Why do all sequences represent functions?

Answers

Answer 1

Basically, a sequence is a function whose domain is set of natural numbers and co-domain is set of real numbers.

Function:

A function relates each element of a set with exactly one element of another set (possibly the same set)

Real numbers:

Real numbers can be defined as the union of both rational and irrational numbers. They can be both positive or negative and are denoted by the symbol “R”.

Domain

Domain is the set of all possible inputs of a function.

Co - Domain:

Co - domain is the set of its possible outcomes or results.

Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. Formally, a sequence can be defined as a function from natural numbers (the positions of elements in the sequence) to the elements at each position.

That's why, every sequence must be the function itself.

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Related Questions

1. Ralf and Susie share $57 in the ratio 2:1.
(a) Calculate the amount Ralf receives.
(b) Ralf gives $2 to Susie.
Calculate the new ratio Ralf's money: Susie's money.
Give your answer in its simplest form

Answers

Ralf receives total amount of 38$.

Susie receives total amount of 19$.

What do you mean by amount?

Raff gets 2x

Suzie gets x

2x + x = 57 dollars

3x = 57 dollars

x = 19 dollars

2x = 38 dollars

Aggregation attempting to calculate the time it will take by looking at the overall number or quantity.

To sum up to a total is the definition of amount. A restaurant bill for four individuals that totals $50 is an example of the costs of four meals that come to $50.

To achieve success or importance. The words "amount to anything" or "amount to something," which both indicate the same thing, are almost always used.

Amount can be a noun or a verb, as was said above. Use of the noun: Add a little water to the dish. The quantity of food required vary each dog. It is three bucks and change, to be exact.

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what is the common denominator of 3/5, 4/9, 6/7?

Answers

Answer: hi! for the denominators (5, 9, 7) the least common multiple

Step-by-step explanation:

(LCM) is 315.

LCM(5, 9, 7)

Therefore, the least common denominator (LCD) is 315.

Calculations to rewrite the original inputs as equivalent fractions with the LCD:

3/5 = 3/5 × 63/63 = 189/315

4/9 = 4/9 × 35/35 = 140/315

6/7 = 6/7 × 45/45 = 270/315

Does anyone know this answer??

Answers

Answer: 2y-13

Step-by-step explanation: 2y => double of lenght
-13 => less than

helppp me solveeeeeee this ty 50+pnts

Answers

Answer:

1. 47
2. 4

Step-by-step explanation:

1. 4a + 5b

4(8) + 5 (3)

32+ 15
=47

2. 3a/2b
3(8)/2(3)
24/6
=4

Joe's employer will reimburse him $0.17 per mile driven. If Joe drives 185.74 miles on a business trip, what is his mileage reimbursement? Round your answer to the nearest cent.

Answers

how do you not know how to do this

0.17 times 185 = $136.9 or $137

(0.74 is not 1 mile)

Answer:

$31.58

Step-by-step explanation:

Reimburse for 1 mile,

→ $0.17

Then reimbursement for 185.74 miles,

→ 185.74 × 0.17

→ 31.5758

→ $31.58

Hence, the answer is $31.58.

Determining a Segment Length

how do i solve 4x-1

Answers

TQ is the same as TS which is 26

Fatoumata has a collection of 280 coins. How many coins represent 20% of her
collection?
Divide/scale down to solve for the missing percent.

Answers

The coins that represent the 20 5 of her coins that is 280 are 56 coins.

We know that:

Fatoumata has a collection of 280 coins.

Now, we need to tell how many coins will be its 20 %.

For this we will calculate 20 percent of 280

So, number of coins = N will be:

N = 20 % of 280

N = 20 % × 280

N = 20 / 100 × 280

N = 2 × 28

N = 56 coins

Therefore, we get that, the coins that represent the 20 5 of her coins that is 280 are 56 coins.

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Evaluate each expression so the equation is 8b-a and a=4 and b=6

Answers

Answer: 44

Step-by-step explanation: basically replace b with 6 and a with 4 in the expression 8b-a, which turns out to be 8(6)-(4). We're subtracting 4 from the product of 8(6), which is 48. 48-4 = 44

Help
me solve this pls

Answers

The constant of proportionality is 28.2.

How to calculate the constant of proportionality?

It should be noted that the miles driven and the number of gallons used has been given.

