Show every subsequence of a subsequence of a given sequence is itselfa subsequence of the given sequence. Hint: Define subsequences asin (3) of Definition 11.1 g

Answers

Answer 1

Answer: Suppose that [tex]S_{n}[/tex],  [tex]K_{n}[/tex] and [tex]A_{n}[/tex] are all sequences, also suppose that  [tex]A_{n}[/tex] ⊂ [tex]K_{n}[/tex] ⊂ [tex]S_{n}[/tex]  ∀ [tex]n[/tex] ∈ [tex]Z^{+}[/tex]. This implies that [tex]A_{n}[/tex] ⊂ [tex]S_{n}[/tex] as required. 

Step-by-step explanation:

If you suppose that [tex]S_{n}[/tex],  [tex]K_{n}[/tex] and [tex]A_{n}[/tex]  are all representing three sequences respectively, and you also suppose that  [tex]A_{n}[/tex] is a subset (in other words subsequence) of [tex]K_{n}[/tex] and [tex]K_{n}[/tex]  is a subset (in other words subsequence) of [tex]S_{n}[/tex], where n takes its values from the set of positive integers. We can safely say that [tex]A_{n}[/tex] is a subsequence of [tex]S_{n}[/tex] and this can demosnstrated mathematically as follows:

Suppose that [tex]S_{n}[/tex],  [tex]K_{n}[/tex] and [tex]A_{n}[/tex] are all sequences, also suppose that  [tex]A_{n}[/tex] ⊂ [tex]K_{n}[/tex] ⊂ [tex]S_{n}[/tex]  ∀ [tex]n[/tex] ∈ [tex]Z^{+}[/tex]. This implies that [tex]A_{n}[/tex] ⊂ [tex]S_{n}[/tex] as required. 


Related Questions

A bakery cooks 15 cakes in 3 hours. At this rate, how many cakes can they bake in 8 hours?

Answers

Answer:

40

Step-by-step explanation:

IMPLAYER
Every day after ser daily walk, Dena drinks 1.06 liters of water. Which decimal is equivalent to 1.06?
A 1.6
O
B. 1.600
C. 1.060
D. 1.006

Answers

Answer:

C. 1.060

Explanation:

r Which decimal is equivalent to 1.06? Well, if you look at it, c. 1.060 is just 1.06 with a zero added at the end... And we all know zeros have no value. So you can technically just take off the zero at the end and have 1.06. But this is a multiple-choice so you don't get to choose whether or not to take the zero off. So yeah, the answer is c.

Please mark brainliest!

¿Cuál es la desigualdad de 3 x - 4> 4-4-3 x

Answers

3 x - 4> 4-4-3
3x-4>-3
suma 4 a ambos lados:
3x>1
dividir 3 en ambos lados:
x>1/3

Consider the following graph of an exponential function.

Answers

Answer:

A= All are real numbers

B=y>-2

c= the graph is not increasing

d= the graph is decreasing for all real numbers of x

none for both

Step-by-step explanation:

A= All are real numbers

B=y>-2

c= the graph is not increasing

d= the graph is decreasing for all real numbers of x

none for both

whats 2 plus 2? do u know?

Answers

I think it might be 4.. I’m not sure tho

Write the number 0.0049 in scientific notation.

Answers

Answer:

= 4.9*10^-3

Step-by-step explanation:

Hope it helpzzz

4.321 × 12.34 AND IF YOU ANSWER YOU GET 10 POINTS JUST PLS HELP

Answers

Answer:

53.32114

Step-by-step explanation:

This problem illustrates the limit derivation of a Poisson distribution from Binomial distributions. Suppose an average of 66 arrivals occur during a 30 minute interval. To count arrivals, divide the 30 minute interval into nn sub-intervals. On the previous problem, you found the probability pp of one arrival during a single sub-interval for each n given. Now, compute the (estimated) probability that there will be, in fact, exactly 6 arrivals during a 30 minute interval, with each probability model:

a. Using Binomial with n=30, the chance of 6 arrivals is estimated as:__________
b. Using Binomial with n=60, the chance of 6 arrivals is estimated as:__________
c. Using Binomial with n=100n=100, the chance of 6 arrivals is estimated as:________
d. Using Poisson, the chance of 6 arrivals is estimated as:________

Required:
Use a probability calculator, and enter answers in decimal form, rounded to at least four places after the decimal.

Answers

Answer:

1. 0.1795

2. 0.1693

3. 0.1657

4. 0.1606

Step-by-step explanation:

This problem was solved using the binomial distribution

1.

N = 30

P = 6/30 = 0.2

Using binomial distribution

30C6 x 0.2⁶ x 0.8²⁴

= 593775 x 0.000064 x 0.004722

= 0.1795

2.

N = 60

P = 6/60 = 0.1

60C6 x 0.1⁶ x 0.9⁵⁴

= 50063860 x 0.000001 x 0.00338139

= 0.1693

3.

N = 100

100C6 x 0.06⁶ x 0.94⁹⁴

= 1192052400 x 0.000000046656 x 0.00297864

= 0.1657

4.

