in class, we proved that the number of ways of tiling a $1 \times n$ rectangle with $1 \times 1$ and $1 \times 2$ tiles is $f {n 1}.$ (a) use a tiling argument to give a combinatorial proof that \[f 1 f 2 f 3 \dots f n

Answers

Answer 1

Here is a straightforward recursion you may employ to calculate the value.

let's use rectangles with integer aspects to represent the quantity of tilings of a $2 instances n$ rectangle as $T(n)$. There are $22n-2$ techniques to accomplish this if no rectangles of height $2$ are hired, wherein case we lessen to two wonderful times of the $1 times n$ state of affairs. If no longer, we set a situation based at the top-proper rectangle's $2 height. With the preliminary conditions $T(0)=1$ and $T(1)=2$, this results in $$T(n)=22n-2+sum k=0n-1 T(okay)+sum 0leq k ell leq n-1T(ok)22(n-ell-1)$. The center term inside the recursion corresponds to the case where the rightmost rectangle of top $2$ is absolutely the rightmost rectangle inside the tiling.

It should be noted that the formula $2n-1$ for the $1 times n$ case is incorrect if $n=0$.

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Related Questions

The square below represents one whole. What percent is represented by the shaded area?

Answers

Answer:

29%

Step-by-step explanation:

There are 100 boxes. 29 of them are shaded in, so we can divide that by 100.

29/100=0.29

0.29 is equal to 29%

The Daily Smile store sells bouquets in which 2 out of 5 are white. How many total daisies are there if 8 daisies are white?

Answers

The answer is 28 total daisies

please help question is in the image!

Answers

x1 = 4 x2 = -4

substitute the values into the given equations!!

(4 + (-4)) / 2 = (0 / 2) = 0

y1 = -5 y2 = 5

(-5 + 5) / 2 = (0 / 2) = 0

midpoint = (0, 0)

bold values - box answers :D

Solve the literal equation for x.
13. x + 5y = 2
14. 2x + 5 = 12y + 9

Answers

Answer:

x=2

Step-by-step explanation:

You would use substitution. In which x =-5y +2 and x = 6y+2. -5y + 2 = 6y + 2. So would solve for y value then plug it into the equation to solve x.

WRITING A quadratic function is increasing on (- ∞ ,2) and decreasing on (2, ∞). Is the vertex the highest or lowest point on the parabola? Explain.

Answers

The vertex of the parabola of the quadratic function that is increasing in the interval (-∞, 2), and decreasing in the interval (2, ∞), is the highest point on the parabola.

How can the type of vertex be found from the description of the quadratic function?

The given description of the quadratic function is presented as follows;

The interval the function is increasing = (-∞, 2)

The interval the function is decreasing = (2, ∞)

The graph of the function is therefore increasing from -∞ up to the point just before 2.

The graph of the function is decreasing from the point just after 2 to infinity.

The point 2 is therefore the highest point of the graph and also, the vertex of the quadratic function.

Therefore;

The vertex of the parabola of the quadratic function is the highest point

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Which equation represents a line through (4, -6) and (0, 2)?

Answers

Answer: C

Step-by-step explanation: Substitute four and zero in each of the choices and see if the sum becomes negative six and two, respectively. If it does, then the equation represents the line.

Third equation substitution:

x = 4

y = -2(4) + 2

y = -8 + 2

y = -6

x = 0

y = -2(0) + 2

y= 0 + 2

y = 2

Therefore, the answer is C.

Note: I skipped to the third equation because the other equations are false.

Dana saved 450 for food for her upcoming vacation. the breakfast was included with their hotel, but lunch and dinner are not. when dana cooks lunch or dinner it costs on average 10 . when the family goes to a restaurant for lunch or dinner it costs on average 40 . what is the maximum number of meals the family can eat at a restaurant.

