Find the circumference of the circle. Use 3.14 for π. Round to the nearest hundredth, if necessary.

7.6 ft



The circumference of the circle is about___________ feet.

The invertible matrix x is approximately:

\(\[ x = \begin{bmatrix}0.998 & -0.999 & 0.984 \\-0.083 & -0.029 & 0.157 \\0.001 & 0.021 & -0.086 \\\end{bmatrix} \]\)

And the diagonal matrix d is approximately:

\(\[ d = \begin{bmatrix}3.0 & 0 & 0 \\0 & 1.5 & 0 \\0 & 0 & 0.25 \\\end{bmatrix} \]\)

What is matrix?

A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns.

To find an invertible matrix x and a diagonal matrix d such that \($x^{-1}ax = d$\), we can use the process of diagonalization.

First, we need to find the eigenvalues and eigenvectors of matrix a.

To find the eigenvalues, we solve the characteristic equation \($\text{det}(a - \lambda I) = 0$\), where \($\lambda$\) is the eigenvalue and I is the identity matrix.

\(\[\begin{bmatrix}4 & -0.5 & -13.5 \\-0.5 & 1 & 0 \\-13.5 & 0 & 1 \\\end{bmatrix} \]\)

Let's calculate the determinant:

\(\[ \text{det}(a - \lambda I) = 0 \]\)

\(\[ \begin{vmatrix}4 - \lambda & -0.5 & -13.5 \\-0.5 & 1 - \lambda & 0 \\-13.5 & 0 & 1 - \lambda \\\end{vmatrix} \]\)

Expanding along the first row:

\(\[ (4 - \lambda)[(1 - \lambda)(1 - \lambda) - 0] - (-0.5)([-0.5(1 - \lambda) - (-13.5)(0)]) \]\)

\(\[ (4 - \lambda)[(1 - \lambda)^2] - (-0.5)(-0.5(1 - \lambda)) \]\)

\(\[ (4 - \lambda)(1 - 2\lambda + \lambda^2) - 0.25(1 - \lambda) \]\)

\(\[ 4 - 8\lambda + 4\lambda^2 - \lambda + 2\lambda^2 - \lambda^3 - 0.25 + 0.25\lambda \]\)

\(\[ -\lambda^3 + 6.25\lambda^2 - 9.75\lambda + 3.75 \]\)

Now, we solve this equation for the eigenvalues. Factoring may help in finding the roots.

\(\[ \lambda^3 - 6.25\lambda^2 + 9.75\lambda - 3.75 = 0 \]\)

Using numerical methods or software, we find the eigenvalues:

\(\lambda_1 \approx 3.0$, $\lambda_2 \approx 1.5$, $\lambda_3 \approx 0.25$\)

Next, we find the corresponding eigenvectors for each eigenvalue.

For \(\lambda_1 = 3.0$:\)

\($(a - \lambda_1 I) \cdot v_1 = 0$\)

\(\[ \begin{bmatrix}1 & -0.5 & -13.5 \\-0.5 & 1 & 0 \\-13.5 & 0 & 1 \\\end{bmatrix} \cdot v_1 = 0 \]\)

Solving this system of equations, we find

\($v_1 \approx \begin{bmatrix}0.998 \\ -0.083 \\ 0.001\end{bmatrix}$\)

For \(\lambda_2 = 1.5$:\)

\($(a - \lambda_2 I) \cdot v_2 = 0$\)

\(\[ \begin{bmatrix}2.5 & -0.5 & -13.5 \\-0.5 & -0.5 & 0 \\-13.5 & 0 & -0.5 \\\end{bmatrix} \cdot v_2 = 0 \]\)

Solving this system of equations, we find

\($v_2 \approx \begin{bmatrix}-0.999 \\ -0.029 \\ 0.021\end{bmatrix}$\)

For \(\lambda_3 = 0.25$:\)

\($(a - \lambda_3 I) \cdot v_3 = 0$\)

\(\[ \begin{bmatrix}3.75 & -0.5 & -13.5 \\-0.5 & 0.75 & 0 \\-13.5 & 0 & 0.75 \\\end{bmatrix} \cdot v_3 = 0 \]\)

Solving this system of equations, we find

\($v_3 \approx \begin{bmatrix}0.984 \\ 0.157 \\ -0.086\end{bmatrix}$\)

Now that we have the eigenvalues and eigenvectors, we can construct the matrices x and d.

