Where is the graph of f(x)= 4LX-3]+ 2 discontinuous?
all real numbers
all integers
only at multiples of 3
only at multiples of 4

Where Is The Graph Of F(x)= 4LX-3]+ 2 Discontinuous?all Real Numbersall Integersonly At Multiples Of

Answers

Answer 1

Answer:B all integers

Step-by-step explanation: took the test

Answer 2

The option second all integers are correct because for every value of the x the function will always give an integer value.

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function

f(x)= 4[X-3]+ 2

f(x) represents the greatest integer function, which means for every value of the x the function will always give an integer value.

The function will be discontinuous for all integers.

Thus, the option second all integers are correct because for every value of the x the function will always give an integer value.

Learn more about the function here:

brainly.com/question/5245372

#SPJ2


Related Questions

A jar contains 6 blue gumballs, 4 yellow gumballs, and 8 red gumballs. What is the probability of choosing a yellow gumball and then a red gumball if the first gumball is placed back into the jar before the second is chosen?

Answers

Answer:

2/9 or 22.22% and 4/9 or 44.44%

Step-by-step explanation:

6+4+8=18   4/18=2/9   8/18=4/9

00:00
Which is greater: 10 centimeters or 103 millimeters? How much greater?

Answers

Answer:

103 is greater by .3

Step-by-step explanation:

103 mm equals 10.3 cm so it is greater by .3

A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let Y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation.
y
p(x, y) 0 1 2
x 0 0.10 0.03 0.01
1 0.08 0.20 0.06
2 0.05 0.14 0.33
(a) Given that X = 1, determine the conditional pmf of Yi.e., pY|X(0|1), pY|X(1|1), pY|X(2|1). (Round your answers to four decimal places.)
y 0 1 2
pY|X(y|1)
(b) Given that two hoses are in use at the self-service island, what is the conditional pmf of the number of hoses in use on the full-service island? (Round your answers to four decimal places.)
y 0 1 2
pY|X(y|2)

Answers

Answer:

(a)

[tex]\begin{array}{cccc} {y} & {0} & {1} & {2} & {p(y|1)} &{0.2353}&{0.5882} & {0.1765}\ \end{array}[/tex]

(b)

[tex]\begin{array}{cccc} {y} & {0} & {1} & {2} & {p(y|2)} &{0.0962}&{0.2692} & {0.6346}\ \end{array}[/tex]

Step-by-step explanation:

Given

[tex]\begin{array}{ccccc}{} & {y} & { } & { }& { } & {x} & {0} & {1} & {2} & {total} & {0} &{0.1}&{0.03} & {0.01} & {0.14} & {1} &{0.08}&{0.20} & {0.06} &{0.34}& {2} &{0.05}&{0.14} & {0.33} &{0.52 } \ \end{array}[/tex]

Solving (a): Find PMF of y if x = 1

This implies that, we consider the dataset of the row where x = 1 i.e.

[tex]\begin{array}{ccccc}{} & {y} & { } & { }& { } & {x} & {0} & {1} & {2} & {total} & {1} &{0.08}&{0.20} & {0.06} &{0.34} \ \end{array}[/tex]

The PMF of y given x is calculated using:

[tex]Py|x(yi)=P(y=y_i|x)=\frac{P(y=x_i\ \&\ x)}{P(x)}[/tex]

When x = 1

[tex]P(x) = 0.34[/tex] --- the sum of the rows

So, we have:

[tex]Py|x(yi)=P(y=y_i|x)=\frac{P(y=x_i\ \&\ x)}{0.34}[/tex]

For i = 0 to 2, we have:

[tex]i = 0[/tex]

[tex]P(y=0|x)=\frac{P(y=0\ \&\ x = 1)}{0.34}[/tex]

[tex]P(y=0|x)=\frac{0.08}{0.34}[/tex]

[tex]P(y=0|x)=0.2353[/tex]

[tex]i =1[/tex]

[tex]P(y=1|x)=\frac{P(y=1\ \&\ x = 1)}{0.34}[/tex]

[tex]P(y=1|x)=\frac{0.20}{0.34}[/tex]

[tex]P(y=1|x)=0.5882[/tex]