Answers

The maximum number of meals the family can eat at the restaurant is 11

Amount saved by Dana for her upcoming vacation = 450

Average cost when Dana cooks lunch or dinner  = 10

Average cost when the family goes to a restaurant for lunch or dinner = 40

Maximum number of meals the family can have at the restaurant  = Amount saved by Dana/Average cost of a meal when the family goes to a restaurant

=450/40

= 11.25 or 11

So, the maximum number of meals the family can eat at the restaurant is 11 with a budget of 450.

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Which numbers are a distance of 3 units from 12 on a number line?














Select each correct answer.

Answers

Answer:

9 and 15

Step-by-step explanation:

ans should be 9 and 15

i dun really understand what this qns wants u to find really bad qns to test

joe and millie each have some baseball cards, and ¾ of the number of cards joe has is equal to 2/3 of the number of cards millie has. what is the least number of cards they could have altogether?

Answers

So, the least number of cards they could have altogether is any value of integer Z, that is ranging from (0→∞). If starting from n=1, then X=8 and Y=9.

What is an integer?

A whole number that can be either positive, negative, or zero is known as an integer.

Let Joe has x no. of cards,

then,

Millie has (3/4)x cards.

In that case, Let millie has a total y no. of cards,

then, Joe has (2/3) y cards.

This means that,

(3X)/4 = (2Y)/3

The alternate form shall be:

X = (8 Y)/9

(3 X)/4 - (2 Y)/3 = 0

Real solution:

Y=(9X)/8

Integer Solution shall be:

X=8n, Y=9n, n∈Z, where Z is the set of integers.

So, the least number of cards they could have altogether is any value of integer Z, that is ranging from (0→∞). If starting from n=1, then X=8 and Y=9.

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cos x + sin x tan x = sec x

Answers

Answer:

Dear Friend

To prove the given equation

50 points mathamatics last question for the day

Answers

10² = 100

28.007 × 100 / 2800.7

third option = 2,800.7

Answer: The answer is within the picture!

Step-by-step explanation:

Brooke and her mom are 21 years apart in age. The sum of their ages I'd 49. How old are Brooke and her mom

Answers

Answer: her mom is 35 and she is 14.

4(4 – 12x) – 2(x – 12) + 5x = –50?

Answers

The value of x of the given equation is 2.

What is equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.

Given:

The given equation is

4(4 – 12x) – 2(x – 12) + 5x = –50

We have to find the value of x.

According to given question we have

4(4 – 12x) – 2(x – 12) + 5x = –50

Rearrange terms we get,

4(– 12x+4) – 2(x – 12) + 5x = –50

Distribute we get,

-48x+16-2x+24+5x=-50

Compare the like terms we get,

-45x=-50-40

-45x=-90

x=2

Therefore, the value of x of the given equation is 2.

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consider the question: what is the probability of getting a 7-card poker hand (order doesn’t matter) that contains at least two 3-of-a-kind (3-of-a-kind means three cards of the same rank). for example, this would be a valid hand: ace of hearts, ace of diamonds, ace of spaces, 7 of clubs, 7 of spades, 7 of hearts and queen of clubs. (note that a hand consisting of all 4 aces and three of the 7s is also valid.)

Answers

The probability of getting a 7-card poker hand that contains at least two 3-of-a-kind is 0.0013

For given question,

We need to find the probability of getting a 7-card poker hand that contains at least two 3-of-a-kind.

Total number of cards = 52

If a 7-card poker hand contains at least two 3-of-a-kind,

3-of-a-kind means the three cards of the same rank.

The expression for the probability is,

[tex]P=\frac{ ^7C_3}{ ^{52}C_4} +\frac{ ^7C_2}{ ^{52}C_5} +\frac{ ^7C_1}{ ^{52}C_6}\\\\P=0.0013[/tex]

So, the required probability is 0.0013

Therefore, the probability of getting a 7-card poker hand that contains at least two 3-of-a-kind is 0.0013

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help pls its algebra quick

Answers

Answer:

B

Step-by-step explanation:

Graph is positive and y intercept is on negative 2.