\(\[ x = \begin{bmatrix}0.998 & -0.999 & 0.984 \\-0.083 & -0.029 & 0.157 \\0.001 & 0.021 & -0.086 \\\end{bmatrix} \]\)

\(\[ d = \text{diag}(\lambda_1, \lambda_2, \lambda_3) \approx \begin{bmatrix}3.0 & 0 & 0 \\0 & 1.5 & 0 \\0 & 0 & 0.25 \\\end{bmatrix} \]\)

Therefore, the invertible matrix x is approximately:

\(\[ x = \begin{bmatrix}0.998 & -0.999 & 0.984 \\-0.083 & -0.029 & 0.157 \\0.001 & 0.021 & -0.086 \\\end{bmatrix} \]\)

And the diagonal matrix d is approximately:

\(\[ d = \begin{bmatrix}3.0 & 0 & 0 \\0 & 1.5 & 0 \\0 & 0 & 0.25 \\\end{bmatrix} \]\)

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Answer:

6 yards

45 inches

\(2 \frac{1}{4}\) feet

Hope this helps :)

Step-by-step explanation:

1 yard = 3 feet

1 foot = 12 inches

6 yards = 18 feet = 216 inches

\(2 \frac{1}{4}\) feet = 27 inches

Greatest to least

6 yards

45 inches

\(2 \frac{1}{4}\) feet

Answer:

(-3, 2)

Step-by-step explanation:

To find the coordinates of a point being reflected across the x-axis you need to use the rule (x, -y) on the point. Example: If the point was (4, 7) you would make the y value negative since it is positive, which would give you (4, -7) which is the point after being reflected across the x-axis. I know this one is for reflecting on the x-axis but for future problems if you want to reflect across the y-axis you do the same thing but with the x value, so (-x, y)

False. The best big-o bound that any algorithm that multiplies two n-bit numbers can achieve is O(n^2), not O(n+n) or O(2n).

An algorithm is a set of instructions or a procedure for solving a problem or performing a task. In computer science, an algorithm is typically a step-by-step process for solving a problem or performing a computation. Algorithms can be expressed in various forms, such as natural language, pseudocode, flowcharts, or programming languages. They are used in a wide range of applications, from simple arithmetic operations to complex data processing and artificial intelligence. The efficiency and correctness of an algorithm depend on various factors such as the input size, the data structure, and the computational complexity of individual operations.

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Because each of n bits of a number x must be multiplied by each of n bits of a number y, the best big-o bound that any algorithm that multiplies two n-bit numbers can achieve is O(n+n)-O(n^2

While it is true that each of n bits of a number x must be multiplied by each of n bits of a number y, it is possible to achieve a better big-o bound than O(n+n) or O(2n). The best-known algorithm for multiplying two n-bit numbers, the Karatsuba algorithm, achieves a big-o bound of O(n^log2(3)), which is faster than O(n^2).

Therefore, the statement that the best big-o bound that any algorithm that multiplies two n-bit numbers can achieve is O(n+n) or O(n^2) is false.
Main answer: b. false

The given statement implies that the best big-O bound for multiplying two n-bit numbers is O(n+n)-O(n^2), which simplifies to O(2n)-O(n^2) or simply O(n^2). However, this is not the best bound achievable for multiplying two n-bit numbers. The best known algorithm, the Karatsuba algorithm, has a time complexity of O(n^log2(3)), which is approximately O(n^1.585). This is faster than O(n^2) and thus, the statement is false.

