distribution is given by u = 1/θ .
In the question it is 22 seconds.
So, the value of θ is 1/22.
Now, we have to find P(X<30) where X is the random variable denoting the calling time in seconds.
P(X<30) is nothing but F(x) at x = 30 seconds, i.e. cumulative distribution function. For an exponential distribution , F(X) is given by -
P(X<x)= F(X) = 1- e^(-θ x) , where x>0.
Putting θ = 1/22 and x= 30 in F(X) , we get -
F(X) = 1-e[(-1/22)30] = 1- 0.2555 = 0.7445 which is P(X<x) = P(X<30) = 0.7445.
So, the probability that a randomly selected call time will be less than 30 seconds is approximately 0.7445.
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The probability that a randomly selected call time will be less than 30 seconds is approximately 0.7445.
The problem involves exponential distribution which is a standard continuous distribution. The probability density function of this distribution is given by -
f(x) = θe^(-θx) ; where θ is a parameter and characteristic of the distribution, x is the random variable.
Also, the mean for an exponential distribution is given by u = 1/θ.
In the question, it is 22 seconds.
So, the value of θ is 1/22.
Now, we have to find P(X<30) where X is the random variable denoting the calling time in seconds.
P(X<30) is nothing but F(x) at x = 30 seconds, i.e. cumulative distribution function. For an exponential distribution , F(X) is given by -
P(X<x)= F(X) = 1- e^(-θ x) , where x>0.
Putting θ = 1/22 and x= 30 in F(X) , we get -
F(X) = 1-e[(-1/22)30] = 1- 0.2555 = 0.7445 which is P(X<x) = P(X<30) = 0.7445.
So, the probability that a randomly selected call time will be less than 30 seconds is approximately 0.7445.
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Find the value of x. 72 Degree x+4
Answer: x = 104
Step-by-step explanation:
Write the equation of the line in slope-intercept form (y=mx+b):
Answer: y = 3x + 0 OR y = 3x
Step-by-step explanation:
M = slope. rise/run. compare the points on the line by how much they rise and how much they run. In this case it is 3/1 (3). the B = the y-intercept. (the point where the line meets the y line, in this case the line meets at the origin which is 0.)
the numbers, if any, at which f has a relative maximum. what are these relative maxima?
Using the graph of the function f, the relative maxima of function is at x = 3 and is equal to 6.
The graph of the function f is given below:
A relative maximum occurs at an x-coordinated position when the function value is higher than it is compared to nearby places. At that time, the function value is at its relative maximum (y coordinate).
A relative minimum occurs at an x-coordinated location where the function value is the lowest in relation to its neighbors.
The Relative maximum is determined by y's maximum value.
In the graph we can see that;
The greatest value of the y value for x = 3 is 6.
As a result, the function's relative maximum is at x = 3 and is equal to 6.
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The complete question is:
The graph of a function f is given. Use the graph to find each of the following.
The numbers, if any, at which f has a relative maximum. What are these relative maxima?
Malcolm and his father want to build a frame for their favorite poster. What strategy could they use to find out how much framing material they will need?
1.
Please solve this question.
Answer: The answer is 3.
Step-by-step explanation:
As a fraction in simplest terms, what would you multiply the first number by to get the second?
First number:
32
Second number:
51
Answer:
1.59375
Step-by-step explanation:
51 divided by 32 which is 1.59375
to check if you are right you do 1.59375 times 32 which equals to 51
i can do this one i am just too lazy
Answer: 7/2
Step-by-step explanation: An easy way to calculate slope with two given points is to count the rise (y) between the points (7). Then count the run (x) between the points (2). Then put the rise over the run. 7/2
What's the answer and how do you solve for the answer?
The solution to the exponential inequality in this problem is given as follows:
x < 1.72.
How to solve the exponential inequality?The exponential inequality for this problem is defined as follows:
3^(4x - 5) < 8.
The number 8 is not a base of 3, hence the way to isolate the variable x is applying the log of base 3 to both sides, as follows:
log3(3^(4x - 5)) = log3(8)
4x - 5 = log3(8)
The logarithm of base 3 of 8 can be obtained applying the change of base property, as follows:
log3(8) = log(8)/log(3)
log3(8) = 1.893.
Hence the inequality is solved as follows:
4x - 5 < 1.895
4x < 6.896
x < 6.896/4
x < 1.72.
