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

Find the perimeter of the figure.
7 mi
7 mi

Answers

Answer:

28mi

Step-by-step explanation:

The shape given is a square because all the internal angles are the same. Also, all the sides are equal;

   The perimeter of a square is given as;

          = 4L

Where L is the dimension of the sides

L in this problem is 7mi

Input the parameter and solve;

            Perimeter  = 4  x  7 = 28mi

By the end of Tina’s bike ride, she traveled a distance of 40 kilometers. How many miles did Tina ride? (1 mile ≈ 1.6 kilometers)

help plz brainless you help me

Answers

Answer:

24.85 or rounded to 24.9

Step-by-step explanation:

Conversion

K H D____D C M

The number of miles did Tina ride when (1 mile ≈ 1.6 kilometers) so it should be considered as the 25 miles.

Calculation of the number of miles:

Since

By the end of Tina’s bike ride, she traveled a distance of 40 kilometers.

And we know that

1 mile ≈ 1.6 kilometers

So,

[tex]= 40 \div 1.6[/tex]

= 25 miles

hence, The number of miles did Tina ride when (1 mile ≈ 1.6 kilometers) so it should be considered as the 25 miles.

Learn more about miles here: https://brainly.com/question/13208356

A young reptile is 0.6 foot long. An adult reptile is 19.5 times as long. How many feet longer is the adult reptile than the young reptile?

Answers

0.6ft x 19.5 = 11.7 ft
11.7ft-0.6ft = 11.1 ft
answer is 11.1 ft longer

Please help me if you know it thank you so much

Answers

Answer:

a) 9 beats

b) 9 beats per minute

c) y=9x

d) 180 times

what does they y represent in the equation y=mx+b​

Answers

Answer:

The y-intercept of this line is the value of y at the point where the line crosses the y axis.

Step-by-step explanation:

The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept.

57.99 The 9 in the hundredths place is _______ the value of the 9 in the tenths place.

Answers

Answer:The 9 in the hundredths place is 0.1x the value of the 9 in the tenths place.

Step-by-step explanation:

Every place going forward is 10x forward, so this means that every place going backwards is 0.1x.

Answer:

1/10th

Step-by-step explanation:

The slope of a line is ¾. A different line passes through the points (6, 3) & (-1, 5). Are the lines parallel? Why or why not?

Answers

Answer:

B. They are not parallel because their slopes are not equal.

Step-by-step explanation:

Find the slope of the line that runs through points (6, 3) and (-1, 5):

[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 3}{-1 - 6} [/tex]

[tex] slope (m) = \frac{2}{-7} = -\frac{2}{7} [/tex]

Since the slope of the line that passes through points (6, 3) and (-1, 5) is not the same with line that has a slope of ¾, therefore, both lines cannot be parallel.

The answer is "B. They are not parallel because their slopes are not equal."

y=3x+22
x is equal to 225

Answers

9514 1404 393

Answer:

  y = 697

Step-by-step explanation:

Put the value of x into the equation and do the arithmetic.

  y = 3·225 +22 = 675 +22

  y = 697

a tourist information center charges $10 per hour to rent a bicycle

Answers

whats the question? I think you forgot to type it

Answer:

10per the other side of alloys

The only expression 3(2x+7)-4(-3x+5) is equal (=) to

Answers

Answer:

18x + 1

Step-by-step explanation:

3(2x + 7) -4(-3x +5)

6x + 21 + 12x - 20

6x + 12x + 21 - 20

18x + 1

Answer:

18x+1

Step-by-step explanation:

3(2x+7)-4(-3x+5)= 6x+21+12x-20

Combine Like Terms:

6x+12x= 18x

21-20=1

=18x+1

Sebastian drove for 2.2 hours at an average rate of 43.5 miles per hour. He calculates that he drove 95.7 miles. He knows the answer should be near 80, because 40 times 2 is 80. Which best explains Sebastian’s actual solution?

Answers

Answer: A. The actual product is reasonable because it is near 80 but greater than 80. Both factors were rounded down, making the estimate lower than the actual product.

Step-by-step explanation:

Answer: A. The actual product is reasonable because it is near 80 but greater than 80. Both factors were rounded down, making the estimate lower than the actual product.

Step-by-step explanation:

help me please thank you​

Answers

24 blueberries. 24:60=2:5

If a =
3
5
, b = 3, c = 1, d = 5, which equality is true?

A)
d
a
=
b
c
B)
a
b
=
c
d
C)
b
a
=
c
d
D)
a
d
=
b
c

Answers

Answer:

could you give a picture of the problem. cause I may be able to help but I cant really understand the question with what you typed

Answer:

D

Step-by-step explanation:

just took this test

SOMEONE HELP WITH MY LAST TWO PROBLEMS

Answers

Answer:

What are your last 2 problems m8

Step-by-step explanation:

Question 4
5 pts
4. Cassie has 45 marbles. Abdul has m If Cassie has 9 times as many
marbles as Abdul. Choose the equation that correctly represents the
number of marbles Abdul has.
O 9 x m = 45
O 45 - 9 = m
O C. 9+ m = 45
O D. 9 x 45 = m

Answers

Answer:

8 x m = 45

Step-by-step explanation:

cassie has 9 times which means multiplcation so its the first one

PLZ HURRY IT'S URGENT!!
What is the y-intercept of the line?
y=2/3x+4
options:

0

1

2/3

4

Answers

Answer:

4

Step-by-step explanation:

y intercept is always the value without a coeffiecent

Answer:

ITS 4

Step-by-step explanation:

Regina used nuts and fruits to make a snack mix. The graph below shows the quantities used for each serving

What do the points on the graph mean in this context? Select all that apply.