Therefore, the constant of proportionality will be:

= Miles driven / Gallons used

= 930.6 / 33

= 28.2

Therefore, the constant of proportionality is 28.2.

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Solve for the value of r.
52°
(4r-6)⁰

Answers

The value of r is 11°

How to determine the value

From the information given, we have that;

52°(4r-6)⁰

Both angles are complementary angles.

It is important to note that complementary angles sum up to 90 degrees

Then, we have;

52 ° + 4r - 6° = 90°

collect like terms

4r + 46° = 90 °

4r = 90 - 46

4r = 44

Make 'r' the subject of formula

Divide both sides by 4

4r/4 = 44/4

r = 11°

Thus, the value of r is 11°

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q+10q+4q q+10q+4qq+10q+4q

Answers

3q+30q+12q = 45q

Hope that helped :)

Answer:

35q+8qq

Step-by-step explanation:

i know is ryt

but y did u separate de first 4's other q like dat?

Solve the formula for the indicated variable

A=LWH for H

H=

Answers

Answer:

Step-by-step explanation:

[tex]A=LWH\\[/tex]

Divide both parts of the equation by LW:

[tex]\displaystyle\\\frac{A}{LW} =H\\\\Thus,\\\\H=\frac{A}{LW}[/tex]

The diorama of a town uses the scale 5 inches : 10 miles. If the diorama measures approximately 60 inches across, what is the approximate measure of town?

Answers

Answer: 120 miles

Step-by-step explanation:

      We will set up a proportion to solve.

 Set up a proportion:

[tex]\displaystyle \frac{5\text{ inches}}{10\text{ miles}} =\frac{60\text{ inches}}{x\text{ miles}}[/tex]

 Cross-multiply:

5 * x = 60 * 10

 Multiply:

5x = 600

 Divide both sides by 5:

x = 120 miles

During 1 hour of television there are 12 commercials. If you watch 3 hours of television how many commercials will there be (please explain in numbers

Answers

Answer: 36

Step-by-step explanation: the reason why is that if each hour there is 12 commercials then by the third hour there will be 36 we can also use multiplication 12x3=36  I hope that helps

suppose you have two bags of marbles that are in a box. bag 1 contains 7 white marbles, 6 black marbles, and 3 gold marbles. bag 2 contains 4 white marbles, 5 black marbles, and 15 gold marbles. the probability of grabbing the bag 1 from the box is twice the probability of grabbing the bag 2. if you close your eyes, grab a bag from the box, and then grab a marble from that bag, what is the probability that it is gold?

Answers

The probability that it is gold is (1/3).

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability. If two events are mutually exclusive, then there is a 0 percent chance that they will both happen at the exact moment. Two events are said to be mutually exclusive if they share no elements (their intersection is the empty set). Consequently, P(A∩B)=0.

Let A be the event that a gold marble is picked.

Let B₁ and B₂ be the event that the first bag is chosen and the second bag is chosen respectively.

Given: P (B₁ ) = 2.P(B₂)

Also, P(B₁) + P(B₂) = 1

∴ 2P(B₂) + P(B₂) =1

3P(B₂) = 1

P(B₂) = 1/3 and  P(B₁) = 2/3

Now

P(A)

= P(A∩(B₁∪B₂))

= P[(A∩B₁)∪(A∩B₂)]

Probability adds up because the events are mutually exclusive

= P(A∩B₁) + P(A∩B₂)

= P(B₁). P(A/B₁) + P(B₂). P(A/B₂)

= (2/3)×(3/16) + (1/3)×(15/24)

= (1/3)

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8) the lion at the zoo became ill and lost 6 pounds every week for 3 weeks. in the fourth week, she began to feel better and gained 5 pounds. write and find the value of an expression for the change in the lion's weight.

Answers

Answer:

w - 13.

Step-by-step explanation:

Change in weight

= w - 3(6) + 5   where w is her original weight.

= w - 18 + 5

= w - 13.

tickets to the zoo cost $4 for children, $5 for teenagers and $6 for adults. in the high season, 1200 people come to the zoo every day. on a certian day, the total revenue at the zoo was $5300. for every 3 teenagers, 8 children went to the zoo. how many teenagers went to the zoo? a. 100 teenagers c. 300 teenagers b. 200 teenagers d. 400 teenagers please select the best answer from the choices provided a b c d

Answers

300 teenagers went to the zoo.

