answer the gaps/questions attached

The experimental probability that the next student Judith talks to will pick red is 1/2.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means.

Given that,

Yellow = 2

Red = 5

Blue = 3

Finding the experimental probability

Total number of trials = 2+5+3 = 10

Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes

Probability = red/ Total number of trials = 5/10 = 1/2

Thus, the experimental probability that the next student Judith talks to will pick red is 1/2.

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Answer:

1/2

Step-by-step explanation:

Therefore , the solution of the given problem of equation comes out to be it mean that you owe 36 amount of money to bank.

When the equals sign (=) is used to denote equality, an algebraic theorem resembles a rule joining two statements. An algebraic equation is a factual assertion that shows the equivalence of multiple numerical variables. The values ob d + 6 and 12 are separated by an equal sign in the calculation data logger + 6 = 12. The number of syllables that correspond to each side of each letter can be expressed numerically. The message of a symbol is frequently its complete opposite.

Here,

Given :

After a few weeks, you create and calculate an equation

so determine how much money is in your bank account.

M equals -36, as you discover.

Thus,

It mean that you owe 36 amount of money to bank.

Therefore , the solution of the given problem of equation comes out to be it mean that you owe 36 amount of money to bank.

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you can use math away app

Most accurate statement is "The plane clears the tower with about 6 yards to spare". So the option c is correct.

In the given question, a plane travels 1500 yard before lifting off the ground.

If the plane continues on the runway, it is 600 more yard to the control tower, which is 198 feet high.

Instead, the plane takes flight and travels 603 yards.

Initial distance traveled = 1500

Yards to control tower = 600

Height of control tower = 198 feet

Height of control tower = 198×3 yards

Height of control tower = 594 yards

If the airplane's rate of ascent is proportionate to the distance flown, then 1 yard of length equals 1 yard of height achieved.

The height of the plane would be 600 yards after flying 600 yards to the location of the control tower.

So, Difference in height = Height of plane - Height of tower

Difference in height = 600 yards - 594 yards

Difference in height = 6 yards

Hence, most accurate statement is "The plane clears the tower with about 6 yards to spare". So the option c is correct.

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The area of the rectangular pen is represented by the quadratic equation [tex]A(w) = 50w - w^{2}[/tex].

Let w be the width of rectangular pen.

We have been given that a farmer has 100 m of fencing to enclose a rectangular pen. This means that perimeter of pen is 100 meter.

Since the perimeter is 2 times the length and width of rectangle.

Perimeter of a rectangle = 2 (Width + Length)

Upon substituting our given values in above formula we will get,

[tex]100 = 2(w + length)\\50 = w + length\\50-w = Length[/tex]

Area of a rectangle = Width x Length

[tex]Area of a rectangle = w (50-w)\\= 50w - w^{2}[/tex]

Let us represent area in terms of width of rectangle as:

[tex]A(w) = 50w - w^{2}[/tex]

Therefore, the area of the rectangular pen is represented by the quadratic equation [tex]A(w) = 50w - w^{2}[/tex].

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If you want to make 1/2 the recipe, then [tex]1\frac{11}{16}[/tex] tablespoon of sugar you need.

In the given question, a recipe calls for [tex]3\frac{3}{8}[/tex] tablespoons of sugar.

If you want to make 1/2 the recipe, then we have to find how much sugar you need.

As given that;

1 recipe = [tex]3\frac{3}{8}[/tex] tablespoons of sugar

Before solving the question, we convert the mixed fraction into simple fraction.

To convert in simple fraction we multiply 3 by 8 then we add 3 on the result of multiplication of 3 and 8.

1 recipe = 27/8 tablespoons of sugar

We have to find sugar need for making 1/2 recipe.

1/2 recipe = [tex]\frac{27}{8}\times\frac{1}{2}[/tex] tablespoons of sugar

1/2 recipe = 27/16 tablespoons of sugar

1/2 recipe = [tex]1\frac{11}{16}[/tex] tablespoons of sugar

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The top 15 Excel functions are SUM, AVERAGE, COUNT, MAX, MIN, IF, VLOOKUP, CONCATENATE, INDEX, MATCH, ROUND, TEXT, OFFSET, TODAY, and RAND.

