Renae has been playing Tower of Hanoi and has noticed that the minimum number of moves it takes to defeat the game is related to the number of disks she must move. She has recorded her observations below. Write an equation that describes this pattern. Show your work.


Number of Disks in the Tower ║Minimum Number of Moves

1 ║1

2║ 3

3 ║7

4 ║15

5 ║31

Answers

Answer 1

Answer:

[tex]y = 2^x - 1[/tex]

Step-by-step explanation:

Let the number of disks be x and the minimum number of moves be y.

[tex]y = 2^x - 1[/tex]

When x = 1: y = 1

[tex]y = 1 = 2 - 1 = 2^1 - 1[/tex]

When x = 2: y = 3

[tex]y = 3 = 4 - 1 = 2^2 - 1[/tex]

When x = 3: y = 7

[tex]y = 7 = 8 - 1 = 2^3 - 1[/tex]

When x=4: y = 15

[tex]y = 15 = 16 - 1 = 2^4 - 1[/tex]

When x = 5: y = 31

[tex]y = 31 = 32 - 1 = 2^5 - 1[/tex]

Notice that for each derived expression of y, the exponent of 2 is being replaced by the value of x.

The general equation is: [tex]y = 2^x - 1[/tex]


Related Questions

Everyone will have juice in party and you have 10 liters of a juice blend (mixture of
pure juice and water) that is 60% pure juice.
1. How many liters of pure juice need to be added in order to make a blend that is 75% juice?
2. How many liters of pure juíce need to be added in order to make a blend that is 90% juice?

Answers

Answer: you added 6 liters of juice

Step-by-step explanation:

You have 10 liters of a juice blend that is 60% juice. How many liters of pure juice need to be added in order to make a blend that is 75% juice?

Ten liters of a juice blend at 60% juice means you also have ten liters of a juice blend at 40% water. 10 x .40 yields 4 liters of water in your blend.

A juice blend of 75% has a water content of 25%. So the same 4 liters of water must represent 25% of the blend after adding more juice.

4/.25 = 16 liters. 16 x .75 = 12.

12 + 4 = 16.

That means after adding your juice you will have 16 liters of blend at 75% juice.

You originally had 10 liters at 60% and now you have 16 liters at 75% . Subtracting 10 from 16 means you added 6 liters of juice.

A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.
-9x-8y= 41
-9x-2y=71

Answers

Answer:

I think it is add to eliminate x

Answer:

Step-by-step explanation:

4.913 rounded to the nearest tenth

Answers

Answer:

4.9

..........................

HELP PLEASE!!
Solve the system of equations below by graphing.
y= x - 3
y=-5/2x + 4

Answers

(x,y) = (9/2,3/2) is final results ig
Well, you can set them together like...

x-3 = -5/2 +4

Multiply both sides of equation by 2 to remove the fraction...

2(x-3)= 2(-5/2x+4)

2x-6 = -5x+8

Move the terms together...

2x+5x = 8 + 6

7x = 14

So....

x = 2

Answer this question:What is the difference between 9 < x and 9 = x? Explain.

Answers

9 < x

this means that x is a larger number than 9

9 = x

this means that x is equal to 9

GIVING BRAINLIEST FOR BEST ANSWER!!!
In two paragraphs, explain how Vietnam’s political boundaries, affiliations, and alliances changed from the end of World War II to 1975, when the country finally achieved independence. Based on your research, include the causes and effects of foreign aggression on Vietnam during this period.

Answers

Answer:

Vietnam got its independence from France on 2 September 1945. during second world war, France becomes weak and cannot control Vietnam so France evacuated from Vietnam completely and Vietnam got its independence. Vietnam's political boundaries meets with China, Indonesia, Cambodia and Thailand.

Step-by-step explanation:

Una fábrica produce 12 480 borradores cada semana. Estos artículos se venden empacados en cajas de una docena. ¿Cuántas cajas de borradores saldrán a la venta cada semana?

Answers

dhdirkkrfnfof. jeoxjfiwidodod . didof



A bag contains 2 5/8 pounds of candy. If the candy is equally distributed to point
seven children, how many pounds will each child get?"
3/7
3/8
3/9
3/10

Answers

The correct answer is 3/8

area of a square with 1m side is?​

Answers

Answer:

1 meter

Step-by-step explanation:

Okay so, all sides of a square are equal right? And is one side is 1 meter, then all of the sides are 1 meter. Your multiplying one by itself, making the answer pretty easy to find out.

Choose all the properties of a square

Answers

Answer:

Opposite sides are parallel. All sides are congruent. All angles are congruent. Diagonals bisect each other. Consecutive angles are supplementary. Diagonals are perpendicular and congruent.

Step-by-step explanation:

A square is a special shape in which all angles, sides, and diagonals are congruent to one another. Therefore, all sides and angles are congruent, the diagonals cross in the middle of the square making them perpendicular, the diagonals bisect each other in the middle, and they are supplementary because they are parallel.

x - 3( 2 - 3x)=2 ( 5x - 2)

Please solve !!