A shop displays a total of 50 type A and type B mice. The cost of a type A mouse is $6 and that of a type B mouse is $13. If the total cost of all 50 mice is $433, find the number of type A mice displayed. The answers is 31​

Answers

31 Type A
19 Type B

A+B= 50

6a+13b=433

a =31, b=19

ill give uu crown if you answer this for me

Answers

Formula for slope: y2-y1/x2-x1

Answer: 1/2

Answer:

Given,points (0,3)and(10,8)

Step-by-step explanation:

slope(m)=

[tex] \frac{y2 - y1}{x2 - x1} [/tex]

=

[tex] \frac{8 - 3}{10 - 0} [/tex]

=

[tex] \frac{5}{10} [/tex]

=

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

The slope is 1/2.

If the answer is correct please mark brainliest

The man has 2 he loses one how many does he have left

Answers

Answer:

1

Step-by-step explanation:

If a person has 2 apples and gives someone 1 which is 2-1=1

PLEASE HELP ME ITS DUE IN 10 MINUTES (I'm in 5th BTW!!!)​

Answers

Answer:

1st box: 2000

2nd box: 1

3rd box: 22.99

4th box: 0.11

5th box: 23

Step-by-step explanation:

It's simply splitting up the 2000 and 1, and then diving them by 87 each.
After that you can divide them and round to the nearest 10th, and add them to get 23.

The sum of three lengths of a fence ranges from 45 to 60 inches. Two side lengths are 9 and 18 inches. If the length of the third side is x inches, write and solve a compound inequality to show the possible lengths of the third side.
a. 9 ≤ x ≤ 18
b. 18 ≤ x ≤ 33
c. 36 ≤ x ≤ 42
d. 45 ≤ x ≤ 60

Answers

The solution to a compound inequality to show the possible lengths of the third side is 18 ≤ x ≤ 33.

What is Compound Inequality?

Two or more inequalities are connected together with or or and to form a compound inequality (also known as a combined inequality).

A value must only make one aspect of an inequality true in order to be the solution to an or inequality. An inequality's solution must make both portions true in order to be effective.

According to the given values;

given parameters are

Range = 45 to 60 inches

Sides = 9, 18 and x

The sum of the three sides is

sum=9 + 18 + x

Evaluate

Sum = 27 + x

Recall that

Range = 47 to 60 inches

So, we have

45 ≤ 27 + x ≤  60

Subtract through by 27

So, we have

18 ≤ x ≤ 33

Hence, the solution to a compound inequality to show the possible lengths of the third side is 18 ≤ x ≤ 33.

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24-{[16-(8-1)]×2 please answer

Answers

Answer:

4

Step-by-step explanation:

It look like your are missing a bracket.

Do the inner most parentheses first.

24 -(16 -(7))x2

24 - 9 x 2

24 -18

4

Which algebraic expression is equivalent to the expression below?

4(4x + 5) + 4(11 - x)

A.
20x + 64
B.
12x + 24
C.
12x - 64
D.
12x + 64

Answers

Answer:

D. 12X + 64

Step-by-step explanation:

4(4x+5)+4(11-x)

4(4x+5)+4(11−x)

4(4x + 5) + 4(11 - x)

1 Expand by distributing terms.

16x+20+4(11-x)

16x+20+4(11−x)

2 Expand by distributing terms.

16x+20+44-4x

16x+20+44−4x

3 Collect like terms.

(16x-4x)+(20+44)

(16x−4x)+(20+44)

4 Simplify.

12x+64

12x+64

Answer:

D. 12x + 64

Step-by-step explanation:

expand the brackets by multiplying:

= 16x + 20 + 44 - 4x

= 12x + 64

brainliest pls :,)

Describe at least two differences between constructing an inscribed regular hexagon and constructing an inscribed square.

100 points and brainliest

Answers

There are some differences in the process of constructing a inscribed square and a hexagon inside a circle.