1. SUM: Add up the values in a range of cells

2. AVERAGE: Calculate the mean of a range of cells

3. COUNT: Count the total number of cells in a range

4. MAX: Find the maximum value in a range of cells

5. MIN: Find the minimum value in a range of cells

6. IF: Perform different actions based on whether a condition is met

7. VLOOKUP: Look up the value of a cell in another table

8. CONCATENATE: Join two or more cells together

9. INDEX: Return a value from a given range of cells

10. MATCH: Find the position of a value in a range of cells

11. ROUND: Round a number to a specified number of decimal places

12. TEXT: Format a number or value as text

13. OFFSET: Return a range of cells at a given offset from another cell

14. TODAY: Return the current date

15. RAND: Generate a random number

The top 15 Excel functions are SUM, AVERAGE, COUNT, MAX, MIN, IF, VLOOKUP, CONCATENATE, INDEX, MATCH, ROUND, TEXT, OFFSET, TODAY, and RAND, which are used for various tasks such as adding up values, calculating the mean, counting cells, finding maximum/minimum values, looking up values in another table, joining cells together, returning a value from a given range, finding the position of a value, rounding numbers, formatting values as text, generating a random number, and returning the current date.

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The combination is the way to find a number of different committees. The different number of committees is 120.

What is the combination?

A combination is a method of selecting items from a collection where the order of selection is irrelevant.

The combination is defined as "an arrangement of objects in which the order in which the objects are chosen is unimportant." The combination means "selection of things," where the order is irrelevant.

Given that the total number of teachers is 10.

The number of members of the committee is 3.

The formula of combination is nCr = n!/[r!(n-r)!]

Where n is the total number of objects and r is the number of objects those are selected.

In the question, n=10, r=3

The different committees is ₁₀C₃

=10!/3!(10-3)!

=10!/3!7!

=120

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Answer:

6.97%

Step-by-step explanation:

a) To work out the value of x, we can use the information given that "Marry is three times more likely to score 2 points than to score 1 point". We know that the probability of scoring 1 point is x, and the probability of scoring 2 points is 3x.

So we can set up the equation:

3x = probability of scoring 2 points

x = probability of scoring 1 point

We know that 3x = probability of scoring 2 points = 0.16

So we can solve for x by dividing both sides by 3:

x = 0.16 / 3 = 0.05333

b) To work out the probability of Mary scoring a total of 8, we can use the information from the table and the formula for the probability of a specific outcome when playing the game twice.

We know that the probability of scoring 4 points in one game is 0.21, so the probability of scoring 4 points twice is (0.21)^2 = 0.0441

We also know that the probability of scoring 2 points in one game is 3x = 3(0.05333) = 0.16, so the probability of scoring 2 points twice is (0.16)^2 = 0.0256

We can add these probabilities together to find the total probability of scoring 8 points:

0.0441 + 0.0256 = 0.0697 or 6.97%

So the probability of Mary scoring a total of 8 is 6.97%.

The length of the side of the smaller square is 7 inches.

Let x be the length of the side of the smaller square.

The length of each side of a square is 3 inches more than the length of each side of a smaller square. Thus the length of the side of the larger square is

(x + 3) inches.

The area of the smaller square is

x^2 square inches.

The area of the larger square is

(x + 3)^2 square inches.

We can set up the equation:

x^2 + (x + 3)^2 = 149

Expanding and simplifying the equation gives:

x^2 + x^2 + 6x + 9 = 149

Combining like terms:

2x^2 + 6x - 140 = 0

Using the quadratic formula, we can solve for x:

x = (-b ± √(b^2 - 4ac)) / 2a

x = (-6 ± √(6^2 - 4 * 2 * (-140))) / 2 * 2

x = (-6 ± √(36 + 1120)) / 4

x = (-6 ± √(1156)) / 4

x = (-6 ± √(596)) / 4

x = (-6 ± 34) / 4

x = -10 or x = 7

The side length of the smaller square can't be negative, so x = 7 inches.

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The unit rate of the relationship between the amount of water pumped and time is the amount of water pumped in one minute for 14 hours.

To calculate unit price, you need to divide the first term (quantity) by the second term (unit). The resulting value is the unit price.

