Proof that the formula Fn = Fn-1 + Fn-2 works
Fibonacci python

Answers

Answer 1
Umm— fn-1+Fn-2?? Fibonacci python
Answer 2
= f6 .

IV. The sum of the first n Fibonacci numbers with even indices is

f2 + f4 + ... + f2n = f2n+1 - 1.

Proof:

From II,

f1 + f2 + f3 + ... + f2n = f2n+2 - 1.

When we subtract the result from III, we get the desired result.

Example:

f2 + f4 + f6 + f8 + f10 + f12 = 1 +3 + 8 + 21 +55 +144

= 232

= f13 - 1 .

V. The sum of all (fn+1)/ (fn )

converges to the Golden Ratio.

3/1 + 5/3 + 8/5 + 13/8 .... converges to ) / 2.

Proof that Rn converges to the Golden Ratio:

Let R = lim Rn as n approaches infinity

= lim f n+1 / f n as n approaches infinity

= lim fn + fn-1 /fn as n approaches infinity

= lim (1 + fn-1/ fn) as n approaches infinity

= 1 + lim (fn-1 /fn ) as n approaches infinity

= 1 + 1/ lim (fn-1 /fn ) as n approaches infinity

= 1 + 1/R

So, R = 1 + 1/R,

or R^2 = R + 1,

R^2 - R - 1 = 0,

R = ( ) / 2

= ( ) / 2

Since Rn is positive, Rn = ( ) / 2 .

Thus, Rn converges to the Golden Ratio.

Related Questions

Express each of the following fractions as percentages
12/25
solution for class 7

Answers

Like we did in the previous problem, divide and multiply by 100:
12 / 25 = 0.48
As a percentage, we multiply by 10p;
0.48 *100 = 48

[tex]\\ \sf\longmapsto \dfrac{12}{25}\times 100[/tex]

[tex]\\ \sf\longmapsto \dfrac{12\times 100}{25}[/tex]

[tex]\\ \sf\longmapsto \dfrac{1200}{25}[/tex]

[tex]\\ \sf\longmapsto 48\℅[/tex]

PLzzzzz help im giving 30 points

Answers

Answer:

0.25

Step-by-step explanation:

-2 + 2= 0

-0.25 + 0.5= 0.25

O.25 is your answer I took this homework before

I need help please thank you <:

Answers

Answer:

B

Step-by-step explanation:

We have the following

- 3,210,000

- 420,000

- 1,100,000,000

Now we rearrange the numbers as asked from least to greatest.

- 420,000

- 3,210,000

- 1,100,000,000

They answer should be B

A pair of equations is shown below:

y = 2x − 1
y = 4x − 5

Part A: In your own words, explain how you can solve the pair of equations graphically. Write the slope and y-intercept for each equation that you will plot on the graph to solve the equations. (6 points)

Part B: What is the solution to the pair of equations? (4 points)

Answers

This kinda took a lot of effort but hope it helps
solved this on a napkin but whatever lol

Please help me with this :) (extra points)

Answers

Step-by-step explanation:

the total distance traveled would be 15

Please help ! I only have 30 more minutes

Answers

1.5 negative and negative

A triangle is going to be reflected over the x-axis and translated 4 units left and 2 units up. Which of the following is a TRUE statement?

A
The image with be larger than the pre-image

B
The image with be smaller than the pre-image

C
The image and pre-image will be congruent

D
The image and the pre-image will not be congruent.

Answers

C. The image and the pre image will be congruent
C
The image and pre-image will be congruent

The volume of a right cylindrical water tank is 5000 cubic meters. The radius of the base of the tank is 20 meters. Find the length in meters, of h, the hight of the tank.
A. 15 m B. 10 m C. 10.5 m D. 12.5 m

Answers

Answer:

D. 12.5

Step-by-step explanation:

Volume of a cylinder is V=pi r^2 h

*assuming that they already divided by pi since it isnt in their volume*

We can substitute our values...