[tex]i = 2[/tex]

[tex]P(y=2|x)=\frac{P(y=2\ \&\ x = 1)}{0.34}[/tex]

[tex]P(y=2|x)=\frac{0.06}{0.34}[/tex]

[tex]P(y=2|x)=0.1765[/tex]

So, the PMF of y given that x = 1 is:

[tex]\begin{array}{cccc} {y} & {0} & {1} & {2} & {p(y|1)} &{0.2353}&{0.5882} & {0.1765}\ \end{array}[/tex]

Solving (b): The interpretation of (b) is to find the PMF of y if x = 2

This implies that, we consider the dataset of the row where x = 2 i.e.

[tex]\begin{array}{ccccc}{} & {y} & { } & { }& { } & {x} & {0} & {1} & {2} & {total} & {2} &{0.05}&{0.14} & {0.33} &{0.52 }\ \end{array}[/tex]

When [tex]x = 2[/tex]

[tex]P(x) = 0.52[/tex]

So, we have:

[tex]Py|x(yi)=P(y=y_i|x)=\frac{P(y=x_i\ \&\ x)}{0.52}[/tex]

For i = 0 to 2, we have:

[tex]i = 0[/tex]

[tex]P(y=0|x)=\frac{P(y=0\ \&\ x = 2)}{0.52}[/tex]

[tex]P(y=0|x)=\frac{0.05}{0.52}[/tex]

[tex]P(y=0|x)=0.0962\\[/tex]

[tex]i =1[/tex]

[tex]P(y=1|x)=\frac{P(y=1\ \&\ x = 2)}{0.52}[/tex]

[tex]P(y=1|x)=\frac{0.14}{0.52}[/tex]

[tex]P(y=1|x)=0.2692[/tex]

[tex]i = 2[/tex]

[tex]P(y=2|x)=\frac{P(y=2\ \&\ x = 2)}{0.52}[/tex]

[tex]P(y=2|x)=\frac{0.33}{0.52}[/tex]

[tex]P(y=2|x)=0.6346[/tex]

[tex]P(y=0|x)=0.0962\\[/tex]

[tex]P(y=1|x)=0.2692[/tex]

[tex]P(y=2|x)=0.6346[/tex]

So, the PMF of y given that x = 1 is:

[tex]\begin{array}{cccc} {y} & {0} & {1} & {2} & {p(y|2)} &{0.0962}&{0.2692} & {0.6346}\ \end{array}[/tex]

when a fraction has a small numerator and a bigger denominator what you notice about the percent

Answers

when a fraction has a small numerator and a bigger denominator, the percent would be a proper fraction.

What is percent?

A percentage is a number or ratio that can be expressed as a fraction of 100 in mathematics. If we need to calculate the percentage of a number, divide it by the whole and multiply by 100.

As a result, the percentage denotes a part per hundred. The term % refers to one hundred percent. The symbol “%” represents it.

Therefore, When a fraction has a small numerator and a large denominator, it is a proper fraction.

Learn more about the percent, refer to:

https://brainly.com/question/28840349

#SPJ1

Swimming Pool B is also rectangular and has a perimeter of 90m. Its length is 25m. What is the width?

Answers

By using the formula for the perimeter, we will get that the width of the pool is 20 meters.

What is the width of the swimming pool?

Remember that for a rectangle of length L and width W, the perimeter is given by the formula:

P = 2*(L + W)

In this case, we know that the perimeter is 90m, and the length is 25m, then we know that:

P = 90m

L = 25m

Replacing that in the formula above we will get:

90m = 2*(25m + W)

now we can solve this for W.

90m/2 = 25m + W

45m - 25m = W

20m = W

The width of the pool is 20 meters.

Learn more about perimeter:

https://brainly.com/question/24571594

#SPJ1

Given that f(x)=x+9 and g(x)=4x
Evaluate:
a) fg(2)
b) gf(2)

Answers

Answer:

f(x)=11

g(x)=8

Step-by-step explanation:

f(x)=(2)+9=11

g(x)=4(2)=8

BRAINLIEST PLEASE

What is 20 minus 2 equal?