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The diagram shows pentagon P, rectangle Q and triangle R drawn on a grid. Pentagon P is enlarged by scale factor 3 from centre (7,8), to form pentagon S. Shapes Q and R are translated so that together the form pentagon S. Shape Q and R are translated so that together the form pentagon S. What are the vectors used to translate shapes Q and R? You must show your working.
The correct answer is option A which is the ordered pair of point P’ will be (8.75, 5.25).
What is scale factor?The scale factor is defined as the proportion of the new image's size to that of the previous image. decision-making.
here, we have,
If pentagon OPQRS is dilated by a scale factor of 7/4 from the origin, to create O’P’Q’R’S’, what is the ordered pair of point P’
Multiply the coordinates of point P by the scale factor 7/4 to get the coordinates of P'.
Given : P(-5,3)
P' (x,y) = P (-5 x 7/4 , 3 x 7/4)
= P(-8.75, 5.25)
Therefore the correct answer is option A which is the ordered pair of point P’ will be (-8.75, 5.25).
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calculate the double integral. (y xy^-2) da r = (x y) 0 ≤ x ≤ 2 0 ≤ y ≤ 2 r
The double integral of (xy y^(-2)) over the region R is equal to 0.
What is double integral ?
The term integral in math is defined as a method of adding or summing up the parts to find the whole and it is basically used to find the volume, area and the central values of many things. Double integrals are a two-dimensional integration method.
The given expression is the integrand of a double integral over the region R defined by the constraints 0 ≤ x ≤ 2 and 0 ≤ y ≤ 2. To calculate this double integral, we would evaluate the following expression:
∬(xy y^(-2)) dA = ∬(xy y^(-2)) dx dy over the region R
We can evaluate this double integral using a change of variables, such as polar coordinates, or using rectangular coordinates.
In rectangular coordinates, we can evaluate the double integral using the following steps:
Evaluate the bounds of integration:
x: 0 to 2
y: 0 to 2
Evaluate the integral with respect to y first, keeping x fixed:
∬(xy y^(-2)) dx dy = ∫(x ∫(y y^(-2)) dy) dx, from 0 to 2
Evaluate the inner integral with respect to y:
∫(y y^(-2)) dy = -y^(-1) = -ln(y) + C, where C is an arbitrary constant
Substitute the solution for the inner integral back into the outer integral:
∫(x (-ln(y) + C)) dx = x(-ln(y)) - xC + D, where D is another arbitrary constant
Evaluate the outer integral with respect to x:
∫(x(-ln(y)) - xC + D) dx = (-x^2/2)ln(y) - (x^2/2)C + xD + E, where E is yet another arbitrary constant
Evaluate the constants of integration C, D, and E using the boundaries of integration for x and y:
-ln(2) - 0C + 0D + E = 0
-2ln(2) - 2^2/2 C + 2D + E = 0
Solving the system of equations, we find C = 2ln(2), D = 0, and E = 0
Substitute the values of C, D, and E back into the solution:
(-x^2/2)ln(y) - (x^2/2)C + xD + E = (-x^2/2)ln(y) - x^2ln(2)
Finally, evaluate the integral over the region R by substituting the bounds of integration for x and y:
(-2^2/2)ln(2) - 2^2ln(2) = -4ln(2) + 4ln(2) = 0
So, The double integral of (xy y^(-2)) over the region R is equal to 0.
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how many significant figures would this calculation have if it were completed:
The calculation would have three significant figures, since both original numbers have three significant figure.
The number of significant figures in a calculation is determined by the number of significant figures in the original numbers used in the calculation. For example, if we have the calculation 3.14 + 2.7 = 5.84, the answer will have three significant figures because the original numbers, 3.14 and 2.7, each have three significant figures.
In general, significant figures are determined by counting all non-zero digits, plus any zeros that come between non-zero digits, such as in the numbers 10.0 and 0.07. If a number is a decimal, the zeros after the decimal point are also significant, such as in the number 0.07. Zeros that come before the first non-zero digit are not significant, such as in the number 0.0007.
In the above example, the calculation would have three significant figures, since both original numbers have three significant figures.
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Complete quetion:
What is the number of significant figures in the calculation 3.14 + 2.7 = 5.84?
how to find the period of a function
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or
Jeffrey likes to skate at an ice cream parlor that is due south of his school and due west of his favorite movie theater. If the ice cream parlor is 12 kilometers from his school and the straight-line distance between the school and the movie theater is 13 kilometers, how far is the ice cream parlor from the movie theater?
kilometers
The distance between the ice cream parlor from the movie theater is 5 km.
