give an example of a function that is discontinous at one and only one point in its domain but is continous at every other point

Answers

Answer 1

An example of a function that is discontinuous at one and only one point in its domain but is continuous at every other point is the function f(x) = x^2.

This function is continuous at every point in its domain, which is the set of all real numbers (-infinity < x < infinity). However, at the point x = 0, the function is discontinuous. At x = 0, the function f(x) = x^2 is equal to 0, but if we approach the point x = 0 from the left (x = -0.1, -0.01, etc.), the function is equal to a negative value (-0.01, -0.0001, etc.), and if we approach the point x = 0 from the right (x = 0.1, 0.01, etc.), the function is equal to a positive value (0.01, 0.0001, etc.). This means that the function is not continuous at the point x = 0, and is therefore discontinuous at this point.

The point of discontinuity in this example is an essential discontinuity, which means that it cannot be removed by redefining the function at that point. This is because the function f(x) = x^2 is defined differently for x < 0 and x > 0, and there is no way to redefine the function at x = 0 to make it continuous.

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Related Questions

Calculate the difference and enter below. 3-9

Answers

Answer: -6

Step-by-step explanation: Since 9 is being subtracted from 3, we know that it will be a negative number. So, 9-3 = 6, and a greater number subtracted from a smaller number is a negative number. So, that results in this being -6. I hoped this helped.

[tex]3-9[/tex]

[tex]3+(-9)[/tex]

[tex]=\fbox{-6}[/tex]

[tex]3+(-9)[/tex] on a number line:

Test of Independence 6. Are the factors that contribute to a person's wellbeing, (ie: Friendship and social life, job or primary activity, and health and physical condition), Independent of a person's marital status. See the chart. Marital married Widowed/divorced totals 42 132 49 Factors contribution to a 50 33 110 person's wellbeing. 21 25 58 100 300 a. a. b. b. C. C. d. d. e. e. status single Friendship 41 and social life Job or 27 primary activity Health and physical condition totals 80 120 State the null and alternative hypothesis State the observed values State the expected values Give the p-value Give a conclusion for the hypothesis test. 12

Answers

The conclusion of the hypothesis test is 0.342112

What is meant by hypothesis?

In statistics, hypothesis means an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true.

Here we have given that the factors that contribute to a person's wellbeing, That is Friendship and social life, job or primary activity, and health and physical condition), Independent of a person's marital status.

And we need to find the null and alternative hypothesis and the conclusion of the hypothesis test.

As per the given table of data we have to calculated the p value in order to find the null and alternative hypothesis,

For that we gathered the value of the following,

Number of samples = 9

Then the mean value of data = 83.63

And the standard deviation of the data = 80.475

Then the p - value is calculated as,

p-value ≈ 0.342112

This decision is made at significance level α = 0.05.

Therefore, the result is not statistically significant: there is not enough evidence to reject the null hypothesis.

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give an example of a continuous map with x and y connect that is one to one and honto but is not a homemorphism g

Answers

Let X be the integers with the topology created by declaring a set to be open if either it is a subset of N or it is the entire set Z. Then, we define a map f: X --> X such that f(x) = x- 1 is an example of continuous map is one to one and honto but is not a homemorphism .

What is a bijective function?

A function f: A --> B is said to be bijective or bijection if it satisfies both injective (one-to-one function) and surjective (over-function) properties. Let X be the integers with the topology created by declaring a set to be open if either it is a subset of N or it is the entire set Z. Then, we define a map

f : X--> X such that f(x) = x- 1 ; x∈X (domain)

Now, we show that it is bijective, so

One to One : let x₁ and x₂ belongs to X such that f(x₁) = f(x₂) we have to show x₁= x₂

f(x₁) = f(x₂) => x₁ - 1 = x₂ - 1

=> x₁ = x₂ -1 + 1

=> x₁ = x₂

So, f(x) is one to one.

Onto : let y be a element of X ( co-domain) We can show that there exists x∈A such that f(x)=y. Choose x= f⁻¹(y) and so f(f⁻¹(y))=y. So for all y∈B, there exists an x∈A such that f(x)=y. Therefore, it is onto. Thus, f(x) is one to one and onto and continus( due to polynomial nature) i.e it is a continuous bijection from X to itself, but it is not a

homeomorphism, since the image of N is not open.

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sylvia went on a trip. The number of shirts she packed was 2 fewer than twice the number of pants she packed. The total number of pairs of pants and shirts was 16

Answers

Answer:

She packed 6 pairs of pants and 10 shirts.

Step-by-step explanation:

Say the number of pants is x. Then, the number of pants is 2x-2. Now you have the equation:

x+ (2x-2)=16

Solving this equation gives x=6.