Answers

Answer:

18

Step-by-step explanation:

20-2=18

please brainiest

its 18

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

bye! <3

2(-2b)+2b=-8 what does b equal

Answers

Answer:

b = 4

Step-by-step explanation:

[tex]2(-2b) + 2b = -8[/tex]

Open the brackets & simplify the terms (which were in brackets).

[tex]=> -4b + 2b = -8[/tex]

[tex]=> -2b = -8[/tex]

Divide both the sides by -2

[tex]=> \frac{-2b}{-2} = \frac{-8}{-2}[/tex]

[tex]=> b = 4[/tex]

What is the mode of the quiz scores 2?3?4?5?

Answers

Answer:

2

Step-by-step explanation:

Frequency means the number of times the number appears.

2 appears the most since its frequency is the largest. 2 appeared 5 times.

Answer:

To find the mode, you have to find the number that appears the most.

Here, I see that 2 appears the most.

2 is the mode.

Step-by-step explanation:

There are a lot of lazy students.

I hope you are not one of them!

2 1/12 - 1 5/12
How many are left?

Answers

Answer:

is it 21 or 2 whole?

Step-by-step explanation:

plz clarify the question first i am discombobulated

Helppp can’t figure this one out

Answers

Answer:

x = 5.9

Step-by-step explanation:

Reference angle = 26°

Opposite = x

Adjacent = 12

Apply TO A:

Tan 26 = Opp/Adj

Substitute

Tan 26 = x/12

Multiply both sides by 12

12*Tan 26 = x

5.85279107 = x

x = 5.9 (nearest tenth)

Ques below: please answer that

Answers

The answer is 18 meters per second


990 divided by 55 equals 18

An ice cream store offers waffle cones or sugar cones. Each is equally likely to be chosen.

Which of the following models could be used to simulate this situation?



(HINT: Choose the model with the same number of possible outcomes as cone choices.)

Group of answer choices

A rolling a 6-sided number cube

B spinning a spinner with 3 equal sections

C flipping a coin

D using a random number generator that generates numbers 1 through 9

Answers

Answer:

C

Step-by-step explanation:

hopes it helps you!

Answer:

Flipping a coin

Step-by-step explanation:

It is the best answer, because the other choices do not represent a 50% chance. Rolling a 6-sided number cube would be good if you had 6 things, spinning a spinner would be ideal for 3, and using a number generator would be good for 9 things.

Lena sells two types of fidget toys. The price for each fidget toy A is x and the price for each Fidget B is y. Write an equation that will let her earn a profit of $3500 if she sells 20 of Fidget A and 60 of Fidget B

Answers

Answer:

3500 = 20x + 60y

Step-by-step explanation:

Its just the answer

can someone help me please i really have to do this right now

Answers

Answer: Angles 2 and 4 = 38, Angle 1 = 142

Step-by-step explanation:

Given that angle 3 is equal to 142, the angle between 2 and 3 has to add up to 180. 142 + 38 = 180. The same applies for angle 4 and 3. So, angle 1 + angle 2 has to add up to 180. We already know angle 2, so now we just have to subtract that from 180 to find angle 1.

Beverly Hobbs earns $683 a week she is single and claims 2 allowances what amount is withheld weekly for federal income tax

Answers

Therefore, $52.25 is the answer to the inquiry about what percentage of a person's income is withheld each week for federal income tax.

What is percentage?

A % is a number that indicates how many out of 100 it is, and it can also be expressed as a decimal or a fraction. Put the percentage value in the numerator and 100 in the denominator to convert a percentage to a fraction.

Here,

The Federal Insurance Contribution Act is the American legislative framework in use here, and it contains the criteria and guidelines that are utilized to determine payroll taxes on an employee's paychecks. The social security and Medicare programs are funded through taxation, which is paid by both employers and employees.

The amount of federal income tax deducted from the weekly cheque is:

6.2% from Social Security plus 1.45% from Medicare.

= 7.5 percent of the weekly gross salary.

The amount of federal income tax withheld each week from Beverly Hibbs's $683.00 weekly salary is:

= 0.0765 × 683

= $52.25

Therefore, $52.25 is the answer to the inquiry about what proportion of a person's income is withheld each week for federal income tax.