When constructing a square, we start with a circle. Then draw its diameter through the center of the circle. Now putting compass on end points of this diameter, measuring more than half the length of diameter on the compass, draw 4 arcs above and below the diameter. So we get a perpendicular bisector of the diameter. In total, we get 4 points on the circle. Joining the adjacent points, we get the inscribed square.

When constructing the regular hexagon, start drawing a circle. Put the compass on a point on the circle and measure the radius on it. Now draw an arc on the circle. Putting compass on this new point on the circle draw another arc. Continuing like this, we get a total of  6 arcs giving 6 points on the circle. Join the adjacent points to get an inscribed regular hexagon.

So the differences in constructing the square and the regular hexagon are:

Diameter is used in square whereas radius is enough for the regular hexagonPerpendicular bisector is constructed for square while regular hexagon does not need one.For a square,4 arcs giving 4 points on the circle are needed. But for a regular hexagon 6 arcs giving 6 points are there.

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coach ferguson uses a thermometer to measure the temperature (in degrees fahrenheit) at 20 different locations in the school swimming pool. an analysis of the data yields a mean of 77 degrees fahrenheit and a standard deviation of 3 degrees fahrenheit. recall that ∘c

Answers

1) The standard deviation of the temperature readings in degrees Celsius is 1.66° C.

2) The mean and standard deviation of Ferguson tip distribution is 1.1 and 0.3 respectively.

1) Let, X be the temperature in Fahrenheit and Y be the temperature in Celsius.

Mean = 77° F

[tex]77^\circ \ F=\frac{5\times77}{9}-\frac{160}{9}[/tex]

[tex]= 25^{\circ}C[/tex]

Variance in Fahrenheit is [tex]3^2=9[/tex]

[tex]Var(aX+b)=a^2VarX[/tex]

Here, [tex]a=\frac{5}{9}[/tex] and [tex]b=-\frac{160}{9}[/tex]

[tex]Var(Y)=\frac{25}{81}\times9[/tex]

[tex]=2.77[/tex]

Standard deviation [tex]= \sqrt{Var(X)[/tex]

[tex]= \sqrt{2.77}[/tex]

[tex]= 1.66^{\circ}[/tex]

2) Let, X be the cost of them meal and Y be the tip he gives.

[tex]Y=2+0.1X[/tex]

[tex]E[X]=9, Var[X] = 9[/tex]

Therefore,

[tex]E[Y]=E[2+0.1X][/tex]

[tex]=0.1E[X]+2[/tex]

[tex]=0.1\times9+2[/tex]

[tex]=1.1[/tex]

[tex]Var[Y] = 0.12Var[X] = 0.01\times9=0.09[/tex]

Standard deviation of [tex]Y = \sqrt{Var[Y]}[/tex]

[tex]= \sqrt{0.09}[/tex]

[tex]= 0.3[/tex]

Therefore,

1) The standard deviation of the temperature readings in degrees Celsius is 1.66° C.

2) The mean and standard deviation of Ferguson tip distribution is 1.1 and 0.3 respectively.

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"Your question is incomplete, probably the complete question/missing part is:"

Coach Ferguson uses a thermometer to measure the temperature (in degrees Fahrenheit) at 20 different locations in the school swimming pool. An analysis of the data yields a mean of 77 degrees Fahrenheit and a standard deviation of 3 degrees Fahrenheit. Recall that [tex]C^{\circ}=\frac{5^{\circ}F}{9} -\frac{160}{9}[/tex]. What is the mean temperature reading in degrees Celsius? What is the standard deviation of the temperature readings in degrees Celsius? When Sam goes to a restaurant, he always tips the server $2 plus 10% of the cost of the meal. If Sam's distribution of meal costs has a mean of $9 and a standard deviation of $3, what are the mean and standard deviation of his tip distribution?

find the area of a cylinder with a height of 8 inches and base radius of 4 inches

Answers

Answer is 401.92 cubic inches

Volume of a cylinder formula is

V = TT x radius ^2 x height

V = 3.14 x 4^2 x 8

V = 3.14 x 16 x 8

V = 401.92

Which of the following ordered triples is the solution to the system of equations?