How to find the how many teenagers went to the zoo?

given that

Tickets to the zoo cost $4 for children.

Tickets to the zoo cost $5 for teenagers.

Tickets to the zoo cost $6 for adults.

1200 people come to the zoo every day.

on a certian day, the total revenue at the zoo was $5300.

Let the number of adults be x.

The number of teenagers be y.

and the number of children that went to the zoo 8y/3.

Consider the question

1200 people come to the zoo every day.

x + y + 8y/3 = 1200

now, take L.C.M between y and 8y/3

[tex]x + \frac{(3y + 8y)}{3} = 1200 \\ x + \frac{11y}{3} = 1200[/tex]

now multiply with 3 to this equation.

3x + 11y = 3600 .......................(1)

tickets to the zoo cost $4 for children, $5 for teenagers and $6 for adults.

according to the question

6x + 5y + 32y/3 = 5300

Now take the L.C.M between 5y and 32y/3

6x + 47y/3 = 5300

now multiply with 3 to this equation.

18x + 47y = 15900 ...................(2)

now, multiply equation (1) with 6

18x + 66y = 21600 .....................(3)

now, subtract equation (1) in equation (2)

(18x - 18x) + (66y - 47y) = (21600 - 15900)

19y = 5700

y = 5700/19

y = 300

Hence, the 300 teenagers went to the zoo.

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b is less than or equal to 6.
options are attached

Answers

Answer:

b ≤ 6

This inequality matches the statement, "b is less than or equal to 6."

This is because the sign < tell us that b is going to be less 6, and the line _ tells us that the solution can also be equal to 6.

this visual representation shows the sets of real numbers. classify the number −25. select all terms that are correct. natural whole integer rational irrational −25 natural – negative 25 whole – negative 25 integer – negative 25 rational – negative 25 irrational – negative 25

Answers

Classify the number -25.

Natural, Whole, Integer, Rational, Irrational.

25 is a rational number. This number is a whole that may be expressed as the fraction 25/1.

What is meant by negative number?

This wouldn't be a natural number because -25 is a negative number.

Since -25 isn't a positive number, this wouldn't be a whole number.

the whole number 85 is -85, which is a negative number. -85 is consequently an integer. Negative numbers are rational numbers.

square integers are frequently irrational, -25 is a square root.

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Charlette reads 8 1/3 pages of a book in 10 minutes. What is her average reading rate in pages per minute?

Answers

Answer:

Step-by-step explanation:

8 1/3 pages/10 minutes = 25/3 pages / 10 minutes = 25/30 pages/minute = 5/6 page/minute

. In a triangle, one angle is 5° more than the
measure of the second angle. The third
angle is 10° more than the measure of the
second angle. Find the measure of each
angle angle

Answers

The angles are 60°, 55°, and 65°.

Let the triangle be named ΔABC.Let the angle ∠A be "x".Then, the angle ∠B is equal to ∠A + 5°.The angle ∠B is equal to x + 5°.The angle ∠C is equal to ∠A + 10°.The angle ∠C is equal to x + 10°.The angle ∠C is equal to x + 10°.Using the angle sum property of a triangle, we know that the sum of all the angles in a triangle is equal to 180°.∠A + ∠B + ∠C = 180°(x) + (x + 5°) + (x + 10°) = 180°3x + 15° = 180°3x = 165°x = 55°The angle ∠A is equal to 55°.The angle ∠B is equal to 55° + 5° = 60°.The angle ∠C is equal to 55° + 10° = 65°.

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how many solutions does the equation 3x-1=3x+1 have

Answers

Answer:

0

Step-by-step explanation:

[tex]3x-1=3x+1\\=3x-1-3x=3x+1-3x\\-1=1[/tex]

Due to the fact that the sides are unbalanced, the equation has no true solution.

Cookies are sold in the lunchroom for $2. Ana wants to buy cookies for a group of her friends. If she has $20, write an inequality to show the number of cookies cc she can buy. Use the variable c
As a inequality

Answers

Answer:

2c < 20

Step-by-step explanation:

$2 is the price per cookie so 2c is per every cookie, you multiply by 2 to get the price.

Ana only has $20 so the amount of money she spends has to be less then 20 so the inequality would be 2c < 20

9. Use the graph of the sequence to answer the parts.

a. Is the sequence arithmetic, geometric, or neither Explain.

b. Write a recursive formula for the sequence.

c. Write an explicit formula for the sequence.