5000 = 20^2 h

5000 = 400 h

12.5 = h

IM SO SORRY PLEASE HELP ME!!!

Answers

Answer:B,D i think that's it

Step-by-step explanation: lmk if it was right or wrong

D for sure, and maybe E

Hii! Please helpppp!! This was due like 3 days ago lol

Answers

Fergus has 3 1/4 cups of oats

= 13/4 cups of oats

Oatmeal bars = 2 2/3

= 8/3 cups of oatmeal used

Therefore cups of oats left = 13/4 - 8/3

= 39/12 - 32/12

= 7/12 cups of oats left

She borrowed 1 cup of oats from neighbour

7/12 + 1/1

= 7/12 + 12/12

= 19/12 cups of oats

Blueberry oats muffin = 1 3/4 cups of oats

= 7/4 cups of oats

Total she will have now = 19/12-7/4

= 19/12 - 21/12

= - 2/12

= -1/6

Which means she needs 1/6 cup of oats more

Therefore its option 4

Must click thanks and mark brainliest

Answer:

she needs 1/6 more so the last option! looking at the pic i dont think you need to show the work :)

Step-by-step explanation:

A bag of marbles contains 12 blue marbles, 5 red marbles, and 13 green marbles. if one is selected at random, what is the probability that the selected marble is blue?

A. 0
B. 2/5
C. 13/30
D. 5/6
E. 1

Answers

Answer:

2/5

Step-by-step explanation:

Total marbles=12+13+5=30

P(that the selected marble is blue) = 12/30 = 6/15 = 2/5

I think it’s B sorry if im wrong

Why are the divisibility rules for 2, 3, and 5 very useful for determining prime and composite numbers

1. They are the smallest odd numbers
2. They add up to 10
3. They are prime numbers with nice divisibility rules
4. They multiply to 30
5. They can be multiplied together to make every number

Answers

Answer:

option 3.

Step-by-step explanation:

alright, ima explain each option.

1. "smallest odd numbers" 2 is an even number. that's out of the playing field.

2. "add up to 10" sure, they do add up to 10, but finding prime and composite numbers are all about division and multiplication.

3. this is true. 2, 3, and 5 are all prime numbers, and they have the nice divisibility rules. [ for 2, it has to be even, for 5, it has to end in 0 or 5, and 3 has to have the sum of its digits being divisible by 3. ]

4. they do multiply to 30, but this does not help break the composite numbers down.

5. we cannot make every number with just these. we can not multiply any other whole number to get 7 for per example, because it's a prime number.

sub to gauthmath sub reddit if ya can !

They are prime numbers with nice divisibility rules

Given: UR ∥ ST ∠R, ∠T right angles Prove: ∆RSU ≅ ∆TUS
What you will get:
25 pts
Brainliest

Answers

Here

Angle R = Angle T

UR = ST

US = SU

So using RHS conguerence criteria Triangle RSU conguerent to Triangle TUS

Heres your answer
Hope it helps !

Please answer all these questions right I can’t do them ‍♀️
I will mark you as brainliest if you do!

Answers

Step-by-step explanation:

first take out graph paper then line it

sorry i don't have graph copy right now hope it work

The dot plots below show the test scores of some mathematics students and some science students: Two dot plots are shown one below the other. The top and the bottom plots have the title Mathematics Students and Science Students respectively. Below the line for each dot plot is written Mark. The markings on each line are from 30 to 50 at intervals of 1. For the top plot there are two dots each for 34 and 40 and 1 dot each for 32, 33, 35, 37, and 39. For the bottom plot there are 2 dots each for 43, 46 and 49 and 1 dot each for 41, 42, and 47. Based on visual inspection of the dot plots, which group of students appears to have the larger average score? The mathematics students The science students Both groups are similar. Not enough information is available to draw a conclusion.

Answers

Answer:

Science students

When you find the average both plots using median, mean, or interquartile range, you will find that the score for the science students will always be greater than the score of the mathematics students. This is because none of the mathematics students scored higher than the science students, so the mean will always be greater.