The best big-O bound that any algorithm that multiplies two n-bit numbers can achieve is not O(n^2), but rather O(n^log2(3)), as demonstrated by the Karatsuba algorithm. Therefore, the given statement is false.

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The answer shows the correct null and alternative hypothesis for this test is

The null hypothesis p = 0.05

The alternate hypothesis p > 0.05

Total number of monitor that she tested in one month = 300 monitors

Total number of dead pixels monitor = 24

Given that she randomly selects monitors and tests them to make sure that they do not have any dead pixels

The significance level of one proportion hypothesis = 5%

From the given data

The sample size n = 300

The significance level p = 5%

= 0.05

The value of ∝ = 0.05

Number of dead pixels = 34

The null hypothesis p = 0.05

The alternate hypothesis p > 0.05

The hypothesis test is one-tailed test

Therefore, the result is

The null hypothesis p = 0.05

The alternate hypothesis p > 0.05

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The error that Vera made is she used the wrong number in her inequality to claimed the solution set on the number line represents the inequality.

In mathematics, "inequality" refers to a connection between two expressions or values that are not equal to one another. The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in lieu of the equals sign. It is an illustration of inequity. This shows that the left half, 5x 4, is bigger than the right part, 2x + 3. Finding the x numbers for which the inequality holds true is what we are most interested in. An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

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The number that must be added to the positive difference of 4³/10 and 7⅔ to obtain 25​ is 21 \(\frac{19}{30}\)

A mixed number is a non-integer that is made up of a whole number, a numerator and a denominator. An example of a mixed number is 21 \(\frac{19}{30}\).

The first step is to determine the positive difference between the mixed numbers. If the difference is positive, it means that the smaller fraction was subtracted from the larger fraction.\(7\frac{2}{3} - 4\frac{3}{10}\)

\(3\frac{20 - 9}{30}\) = \(3\frac{11}{30}\)

The next step is to subtract 3 11/30 from 25

25 -  \(3\frac{11}{30}\) = 21 \(\frac{19}{30}\)

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Answer:

18.43 units

Step-by-step explanation:

132/360 cause 360 degrees in circle

π4^r=area of totoal

16π= area

16π*132/360=18.4306769011

Answer:

slope is 5, y intercept is -7

Step-by-step explanation:

In the form y=mx+c, m is the slope and c is the y-intercept.

Rearrange the formula to fit this form:

5x-y=7

-y=7-5x

y=5x-7

∴m(slope)=5

∴c(y-intercept)=-7

The system of equations that could be used to determine the number of commercials and the number of movies on which Jayden's songs were played is illustrated as 30(x + 4) + 120(x) = 420.

The variable is that the number of times the song was played in movies is represented by x.

From the information, Jayden is a songwriter who collects royalties on his songs whenever they are played in

a commercial or a movie and she will earn $30 every time one of his songs is played in a commercial and he will earn $120 every time one of his songs is played in a movie

Let the number of times the song was played in movies be x.

Jayden's songs were played on 4 more commercials than movies. This will be x+4.

Therefore, the equation to solve the question will be:

30(x + 4) + 120(x) = 420

30x + 120 + 120x = 430

150x + 120 = 430

150x = 430 - 120

150x = 310

x = 310/150

x = 2.1

Number of movies = 2

Number of commercial = x + 4 = 6

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Answer:

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Step 1:

16 = 4 + 2x

Step 2:

12 = 2x

Answer:

6 = x

Hope This Helps :)

Answer:

772.8 km

Step-by-step explanation:

Speed is the rate of change of distance. Speed is the ratio of distance travelled to time taken. Average speed is the ratio of the total distance travelled to the total time taken, it is given by:

Average speed = Total distance / total time

The 20 07 train leaves Paris at 20:07 and reaches Montpellier at 23:34. This means that the total time taken is 3 hours 27 minutes, that is 3.45 hours.