2x − y − z = −1

3x + y − z = 2

x + y − 5z = −8

Answers

Answer:

1,1,2

Step-by-step explanation:

The solution to the given system of equations are:{ x = 1, y = 1, z = 2} which is the corrrect answer would be option (A).

What is an equation?

The equation is defined as a mathematical statement with at least two terms that contain variables or values that are equal.

We have been given the system of equations as:

2x − y − z = −1

3x + y − z = 2

x + y − 5z = −8

Isolate the term of x in the equation 2x − y − z = −1, and we get

x = (- 1 + y +z)/2

Substitute the value of x = (- 1 + y +z)/2 in the above both equations,

3(- 1 + y +z)/2 + y − z = 2

(- 1 + y +z)/2 + y − 5z = −8

Simplify the equation to you get,

(5y + z - 3) / 2 = 2

(3y - 9z - 1) / 2 = -8

Isolate the term of y : (5y + z - 3) / 2 = 2 ⇒ y = (-z +7 )/5

Substitute the value of y = (-z +7 )/5 in the equation (3y - 9z - 1) / 2 = -8

(3(-z +7 )/5 - 9z - 1) / 2 = -8

Simplify the equation to you get,

8(-3z + 1)/d = -8

Isolate the term of z : 8(-3z + 1)/d = -8 ⇒ z = 2

Substitute the value of z = 2 in the equation y = (-z + 7) / 5 to simplify to get

⇒ y = 1

Substitute the values of y = 1 and z = 2 in the equation x = (-1 + y + z) / 2 to simplify to get

⇒ x = 1

The solution to the given system of equations are:

{ x = 1, y = 1, z = 2}

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how to solve if 5a=6 and 7b=8, 35ab=
(please explain, i need explaination)

Answers

Answer:

35ab = 48

Step-by-step explanation:

given

5a = 6 ( divide both sides by 5 )

a = [tex]\frac{6}{5}[/tex]

and

7b = 8 ( divide both sides by 7 )

b = [tex]\frac{8}{7}[/tex]

substitute these values for a and b into the expression and simplify

35ab

= 35 × [tex]\frac{6}{5}[/tex] × [tex]\frac{8}{7}[/tex] ( divide 35 and 5 by 5 )

= 7 × 6 × [tex]\frac{8}{7}[/tex]

= 42 × [tex]\frac{8}{7}[/tex] ( divide 42 and 7 by 7 )

= 6 × 8

= 48

b.a slug takes 4.25 minutes to travel 11.2 centimeters. what is the speed of the slug in meters per second? predicted number of significant digits in answer: 2 or 3 answer value: actual number of significant digits:

Answers

Answer:

0.00375 meters per second,

Step-by-step explanation:

0.00375 meters per second, we know this is the answer because, 4.25*60=255 and 255/11.2=0.00375

work out the value of (3.5 x 10^6) ÷ (5 x 10^-3) give your answer in standard form.

Answers

The standard form of  (3.5 x 10^6) ÷ (5 x 10^-3) is 7*10^8

What is standard form?

Any number that we can write as a decimal number, between 1.0 and 10.0, multiplied by a power of 10, is said to be in standard form.

Given:

(3.5 x 10^6) ÷ (5 x 10^-3)

On further solving

3.5 * 10^(6 -(-3)) / 5

3.5* 10^9 /5

0.7 * 10^9

7*10^8

Hence, the standard form is 7*10^8.

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Please help - thanks

Insert parentheses in the appropriate places:

8+ 3-2 ×9 =17
28 ÷ 4+3 × 4+3 =28
5× 3+2 ×6 ÷3 =50
6× 9-4 +3-3 ×4=30
5 ×3+2× 6÷3 =19
5× 3+2×6 ÷3 =25

Answers

Answer:

the answer is 27

Step-by-step explanation:

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