What is the Pythagorean theorem?Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We have,
School
| \
| \
| \ 13 km
12 km \
| \
Ice cream parlor Movie theater
Using Pythagorean theorem.
The distance between the ice cream parlor from the movie theater = x
Now,
13² = 12² + x²
169 = 144 + x²
x² = 169 - 144
x² = 25
x = 5
Thus,
The ice cream parlor from the movie theater is 5 km away.
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At the beginning of the party, there were 1 pizzas. By the end of
the party, there were 4/5 pizzas left. How many pizzas were
consumed during the party?
Show your work here
0.2 pizzas were consumed during the party.
What are the arithmatic calculations?
Arithmetic is the branch of mathematics that deals with basic operations such as addition, subtraction, multiplication, and division, and their properties and applications. Arithmetic calculations are mathematical operations that involve one or more numbers and result in a numerical answer.
To find the number of pizzas consumed during the party, we need to subtract the number of pizzas left at the end of the party from the number of pizzas at the beginning of the party.
At the beginning of the party, there was 1 pizza.
At the end of the party, there were 4/5 pizzas left.
So, the number of pizzas consumed during the party can be calculated as:
1 - 4/5 = 1 - 0.8 = 0.2
Therefore, 0.2 pizzas were consumed during the party.
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Which graph shows the solution to the system of linear equations?
y equals one third times x
x + 3y = −6
The second graph is correct
Answer:
second graph
Step-by-step explanation:
just wanted to help the first person who answered get brainlist
which of the following matrices is not diagonalizable?
Not all square matrices can be diagonalized. If there are just two eigenvectors (up to multiplication by a constant), then the matrix cannot be diagonalized.
A collection of integers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix, are the integers. In addition to several mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics.
In computer graphics, where they have been used to describe picture rotations and other transformations, matrices have vital uses as well.
Thus, Not all square matrices can be diagonalized. If there are just two eigenvectors (up to multiplication by a constant), then the matrix cannot be diagonalized.
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Can somebody PLEASE help me with this? I don’t understand. Show work please
Answer:
B. m2=50 and m3=50
Step-by-step explanation:
Angle m1 and angle m3 combined make a straight line, the angle of a straight line is 180°, so you can do 180-130=50 amd theres you m3. Looking at m1 and m2 its the same thing, we already know m1 is 130° so its the same equation, 180-130=50 and thats m2 angle.
Ps. My hand writing is bad but this is how I solved it.
what is the average cpi for a processor with 3 instruction classes, a, b, and c having relative frequencies of 45%, 35%, and 20% respectively and individual cpi’s of 1, 2, and 4 respectively?
The average CPI of the processor is 1.95, which means that on average, it takes 1.95 clock cycles to execute one instruction.
The average CPI such as cycles per instruction of a processor is a measure of its performance.
In a processor with 3 instruction classes, A, B, and C, with relative frequencies of 45%, 35%, and 20% respectively, and individual CPIs of 1, 2, and 4 respectively, the average CPI can be calculated as follows:
Average CPI = (relative frequency of class A * individual CPI of class A) + (relative frequency of class B * individual CPI of class B) + (relative frequency of class C * individual CPI of class C)
Average CPI = (45% * 1) + (35% * 2) + (20% * 4)
Average CPI = 0.45 + 0.70 + 0.80 = 1.95
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In the following, choose k to create a perfect-square trinomial:
(a) x² - 16x+k
(b) x² + 10x + k
(c) x² - 5x + k
(a) The value of k is 64.
(b) The value of k is 25.
(c) The value of k is 25/4.
What is a trinomial?
An algebraic expression with three terms is called a trinomial. One or more terms in an algebraic expression each have variables and constants. These expressions use separators like +, -, ÷, and × that are symbols or operations. This algebraic expression includes a trinomial, a monomial, a binomial, and a polynomial.
(a)
Given trinomial is x² - 16x+k.
The algebraic identity is (a-b)² = a² -2ab + b²
Now equate a² -2ab + b² with x² - 16x + k.
x² - 16x + k = a² -2ab + b²
Compare both sides:
x² = a², 16x = 2ab, k = b².
