find and solve a recurrence relation for the number of ways to arrange flags on an n-foot flagpole using three types of flags: red flags 2 feet high, yellow flags 1 foot high, and blue flags 1 foot high. page 4 of 8

Answers

Answer 1

Let Fn be the number of ways of arranging such flagpole with the given conditions.

When arranging a flagpole of n feet high, consider the following cases

If the last flag used is a red flag, then the other flags are n-1 foot high, so they can be seen as arranged on a smaller flagpole of n-1 feet high, which can be done in Fn-1 ways.

Similarly, If the last flag used is a gold flag, then the other flags can be seen as arranged on a smaller flagpole of n-1 feet high. This can be done in Fn-1 ways.

If the last flag used is green, the other flags are n-2 feet high, so the flagpole can be arranged in Fn-2 ways.

Using the sum rule, we obtain that Fn = 2Fn-1 + Fn-2 for all n≥3. Listing all the combinations of flags, the initial conditions are F1 = 2 and F2 = 3.

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Related Questions

Help plssssss it due today

Help plssssss it due today

Answers

Answer:

C

Step-by-step explanation:

If I am correct the answer is c

In 2010, your company paid overtime wages or hired temporary help during 32 weeks of the year. Overtime was paid for 26 weeks and temporary help was hired for 15 weeks. If at year’s end an auditor
checks your accounting records and randomly selects one week to check the company’s payroll, what is the probability that the auditor will select a week in which you paid overtime wages and hired
temporary help?

Answers

The probability that the auditor will select a week in which you paid overtime wages and hired is 0.28

In 2010, your company paid overtime wages or hired temporary help during 32 weeks of the year. Overtime was paid for 26 weeks and temporary help was hired for 15 weeks.

What is probablitity?


Probability, can be define as the ratio of favorable outcomes to the n number of total events.

Here, p(a) = Overtime was paid for 26 weeks = 26/32= 0.81
       p(b) =  temporary help was hired for 15 weeks = 0.46
Required probability = P(a) + P(b) - 1
                                  =   0.81 + 0.46 -1
                                  =   0.28

The the required probability that the auditor will select a week in which you paid overtime wages and hired is 0.28

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Multiply. 6/7 ⋅ 4/15

A. 8/35
B. 14/45
C. 5/11
D. I don't know

Answers

Answer:

A

Step-by-step explanation:

Multply = 24/105

Divide by 3

8/35

it'd be 8/35
6•4 = 24
7•15 = 105
simplify and you get 8/35 :)

A group of 25 employees want to go out for a group dinner.
18 employees want to go to Restaurant A.
7 employees want to go to Restaurant B.
Use this information to answer the questions below.
ws the proportion of employees who want to an to Restaurant

Answers

A is 18:25
B is 7:25

i just need help with part B and can you draw the bar diagram for me and the equation

i just need help with part B and can you draw the bar diagram for me and the equation

Answers

The bar diagram of the values is added as an attachment

How to determine the bar diagram

From the question, we have the following parameters that can be used in our computation:

Almonds = 3.64 kgCashews = 2.79 kgPeanuts = 3.44 kgPine Nuts = 2.73 kg

The equation of the above details cannot be determined

This is so because the parameters do not represent a relation

Next, we make the bar graph

See attachment for the bar graph

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i just need help with part B and can you draw the bar diagram for me and the equation

i need answer please SSS SAS AA NOT ENOUGH INFO NOT ENOUGH INFO​

i need answer please SSS SAS AA NOT ENOUGH INFO NOT ENOUGH INFO

Answers

Answer:

Not enough info

Step-by-step explanation:

You don't have enough information to figure it out

Please help for 100 points.

Please help for 100 points.

Answers

By using matrix operations, the resulting matrix is \(4 \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right] - \left[\begin{array}{cc}1&2\\4&5\end{array}\right]\) is  \(\left[\begin{array}{cc}3&6\\12&15\end{array}\right]\).

How to simplify a combination of matrices

In this problem we must simplify a combination of two matrices, this can be done by using properly the fundamental operations for matrices. Matrices are algebraic constructions characterized by a number of row and a number of columns. For instance, there is a matrix with two rows and three columns:

\(\left[\begin{array}{ccc}1&2&3\\4&5&6\end{array}\right]\)

There are two fundamental operations for matrices:

Sum - The respective elements of the same row and the same column of the matrix are summed:

\(\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] + \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] = \left[\begin{array}{ccc}2&4&6\\8&10&12\\14&16&18\end{array}\right]\)

Where C(i, j) = A(i, j) + B(i, j), i is the row index and j is the column index.