For example, if you want to calculate the unit price for a bag of 4 $3 apples, divide the total cost ($3) by the number of apples (4).

$3 / 4 apples = $0.75 / apple

In this example, the unit price is $0.75 per apple. So the price per apple is $0.75.

Given by the equation:

The unit rate of water pumped versus time is the amount of water pumped in one minute, so:

28/2=14

That means 14 gallons of water is being pumped every minute.

Now you can calculate the water pumped in 3/2 minutes like this

14*3/2=21

So in total, water pumped in 12 minutes plus 3/2 minutes gives water pumped in 15/2 minutes.

14*15/2=105

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Answer:

We know that there are 67 students performing in the middle school's production of "Beauty and the Beastly." and 49 of them are 7th and 8th graders.

We can write a proportion to find the percent of 6th grade students in the play:

6th grade students / Total students = s / 100

We know that 49 of the students are 7th and 8th graders, so the number of 6th grade students is 67 - 49 = 18.

Now we can substitute the values in the proportion and solve for s:

18 / 67 = s / 100

To find s, we can cross-multiply and divide:

18 * 100 = 67 * s

1800 = 67 * s

s = 1800 / 67

s = 26.87

Rounding to the nearest tenth of a percent: 26.9 %

So, the percent of 6th grade students that are in the play is 26.9%.

The general solution of the system x' (t) is[tex]X(t)=c_1\left(\left[\begin{array}{c}-5 \\2\end{array}\right] \cos 3 t-\left[\begin{array}{l}1 \\0\end{array}\right] \sin 3 t\right)[/tex][tex]+c_2\left(\left[\begin{array}{c}1 \\0\end{array}\right] \cos 3 t+\left[\begin{array}{c}-5 \\2\end{array}\right] \sin 3 t\right)\end{gathered}[/tex]

The given system of equation is X'A=X

where

[tex]$$A=\left[\begin{array}{cc}-15 & -39 \\6 & 15\end{array}\right]$$[/tex]

Eigenvector of a square matrix is defined as a non-vector in which when a given matrix is multiplied,  it is equal to a scalar multiple of that vector. Let us suppose that A is an n x n square matrix, and if v be a non-zero vector, then the product of matrix A, and vector v is defined as the product of a scalar quantity λ and the given vector, such that:

Where

v = Eigenvector and λ be the scalar quantity that is termed as eigenvalue associated with given matrix A

The values of A are given by

[tex]$|A-\lambda I|=0 \\\left|\begin{array}{cc}-15-\lambda & -39 \\6 & 15-\lambda\end{array}\right|=0 \\[/tex]

[tex](-15-\lambda)(15-\lambda)-(6)(-39)=0 \\[/tex]

[tex]\Rightarrow-(15+\lambda)(15-\lambda)+(6)(39)=0 \\[/tex]

[tex]\\\Rightarrow(15+\lambda)(15-\lambda)-(6)(39)=0 \\\\\Rightarrow 225-\lambda^2-234=0 \\[/tex]

[tex]\Rightarrow-\lambda^2-9=0 \\[/tex]

[tex]\Rightarrow \lambda^2=-9 \\[/tex]

[tex]\Rightarrow \lambda=\pm 3 i[/tex]

Now, eigen vector u corresponding to [tex]$\lambda=3 i$[/tex] is given by

[tex]$$\begin{gathered}{[A-3 i I] u=O} \\{\left[\begin{array}{cc}-15-3 i & -39 \\6 & 15-3 i\end{array}\right]\left[\begin{array}{l}u_1 \\u_2\end{array}\right]=\left[\begin{array}{l}0 \\0\end{array}\right]} \\\\\end{gathered}$$[/tex]

Applying [tex]R_2 \rightarrow R_2-6 R_1[/tex]

[tex]& {\left[\begin{array}{cc}1 & \frac{-39}{-15-3 i} \\0 & 0\end{array}\right]\left[\begin{array}{l}u_1 \\u_2\end{array}\right]=\left[\begin{array}{l}0 \\0\end{array}\right]} \\[/tex]

[tex]& \Rightarrow u_1+\frac{39}{15+3 i} u_2=0 \\[/tex]