MATHEMATICS :

Plot interval = 30 to 50

MEAN :

(34*2) + (40*2) + (32*1) + (33*1) + (35*1) + (37*1) + (39*1) = 324

Sample size, n = (2 + 2 + 1 + 1 + 1 + 1 + 1) = 9

Mean = 324 / 9 = 36

BOTTOM :

SCIENCE :

MEAN : (43*2)+(46*2)+(49*2)+(41*1)+(42*1)+(47*1) =

406

SAMPLE SIZE = (2 + 2 + 2 + 1 +1 +1) = 9

406 / 9 = 45.111

Step-by-step explanation: hope this helps

Easy flat heads plus 43,46,38383

Express each of these percentages as a fraction
158%
solution for class 7

Answers

Answer: 158% = [tex]\frac{158}{100}[/tex] = [tex]\frac{79}{50}[/tex]

Hope it helps :)

79/50!!!!!!!!!!
!! 79/50!!!!!!!!!!
!!

This shape is made of four congruent kites meeting at a point. Calculate the size of Angle K.

Answers

Answer:

k = 115°

Step-by-step explanation:

Hope it helped.

• • •

90 + 2k + 40 = 360

2k = 360-130

2k = 230

k = 115

Angle K = 115

Answered by gauthmath pls make brainliest and comment thanks

please help
a(8x + 2y) = 8ax +

Answers


a(8x + 2y) = 8x

Answer x=-2/0

If g(x) = 1 - ¾ x
find: g(0)

Answers

[tex] \sf \: g(x) = 1 - \frac{3}{4} x \\ \sf \:g(0) = \: ? \\ \\ \sf \: Substitute\: the \: value \: of \: x \: as \: 0 \\ \\ \sf \:1 - \frac{3}{4} (0) \\ \sf \: = 1 - \frac{3}{4} \times 0 \\ \sf \: = 1 - 0 \\ \sf \: = \underline{\bf \: 1}[/tex]

Hope it helps.

RainbowSalt2222

I honestly don’t know

solve for P

P/15=20/25

Answers

Answer:

p=12

Step-by-step explanation:

Cross multiply in order to get answer

What is the value of the expression shown below? 7 + (10 - 4 )^2 divided 4 x (1/2)

Answers

i’m pretty sure 21.5 because you do what is in parentheses first which is 10-4=6, then you square to equal 36 then add 7=43 and divide by 2 bc 4(1/2) is 2 and you get 43/2 which is 21.5

Answer:

43 / 2  = 21  1/2 = 21.5

Step-by-step explanation:

7+(10-4)^2/ 4 (12)        you can either multiply by  4(1/2)/4(12) or do the following

Subtract 4 from 10 to get 6.

7+6^2 / 4×(  1/2)  

Calculate 6 to the power of 2 and get 36.

7+36 / 4×(  1/2  )  

Add 7 and 36 to get 43.

43 / 4× 1/2  

 Multiply 4 and    1/2   ​ to get 2.

43 / 2  = 21  1/2 = 21.5

 

Write two equivalent ratios using four different types of music in the data table showing. How do you know the ratios are equivalent? ​

Answers

The ratio is equivalent because 1/20 is 5 which means 9/10 is equal
wheres the data table ?

sin0+sin0+2sin0+3sin0
step by step

Answers

Answer:

0

Step-by-step explanation:

the value of sin 0 degree is always equal to 0.

=0+0+2x0+3x0

=0

sin0+sin0+2sin0+3sin0=0

Sinx0+sinx0+2sinx0+3sinx0
Any expression multiplied by 0
equals 0
0+sinx0+2sinx0+3sinx0
0+0+2sinx0+3sinx0
0+0+0+3sinx0
0+0+0+0
0+0+0
0+0
0
This did take me a lot of effort to write but hope it helps

I really need help with this

Answers

Answer:

8/5

Step-by-step explanation:

There are 8 jokers combined, and 5 decks, so the mean is 8/5.