Given that average speed is 224 km/h, hence:

Average speed = total distance / total time

224 km/h = total distance / 3.45 h

total distance = 224 * 3.45 = 772.8 km

Answer: 112.5

Step-by-step explanation: When line AB and CD intersect at point E, angle AEC equals BED so you set them equal to each other and find what x is. 5x -20 = x + 50, solving for x, which gives you 17.5. Finding x will tell you what AEC and BED by plugging it in which is 67.5. Angle BED and BEC are supplementary angles which adds up to 180 degrees. So to find angle CEB, subtract 67.5 from 180 and you get 112.5 degrees.

Let's start by defining the set of natural numbers. The set of natural numbers is the set of positive integers: 1, 2, 3, 4, 5, 6, ... etc. Now we define the set n2 which is the set of all ordered pairs (a,b) where a and b are natural numbers.

Therefore, every element of the set n2 is of the form (a,b) where a, b ∈ ℕ. We can represent the set n2 as follows:n2 = {(a,b) | a,b ∈ ℕ}Next, let's consider the function f : n2 → n given by f((a,b)) = ab.

This function takes an ordered pair (a,b) and returns its product. To clarify, f is a function that takes an element of n2 (which is an ordered pair of natural numbers) and returns a single natural number.

The function f can be interpreted as mapping an ordered pair of natural numbers (a,b) to their product ab. Therefore, we can write:f : n2 → n f((a,b)) = ab where a,b ∈ ℕNote that the output of the function is a natural number (since the product of two natural numbers is also a natural number).

In conclusion, we have defined the set n2 to be the set of ordered pairs of natural numbers, and the function f((a,b)) = ab takes an ordered pair (a,b) and returns its product.

The output of the function is always a natural number, and the function maps elements of n2 to elements of n.

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Answer:

it is D rectangle i just did the quiz on Edmentum and got it right

Step-by-step explanation:

Answer:

The Slope Equation = y2 -y1 over X2 - X1

Step-by-step explanation:

1.) Pick every graph

2.) Pick any 2 point in the graph

3.) do the slope equation

4.) the answers must be equal  

The carrot ate by Fluffy the bunny at the night will be equal to 2/4 or 1/2.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given information in the question,

Carrot ate by bunny in the morning = 1/4

Then, carrot left after ate by bunny = 1- 1/4 = 3/4

Assume that the amount of carrot ate at the night be x.

Then, the carrot left = 1/4

So, the equation will be,

3/4 - x = 1/4

x = 3/4 - 1/4

x = 2/4 or,

x = 1/2.

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Answer:

y = $8(1.05)^t

Step-by-step explanation:

FV = P (1 + r)^n

FV = Future value

P = Present value

R = rate of increase

N = number of years

y = $8(1.05)^t

Parallel cousins are found in the iroquois system of kinship and are defined as bifurcate merging.

Parallel cousins, or the offspring of one's mother's or father's brothers or sisters, were frequently referred to and regarded in the same way as one's siblings. Contrarily, cross-cousins, or the offspring of one's mother's brothers or father's sisters, were frequently regarded as the best source of children.

Bifurcate merging is the underlying idea of the Iroquois system. The ego divides his family into those on his mother's side and those on his father's side (bifurcation) and combines his father with his brother (A) and his mother with her sister (B) .

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Answer:

Volume is 285

Step-by-step explanation:

We start by calculating the area of the base

Mathematically, we have a rectangle as the base

So, the area of the base will be;

3.75 * 8 = 30

We now multiply this by the height to get the volume

we have this as:

30 * 9.5 = 285

The number of  subscribers they must  sample to obtain this interval is: b) 385.

How to find the sample?

95% confidence interval for z-score is  1.96

Using this formula to find the number of  subscribers  they must sample to obtain this interval

n≥ (zσ/2 ÷ 2ME)²

Where:

n= Sample

zσ = Z-score

ME = margin of error

Let plug in the formula

n≥ [1.96 / 2(0.05)]²

n≥ [1.96 / 0.1]²

= (19.6)²

= 384.16

=385 (Rounded)

Therefore the correct option is B.