Therefore, she packed 6 pairs of pants and 10 shirts.

Hey WRLD... 999

Match each polynomial with its factorization. Type the number of the corresponding polynomial on the line of it’s factorization on the right.

1.
x2 – 2x – 48
_____ (x + 2)(9 – x)

2.
-3x2 + 14x - 8
____ (2 – 3x)(x – 4)

3.
X2 – 10x – 25
_____ (x + 6) (x – 8)

4.
-x2+7x+18
____ 3(x – 7) (x + 7)

5.
X4 – 16
_____ (x – 5)2

6.
3x2 – 147
_____ ( x – 2)( x + 2)( x2 + 4)

Answers

Each equation is expressed and mentioned in its factorized form are given above.

What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.

Given are the polynomials along with their factorized forms.

The polynomials along with their correct factorized forms are as follows -

x² - 2x - 48 → (x + 6) (x – 8)-3x² + 14x - 8 → (2 – 3x)(x – 4)x² – 10x + 25 → (x - 5)²- x² + 7x + 18 → (x + 2)(9 – x)x⁴ - 16 → (x – 2)(x + 2)(x² + 4)3x² – 147 → 3(x – 7) (x + 7)

Therefore, each equation is expressed and mentioned in its factorized form are given above.

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A linear relationship is given in the table below. Determine the slope of the relationship.
-1 / -3/ 2/3/4/7/8/15/10/19

Answers

The slope of the linear relationship will be 2.

What is Equation of line?

The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

A linear relationship is given in the table.

Now,

Let two point on the table are (- 1, - 3) and (2, 3).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (3 - (-3)) / (2 - (-1))

m = 6 / 3

m = 2

Thus, The slope of the linear relationship = 2.

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how do you prove 6^7-6^6+6^5 is divisible by 31

Answers

the same digit. Please note that in order to check the last digit of a5
a
5
you just can ignore all digits but the last one. Thus, you can asume that a
a
has a single digit. You only have to check the fifth power of the numbers 0 to 9. It’s easy and fun, if I may add

Step-by-step explanation:

I don't know if this is valid but

We can think of this problem like

(6^7-6^6+6^5)/31 = x

Where x is a whole number so 6^7-6^6+6^5 is divisible by 31

Multiply each side with 31 :

6^7-6^6+6^5 = 31x

We can turn 6^7 into 6^5 x 6^2

We can also turn 6^6 into 6^5 x 6

So the equation turns into this :

(6^5 x 6^2) - (6^5 x 6) + (6^5 x 1) = 31x

We can factor out the 6^5 out of the left side of the equation, which turns into :

(6^5) x (6^2 - 6 + 1) = 31x

Which is also :

(6^5) x (31) = 31x

Divide each side with 31

6^5 = x

X is obviously a whole number

A local university offers a review course for those who are planning to take the GRE exam. Thirty
percent of the people who took the exam had attended the university's GRE review course. The results
of the test showed that 60% of those who attended the review passed the exam, while among those who
did not attend the course, only 20% passed the exam. An individual has passed the exam. Knowing this,
what is the probability that he attended the review course?

Answers

The probability that an individual attended the course given he passed

is 37.5%.

What is conditional probability?

Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.

We know the probability of A given B is P(A/B) = P(A∩B)/P(B).

Let, The number of students be 100.

Given, Thirty percent of the people who took the exam had attended the university's GRE review course which is 30 and hence 70 people did not attend the review course.

60% of those who attended the review passed the exam,

= (60/100)×30.

= 18 people.

20% who passed the exam did not attend the review course.

= (20/100)×70.

= 14.

So, The no. of people who passed is (18 + 14)/100 = 32/100 = 0.32.

The probability that a student passed and taken the course is (18/30)×(14/70) = 0.12.

Therefore, Given that he passed, the likelihood that someone took the course is = (0.12/0.32) = 0.375 Or 37.5%.

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pls do this qwick

What is the product of (−23)(18)(−4)?

−1,656
−322
74
1,656

Answers

Answer:

1656

Step-by-step explanation:

Answer: 1656

Step-by-step explanation:

just trust me, that's the answer! I did the same question.

Indicate whether a binomial distribution is a reasonable probability model for the random variable X. give your reasons in each case.
joey buys a virginia lottery ticket every week. x is the number of times in a year that he wins a prize.

Answers

The given statement is a reasonable probability model because it fulfills the 4 conditions of binomial distribution.

How to identify binomial distribution model?

The conditions for binomial distribution are;

1: The number of observations n must be fixed.

2: Each observation must be independent.

3: Each observation must represent one of two outcomes ("success" or "failure").

4: The probability of "success" p must be the same for each outcome.

