Use the value of phi = 1.618 to predict the 23rd number in the Fibonacci sequence. The 22nd number in the sequence is 17,711.

- 10,946

- 17,711

- 22,897

- 28,656

Answers

Answer 1

Given:

[tex]\phi=1.618[/tex]

22nd number in Fibonacci sequence = 17,711

To find:

The 23rd number in the Fibonacci sequence.

Solution:

The nth term of a Fibonacci sequence is:

[tex]f_n=\dfrac{\phi^n-(1-\phi)^n}{\sqrt{5}}[/tex]

Substituting [tex]\phi=1.618, n=21[/tex], we get

[tex]f_{21}=\dfrac{(1.618)^{21}-(1-1.618)^{21}}{\sqrt{5}}[/tex]

[tex]f_{21}=\dfrac{(1.618)^{21}-(1-1.618)^{21}}{\sqrt{5}}[/tex]

[tex]f_{21}=10941.1724024[/tex]

[tex]f_{21}\approx 10941[/tex]

Now,

[tex]f_{23}=f_{21}+f_{22}[/tex]

[tex]f_{23}=10941+17711[/tex]

[tex]f_{23}=28652[/tex]

It is about 28,656. Therefore, the correct option is D.


Related Questions

2x + 2x + 5x + 5x= please answer quick it's very hard and I like the game to answer please and thank you.

Answers

Answer:

14x I answered your question thank you for the points appreciate it

Answer:

2x+2x+5x+5x=14x

Ans: 14x


The table shows the proof of the relationship between the slopes of two perpendicular lines. What is the missing statement in step 2?

Answers

Answer:

[tex]\frac{AB}{BC} = \frac{CE}{ED}[/tex]

Step-by-step explanation:

Given

The attached proof

Required

Complete the missing piece

In (a), we have:

[tex]\triangle ABC \to \triangle CED[/tex]

This implies that, the following sides are similar:

[tex]AB \to CE[/tex]

[tex]AC \to CD[/tex]

[tex]BC \to ED[/tex]

An equation that compares the triangle can be any of:

[tex]\frac{AB}{BC} = \frac{CE}{ED}[/tex]

[tex]\frac{AB}{AC} = \frac{CE}{CD}[/tex]

.....

From the options;

[tex]\frac{AB}{BC} = \frac{CE}{ED}[/tex] is true

How do I do this formula

Answers

Answer:

Step-by-step explanation:

your solution is almost true h=V/πr^2 but the final answer is 36/9π= (4π)cm

--->4×3.14=12.56cm

A certain list of movies were chosen from lists of recent Academy Award Best Picture winners, highest grossing movies, series movies (e.g. the Harry Potter series, the Spiderman series), and from the Sundance Film Festival and are being analyzed. The mean box office gross was $138.64 million with a standard deviation of $11.2526 million. Given this information, 98.49% of movies grossed greater than how much money (in millions)

Answers

what is the question?

the radius of the right circular cylinder shown below is growing at a rate of 2ft/min while it's height is shrinking at 3ft/min. At what rate is the volume of the cylinder changing, with respect to time, when the radius is 4ft and the volume is 32 ft cubed.

Answers

Answer:

The volume is decreasing at a rate of about 118.8 cubic feet per minute.

Step-by-step explanation:

Recall that the volume of a cylinder is given by:

[tex]\displaystyle V=\pi r^2h[/tex]

Take the derivative of the equation with respect to t. V, r, and h are all functions of t:

[tex]\displaystyle \frac{dV}{dt}=\pi\frac{d}{dt}\left[r^2h\right][/tex]

Use the product rule and implicitly differentiate. Hence:

[tex]\displaystyle \frac{dV}{dt}=\pi\left(2rh\frac{dr}{dt}+r^2\frac{dh}{dt}\right)[/tex]

We want to find the rate at which the volume of the cylinder is changing when the radius if 4 feet and the volume is 32 cubic feet given that the radius is growing at a rate of 2ft/min and the height is shrinking at a rate of 3ft/min.