To know more about percentage , visit

brainly.com/question/20260562

#SPJ1

Which expression results in a rational number?

Answers

Answer:

3

Step-by-step explanation:

It equal .4, which is rational because it doesn't repeat.

Answer:

3

Step-by-step explanation:

dave earns $200 per week plus 4.1 commission. He sold $5175.50 in the month of February. What is his gross monthly earinings for february?

Answers

The gross monthly earnings for February will be $1012.2

How to illustrate the expression?

It should be noted that gross monthly earnings simply means the earnings that an individual makes for a particular month.

In this case, Dave earns $200 per week plus 4.1 commission. He sold $5175.50 in the month of February. His gross monthly earnings for February will be:

= ($200 × 4) + (4.1% × $5175.50)

= $1012.2

Therefore, $1012.2 will be the earnings.

Learn more about expressions on;

brainly.com/question/723406

#SPJ1

Captain Crunch costs $3.50, while a pack of gourmet oatmeal costs $2.50. If $25 of
breakfast food was purchased and 8 total items were purchased, how many oatmeal
packets must have been bought?

Answers

Answer:

I believe the answer is 3

Step-by-step explanation:

1) 3.50 * 5 = 17.50

2) 2.50 * 3 = 7.50

3) 17.50 + 7.50 = 25

Answer:

Step-by-step explanation:

given:

25 = 3.5x + 2.5y

8 = x +y

use substitution to solve

8-x = y

25 = 3.5x + 2.5(8-x)

25 = 3.5x + 20-2.5x

5 = 1x

x = 5

they bought 5  Captain Crunch  :P  yes,  Captain Crunch is sooooo good

and 3 yucky oatmeal packets  :P  

so 3 packets of oatmeal  :)

Help!! Like what even is this

Answers

The new transformation coordinates are B""(6, 15), C""(-3, 12), and Dilate k=3 by multiplying both x and y by 3.

what is coordinates ?

When locating points or other geometrical objects precisely on a manifold, such as Euclidean space, a coordinate system is a technique that uses one or more integers or coordinates. Locating a point or item on a two-dimensional plane requires the use of coordinates, which are pairs of integers. Two numbers called the x and y coordinates are used to describe a point's location on a 2D plane. a collection of integers that represent specific locations. The figure often has two numbers. The first number denotes the front-to-back measurement, while the second number denotes the top-to-bottom measurement. For example, in (12.5), there are 12 units below and 5 above.

given

For point B,

B(1,2) → B'(1 , -2) → B"( 2, -5) → B""( 6 ,-15)

For point C,

C(-2,1) → C'( -2 , -1) → C"( -1 , -4 )→ C"" ( -3 , -12)

In order to reflect a point across the x-axis, keep the x coordinate constant while changing the y coordinate to its opposite.

<1, -3> the following translations: Add 1 to x, take 3 away from y.

Add 3 to both x and y to dilate k=3.

To know more about coordinates visit:

https://brainly.com/question/27749090

#SPJ1

please answer this question right now ​

Answers

Answer:

6) c

7) d

Step-by-step explanation:

6) 25 + 15= 40

40+35=75

Php. 75

7) 29•3=87

150-87=63

Php. 63

Hope this helps!


Two alien spaceships start traveling toward each other from space stations that are 710,000 km apart. The first spaceship started an hour before the second spaceship and is traveling at 110,000 km/hr. In how many hours will the two spaceships meet if the second spaceship is traveling at 90,000 km/hr?


The spaceship will meet in how many hours?

Answers

The time that it will take for the spaceships to meet is given as follows:

3 hours.

How to model the situation?

Each of the spaceships is traveling at a constant rate, hence linear functions are used to model the situation.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the parameters are given as follows:

The slope m represents the velocity.The intercept b represents the initial position.

The positive direction is considered from the first spaceship towards the second spaceship.

The first spaceship started an hour before the second spaceship and is traveling at 110,000 km/hr, hence the difference when the second spaceship starts traveling is given as follows:

710,000 - 110,000 = 600,000 km.

Then the functions are given as follows:

x1(t) = 110t.x2(t) = 600 - 90t. (negative as they travel in opposite direction).