[tex]& \Rightarrow u_1=-\frac{13}{5+i} u_2=-\frac{13}{5+i} * \frac{5-i}{5-i} u_2=-\frac{13(5-i)}{26} u_2=-\frac{5-i}{2} u_2 \\[/tex]

Thus, by choosing [tex]$u_2[/tex]=1 eigenvector corresponding to [tex]$\lambda=3 i$[/tex] is [tex]$$u=\left[\begin{array}{c}-\frac{5-i}{2} \\1\end{array}\right]$$[/tex]

[tex]R_1 \rightarrow \frac{1}{-15+3 i} R_1 \\[/tex]

[tex]{\left[\begin{array}{cc}1 & \frac{-39}{-15+3 i} \\6 & 15+3 i\end{array}\right]\left[\begin{array}{l}v_1 \\v_2\end{array}\right]=\left[\begin{array}{l}0 \\0\end{array}\right]} \\[/tex]

Applying [tex]R_2 \rightarrow R_2-6 R_1 \\[/tex]

[tex]{\left[\begin{array}{cc}1 & \frac{-39}{-15+3 i} \\0 & 0\end{array}\right]\left[\begin{array}{l}v_1 \\v_2\end{array}\right]=\left[\begin{array}{l}0 \\0\end{array}\right]} \\[/tex]

[tex]\Rightarrow v_1+\frac{39}{15-3 i} v_2=0 \\\Rightarrow v_1=-\frac{39}{15-3 i}[/tex]

[tex]\begin{gathered}\Rightarrow v_1+\frac{39}{15-3 i} v_2=0 \\\v_2=-\frac{13(5+i)}{26} \\\Rightarrow v_1==-\frac{5+i}{2}\end{gathered}$$[/tex]

Thus, by choosing [tex]$v_2=1$[/tex] eigenvector corresponding to [tex]$\lambda=-3 i$[/tex] is

[tex]$$v=\left[\begin{array}{c}-\frac{5+i}{2} \\1\end{array}\right]$$[/tex]

Hence, the general solution is given by

[tex]X(t)=c_1 e^{3 i t} u+c_2 e^{-3 i t} v \text { [using } e^{i t}=\cos t+i \sin t \\[/tex]

[tex]X(t)=c_1\left[\begin{array}{c}-\frac{5-i}{2}(\cos 3 t+i \sin 3 t) \\(\cos 3 t+i \sin 3 t)\end{array}\right]+c_2\left[\begin{array}{c}-\frac{5+i}{2}(\cos 3 t-i \sin 3 t) \\(\cos 3 t-i \sin 3 t)\end{array}\right] \\[/tex]

[tex]X(t)=c_1\left[\begin{array}{c}-\frac{5}{2}(\cos 3 t+i \sin 3 t)+\frac{i}{2}(\cos 3 t+i \sin 3 t) \\(\cos 3 t+i \sin 3 t)\end{array}\right][/tex][tex]+c_2\left[\begin{array}{c}-\frac{5}{2}(\cos 3 t-i \sin 3 t)-\frac{i}{2}(\cos 3 t-i \sin 3 t) \\(\cos 3 t-i \sin 3 t)\end{array}\right] \\[/tex]

[tex]X(t)=c_1\left[\begin{array}{c}-\frac{5}{2} \cos 3 t-\frac{5 i}{2} \sin 3 t+\frac{i}{2} \cos 3 t-\frac{1}{2} \sin 3 t \\\cos 3 t+i \sin 3 t\end{array}\right][/tex][tex]+c_2\left[\begin{array}{c}-\frac{5}{2} \cos 3 t+\frac{5}{2} i \sin 3 t-\frac{i}{2} \cos 3 t-\frac{1}{2} \sin 3 t \\\cos 3 t-i \sin 3 t\end{array}\right ][/tex]

[tex]X(t)=c_1\left(\left[\begin{array}{c}-5 \\2\end{array}\right] \cos 3 t-\left[\begin{array}{l}1 \\0\end{array}\right] \sin 3 t\right)[/tex][tex]+c_2\left(\left[\begin{array}{c}1 \\0\end{array}\right] \cos 3 t+\left[\begin{array}{c}-5 \\2\end{array}\right] \sin 3 t\right)\end{gathered}[/tex]

Therefore, the general solution of the system X(t) is [tex]X(t)=c_1\left(\left[\begin{array}{c}-5 \\2\end{array}\right] \cos 3 t-\left[\begin{array}{l}1 \\0\end{array}\right] \sin 3 t\right)[/tex][tex]+c_2\left(\left[\begin{array}{c}1 \\0\end{array}\right] \cos 3 t+\left[\begin{array}{c}-5 \\2\end{array}\right] \sin 3 t\right)\end{gathered}[/tex].