In other words, we want to find dV/dt when r = 4, V = 32, dr/dt = 2, and dh/dt = -3.

Since V = 32 and r = 4, solve for the height:

[tex]\displaystyle \begin{aligned} V&=\pi r^2h \\32&=\pi(4)^2h\\32&=16\pi h \\h&=\frac{2}{\pi}\end{aligned}[/tex]

Substitute:

[tex]\displaystyle\begin{aligned} \frac{dV}{dt}&=\pi\left(2rh\frac{dr}{dt}+r^2\frac{dh}{dt}\right)\\ \\ &=\pi\left(2(4)\left(\frac{2}{\pi}\right)\left(2\right)+(4)^2\left(-3\right)\right)\\\\&=\pi\left(\frac{32}{\pi}-48\right)\\&=32-48\pi\approx -118.80\frac{\text{ ft}^3}{\text{min}}\end{aligned}[/tex]

Therefore, the volume is decreasing at a rate of about 118.8 cubic feet per minute.

By way of tree diagram determine all likely outcome when a fair die is tossed

Answers

Step-by-step explanation:

hope it helps

brainliest please

Can someone answer these?

Answers

Answer: hello there here are your answers:

5.d associate property of addition

6.b multiplicative identify

7. c Additive identify

Step-by-step explanation:

5) they are just changing up the number in the ()

6) Its the same number or equation on both sides just wrote different

7) that in a given mathematical system leaves unchanged any element to which it is added.

hope this help have a good day bye!

how much water consumed by Aguilar family as shown in the meter reading

Answers

Answer:

?????????????????

Step-by-step explanation:

????????

8. Discount: An auto dealer paid $8730 for a
large order of special parts. This was not the
original price. The amount paid reflects a 3%
discount off the original price because the
dealer paid cash. What was the original price
of the parts?

Answers

Answer: 5,987

Step-by-step explanation:

PLEASE ANSWER QUICKLY Find the distance between points (4, 2) and (7, 2) on the coordinate
plane.

Answers

Answer:

3 units

Step-by-step explanation:

(4,2) (7,2)

Subtract 4 from 7 = 3

Subtract 2 from 2 = 0

This means that (7,2) is 3 units up from (4,2).

:) ur welcome

Answer:

Step-by-step explanation:

D=√(x2-x1)²+(y2-y1)²

D=√(7-4)²+(2-2)²

D=√(3)²+0

D=3²*½

D=3

Suppose your dean of admissions is considering surveying high school seniors about their perceptions of your school to design better informational brochures for them. What are the advantages and disadvantages of doing (a) telephone interviews and (b) an Internet survey of seniors who have requested information about the school

Answers

Answer and explanation:

Advantages of telephone interviews:

They are more convenient than face to face interviews

They are alot more cost-effective

There is a wider geographical access as you can reach people in other countries too

Disadvantages of telephone interviews:

Questions become has limited complexity as opposed to face to face interviews

It may be somewhat intrusive for customers and there could also be interference from noise in the background. Also bad connection issues.

Advantages of internet survey:

Increased geographical access leading to high response rate.

Alot more convenient and flexible than face to face interviews

Low cost advantages

Disadvantages of internet survey:

Inability for individuals who are not online to participate

Non response bias

Limited complexity of questions, usually close ended questions

A boy leaves station X on a bearing of 035' to station Y. which is 21km away. He then travels to another station Z on a bearing of 125 degrees . If Z is directly East of X, what is the distance from X to his present position?​

Answers

9514 1404 393

Answer:

  36.6 km

Step-by-step explanation:

We assume the initial bearing of the boy is 35°. Then he will make a 90° turn to a heading of 125°. A diagram shows the distance of interest is the hypotenuse of a right triangle in which 35° is the angle opposite the side of length 21 km.

The relevant trig relation is ...

  Sin = Opposite/Hypotenuse

  sin(35°) = (21 km)/XZ

  XZ = (21 km)/sin(35°) ≈ 36.61 km

The distance from X to Z is about 36.61 km.