For every 3 cups of fruit, there is 1 cup of nuts.

For every 1 cup of fruit, there are 3 cups of nuts.

For every 2 cups of fruit, there are 6 cups of nuts.

For every 6 cups of fruit, there are 2 cups of nuts.

For every 12 cups of fruit, there are 4 cups of nuts.

Answers

Answer: 1st, 4th & 5th .

Answer:

1st, 4th, and 5th

Step-by-step explanation:

Shen is on the swim team. Each week he swims a total of 5000 meters. How many kilometers does he swim each week?
Be sure to include the correct unit in your answer.

Answers

Answer:

5 km

Step-by-step explanation:

to convert m to km you have to divide by 1000.

5000/1000=5

hope this helps!

**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

Select all the expressions that are rational numbers.
a. 3.14159…
b. –9.1234567123…
c. –9.293847210103938…
d. 227
e. –26

Answers

Answer:

d,e

Step-by-step explanation:

rational numbers are positive and negative whole numbers.

Answer:

d,e

Step-by-step explanation:

find 759 divided by 3

Answers

Answer:

253 .....is that it??

Step-by-step explanation:

Answer:

253!

Step-by-step explanation:

Plz help :( I need the negative if y plz show steps 6X plus 6Y equal 83/9 upper 2N

Answers

Answer:

x=8

Step-by-step explanation:

Simplifying

Combine like terms

Solving

simplify 3 · 32 + 8 ÷ 2 − (4 + 3)

Answers

Answer:

= 93

Step-by-step explanation:

Calculate within parentheses:

(4+3)

= 7

Simplify:

= 3 * 32 + 8 ÷ 2 - 7

Multiply and divide (left to right):

= 96 + 8 ÷ 2 - 7

Multiply and divide (left to right):

= 96 + 4 - 7

Add and subtract (left to right):

= 93

The net of a rectangular shipping box is shown.

What is the surface area, in square centimeters, of the box?

Answers

Answer:

It would be 376.

What does it mean to divide a number by
a fraction (e.g., ¾)?

Answers

Answer: You can divide a number by a fraction by flipping over the fraction and multiplying them together.

Step-by-step explanation:

For example:

Lets say we wanted to divide 8 by 3/4

8÷[tex]\frac{3}{4}[/tex]

Change the division symbol into multiplication, and flip over the fraction (a great way to remember doing this is to remember the phrase Copy Dot Flip - Copy the first digit as it is, put a dot for multiplication, and then flip the fraction over)

8 ·[tex]\frac{4}{3}[/tex]

Now, just multiply and reduce/simplify the fraction if needed

Final answer is [tex]\frac{32}{3}[/tex], no need to simplify or reduce

Hope that helps!!

Oct 16, 10:30:54 AM
A rocket is shot into the air. The function f (x) = -16x2 + 64x + 8 gives the
height of the rocket (in feet) as a function of the rockets horizontal distance from
where it was initially shot.
a. What was the initial height of the rocket when it was shot?
b. What is the maximum height the rocket reaches in the air?
a. The initial height of the rocket was
feet.
b. The maximum height the rocket reaches is
feet.

Answers

Answer:

A) 8 feet.

B) 72 feet

Step-by-step explanation:

We have the function [tex]f(x)=-16x^2+64x+8[/tex] which gives the height of the rocket (in feet) as a function of the rocket's horizontal distance.

Part A)

We want to find the initial height of the rocket when it was shot.

At the initial height, the rocket has not moved anywhere. So, the horizontal distance will be 0.

Therefore, to find the initial height, we will substitute 0 into our function. This yields:

[tex]f(0)=-16(0)^2+64(0)+8[/tex]

Evaluate:

[tex]f(0)=8[/tex]

Therefore, the initial height was 8 feet.

Part B)

Notice that our function is a quadratic.

Therefore, the maximum height will be given by the vertex of our quadratic.

To find the vertex, we use:

[tex](-\frac{b}{2a},f(-\frac{b}{2a}))[/tex]

Let's label our coefficients. We have [tex]-16x^2+64x+8[/tex]

Therefore, a=-16, b=64, and c=8.

Substitute them into the vertex formula to find the x-coordinate:

[tex]x=-\frac{64}{2(-16)}\\\Rightarrow x=64/32=2[/tex]

Now, to find the maximum height, substitute 2 back into our function f(x):

[tex]f(2)=-16(2)^2+64(2)+8[/tex]

Evaluate:

[tex]f(2)=-16(4)+64(2)+8\\\Rightarrow f(2)=-64+128+8\\\Rightarrow f(2)=72\text{ feet}[/tex]

Therefore, the rocket reaches a maximum height of 72 feet.