Answers

The recursive formula for the sequence is T(n+1) = Tn - 3 where T1 = 19 and the explicit formula for the sequence is Tn = 22 - 3n

a. Is the sequence arithmetic, geometric, or neither

On the given graph, we have the following points

19, 16, 13, 10, 7

These points represent the nth term of the sequence

See that the points have a common difference of -3

Hence, the sequence is an arithmetic sequence

b. Write a recursive formula for the sequence.

In (a), we have

T1 = 19

d = -3

So, we have

T2 = T1 + d

This gives

T2 = T1 - 3

Express 2 as 1 + 1

So, we have

T(1+1) = T1 - 3

Express 1 as n

So, we have

T(n+1) = Tn - 3

Hence, the recursive formula for the sequence is T(n+1) = Tn - 3 where T1 = 19

c. Write an explicit formula for the sequence.

In (a), we have

T1 = 19

d = -3

So, we have

Tn = T1 + (n - 1)d

This gives

Tn = 19 + (n - 1) * -3

Evaluate

Tn = 19 + 3 - 3n

Evaluate the sum

Tn = 22 - 3n

Hence, the explicit formula for the sequence is Tn = 22 - 3n

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50 POINTS!
Solve for x (and you only have to do odd numbers if you want):
1. 3(x+2)=21
2. 5(2x-1)=-25
3. -4(3x-5)=-16
4. -2(4-x)-5=11
5. 3(-6x+7)+4x=-7
6. 2(3x-4)+5(2x+3)=-9
7. 5(x+9)=65
8. 1/2(x-3)=-4
9. 5x+2(x-6)+7=2
10. 9(x+3)-14x-15=52

Answers

1.x=5

2.x=-2

3.x=3

4.x=12

5.x=2

6.x=-1

7.x=4

8.x=-5

9.x=1

10.x=-8

Pls correct me on any of these if I made a mistake

In the diagram below, AB is parallel to CD. What is the value of x?

Answers

Answer:

Can I see the diagram?

Step-by-step explanation:

The midpoint of AB is M(3, -1). If the coordinates of A are (5, 1) what are the coordinates of B?

Answers

The coordinates of B is (1,-3) .

A midpoint formula is a formula used to identify the midpoint between two data points. Except for geometry, research in  economics uses this calculation to calculate elastic moduli, etc.The Midpoint Formula is given by [tex](x, y)=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex] where, [tex](x_1,y_1)[/tex] are the coordinates of the first point and  [tex](x_2,y_2)[/tex] are the coordinates of the second point.

It is given that midpoint of AB is (3, -1) and coordinates of A is (5, 1) .

Let the coordinate of B be (x, y) .

By using midpoint formula , we get

[tex](3, -1)=(\frac{5+x}{2} , \frac{y+1}{2} )\\[/tex]

On comparing , we get the x- coordinate

   [tex]\frac{5+x}{2} =3\\\5+x=6\\x=1[/tex]

On comparing , we get the y- coordinate

[tex]\frac{1+y}{2} =-1\\\\1+y=-2\\y=-3[/tex]

Hence , the coordinates of B is (1,-3) .

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HELPPP ASAP
What is the product of the solutions to the equation?
(2x +4) = 14
A 45
B 81
C 0
D -81
E -45

Answers

Answer:

no answer

Perhaps: E -45

Step-by-step explanation:

(2x + 4) = 14

2x + 4 = 14

2x = 10

x = 5

This equation has only 1 solution.

There cannot be the product of the "solutions" when there is only 1 solution.

Perhaps you meant this (absolute value, not parentheses):

What is the product of the solutions to the equation?

|2x +4| = 14

A 45

B 81

C 0

D -81

E -45

|2x + 4| = 14

2x + 4 = 14 or 2x + 4 = -14

2x = 10  or  2x = -18

x = 5 or x = -9

The product of 5 and -9 = -45

Answer: E -45

a game in which one person tries to trap another in a mistake, lie, or some other type of negative situation is known as a game

Answers

Answer:

"Wooden leg" is the correct answer.

Helpppppppp 27 points MATHH

Answers

Answer:

y

Step-by-step explanation:

x^(-7) * x^7 * y^(-6)/y^(-7)=

x^(-7+7) * y^(-6-(-7))=

x^0 * y^(-6+7)=

1 * y^(7-6)=

y^1=y

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