Scalar mutiplication - Every element of the matrix is multiplied by a scalar:

\(2 \cdot \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] = \left[\begin{array}{ccc}2&4&6\\8&10&12\\14&16&18\end{array}\right]\)

Where B(i, j) = k · A(i, j), k is the scalar.

Now we show the complete procedure to find the simplified expression:

\(4 \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right] - \left[\begin{array}{cc}1&2\\4&5\end{array}\right]\)                         Given

\(4 \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right] + (- 1) \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right]\)               Definition of subtraction

\(\left[\begin{array}{cc}4&8\\16&20\end{array}\right] + \left[\begin{array}{cc}- 1&- 2\\- 4&- 5\end{array}\right]\)                     Scalar multiplication

\(\left[\begin{array}{cc}3&6\\12&15\end{array}\right]\)                                             Sum of matrices / Result

The simplifed form of the matrix is \(4 \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right] - \left[\begin{array}{cc}1&2\\4&5\end{array}\right]\) is  \(\left[\begin{array}{cc}3&6\\12&15\end{array}\right]\).

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I need help with these question my teacher doesnt explains that well

I need help with these question my teacher doesnt explains that well

Answers

the formulam of the volume is

\(V=\frac{\pi\times r^2\times h}{3}\)

where r is the radius and h the height

r=3/5 because is the half of diameter

h=10

so replacing

\(\begin{gathered} V=\frac{\pi\times(\frac{3}{5})^2\times10}{3} \\ \\ V=\frac{\pi\times\frac{9}{25}\times10}{3} \\ \\ V=\frac{6}{5}\pi\approx3.78 \end{gathered}\)

the volume of the cone is 3.78 square millimeters

\(\frac{\frac{9}{25}\times10}{3}=\frac{\frac{90}{25}}{\frac{3}{1}}\)

the red multiplication is the numerator and green the denomintor

\(\frac{90\times1}{25\times3}=\frac{90}{75}\)

simplify by 15

\(\frac{\frac{90}{15}}{\frac{75}{15}}=\frac{6}{5}\)

and then add the pi

I need help with these question my teacher doesnt explains that well

solve each equation for the variable

solve each equation for the variable

Answers

X=36

Hope this helps, if I’m right :p

The volume of this cone is 83.7 cubic meters. Find the DIAMETER. SHOW ALL WORK

The volume of this cone is 83.7 cubic meters. Find the DIAMETER. SHOW ALL WORK

Answers

There for the diameter is 2(4.8 )= 9.6 ft

The volume of this cone is 83.7 cubic meters. Find the DIAMETER. SHOW ALL WORK

Given: Volume of the cone is 83.7 m³

We know that:

\(\bigstar \ \ \boxed{\sf{\textsf{Volume of cone is given by} : \dfrac{\pi r^2h}{3}}}\)

where r is the radius of the cone and h is the height of the cone

Given: Height of the cone = 5m

Substituting the values in the formula, we get:

\(\sf{\implies \dfrac{\pi r^2(5)}{3} = 83.7}\)

\(\sf{\implies \pi r^2 = 83.7 \times \dfrac{3}{5}}\)

\(\sf{\implies \pi r^2 = 83.7 \times 0.6}\)

\(\sf{\implies \pi r^2 = 50.22}\)

\(\sf{\implies r^2 = \dfrac{50.22}{\pi}}\)

\(\sf{\implies r^2 = 16}\)

\(\sf{\implies r = 4}\)

We know that : Diameter is two times the radius

⇒  Diameter of the Cone is 8 meters

problem 7.2. cox-ross-rubinstein (crr) the cox-ross-rubinstein model is a binomial tree in which the up and down factors are given as u

Answers

The Cox-Ross-Rubinstein (CRR) model is a mathematical model used in finance to evaluate the potential future value of an asset or portfolio. The model is based on the concept of a binomial tree.

What is a binomial tree?

A binomial tree is a mathematical model used in finance to estimate the probable future value of an asset or portfolio. The notion of a binomial, a mathematical expression with two potential outcomes, forms the foundation of the model. In a binomial tree, the future value of the asset is defined by two potential outcomes at each time step: a "upper" element and a down factor. The underlying variables that affect the asset, such as interest rates and market circumstances, dictate the up and down components. Reflecting This enables investors to assess the advantages and dangers of a possible investment and come to wise judgments.