Now, we are given the statement;

Joey buys a Virginia lottery ticket every week. x is the number of times in a year that he wins a prize.

From that statement, we can tell that the number of observations is fixed at 52 weeks since a year is made up of 52 weeks.

Secondly, we can say that there could be success by winning a price or failure by not winning the price.

Each weekly observation is independent.

The probability is the same for each outcome.

Thus, we conclude that since it fulfills all the four conditions then it is a binomial model.

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4. The diagram shows a right triangle and the lengths of two of its sides in inches.
11.9
d
¡0m
7.9 in.
Which measurement is closest to the value of din inches?

Answers

Answer:

Step-by-step explanation:

Read the following prompt and type your response in the space provided.
Kim's teacher has marked this problem as one to recheck, but Kim cannot determine what she has done incorrectly. Identify Kim's error and write a correct solution.

Six less than 2 times a number is 50. What is the number?

2x – 6 = 50 (line 1)

2x – 6 – 6 = 50 – 6 (line 2)

2x = 44 (line 3)

2x ÷ 2 = 44 ÷ 2 (line 4)

x = 22 (line 5)

Answers

Kim’s error was in line 2 when she subtracted 6 instead of adding it. To cancel out -6, you would have to ADD 6, not subtract. So doing what Kim did would actually just make the problem 2x - 12 = 44, not have gotten rid of the -6.
If Kim had added 6 instead, she would’ve gotten
2x - 6 + 6 = 50 + 6 in line 2
2x = 56 in line 3
2x / 2 = 56 / 2 in line 4
x = 28 in line 5

(100 points plus brainliest) A proportional relationship between the number of pounds of potatoes (x) and the price in dollars (y) is graphed, and the ordered pair (4, 3) is on the graphed line

what is the price of 1 pound of potatoes? SHOW YOUR WORK

Answers

Answer: $0.75

Step-by-step explanation:

-We know that the line must also contain the point (0,0), as 0 pounds of potatoes would cost $0. Thus we can find the slope of the line and write an equation:

slope = Δy/Δx = (3-0)/(4-0) = 3/4

y = (3/4)x

(The y-int (aka b) is 0 since the line passes through (0,0))

Plugging in 1 yields $0.75

Answer:

$0.75 per pound

-------------------------------------------------------

Proportional relationship equation:

y = kx, where k-constant of proportionality

Given point (4, 3).

Use its coordinates to find the value of k:

3 = 4kk = 3/4k = 0.75

This is representing the price of 1 pound of potatoes.

Simplify (-3x^4) (-4x^2)

Answers

Remove all -
Proceed with equation

12x^6

Final answer

Step-by-step explanation:

(-3x⁴)(-4x²)

as multiplication is commutative (that means the sequence of the factors is irrelevant), we get

-3×-4×x⁴×x²

we can combine everything of the same type (constants or variable names).

-3×-4 = 12

remember, -×- = +

x⁴×x² = x⁶

remember, when multiplying terms with the same base variable, we can simply add the exponents.

why ? because an exponent is a short way of saying that the base variable has to be multiplied by itself that many times.

e.g.

a³ = a×a×a

a⁷ = a×a×a×a×a×a×a

a³×a⁷ = a×a×a × a×a×a×a×a×a×a = a¹⁰

that's why.

so, the complete simplified expression is

12x⁶

Here are the shopping times (in minutes) for each of fifteen shoppers at a local grocery store. Shopping times (in minutes) 29 35 27 26 24 20 37 34 24 33 24 36 32 18 31 (b) Construct a histogram for the data. (a) Complete the grouped frequency distribution for the data. (Note that the class width is 5.) Frequency Shopping times (in minutes) Frequency 18 to 22 23 to 27 OOOO 28 to 32 33 to 37 18 to 22 23 to 27 28 to 32 Shopping times in minutes) 33 to 37 X 5 ? xo?

Answers

Frequency is the number of occurrences of a repeating event.

What do you mean by frequency?

The frequency of an occurrence or a value is the number of times it happens. A frequency table is a list of objects with the frequency of each item shown in the table.

The information that is gathered is called data. The quantity of occurrences of an event or value is referred to as its frequency. A frequency table is a table that lists items and displays how frequently each item happens.

The number of times a specific data value occurs is the frequency of that data. We use f to symbolise the frequency of a data value.

As an illustration, the grade A is said to occur frequently if five students received an A in science.

Here we have the events:

shopping time between occurrences frequency

18 to 22: 20, 18 2

23 to 27: 27, 24, 26, 24, 24 5

28 to 32 29, 31 2

33 to 37 37, 34, 35, 33, 36, 32 6

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What number is 0.1 less than 15.2?