Poisson distribution was used here

e^-6(6)⁶/6!

= 0.1606

Please help 60 Points!!!!!!!! my school is glitched :C

Answers

Answer:

its the two that are glitched because its not any of the other ones

Step-by-step explanation:

Answer:

reload

Step-by-step explanation:

* Which answer choice describes y = -3x² +7x - 2​

Answers

This is the answer for that question:
Y=-(3x-1)(x-2)

Answer:

y = -[tex]3^{2}[/tex] + 7x - 2

Step-by-step explanation:

-9-2= -11

y = -11 +7x

+11

y+11 = 7x

/7

1.57142857143= x

SOMEONE HELP PLZ BRAINLIEST

Answers

Answer:

f = 3n = -16h = -10z = 7.5x = 54v = -12[tex]d = -\frac{417}{25}[/tex]  w = -27.6t = -5w = 43

I hope this helps!

Answer:

F=3

n= -16

h= -10

z =7.5

x=54

v= -12

d= -416÷25

w= -27.6

t= -5

w= 43

If f(x) = 2x2 + x-1, then f(-5)
= ?

Answers

Answer:

-54

Step-by-step explanation:

(-5)^2 = -25

2(-25)+ -5 +1 =-54

Answer:

f(-5) = -2

Step-by-step explanation:

f(-5) = 2x2 + -5 -1

f(-5) = 4 - 6

f(-5) = -2

what is the answer to the first one? pls help

Answers

Answer:

Step-by-step explanation:

14.75 - 8.85 = 5.9

5.9/2

5.9/2 sssssssssssssss

what is 0.067 reccuring as a fraction

Answers

Answer:

67/1000

Step-by-step explanation:

How to translate 0.067 to a fraction:

So you can there is the tenths place (which is considered 0 on the decimal behind the point.) The hundredths place (where the 6 is placed), and the thousandths place (where the 7 is placed.)

Since the 7 is placed at the thousandths place, that means the denominator would be 1000. The number behind the point is .067.

So the fraction would be this:

67/1000

(Also it's at it's simplest form.)

Ray AB is the angle bisector of

Answers

Answer:

Angle CAD

Ray AB is bisecting angle CAD.

(4x+1) = 64

because by getting the angle bisector you are able to get 16 which is X

What is 14 + (8y + 2) =

Y=5

Answers

Answer:

not sure but i think 64 ?

14+((8x5)+2)=14+42=56

About Each statement below involves odd and even integers. An odd integer is an integer that can be expressed as 2k+1 , where k is an integer. An even integer is an integer that can be expressed as 2k , where k is an integer. Prove each of the following statements using a direct proof.

a. The sum of an odd and an even integer is odd.
b. The sum of two odd integers is an even integer.
c. The square of an odd integer is an odd integer.
d. The product of two odd integers is an odd integer.

Answers

Answer:

a. The sum of an odd and an even integer is odd: 3 + 2 = 5

b. The sum of two odd integers is an even integer: 3 + 5 = 8

c. The square of an odd integer is an odd integer: 3² = 9

d. . The product of two odd integers is an odd integer.: 3 x 5 = 15

Step-by-step explanation:

Proving the following statements using a direct proof;

a. The sum of an odd and an even integer is odd:

let the odd integer = 3

let the even integer = 2

3 + 2 = 5

5 is an odd integer, proved

b. The sum of two odd integers is an even integer.

let the first odd integer = 3

let the second odd integer = 5

3 + 5 = 8

8 is an even integer, proved

c. The square of an odd integer is an odd integer. .

let the odd integer = 3

3² = 9

9 is an odd integer, proved

d. The product of two odd integers is an odd integer.

let the first odd integer = 3

let the second odd integer = 5

3 x 5 = 15

15 is an odd integer, proved

Answer:

a. The sum of an odd and an even integer is odd: 3 + 2 = 5

b. The sum of two odd integers is an even integer: 3 + 5 = 8

c. The square of an odd integer is an odd integer: 3² = 9

d. . The product of two odd integers is an odd integer.: 3 x 5 = 15

Step-by-step explanation:

Proving the following statements using a direct proof;

a. The sum of an odd and an even integer is odd:

let the odd integer = 3

let the even integer = 2

3 + 2 = 5

5 is an odd integer, proved

b. The sum of two odd integers is an even integer.

let the first odd integer = 3

let the second odd integer = 5

3 + 5 = 8

8 is an even integer, proved

c. The square of an odd integer is an odd integer. .

let the odd integer = 3

3² = 9

9 is an odd integer, proved

d. The product of two odd integers is an odd integer.

let the first odd integer = 3

let the second odd integer = 5

3 x 5 = 15

15 is an odd integer, proved

Condense to a single logarithm: 4 log9 11 - 4 log9 7.
O log9, (44/28)
O log9, (11/7)^4
O log9, (11/28)
log9 (44/7)

Answers

Answer: Log9,(11/7)^4

Step-by-step explanation:

according to the rules of logarithm

1)Subtraction sign(-) becomes division(÷),while addition(+)becomes multiplication (x)