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By solving a system of equations we will see that the quadratic equation is:

y = 3*x^2 - 10*x - 4

We know that a general quadratic function can be written as:

y = a*x^2 + b*x + c

Here we know that the equation passes through (0, -4), replacing these values:

-4 = a*0^2 + b*0 + c

-4 = c

Then the quadratic equation is:

y = a*x^2 + b*x - 4

Now we can use the other two points (-3, -7) and (2, -12), replacing these values we will get a system of equations:

-7 = a*(-3)^2 + b*(-3) - 4

-12 = a*(2)^2 + b*(2) - 4

We can simplify these equations to get:

-3 = 9a + 3b

-8 = 4a + 2b

We can isolate b on the second equation to get:

2b + 4a = -8

2b = -8 - 4a

b = (-8 - 4a)/2

b = -4 - 2a

Now we can replace that in the other equation to get:

-3 = 9a + 3*(-4 - 2a)

-3 = 9a -12 - 6a

-3 + 12 = 3a

9 = 3a

9/3 = a

3 = a

And the value of b is:

b = -4 - 2a

b = -4 - 2*3

b = -4 - 6 = -10

Then the quadratic equation is:

y = 3*x^2 - 10*x - 4

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On solving the provided question we can say that by equation we have

remain = x+y = 5/8 + 1/8 = 6/8 3/4

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

six whole pizzas, as well as  = 5/8 of another pizza

another one = 1/8 of a whole pizza

Remain -by forming equation

let x = 5/8 of another pizza

and y = 1/8 of a whole pizza

remain = x+y = 5/8 + 1/8 = 6/8 3/4

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The reason why parallel line is so important in our everyday lives is that help us to understand the path of the objects and sides of the various shapes.

Because they allow us to construct congruent angle pair relationships, parallel lines and transversals are crucial to the study of geometry.

Understanding the movement of objects and the sides of various forms is made easier with the aid of parallel lines. For instance, the opposing sides of parallelograms, squares, and rectangles are parallel to one another. The parallel line is frequently employed in the building sector.

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For given function f(x) the y in the graph are f(2) = 4,f(0) = 3 ,f(-6) = -6 and f(4) = 5

A function is described as a relationship between a set of inputs, each of which has a single output. The simplest definition of a function is an association between inputs where each input is connected to a single, unique output. There is a codomain or range for each function. A function is frequently referred to as f(x), where x is the input.

Here,

In the given graph

when x = 2

y = 4

and x = 0

y = 3

Put it in slope formula

=> m =y2 - y1 / x2 -x1

=>  m =1/2

m = 1/2

Now we can just put them into slope formula

y - y₁ = m(x - x₁)

y - 4 = 1/2(x - 2)

y = 1/2(x) -1 + 4

y = 1/2(x) + 3

Now we can just put them into slope formula

y - y₁ = m(x - x₁)

y - 3 = 1/2(x - 0)

y = 1/2(x)  + 3

Thus, the function for given f(x) is solved

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The probability that exactly 4 of the 8 diamonds picked from the bag are real diamonds is 28/256 or 11.1%.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 meaning the event is impossible and 1 meaning the event is certain to occur. Probability theory is used to make predictions and calculate the chances of different outcomes in order to make decisions. Probability theory can also be applied to understand the behavior of complex systems.

This is calculated by first determining the total amount of possible outcomes. Out of the 8 diamonds picked, there are 8C4 = 70 ways in which the 4 real diamonds can be chosen. With 8 real diamonds and 7 fake diamonds, the probability of a real diamond being chosen is 8/15, and the probability of a fake diamond being chosen is 7/15. Therefore, the probability of having exactly 4 real diamonds is 70 x (8/15)^4 x (7/15)^4 = 28/256.