Answers

Answer:

15.1

Step-by-step explanation:

Write the
slope-intercept form of the equation of
the line that passes through the point (1, 2) and
has the slope of 6.

Answers

2=6x1+b this is slope intercept form

Compare the key features of f(x)=2x-3 and the
linear function g shown below.

23. What do the slopes and the y intercepts
indicate about the linear functions f and g?

Answers

Answer:

f slopes was [tex]\frac{3}{2}[/tex] ,the y intercepts was -3

g slopes was [tex]-\frac{1}{3}[/tex],the y intercepts was -2

Step-by-step explanation:

g slopes :

functions g has point (0,-2) and (3,-3)

the slopes =[tex]\frac{-2-(-3) }{0-3} =-\frac{1}{3}[/tex]

URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Question 7

Answers

The first blank as required to be filled in the task content should be filled with; two.

The second blank as required to be filled in the task content should be filled with; 134.1 in³.

What is the volume of the cone?

According to the information given; the diameter of the beachball is; 8 inches. Therefore, it's radius is half that; 4 inches.

On this note, the volume of the beachball which is spherical in shape given by the formula;

Volume of a sphere = (4/3)πr³ where;

Radius, r = 4;

Therefore, volume of beachball is;

4/3 π (4)³ = 256π / 3.

Also, the volume of the cone which is given by the formula;

Volume of a cone = (1/3) π r² h

where; Radius, r = 4 and Height, h = 8.

Therefore, volume of the cone is;

(1/3) π (4²) × 8 = 128π / 3.

On this note, by dividing the volume of beachball by that of cone; we have that;

( 256π / 3 ) / ( 128π / 3 ) = 2.

On this note, the cone will fit into the beachball about 2 times.

Also, the volume of the cone given that; π = 22 / 7 can be evaluated as;

( 128 × 22 ) / ( 7 × 3 )

= 134.1 in³.

Answers

No. The proof is wrong.

Here we are asked to prove all Natural numbers are either even or odd.

Natural numbers start from 1 to infinity.

Hence to prove by mathematical induction, we need to take the base case to be n = 1.

here, 1 = 2X0 + 1, therefore 1 is odd

Then we need to assume that for any integer m < n, m is either even or odd.

Now n > 1

Therefore,

n -1 > 0

Hence n - 1 will be a natural number.

Hence by our earlier assumption where any number smaller than is either even or odd

n - 1 has to be either even or odd.

case 1

here n - 1 is odd

if n - 1 is odd then

n-1 + 1 is a sum of two odd numbers, hence n is even

Case 2- If n - 1 is even

then, n-1 + 1 is a sum of an even and n odd number hence n is odd

Therefore n will either be even or odd.

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when max and evie were counting their items of candy after trik or treating. the total humber of items was at least 90 and at most 115. If Evie had 42 items of candy, which of the following inequalities represents all possible number of items, m, that Max could have had?

Answers

Answer:

48 ≤ m ≤ 73

Step-by-step explanation:

Evie has 42, Max has x.

Total candy = x + 42

90 ≤ x+42 ≤ 115

48 ≤ m ≤ 73

Max can have 48 or more, but no more than 73

The equation the quantity x plus 28 end quantity over 5 equals 3 times x models the workload of a class project, where x is the number of hours each student must contribute. How many hours does each student work on the project?

2 hours
5 hours
7 hours
12 hours

Answers

The number of hours that each student work on the project is 2 hours.

How many hours will be illustrated?

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this situation, the equation the quantity x plus 28 end quantity over 5 equals 3 times x models the workload of a class project, where x is the number of hours each student must contribute.

This will be:

(x + 28) /5 = 3x

Cross multiply

x + 28 = 15x

Collect like terms

15x - x = 28

14x = 28

Divide

x = 28 / 14

x = 2

The number of hours is 2 hours.

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Answer: that answer is right ^

Step-by-step explanation:

A random sample of n measurements was selected from a population with unknown mean and standard deviation o = 20 for each of the situations in parts a through d. Calculate a 95% confidence interval for ju for each of these situations. a. n=70, X = 27 b. n = 150, x= 115 c. n= 80. x = 18 d. n = 80, x=5.33

Answers

The 95% confidence interval for this situation is (0.95, 9.71).

What is the Standard deviation?

The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance.

The formula for Confidence Interval for Population Mean When Population Standard deviation is known

[tex]\bar{x} \pm Z_{a/2} * \frac{\sigma}{\sqrt{n} }[/tex]

α for 95% confidence level = (100-95)/100 =0.05

[tex]Z_{\alpha/2}[/tex] = 0.05/2=0.025

[tex]Z_{\alpha/2}[/tex] = Z0.025 = 1.96

σ = 20

95% Confidence Interval for Population Mean When Population Standard deviation is known