Question 1
1 pts
The function f(x) = 4x + 10 models the amount of money Francis makes when babysitting
for x hours. How much money will he make for 2 hours of babysitting work?
2.
0-2
O-3
O 18

Answers

Answer:

18 would be yr answer

Step-by-step explanation:

Please help ASAP! All questions.

Answers

Answer:

I think i don't really know its been awhile for me.

Step-by-step explanation:

But i think you do 2 x 10 and what ever you get from that you multiply by 5 and what get from that you divide by 24.

I may not be right.

So please don't hate i tried.

y= -2x - 45. solve for x if y = -10

Answers

Answer:

-17.5

Step-by-step explanation:

-10 = -2x - 45

(add 45 on both sides)

35 = -2x

(divide both sides by -2)

x = -17.5

Find the equation of a line through (-9, 2) perpendicular to y=3x-12
1 point
y=-1/3x-1
y=3x-1
y=1/3x+4
y=-3x-1

Answers

9514 1404 393

Answer:

  y = -1/3x -1

Step-by-step explanation:

The perpendicular line will have a slope that is the negative reciprocal of the slope of the given line. The given line's slope is the coefficient of x: 3. So, the perpendicular line's slope will be ...

  m = -1/3

Only one answer choice has that value as the coefficient of x:

  y = -1/3x -1

Other Questions
What is the capital of N. Ireland? Lateralization refers to the a. number of neurons produced during prenatal development. b. organizational structure of the peripheral nervous system. c. specialization of the two hemispheres of the cerebral cortex. d. plasticity of the spinal cord. PLS HELP ASAP I'LL GIVE BRAINLIST AND 50 POINTS DO NOT USE GOOGLE!!!!!!!!!!!In the novel Crispin, he lives as a serf in Stromford Village. Compare Crispins rights, roles, responsibilities, & limitations as a serf to a person of lower social status in modern times. Use evidence from the novel Crispin-The Cross of Lead and your knowledge of Medieval Europe to support your response. Between which hours does the most significant drop in temperature occur for most patients? Plz ill give BrainliestMalcolm wants to copy images and articles on different animal species and use them to study for a science test. Which online note-taking tool would be the most helpful? online data storage sites electronic sticky notes electronic flash cards web clipping tools Can someone please Help me Read this sentence from the text.China has moved from a closed, centrally planned system to a more market-oriented one.Based on information in the text, describe this process and its consequences. The power generated by an electrical circuit (in watts) as a function of its current x xx (in amperes) is modeled by P ( x ) = 15 x ( x 8 ) P(x)=15x(x8)P, left parenthesis, x, right parenthesis, equals, minus, 15, x, left parenthesis, x, minus, 8, right parenthesis What current will produce the maximum power? what has the U.S customs created to force importing companies like wal-mart to provide more detailed information about The point (1, 5) is reflected across the y-axis. A coordinate plane. What are its new coordinates? HELPPP ASAPPPwrite an equation for each lineline L(the red line)___line p(the blue line)___line m(the black line)___line n(the green line)___ CAN SOMEONE ANSWER MY QUESTION PLS? *I'LL GIVE BRAINLIEST AND 20 POINTS!* NO WRONG ANSWERS AND PLEASE DO YOUR BEST Use the Distributive Property to simplify the expression.1/2(2n+4+6m) Which of the following is both a perfect square and a perfect cube?6416811,000I know the answer is 64, but how? Can someone please explain me to me how to work this out? pleasseeee help........... Demarco and Janine Jackson have been married for 20 years and have four children who qualify as their dependents (Damarcus, Janine, Michael, and Candice). The couple received salary income of $100,000 and qualified business income of $10,000 from an investment in a partnership, and they sold their home this year. They initially purchased the home three years ago for $200,000 and they sold it for $250,000. The gain on the sale qualified for the exclusion from the sale of a principal residence. The Jacksons incurred $16,500 of itemized deductions, and they had $3,550 withheld from their paychecks for federal taxes. They are also allowed to claim a child tax credit for each of their children. However, because Candice is 18 years of age, the Jacksons may only claim the child tax credit for other qualifying dependents for Candice. (Use the tax rate schedules.)Comprehensive Problem 4-55 Parts-c through fa. What would their taxable income be if their itemized deductions totaled $28,000 instead of $16,500?b. What would their taxable income be if they had $0 itemized deductions and $6,000 of for AGI deductions?c. Assume the original facts but now suppose the Jacksons also incurred a loss of $5,000 on the sale of some of their investment assets. What effect does the $5,000 loss have on their taxable income? Solve for the value of x that makes likes r and s parallel. A dog has a mass of 60kg and an acceleration of 2m/s/s. What is the force of the dog? a number multiplied by 5 and increased by 7 the result is 62 Solve for n.n+ 1 = 4(n-8)0 n = 1O n = 80 n = 11n = 16?