8/5 explanation gut above me

Absolute Value – how far or the
[ Select ] Answer | Counter | Number | or distance
a number is from zero.

Answers

Answer:

The last answer or Distance a number is from zero

Step-by-step explanation:

It's this answer because absolute value is just how far a number is from zero for example | -1 | is equal to 1 because -1 is 1 away from zero. Hope this helps :)

Answer:

The last answer or Distance a number is from zero i think i dont know

Step-by-step explanation:

The sum of two consecutive integers is -92. Find the integers.

Answers

Answer:

x = -46.5

x + 1 = -45.5

Step-by-step explanation:

x + x + 1 = -92

2x + 1 = -92

      -1       -1

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

   2x = -93

   ----     ----

    2        2

   x = -46.5

x + 1

(-46.5) + 1

-45.5

Answer:

No solution

Step-by-step explanation:

We can set up an equation where x is the integer and x+1 is the next one

x+x+1=-92

2x+1=-92

2x/2=-93/2

x=-46.5

-46.5+1=-45.5

The problem is that integers do no include decimals so there is no possible whole number. This problem would be possible if it was consecutive odd integers.

The figure shows a line graph and two shaded triangles that are similar:



Which statement about the slope of the line is true?

A. It is fraction 1 over 2 throughout the line.
B. It is 2 throughout the line.
C.The slope from point O to point A is fraction 1 over 2 time the slope of the line from point A to point B.
D. The slope from point O to point A is two times the slope of the line from point A to point B.

Answers

Answer:

Answer is B

just do your work and proof the work and that will give u the right answer

Answer:

it is B

Step-by-step explanation:

it is just B man, trust

Please Help Me! I will give brainly!!


The distance from your front door to the mailbox is 18 4/5 meters. The distance from your front door to your basketball hoop is 13 7/10 meters. How much farther from your front door is the mailbox than the basketball hoop?

Answers

Answer:

5 1/10 meters

Step-by-step explanation:

18 4/5 can be changed to 18 8/10 so

18 8/10 - 13 7/10 = 5 1/10 meters

5 1/10 meters ahhhhhhhhhhhh

50 POINTS
My neighborhood is full of one-way streets. To drive from my house to the grocery store, I have to go 1 block south, then 1 block east, then 5 blocks north, then 2 blocks east. Each block is 1/16 of a mile. How much shorter would my trip be if I could fly like a bird (that is, travel in a straight line)?
I FOUND THE distance for non bird which is 9/16. I wanna apply the pythagoreum theorum and draw a straight line to make it a triangle so I can do so but don't know where to place it

Answers

1/4. . Hope this helps you
Let's suppose that your house is located at (0,0)

1 block south from here puts you at (0, -1/16)

1 block east from here now puts you at (1/16, -1/16)

5 blocks north from here puts you at (1/16, 4/16)

2 blocks east from here puts you at (3/16, 4/16)


You have traveled (1/16) ( 1 + 1 + 5 + 2) = 9 / 16 of a mile

The "straightline" distance between (0, 0) and (3/16, 4/16) =

sqrt [ (3/16^2 + (4/16)^2 ] = sqrt [ 25 / 256] = 5 /16 of a mile

Your trip would be [ 9/16 - 5/16 ] which equals 4/16 simplified equals 1/4 of a mile.

A circle is cut from a square piece of cloth, as shown:

A square, one side labeled as 42 inches has a circle inside it. The circle touches all the sides of the square. The portion of the square outside the circle is shaded.

How many square inches of cloth are cut from the square? (π = 3.14)

131.88 in2
168.00 in2
1,384.74 in2
1,764.00 in2

Answers

Answer:

A

Step-by-step explanation:

I think you are supposed to do is 42x3.14=131.88 so the answer is 131.88

hope this helps :)

Answer:

Step-by-step explanation:

Given the choices of answers we have to consider that:

The cloth is cut from the square = Area of circle

Area of circle = π r² = 3.14 * 21² = 1,384.74 in²

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