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A graph is called a regular graph if the degree of each vertex is equal.

N complete vertices make up an (N-1) regular graph.

Proof: Each vertex in a complete network with N vertices is connected to each of the (N-1) remaining vertices. Therefore, each vertex's degree is (N-1). The graph is hence (N-1) Regular.

If the degree of each vertex is equal, a graph is said to be a regular graph. If the degree of each vertex is K, a graph is said to be K regular.

A regular graph in graph theory is one in which every vertex has the same number of neighbors or the same degree of valency. The stronger requirement that each vertex's indegree and outdegree be equal must also be met by a regular directed graph.

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The method proposed is not fair, it can be adjusted by giving each sibling equal chance of winning.

What is algebra ?

Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It includes the study of operations such as addition, subtraction, multiplication, division, and the extraction of roots, as well as the properties of operations such as commutativity, associativity, and distributivity.

The method proposed by Alan is not fair because it does not take into account the probability of each outcome. The product of the outcomes being even or odd does not guarantee an equal probability of winning for both siblings. To make it fair, each sibling should have an equal chance of winning. A fair method could be to have the arrow spun once, and the sibling whose number is spun gets to choose the new pet. Another fair method could be to have a coin flipped, and the sibling whose side of the coin is facing up gets to choose the new pet.

So , The method proposed is not fair, it can be adjusted by giving each sibling equal chance of winning.

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The cost of hiring the car in pounds Nina hired is  £210.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Nina hired a car in the United States. The cost of hiring the car was $294.

Now, To covert the dollar into pounds, we have to multiply the total amount in dollars by the unit conversion rate which is, £1 = $1.4 ⇒ $1 = £(1/1.4),

Therefore,

$294 is equal to £(294/1.4) = £210.

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The correct unit of measure for the mean of the sampling distribution of I is A. Dollars.

The original distribution of prices for the car model is given in dollars, and the mean of the sampling distribution represents the average price of a random sample of 4 cars from that distribution. Hence, the correct unit of measure should be in dollars also.

In statistics, the mean is a measure of central tendency that represents the average value of a dataset. It is calculated by adding up all the values in a dataset and dividing by the number of observations. The formula for the mean of a dataset is:

mean = (sum of observations) / (number of observations)

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The fourth term of the resulting four-term sequence is 206.

Let the four terms of the arithmetic sequence be a a+d, a+2d, and a+3d (where d is common difference)

Let the four terms of the geometric sequence be b, br, br^2, and br^3 (where r is the common ratio)

An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is always the same. The difference is called the common difference.

The resulting four-term sequence is a+b, a+d+br, a+2d+br^2, a+3d+br^3

Given that the first three terms of the resulting four-term sequence are 57, 60, and 91, we can set up the following equations:

a + b = 57

a + d + br = 60

a + 2d + br^2 = 91

By substituting the first equation into the second and third equations we get:

d + b(r-1) = 60 - 57 = 3

2d + b(r-1)^2 = 91 - 57 = 34

By substituting the first equation and the second equation into the third one we get:

2(3) + b(r-1)^2 = 34

6+b(r-1)^2 = 34

b(r-1)^2 = 28

Note that either b=28 or b=7. We proceed with casework:

If b=28, then r=2,a=29, and d=25.The arithmetic sequence is 29,4,-21,-46, arriving at a contradiction.

If b=7, then r=3,a=50, and d=-11.The arithmetic sequence is 50,39,28,17, and the geometric sequence is 7,21,63,189. This case is valid.

Therefore, The fourth term of the resulting four-term sequence is [tex]a+3d^{2}+br^{3}= 17 +189 =206[/tex].

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The algorithm completes in an acceptable amount of time because it will draw n forms in around n2 steps.

A mathematical algorithm is a process that describes a series of steps that can be used to accomplish a mathematical computation. A typical illustration of a mathematical algorithm would be the step-by-step process used in long division. A set of instructions called an algorithm is used to solve a problem or complete a task. An algorithm is a set of instructions that spells out how to carry out a task. An algorithm can be thought of as a series of detailed instructions that result in a predictable pattern in a set of numbers or in lines of code.

given

Which of the following best describes the algorithm for drawing n forms, where n is a very big number  based on the numbers in the table.