Answers

Step-by-step explanation:

I hope that this helps:)

x-6+9x=10x-4

10x-6=10x-4

-6=-4

Tha statement is false for any value of x

x=0 no solution

Three cylinders have a volume of 2826 cm. Cylinder A has a height of 900 cm. Cylinder B
has a height of 225 cm. Cylinder C has a height of 100 cm. Find the radius of each cylinder.
Use 3.14 as an approximation for T.

Answers

Answer:

the radius of each cylinder is 1 cm, 2 cm and 3 cm respectively

Step-by-step explanation:

The computation of the radius of each cylinder is shown below:

As we know that

The Volume of the cylinder = πr^2h

The radius would be

[tex]=\sqrt{ \frac{V}{\pi h} }[/tex]

For cylinder A

[tex]=\sqrt{\frac{2826}{3.14\times 900} }[/tex]

= 1 cm

For cylinder B

[tex]=\sqrt{\frac{2826}{3.14\times 225} }[/tex]

= 2 cm

For cylinder C

[tex]=\sqrt{\frac{2826}{3.14\times 100} }[/tex]

= 3 cm

Hence, the radius of each cylinder is 1 cm, 2 cm and 3 cm respectively

what is 40 percent of 90 percent

Answers

Answer:0.36

or 36

Step-by-step explan: used calculator

Multiply (x+9)2 need help ASAP​

Answers

Answer:

2+18

Step-by-step explanation:

(x + 9)2      distribute 2 · x = 2x and 9 · 2 = 18.

2x + 18, is the answer.

If you have any further question, please reach out to me :)

What’s the perimeter

Answers

Answer:64

Step-by-step explanation:

Answer:

64 is the answer :)

Step-by-step explanation:

i hope its correct

I’m confused I’m not sure which one it is

Answers

Answer:

A.55

Step-by-step explanation:

Because DE parallel to AC m(<B) common angle So ABC similar to DBEm(<D) = m(<A) = 180 - (60 + 65) =55

solve а) 3х - 5 = 13​

Answers

Answer:

6

Step-by-step explanation:

3х - 5 = 13

     +5   +5

3x=18

/3   /3

x=6

I honestly don’t know how to do this I need help

Answers

Answer:

the answer is 90

Step-by-step explanation:

hope it helps

have a nice day ^_^

Answer:

It is 90 degrees.

Step-by-step explanation:

It is one fourth of 360 degrees, which is 90 degrees.

Hope that helps!

how are below 0, -10 and -20 related?
PLEASE HELP!!!!

Answers

Answer:

It’s a way to show how things are related. It may be a mathematical pattern.

Step-by-step explanation:

Find the equation of the circle that has center (-4,3) and passes through 3,-3

Answers

Answer:

(x+4)^2+(y-3)^2 = 85

Step-by-step explanation:

The standard form of equation of a circle is expressed as;

(x-a)^2 + (y-b)^2 = r^2

(a, b) is the center

r iis the radius

Get the radius

Radius is the distance between the two points

r^2 = (-3-3)^2 + (3-(-4))^2

r^2 - (-6)^2+(7)^2

r^2 = 36+49

r^2 = 85

Substitute (-4, 3) and r^2 = 85 into the formula

(x-(-4))^2 + (y-3)^2 = 85

(x+4)^2+(y-3)^2 = 85

This gives the required equation

how many pints are in a cup?

Answers

There are 2 cups in a pints

Answer:

0.4 Pints

Step-by-step explanation:

Write an equation in slope-intercept form for the line with slope 3/5 and y-intercept -9

Answers

Y=3/5x -9 I’m pretty sure it’s this

simplify the expression 3(j+2)-2​

Answers

Answer: (3j + 6) or 3j + 4

Step-by-step explanation:

You distribute the 3 inside the parentheses and you could subtract the 2

Step-by-step explanation:

I hope this helps. 3j+6-2= 3j+4

1. what is the equation of a line that has an x-intercept of 2 and a y-intercept of 8

Answers

Answer:

B

Step-by-step explanation:

x- intercept = 2  .So, Coordinate(2 , 0)

y-intercept = 8 . So, Coordinate (0, 8)

[tex]Slope = \frac{8-0}{0-2}\\\\=\frac{8}{-2}\\\\=-4[/tex]

Slope y-intercept form: y = mx + b  {Here, b is y-intercept}

y = -4x + 8

8(12+a) its asking for the distributive property to simplify the expression​

Answers

Answer:

96+8a

Step-by-step explanation:

8*a=8a

8*12=96

combine them

96+8a

The scale of a map is 1 cm: 75 km. What is the actual distance between two towns that are 4 cm apart on the map?

Answers

Answer:

300

Step-by-step explanation:

(75*4)/1

What is the total weight, w, of 5 bags of soil?

Answers

Answer:200

Step-by-step explanation: I typed this and got it right

How do i graph y=2x+5 ?

Answers

Answer:

y/2

Step-by-step explanation:


Find the value of x.
25
65°

Answers

Answer:

The answer is x= 10.6

Step-by-step explanation:

because C and D are both bigger numbers then the side that is given so those are eliminated and you're left with A and B and there is no way it can be B because thats to big of a number so its A

What are the zeros of the function h(x)=2x2+x−15
?

A
x=−3andx=−52
B
x=−3andx=52
C
x=−52andx=3
D
x=52andx=3

Answers

the correct answer is B x=-3 and x= positive 5/2
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