They will meet when:

x1(t) = x2(t).

Hence:

110t = 600 - 90t

200t = 600

t = 600/200

t = 3 hours.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

The time that it will take for the spaceships to meet is given as follows:

3 hours.

How to model the situation?

Each of the spaceships is traveling at a constant rate, hence linear functions are used to model the situation.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the parameters are given as follows:

The slope m represents the velocity.

The intercept b represents the initial position.

The positive direction is considered from the first spaceship towards the second spaceship.

The first spaceship started an hour before the second spaceship and is traveling at 110,000 km/hr, hence the difference when the second spaceship starts traveling is given as follows:

710,000 - 110,000 = 600,000 km.

Then the functions are given as follows:

x1(t) = 110t.

x2(t) = 600 - 90t. (negative as they travel in opposite direction).

They will meet when:

x1(t) = x2(t).

Hence:

110t = 600 - 90t

200t = 600

t = 600/200

t = 3 hours.

More can be learned about linear functions at brainly.com/question/24808124

#SPJ1

How are they equivalent?

Answers

Answer:

A

Step-by-step explanation:

When you distribute what is in the parentheses you get 2.5m + 7m=9.5m, and then you add that to m aka 1m, which is 10.5m and they both end with -2.

Find the missing fraction worksheet 5 1/2 + ? = 7

Answers

Answer:

1 1/2

Step-by-step explanation:

7-5 1/2 is 1 1/2 so 1 1/2+5 1/2 -7

Jason bought 3/4 of jelly beans for $12.60 how much would a pound cost Jason

Answers

$16.80 because $4.20 x 3 = $12.60 and $12.60 + $4.20 = $16.80

In a class of 30 students, 6 have a brother and 12 have a sister. There are 14 students
who do not have any siblings. What is the probability that a student chosen randomly
from the class has a brother and a sister?
HELPPPPPP

Answers

30 students

14 have no siblings

that leaves 16 with siblings

6 have brothers and 12 have sisters which = 18 so 2 of the students have both a brother and a sister

2/30 students have a brother and a sister

1/15 chance

14. Find ST, 5 points plz

Answers

Answer:

7 Can I have brainliest

Step-by-step explanation:

7 find the ST , good luck!

100 POINTS TO WHOEVER ANSWERS CORRECT

if you could ask any 2 questions about a 5th degree polynomial function what would they be and why. HURRY

Answers

Answer:

Why is there no general symmetry?

Does it always take  six points or six pieces of information to describe a quintic function?

Why are the roots not solvable by radicals?

I really don't know the "why", I just steer away from them when I can.

What is the following difference?
2ab(√/192ab²)-5[√/81a¹b³
O-3ab √3ab²
O 18ab² (2/3a)-45a2b² (2√3b)
0-7ab(2√3ab²)
O
8ab(√3ab²-15ab² (2√3ab)

Answers

Expressions with equal values are considered equivalent expressions. the difference is 2ab(√/192ab²)-5[√/81a¹b³ is -7ab(2√3ab²)

what are expressions ?

In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted.

given

Rewrite the above expression as:

[tex]2ab\sqrt[3]{3*4^{3} *ab^{2} } - 5\sqrt[3]{3*3^{3} * a^{4}b^{5} }[/tex]

Evaluate the cube roots

[tex]2ab {4\sqrt[3]{3ab^{2} } } - 5 {3ab\sqrt[3]{3ab^{2} }[/tex]

Evaluate the differences

-7ab(2√3ab²)

Expressions with equal values are considered equivalent expressions. the difference is 2ab(√/192ab²)-5[√/81a¹b³ is -7ab(2√3ab²)

To know more about expressions visit :-

brainly.com/question/14083225

#SPJ1

Select the correct answer from each drop-down menu. Graph of a four-sided polygon on a coordinate plane at A (minus 1, minus 1), B (0, 1), C (2, 2), and D (2, minus 1). In the figure, polygon ABCD is dilated by a factor of 2 to produce A′B′C′D′ with the origin as the center of dilation. Point A′ is at (-2, -2) , and point D′ is at (4, -2) .