Because it will take around n2 steps to draw n forms, the algorithm completes in a fair length of time.

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Answer:

Step-by-step explanation:

1

The linear function that passes through (9, 12) and is perpendicular to y=4  is given as follows:

x = 9.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

The line y = 4 is an horizontal line, hence a perpendicular line will be a vertical line, which has the format given as follows:

x = c.

The point is (9,12), meaning that the x-coordinate is of 9, and thus the constant c is given as follows:

c = 9.

Hence the equation is:

x = 9.

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Answer:

4

Step-by-step explanation:

24*1/6=4

Answer:

Your answer is 4

24/6

6×4=24

The type of system of linear equations with infinitely many solutions is called a homogeneous system of linear equations.

A system of linear equations is a set of two or more equations with two or more variables that are related to each other. When a system of linear equations has an infinite number of solutions, it is called a homogeneous system of linear equations. This is because all the equations in the system are multiples of each other, so any solution of one equation is also a solution for all the other equations.

The type of system of linear equations with infinitely many solutions is called a homogeneous system of linear equations.

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By solving the given initial value the value of x(t) is [tex]\frac{F_0}{2 \omega^2}[/tex] (sinωt - ωt cosωt)

As per the data given in the question the given differential equation will be:

[tex]\frac{d^{2} x}{dt^{2} }[/tex] + [tex]\omega^2 x=f_0[/tex] sin ωt,

x(0) = 0, x'(0) = 0

Now we have to determine the value of x(t).

Consider the differential equation:

x'' + [tex]\omega^2 x=f_0[/tex] sin ωt, x(0) = 0, x'(0) = 0.

In order to translate a given derivative function with a real variable t into a complex function with a variable s, one uses the Laplace transformation.

Laplace transformation is important in the design of control systems. It is necessary to perform Laplace transforms on several functions in order to analyze the control system.

Apply Laplace transformation on both sides,

[tex]&\left(s^2 L\{x(t)\}\right.\left.-s y(0)-y^{\prime}(0)\right)+\omega^2 \mathcal{L}\{x(t)\}=\frac{F_0 \omega}{s^2+\omega^2} \\[/tex]

[tex]&\left(s^2+\omega^2\right) \mathcal{L}\{x(t)\}=\frac{F_0 \omega}{s^2+\omega^2} \\[/tex]

[tex]& \mathcal{L}\{x(t)\}=\frac{F_0 \omega}{\left(s^2+\omega^2\right)^2} \\[/tex]

[tex]& x(t)=F_0 \omega \mathcal{L}^{-1}\left\{\frac{1}{\left(s^2+\omega^2\right)^2}\right\} \\[/tex]

[tex]& \Rightarrow x(t)=\frac{F_0 \omega}{2 \omega^3}[/tex] (sin ωt -ωt cos ωt)

[tex]& \Rightarrow x(t)\left.=\frac{F_0}{2 \omega^2}[/tex] (sin ωt -ωt cos ωt)

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Solve the given initial-value problem. [tex]\frac{d^{2} x}{dt^{2} }[/tex] + [tex]\omega^2 x=f_0[/tex] sin ωt, x(0) = 0, x'(0) = 0 and x(t)=?

Three circles of radius s are drawn in the first quadrant of the xy-plane.

[tex]$r/s$\\[/tex] =9/1 =9

Set [tex]$s$[/tex] =1 so that we only have to find [tex]$r$[/tex].

Draw the segment between the center of the third circle and the large circle; this has length [tex]$r+1$[/tex]. We then draw the radius of the large circle that is perpendicular to the x-axis, and draw the perpendicular from this radius to the center of the third circle.

This gives us a right triangle with legs [tex]$r-3,r-1$[/tex]and hypotenuse [tex]$r+1$.[/tex]

The Pythagorean Theorem yields:

[tex]$(r-3)^2 + (r-1)^2 = (r+1)^2$$r^2 - 10r + 9 = 0$$r = 1, 9$Quite obviously $r > 1$, so $r = 9 \boxed{(D)}$.[/tex]

Three circles of radius s are drawn in the first quadrant of the x y -plane.

[tex]$r/s$\\[/tex] =9/1 =9

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