16 = 2b
b = 8
Taking square on both sides:
b² = 64
(b)
Given trinomial is x² + 10x + k.
The algebraic identity is (a+b)² = a² +2ab + b²
Now equate a² -2ab + b² with x² + 10x + kk.
x² + 10x + k = a² + 2ab + b²
Compare both sides:
x² = a², 10x = 2ab, k = b².
10 = 2b [Since x = a]
b = 5
Taking square on both sides:
b² = 25
(c)
Given trinomial is x² - 5x + k.
The algebraic identity is (a-b)² = a² -2ab + b²
Now equate a² -2ab + b² with x² - 5x + k.
x² - 5x + k = a² -2ab + b²
Compare both sides:
x² = a², 5x = 2ab, k = b².
5 = 2b [Since x = a]
b = 5/2
Taking square on both sides:
b² = 25/4
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Mrs. Chauvet has an unfair number cube that lands with 6 facing up 40% of the time. Let x = the number of times that she rolls a 6 among 3 trials. Here is a binomial probability table for this setting. X 0 1 2 3 p(x) 1(0. 6)3 3(0. 4)(0. 6)2 3(0. 4)2(0. 6) 1(0. 4)3 complete this statement: x = 1 means that we roll exactly 6 in the 3 trials. That means we have success and failures.
X = 1 means that we roll exactly 6 in the 3 trials. This means that the probability of rolling a 6 in this situation is 3(0.4)(0.6)2.
The probability of rolling a 6 in any given trial is 0.6 since Mrs. Chauvet's cube is unfair. The probability of getting a 6 in two of the three trials is 3(0.4)(0.6)2, while the probability of rolling a 6 in all three trials is 1(0.6)3. This means that the chance of rolling a 6 in any combination among three trials is the sum of the probabilities of rolling a 6 in each trial (0.6 + 0.6 + 0.6 = 1.8).
The probability of rolling a 6 exactly once in three trials is 3(0.4)(0.6)2, which is the probability of getting a 6 in one of the three trials and not getting a 6 in the other two.
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pls answer will mark brainliest
what are the domain and range of the function f(x) = √ x-7+9?
Domain : { x ∈ R : x ≥ 7 }
Range: { f ∈ R : f ≥ 9 }
Given function is:
f(x) =
Firstly find the domain of the given function.
Domain is set of all real x's values where given function is defined.
In other words, we exclude all the x's values from all real values where function is undefined.
In case of square root function, inside the square root given expression must be greater or equal to zero.
So,
x - 7 ≥ 0
Solve for x
x ≥ 7
So, domain is all real x when x ≥ 7.
Now find the Range of this function.
Range is set of all output values.
So, lowest value of out put is 9 when x is 7
and maximum value of the function is infinite.
So, Range is all real f's values when f ≥ 9.
The length of a rectangular i three time it width, and the height i four more than the width. Write an expreion for the volume of the rectangular prim in term of width
An expression for the volume V of the rectangular prism in terms of its width w is V = ( 3W³ + 12W² ) Units³
What is the rectangular prism?A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.Its length, width, and height are its three dimensions. Rectangular tissue boxes, school notebooks, laptops, fish tanks, big buildings like freight containers, rooms, storage sheds, etc. are a few instances of rectangular prisms in daily life.A three-dimensional object called a rectangular prism has rectangles on each of its faces. The rectangular prism is a cube if all of its faces are squares. A rectangular prism's volume is a measurement of the inside volume.Given data :
we know that
The volume of a rectangular prism is equal to
V = LWH ------> Equation A
where
L is the length
W is the width
H is the height
we know that
L = 3W ----> Equation B
H = W + 4 ------> Equation C
substitute equation B and equation C in equation A
V = ( 3W ) (W) ( W + 4 )
Apply distributive property
V = ( 3W³ + 12W² ) units³
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Which is completely factored form of 4x^3+10x^2-6x ?
A. 2(x+3)(2x-1)
B. 2x(x+3)(2x-1)
C. 2x(x-3)(2x-1)
D. 2(x-3)(2x+1)
The fully factored form of the equation is 2x(x + 3) (2x - 1) that is option B.
Synthetic division and the rational root theorem can be used to demonstrate this. According to the rational root theorem, p must divide the constant term and q must divide the leading coefficient if p/q is a rational root of the polynomial f(x). The constant term in this example is -6, the leading coefficient is 4, and the potential rational roots are 1, 2, 3, and 6.