2) the number in front of the log figure becomes an indices

Answer:

log9 (11/7)4

Step-by-step explanation:

got it right on the test

last year, emilia went bowling several times and earned an average score of 100 points. this year, after taking a class at school, her average is now 98% higher. what is her current average?​

Answers

198 is the answer I think

Three high school participated in a study to evaluate the effectiveness of a new computer-based mathematics curriculum. Four 24-student sections of freshman algebra were available for the study. The two types of instruction (standard curriculum, computer-based curriculum) were randomly assigned to the four sections in each of the three schools. At the end of the term, a standard mathematics achievement test was given to each of the 24 students in each section.
a. Is this study experimental, observational, or mixed experimental and observational? Why?
b. Identify important factors, factor levels, and/or factor-level combinations.
c. Classify these factors as within- or between-subjects
d. what’s the dependent measures?
e. What is the basic experiment unit of study?

Answers

Answer:

Given that;

There are three high schools, each having four sections of every 24 students

the 2 types of instructions are Standard curriculum  & computer based curriculum

a)

this study is experimental

this is because the study did not just observe the student's performance but randomly assign the performance to different techniques that have some certain control over the technique of teaching and then observe their performance afterwards

b)

-important  factors are; high schools, instruction type and scores

- Highschool has 2 levels: level one there are three high schools,  level 2 each having four sections of every 24 students

-instruction type: has one level which is  divided into two namely; standard base and computer based

Scores: doesn't have levels

c)

there are 3 schools and 4 sections  so the factor high school has between subjects components

factor instruction type also has between subjects because there are two different types available

there are 24 students in each section which are within subjects

d)

the score on the test  is the dependent measures

e)

“STUDENT” in each section is he basic experiment unit of study

Lucy, charlie, and Michael have a total of $95 in their wallet. Charlie has $10 more than lucy. Michael has 3 times what Lucy has. How much does each have?

Answers

I don,t I wish I could help but maybe us Socratic

60th Term of -10,8,26,...

Answers

Answer:

60th term is 1052

Step-by-step explanation:

position to term rule : position number multiplied by 18 then minus 28 (  position number × 18 - 28)

60 × 18 - 28

Help me please!!..,,

Answers

Answer:

A.

Step-by-step explanation:

1.5 x 0.1 = 0.15

0.15 inches

Dont know if this is for sure right. Hope it is.

pleas help me ill give brainleyest

Answers

Answer:

11.8% Decrease

Step-by-step explanation:

I googles it i am sorry if it's not right

Is .09 greater then .0003

Answers

Answer:

Yes

Step-by-step explanation:

For ease, let's multiply these by 10,000.

0.09 • 10,000 = 900.00 = 900

0.0003 • 10,000 = 3.00 = 3

900 is clearly greater than 3. Therefore, 0.09 is greater than 0.0003.

Kyle invested $ 500 and received $ 650 after three years. What had been the interest rate?

Answers

Answer:
216 2/3 : 1
1= one year

Since Kyle invested $500 and received $650 after three years, the value of Kyles's interest rate is 43.3%.

Given the following data:

Principal = $500Simple interest = $650Time = 3 years

To calculate the value of Kyles's interest rate:

Mathematically, simple interest is given by the formula:

[tex]S.I = \frac{PRT}{100}[/tex]

Where:

S.I is the simple interest.P is the principal amount.R is the interest rate.T is the time measured in years.

Making R the subject of formula, we have:

[tex]R = \frac{100S.I}{PT}[/tex]

Substituting the given parameters into the formula, we have;

[tex]R = \frac{100 \times 650}{500 \times 3}\\\\R = \frac{65000}{1500}[/tex]

Interest rate, R = 43.3%

Read more: https://brainly.com/question/22621039?referrer=searchResults

**PLEASE HELP THIS IS DUE TODAY** when the sun's declination is at the highest point, what direction does the sun rise and set?​

Answers

june 22 the declination reaches a maximum of 24.45° on june 22 summer solstice in the northern hemisphere and a minimum of -23.45 on december 21-22 winter solstice in the northern hemisphere. the sun, the moon, the planets and the stars all rise in the east and set in the west. and that’s because earth spins towards the east

Solve each of the following equations for the missing variable.
-2.5x – 10 = 40
O x = 20
O x= -20
O 50
-50

Answers

Answer:

-20

Step-by-step explanation:

-2.5x = 40 + 10

- 2.5x = 50

x = 50/-2.5 = -20

Hi hi I hope you know I’m not doing anything right

Find f(5). f(x) = x2 + 2x
Help please

Answers

Answer:

Your answer is: 15

Your equation would have f(5) = x^2 + 2x

Substitute the given value into the function and evaluate.

Step-by-step explanation:

Hope this helped ; )

HELP ME PLSSS SOMEONE HELPP ILL GIVE BRAINLIEST

tom sold 3 cars ( a total value of $112,500) in the month of january. it is paid only by commission for its seller. he receives a commission of 7%. what is tom’s salary for the month of january?

Answers

Answer:

First multiply 112,500 times 3 (because of the 3 cars) answer should be $337,500

Then do the percentage (7%) $23,625

I believe that 23625 is the answerrr

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