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let s be a set of n segments in the plane. a line ? that intersects all segments of s is called a transversal or stabber for s.

Answers

Suppose 's' be a collection of 'n' plane segments. It is true to say that a transversal as well as stabber for 's' is a line that crosses every segment of 's'.

Explain the term transversal?

A transversal in geometry is a line, ray, as well as line segment that, on a plane, overlaps other lines, rays, including line segments at various locations.

A transversal is a line that, at two different locations in the geometry, cuts through two lines within the same plane. Various sorts of angles in pairs, including successive internal angles, corresponding angles, and alternate angles, are produced by a transversal intersection between two lines.

Thus, if 's' be a collection of n plane segments. It is true to say that a transversal as well as stabber for 's' is a line that crosses every segment of s.

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The midpoint of line segment AB is (1,2). if the coordinates of A are (1,0) what are the coordinates of B

Answers

The required coordinate of B will be at (1, 4)

When a point bisects a line, it cuts the line into two equal parts and the point on that line is known as its midpoint. The expression for calculating the midpoint of a line is expressed as;

\(M(X, Y)= [{ \frac{x_2+x_1}{2} , \frac{y_2+y_1}{2} ]\) where:

\(X =\frac{x_2+x_1}{2} \\Y=\frac{y_2+y_1}{2}\)

From the question, we are given the following coordinate points

\(X=1\\x_1=1\\\)

Get x₂;

\(X =\frac{x_2+x_1}{2}\\1 =\frac{x_2+1}{2}\\2=x_2+1\\x_2=2-1\\x_2=1\\\)

Get y₂;

\(Y =\frac{y_2+y_1}{2}\\2 =\frac{y_2+0}{2}\\2 \times 2=y_2+0\\4=y_2+0\\y_2=4\\\)

Hence the coordinate of B will be (1, 4)

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The midpoint of line segment AB is (1,2). if the coordinates of A are (1,0) what are the coordinates

Find the slope of the line containing the points (-2, -7) and (6,3)

Answers

Answer: slope (m) = 1.25

Step-by-step explanation: m= 10/8 = 5/4 = 1.25

Answer:

          = 10 over 8 (10/8) or 1.25

Step-by-step explanation:

slope = y2 - y1 over x2 - x1

          = 3 - (-7) over 6 - (-2)

you're welcome :)

Please help me I forgot how to do it

Please help me I forgot how to do it

Answers

Answer:

b

Step-by-step explanation:

Answer : b




Explanation : it wouldn’t make sense for them to be the other ones

Saeng wants to run the 100-meter-dash in a certain number of seconds. The table shows the change in times from her goal and her actual times for five races. Between which two race numbers is Saeng's third race?​

Answers

Spewing wants to run the 100 meter dash in a certain number of seconds.the table shows the change

Each of the figures are similar. Find the missing length

Each of the figures are similar. Find the missing length

Answers

Answer:

63

Step-by-step explanation:

the first one is 9x bigger then the second one

so 7x9 is 63

The chester company will increase its automation for the cell product by 2.0. assuming no further change in capacity, how much will this investment in automation cost?
a. $10,000,000
b. $20,000,000
c. $8,750,000
d. $17,500,000

Answers

Investment in automation cost = $8,750,000 when there

no further change in capacity.

Every three-dimensional object occupies some space. This space is measured in terms of its volume. Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Following are the informations of Cent:

Current automation = 7%

Capacity of next round = 1,100

New automation = 7 + 2 = 9

Investment in automation cost = Capacity * (4 * (New automation - previous automation)) * 1000

= 1,100 * (4 * (9 - 7)) * 1,000

= 1,100 * (4 * 2) * 1000

= 1,100 * 8 * 1,000

= $8,800,000.

Investment in automation cost = $8,800,000.

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Which expression is equivalent to -66.1 - (-55.6)?

Which expression is equivalent to -66.1 - (-55.6)?