_____

The attached diagram has the angles measured in the usual way for a Cartesian plane: CCW from the +x axis. This will correspond to bearing measures if we relabel the axes so that +x is North, and +y is East.

Si dos angulos son conjugados entre paralelas entonces son suplementarios es verdadero o falso

Answers

Si dos angulos son conjugados entre paralelas entonces son suplementarios es verdadero o falso

Step-by-step explanation:

no worries skills development and implementation of the year in a while and I am looking for an appointment with the other day

At the 6th grade school dance, there are 132 boys, 89 girls, and 14 adults. What is the ratio of students to adults at the school dance?​

Answers

9514 1404 393

Answer:

  221 : 14

Step-by-step explanation:

The ratio is ...

  students : adults = (boys + girls) : adults = (132 +89) : 14 = 221 : 14

__

That's about 15.8 to 1.

Answer:

221:14

Step-by-step explanation: 132+89=221 (students) and 14 adults and the order is students to adults so 221:14

Find the angle θ between ???? and ???? if ????⋅????=12‖????‖⋅‖????‖. (Use symbolic notation and fractions where needed. Give your answer in terms of π. )

Answers

Answer: hello your question is poorly written below is the complete question

Find the angle between and if ⋅=3√2‖‖⋅‖‖.

(Use symbolic notation and fractions where needed. Give your answer in terms of . )

answer :

∅ = π / 6

Step-by-step explanation:

V .W = [tex]\frac{\sqrt{3} }{2} || V ||. ||W||[/tex]

Hence

∅ = cos^-1 ( [tex]\frac{\frac{\sqrt{3} }{2} || V ||. ||W||}{||V||.||W||}[/tex]

∅ = cos^-1 ( [tex]\frac{\sqrt{3} }{2}[/tex] )

∴ ∅ = π / 6

A number is divisible by 3 if the sum of the digits of the number is divisible by 3.

Answers

I believe the answer the the question A number is divisible by 3 if the sum of the digits of the number is divisible by 3. Is 504, it makes sense

round 3,236 to the nearest hundred

Answers

Answer:

3,200

Step-by-step explanation:

3 is less than 5 so you round down to 3,200

3,200. You’re asked to the nearest hundred so you focus on 3 only. Since 3 is less than 5, it becomes 0. So 3,236 to the nearest hundred is 3,200.

21. The mean salary of twelve men is $58,000, and the
mean salary of eight women is $42,000. Find the
mean salary of all twenty people.

Answers

$50000 is mean salary of 20 people

(58000 + 42000)/2 = 50000

Find the value of y .
Please help !

Answers

9514 1404 393

Answer:

  (b)  √55

Step-by-step explanation:

The right triangles in this geometry are all similar, so the ratio of long side to short side is the same:

  y/5 = 11/y

  y² = 55 . . . . . . multiply by 5y

  y = √55 . . . . . take the square root

__

And x=4√5 by looking at ratios of short side to hypotenuse.

if the smaller side of a rectangle was increased by 7 cm, it would be exactly 55% of the 110 cm longer side. Find the area of the rectangle

Answers

Answer:

5886 cm

Step-by-step explanation:

start by finding 55% of 110 which is 60.5. then subtract by 7 and then you get 53.5

then multiply 53.5 by 110 = 5885 cm

Consider a relation on the set of all states in the United States given by: two states are related if they have a border in common. Is it an equivalence relation

Answers

Answer:

Yes it is an equivalence relation

Explanation:

An equivalence relation is a binary relation between two values that are symmetric, transitive and reflexive. In other words, when we say a value x is equal(using "=") to a value y, there is an equivalence relation between them.

Example, given set {x, y, z} where ~ means equivalence:

x ~ y if y ~ z means symmetric

since x ~ y and y ~ z, then x ~ z means transitive

x ~ x means reflexive

Equivalence relations share a common attribute or attributes(example, a satisfying condition)

The above condition that two states are related from the set of all US states if they have a border in common satisfies the condition of equivalence listed hence it is an equivalence relation.

what is 1.8 in written notation

Answers

Answer:

The answer is 1/8

Find the 11th term of the sequence

3, -6, 12, -24,...