When we divide 4x3 + 10x2 - 6x by 2x - 1 using synthetic division, we arrive at the following result:
4x^3 + 10x^2 - 6x = (2x - 1) (2x^2 + 8x + 6)
We can then factor the remaining quadratic, 2x^2 + 8x + 6, as (x + 3)(2x + 2).
Thus, the completely factored form of 4x^3 + 10x^2 - 6x is:
4x^3 + 10x^2 - 6x = 2x(x + 3)(2x - 1)
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a coin is flipped 30 times. what is the probability of getting 15 or more heads? round answer to 4 decimal places. answer:
The probability of getting 15 or more heads is :
P (Z > -0.18) = 1 - 0.4289 = 0.5714
Now, According to the question:
Normal Approximation to Binomial:
The normal distribution is used to approximate for the binomial distribution. The condition when binomial distribution is approximated to normal is that n should be large and probability should be close to 0.5
"Information available from the question"
n = 30
Probability, p(heads) = 1/2
Since sample size is large, we check for normal approximation.
np = 30(1/2) = 15
and, n(1 - p) = 30(1 - (1/2)) = 15 both are greater than 5, we use normal approximation.
Mean, μ = np = 30(1/2) = 15
Standard deviation, σ = [tex]\sqrt{np(1-p)}[/tex]
Standard deviation, σ = [tex]\sqrt{30(1/2)(1-1/2)}[/tex]
Standard deviation, σ =2.739
We have to find P (X ≥ 15). Using continuity correction, we deduct 0.5
P(X ≥ 15) = P(X > 14.5)
The respective Z-score with X = 14.5 is
Z = (x - μ)/ σ
Z = (14.5 - 15)/2.739
Z = -0.18
Now, we use z-tables to find probability greater than -0.18
P (Z > -0.18) = 1 - 0.4289 = 0.5714
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PLEASE HURRY LIMITED TIME, TEST QUESTION!!!!
Question- Given circle C with center (3, 4) and radius of 2, and circle D with center (-2,1) and radius of 10, what sequence of transformations should be used to prove circle C is similar to circle D by mapping C onto D? Show all work and explain your reasoning.
Answer:
Translation and dilation
Step-by-step explanation:
Translation because the points move spaces on the graph, and dilation because it gets bigger/smaller than the other.
what angle is 6y+2=8y-14
Answer:
y = 8
Step-by-step explanation:
6y+2 = 8y-14
2 = 2y - 14
16 = 2y
y = 8
The baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 0.25, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.
Equally likely and unlikely
Likely
Unlikely
This value is not possible to represent probability of a chance event.
Answer:
Step-by-step explanation:
Assuming the oatmeal raisin and sugar cookies have an equal probability, it is less likely that a chocolate chip cookie will be picked since the other two cookies have a 37.5% chance of being picked. Despite this, it is still both likely and unlikely since it is only a small difference.
To conclude, it depends on what your teacher or textbook think. If they think a 12.5% difference between the other two cookies means that chocolate chip is unlikely, then it's unlikely. In my opinion, it is not equally but near equally likely and unlikely.
i need help please thanks
The inequality equation is y ≤ -2x + 1 and the graph is plotted
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
y ≤ -2x + 1 be equation (1)
when the inequality is solved ,
y = -2x + 1 , where the slope of the line is m = -2
Therefore , the value of A is -2x + 1 and the graph is plotted
Hence , the inequality equation is y ≤ -2x + 1
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How do you show that f is continuous on − [infinity] [infinity]?
It follows that continuity at infinity is provided by having the same limit while approaching it from either side, i.e., the limit towards + and, which makes sense based on your understanding.
When a function can be extended to P1, it is said to be "continuous at infinity" (R).
What is the limit?Calculus's idea of the limit describes how a function behaves as its input gets closer to a particular value. As long as the limit is present, the value that f(x) approaches as x moves closer to c is represented by the notation lim(x -> c) f(x), which stands for the limit of a function at the point x = c.
You must demonstrate that all three of the following conditions are true in order to prove that a function f is continuous on an interval:
Every point in the interval has f specified, and the interval has f's bound.
For each and every > 0, there is a corresponding > 0 such that |x - c| implies |f(x) - f(c)| for all x and all c in the interval.
F is considered to be continuous on the interval if these requirements are met.
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