Answers

The coordinates of the vertices of polygon A'B'C'D' after the dilation are given as follows:

A'(-2, -2), B'(0, 2), C'(4,4), D'(4,-2).

What is a dilation?

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

The vertices of the original polygon for this problem are given as follows:

A(-1,-1), B (0, 1), C (2, 2), and D (2, -1).

The scale factor for the dilation in this problem is given as follows:

k = 2.

Hence the coordinates of the vertices of polygon A'B'C'D' after the dilation are given as follows:

A'(-2, -2), B'(0, 2), C'(4,4), D'(4,-2).

(as each coordinate of each vertex was multiplied by the scale factor of 2).

Missing Information

The problem is incomplete, hence the coordinates of the vertices of the image after the dilation were obtained to show how the dilation works.

More can be learned about dilation at brainly.com/question/3457976

#SPJ1

Other Questions
What do you believe our lives would be like today IF the Articles of Confederation had NOT be replaced with the US Constitution Solve 345=Please help me ASAPthe due date of my assignment is tomorrow . How many grams of Fe2O3 can be produced from 180 g Fe ? 480 over 840 turning it into the lowest term Requirements: Create and write (in Spanish, of course) your own original story. You can use vocabulary from the medical unit, the childhood unit, and the vacation unit. You are telling a story, therefore you must use the preterite and the imperfect tenses.Background information (imperfect)Secondary setting with interrupter (imperfect then preterite)Series of events in the preterite (preterite, preterite, preterite)2nd series of events in the preterite (preterite, preterite, preterite)Resolution or Ending (preterite-events and imperfect-feelings)Verbs must be typed in red for the preterite and typed in blue for the imperfect Help please look at picture^^ Meant this question sorry. how do you know if there is an elephant in your fridge? What is the center of a circle (x y) with the equation (x + 3)^2 + (y 5)^2 = 16 A thesis statement is usually introducedas the last sentence of an essayat the end of the introductionas the first sentence of an essayin the body of the essay Which component of the communication model is responsible for initiating the transaction and encoding the message Read the effect.Julia stopped her car at the parks visitor center to get a map and ask directions to her friends campsite.Which sentence states a corresponding cause?She was unfamiliar with the park layout.She packed marshmallows to roast over the fire.She followed the dirt road until she saw her friend waving.She asked the park ranger to mark her course on the map. The nurse is reinforcing health care provider education on the technique for an amniocentesis. Which piece of equipment will the nurse have ready 2) Julie wants to purchase swim lessons for her son. There are four different stores that offer swim lessons. Based on the lowest cost per minute, which store has the BEST deal ?Store A: $25 for a 45 minute lesson, Store B: $30 for a 1 hour lesson, Store C: $45 for a 1.5 hour lesson, and Store D: $80 for three 1 hour lessons When can we say that we are socially healthy? On August 5, 2021, Wildhorse Furniture shipped 50 dining sets on consignment to Furniture Outlet, Inc. The cost of each dining set was $440 each. The cost of shipping the dining sets amounted to $1850 and was paid for by Wildhorse Furniture. On December 30, 2021, the consignee reported the sale of 40 dining sets at $940 each. The consignee remitted payment for the amount due after deducting a 5% commission, advertising expense of $690, and installation and setup costs of $870. The total profit on units sold for the consignor is In Timbs v. Indiana the Supreme Court ruled ... WILL GIVE BRAINLIESTGroup of answer choicessince Timbs' car was worth much more than the fines, the fines could be paid for with the car.that states could impose excessive fines as long as due process was followed.that seizing Timbs' car was an example of excessive fines and that portion of the Eighth Amendment applies to the states.that the Indiana Supreme Court's decision on the Timbs case was in line with the Eighth Amendment. In 1841-42, thomas wilson dorr agitated for electoral reform and led an insurrection in what state?a. Pennsylvaniab. Virginiac. New Yorkd. Rhode Islande. South Carolina Which of the following is a reason why government is a participant in a market-oriented economy?a. To enforce contracts and protect private propertyb. To promote collusionc. To promote the growth of natural monopoliesd. To provide more inequality in the distribution of incomee. To promote externalities