3072

6144

-6144

-3072

Answers

Answer:

-3072

Step-by-step explanation:

Suppose that all of the points on the circular dartboard shown are equally likely to be hit by a dart. If the radius of the shaded center circle is 1 and the radius of the entire dartboard is 4, what is the probability of throwing a dart and hitting the white part of the board? Round your answer to the nearest whole number.


6%


34%


67%


94%

Answers

Answer:

94%

Step-by-step explanation:

Determine if each statement is always, sometimes, or never true.

Parallel lines are
coplanar.

Perpendicular lines are
coplanar.

Distance around an unmarked circle can
be measured

Answers

Answer:

1) Parallel lines are "ALWAYS"

coplanar.

2) Perpendicular lines ARE "ALWAYS"

coplanar.

3) Distance around an unmarked circle CAN "NEVER" be measured

Step-by-step explanation:

1) Coplanar means lines that lie in the same plane. Now, for a line to be parallel to another line, it must lie in the same plane as the other line otherwise it is no longer a parallel line. Thus, parallel lines are always Coplanar.

2) similar to point 1 above, perpendicular lines are Coplanar. This is because perpendicular lines intersect each other at right angles and it means they must exist in the same plane for that to happen. Thus, they are always Coplanar.

3) to have the distance, we need to have the circle marked out. Because it is from the marked out circle that we can measure radius, diameter and find other distances around the circle. Thus, distance around an unmarked circle can never be measured.

Aron flips a penny 9 times. Which expression represents the probability of getting exactly 3 heads? P (k successes) = Subscript n Baseline C Subscript k Baseline p Superscript k Baseline (1 minus p) Superscript n minus k. Subscript n Baseline C Subscript k Baseline = StartFraction n factorial Over (n minus k) factorial times k factorial EndFraction Subscript 9 Baseline C Subscript 3 Baseline (0.5) cubed (0.5) Superscript 6 Subscript 9 Baseline C Subscript 3 Baseline (0.5) cubed Subscript 9 Baseline C Subscript 3 Baseline (0.5) cubed (0.5) Superscript 9 Subscript 9 Baseline C Subscript 6 Baseline (0.5) Superscript 6

Answers

Answer:

[tex]P(3) = ^9C_3 * 0.5^3 *0.5^6[/tex]

Step-by-step explanation:

Given

[tex]n = 9[/tex] --- number of flips

Required

[tex]P(x = 3)[/tex]

The probability of getting a head is:

[tex]p = \frac{1}{2}[/tex]

[tex]p = 0.5[/tex]

The distribution follows binomial probability, and it is calculated using:

[tex]P(x) = ^nC_x * p^x * (1 - p)^{n-x}[/tex]

So, we have:

[tex]P(3) = ^9C_3 * 0.5^3 * (1 - 0.5)^{9-3}[/tex]

[tex]P(3) = ^9C_3 * 0.5^3 *0.5^6[/tex]

Answer:

Aron flips a penny 9 times. Which expression represents the probability of getting exactly 3 heads?

Answer: A

Step-by-step explanation:

El arquitecto Gómez, dirige el proyecto de remodelación del parque municipal del distrito La Esperanza. La forma del parque está representada por la ecuación polar r(5-3sensθ)=16. El arquitecto planea construir un camino que une los extremos de la parte más ancha del terreno y necesita saber la distancia que existe entre los extremos (considerar que las medidas están en cientos de metros), además en el centro del camino colocará una pileta. Por ello, se requiere obtener las coordenadas de los extremos y del centro en coordenadas rectangulares. Para ayudar al arquitecto Gómez a lograr su objetivo, se deberá seguir la siguiente estrategia:
Pasar la ecuación polar a rectangular (en su forma ordinaria) (2 Puntos)
Hallar el centro, los vértices de la parte más ancha del terreno en la forma rectangular y determinar la distancia entre los vértices (considerar que las medidas están en cientos de metros), utilizando la ecuación cartesiana, hallada en a). (2 Puntos)
Graficar la cónica en el plano cartesiano ubicando las coordenadas de los vértices y del centro. (1 Punto)

Answers

Answer:

thank you for the point too mucheee

You: Your welcome

hey Plz help me fast it's important.