Answers

Answer:

subtracting a negititive is the same as adding so -66.1+55.6

Hope This Helps!!!

work out the area of a semi circle take pi to be 3.142 and five your answer to two decimal places

Answers

Answer:

what are the measurements of the semi circle

Step-by-step explanation:

please help me solve for x and find missing side lengths and angle measures,,

please help me solve for x and find missing side lengths and angle measures,,

Answers

Answer: 90

Step-by-step explanatio

Answer:

the angle measure for angles T and V would be 127 because they are on opposite locations from each other. the angles S and U would 53 because T and U are coplemantery angles (180 degrees) so you subtract. 180-127 to get 53. To find x, on angle S, we simply subtract 1 from 53 (53-1) and divide the answer by 2. To find the lengths of the sides, put them next to each other and separet

them by an equal sign. subtract 3y from both sides of the equation and add 5 to both sides of the equation to get 3y=12. then divide 12 by 3 to get 4 so y=4. Then, simply replace the y with a 4 and solve the equations of the sides.

A bag contains teal and gold marbles. 2 marbles are randomly drawn from the bag. The chance of picking a gold
marble is 20%. If the rst marble picked is gold, there is a 17% chance of picking a gold marble the second time.
If the rst marble picked is teal, there is 26% chance of picking a gold marble the second time.
Create a tree diagram. What is the probability that at least one of the marbles picked is gold? What is the probability that at least one of the marbles picked is teal? What is the probability that one marble picked is gold and the other is teal? What is the probability that both marbles chosen are the same color? What is the probability that the second marble picked is teal?

Answers

Answer: its a 50/ 50 chance

Step-by-step explanation:

Plz helpppppppppppppp plzplzplz​

Plz helpppppppppppppp plzplzplz

Answers

Answer:

Rs. 26,620

Step-by-step explanation:

20,000 * \(1.1^{3}\)

where 1.1 is 10%, because each year it would increase by 1.1

and period 3 is number of years

Will mark brainliest when I can!!​

Answers

Answer:yes

Step-by-step explanation:yes of course (i just want points)

What is the value of x?
B
170
O x = 55°
O x = 60°
O x = 70°
X
С
O x = 110°
A

What is the value of x?B170O x = 55O x = 60O x = 70XO x = 110A

Answers

55 because it is an iscoleses triangle
55 it’s an iscoleses triangle

Find the area of an ellipse with equation \(\frac{x^2}{100} +\frac{y^2}{64} = 1\)

Answers

On solving the provided question, we can say that area of the ellipse equation = \(\pi ab\) = 3.14*10*8 = 251.2 cm sq.

What is equation?

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

area of an ellipse with equation  = \(x^2/100 + y^2/64 = 1\\\)

here, a = 10 and b = 8

area of the ellipse equation = \(\pi ab\) = 3.14*10*8 = 251.2 cm sq.

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21x+7y=42
−5x+5y=10

Answers

Answer:

(1, 6.71)

Step-by-step explanation:

I'm assuming that you need to solve this by substitution or elimination since you didn't include any context in your question, just the equations.

To solve this by elimination, first, decide on a variable you want to get rid of / cancel out. I chose y. To do this, you need to find the least common multiple (LCM) of 7 and 5, which is 35. Now, multiply the top equation, 21x + 7y = 42, by -5. Multiply the bottom equation, -5x + 5y = 10, by 7. Make sure when you multiply that you either make the 5 or the 7 negative so you can cancel out y. I chose to make 5 negative.

After you multiply by the -5 and the 7, rewrite your new equations:

-105x - 35y = -210

-35x + 35y = 70

Now, add the two equations together. When you do this, the y's cancel out and you're left with -140x = -140. Now, divide both sides by -140, and you're left with x = 1. Plug the value of x into one of your original equations. I chose the bottom equation, -5x + 5y = 10.

-5(1) + 7y = 42   ----->   -5 + 7y = 42.

Add -5 to both sides, which gives you 7y = 47. Divide both sides by 7, which gives you y = 6.71.

The last step is to put the values of x and y into a point: (1, 6.71).

Hope this helps!

If number of electricity power failures occur according to a Poisson distribution with an average of 4 failures per 5 months. 12. What is the probability that there will be at least one failure during the coming month

Answers

Answer:

123

Step-by-step explanation:

\(\frac{3}{(x + 4 )} + \frac{4}{(x - 2) (x + 4)}\)

Answers

The answer is 3x-2/x^2+2x-8

A person can pay $14 for a membership to the history museum and then go to the museum
for just $2 per visit. For a member of the history museum, what is the total cost of 3 visits?

Answers

Answer:

$18

Step-by-step explanation:

12+2+2+2=18

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