Answers

Answer:

Step-by-step explanation:

a) 52 is divisible by 4 and 5 - 2 = 3

b) 63 is divisible by 9 and 3*2 = 6 -> ten digit

c) 50 is divisible by 10 and 5 + 0 = 5

d) 72 is divisible by 6 and 7*2 = 14

19. Divide 6/13 by 6/12.
A. 12/13
B. 13/12
c. 1/12
D.9/16

Answers

Answer:

12/13 is the answer

Step-by-step explanation:

I think the answer is A . 12/13

Joan has raised $306 by selling 34 equally priced boxes of chocolate for the team fund-raiser. Which of the following equations can be used to find the price, n, of each box of chocolate?

n ÷ 34 = 306
34n = 306
n − 34 = 306
n + 34 = 306

Answers

Answer:

34n=306

Step-by-step explanation:

Use inverse operation to find it, 306÷34= 9, check again 34(9)=306, so it's correct!

answer 34n=306 hope this helps
Other Questions
Explain the law of conservation of energy. Find the length of BC Why are viruses not living?? Given the following coordinates the glide reflection transformation Which situations can be presented by an exponential function?Select EACH correct answerA.In a structure made of soup cans, each row has 6 more cans that the previous rowB.a doctors office accepts 20 new patients each month C.The value of a motorcycle decrease by 12% each yearD.Every year, the number of online subscribers to a service is 4 times what it was the previous year Which of the following describes transmission of a disease by indirect contact?1. Person A has acne -> Person A and Person B are physically intimate -> Person B does not develop acne2. Person A has a cold -> Person A sneezes near uninfected Person B3. deer has Lyme disease -> tick bites deer -> tick bites uninfected person4. Person A has malaria -> mosquito bites Person A -> mosquito bites uninfected Person B What effect did Kennedy's inaugural speech have on his approval rating?A. increased itB. decreased itC. didn't affect itD. approval ratings weren't measured Round to the nearest penny. $11,579.9998 12. solve for a. help please . Pht biu sau y l ng hay sai? Gii thch? Hai nc c th t c li ch thng mi ngay c khi mt trong hai nc c li th tuyt i. If you could fix one issue in the world what would it be and why? Write 5-7 sentences Which expression is equivalent to^2/9 Quadrilateral ABCD has vertices at A(0,0), B(0,2), C(6,2), and D(6,0). Find the vertices of the quadrilateral after a dilation with scale factor 3/2. Which of the following statements if made by a patient with otitis media External does not indicate the need for further education? A. I will clean my ear with cotton tip applicator or a B. I will take my antibiotics whenever I feel like C. I will avoid potential irritants such as hair care p I will continue to swim Treatment of Chronic Otitis media includes all pointD. I will continue to swim Some diseases/conditions are caused by deficiencies in these nutrients (vitamins). Name one suchdisease, say what element is deficient, and describe the symptoms and treatment. Who usually getsthe disease? Is it more common in certain areas? Solve: 9y+1 = 32y+1 + 54 Pick the word that best completes the following sentence._____ mag Autos.NichtsTschGleichfallsDer Junge Which detail best characterizes the narrators uncle in the excerpt in a journey to the center of the earth This Question: 1 ptThe law of demandshown graphically by ademand curveWhen the price of a good drops, consumers purchase more of it because ofO A. the substitution effect only.OB. neither the income nor the substitution effect.O C. the income effect onlyOD. both the income and substitution effect.Click to select your answerType here to search Problem is in the picture below thank you for your help