The complete question is:

Netflix would like to estimate the proportion of their current subscribers who would pay extra for a premium membership including access to more movies and TV shows. To do this, they plan to calculate a 95% confidence interval to estimate the proportion. They would like a margin of error of .05. How many subscribers must they sample to obtain this interval?

a) 1537

b) 385

c) 192

d) 10

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Answer: 2x+6

Step-by-step explanation: two times a number plus six in other words

Answer: 2a+6

Step-by-step explanation:

Answer:

If your asking which answer the thing is, its 2.

Step-by-step explanation:

Can't explain, I hope you understand . . .

Answer: \(a=110^{\circ}\)

Step-by-step explanation:

By the exterior angle theorem,

\(a+15^{\circ}=125^{\circ}\\\\a=110^{\circ}\)

Using Stokes’ Theorem to evaluate ∫ ⃑∙⃑ ,The value of ∫ ⃑∙⃑ is π.

Let S be the part of the surface z=y² that lies within the cylinder x²+y²=2, with upward orientation. Use Stoke 's theorem to evaluate ∫(C) F·dr, where F(x,y,z)=⟨-2yz,y,3x⟩ and C is the boundary curve of S.

Stoke's theorem states that the line integral of a vector field around a closed curve is equal to the surface integral of the curl of the vector field over the surface bounded by the curve.

∫(C) F·dr=∬(S) curl(F)·dS.For F(x,y,z)=⟨-2yz,y,3x⟩, curl(F)=⟨0,-3,-2y⟩.∬(S) curl(F)·dS=∬(D) curl(F)(r(u,v))·N(r(u,v)) dAwhere D is the projection of S onto the xy plane and N(r(u,v)) is the unit normal vector to S. First, we need to determine the boundary curve of S.

The cylinder x²+y²=2 can be parameterized by x=√2 cos(t) and y=√2 sin(t), 0≤t≤2π. The surface z=y² can be parameterized by r(x,y)=⟨x,y,y²⟩. Then the boundary curve of S is C: r(t)=⟨√2 cos(t), √2 sin(t), 2⟩, 0≤t≤2π. r_x=<-√2 sin(t), √2 cos(t), 0>, r_y=<0,0,1>.So, N(r(u,v))=r_x x r_y=⟨-√2 cos(t), -√2 sin(t), -√2⟩.

Since curl(F) = ⟨0,-3,-2y⟩,curl(F)(r(t)) = ⟨0,-3,-2(2 sin(t))⟩ = ⟨0,-3,-4sin(t)⟩.Now we have ∬(S) curl(F)·dS=∬(D) curl(F)(r(u,v))·N(r(u,v)) dA=∫₀²π ∫₀√2 ⟨0,-3,-4sin(t)⟩ · ⟨-√2 cos(t), -√2 sin(t), -√2⟩ dA=12π∫₀²π(3cos(t)+4sin²(t))dt=12π(3(0)+2)=π.The value of ∫ ⃑∙⃑ is π.

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(x, y) is an element of the set c × d, since x is an element of c and y is an element of d.

Since (x, y) was an arbitrary element in a × b, we can conclude that every element in a × b is also in c × d. Thus, we have shown that if a ⊆ c and b ⊆ d, then a × b ⊆ c × d.

To show that if a ⊆ c and b ⊆ d, then a × b ⊆ c × d, follow these steps:

Step 1: Understand the notation.
a ⊆ c means that every element in set a is also in set c.
b ⊆ d means that every element in set b is also in set d.

Step 2: Consider the Cartesian products.
a × b is the set of all ordered pairs (x, y) where x ∈ a and y ∈ b.
c × d is the set of all ordered pairs (x, y) where x ∈ c and y ∈ d.

Step 3: Show that a × b ⊆ c × d.
To prove this, we need to show that any ordered pair (x, y) in a × b is also in c × d.

Let (x, y) be an arbitrary ordered pair in a × b. This means that x ∈ a and y ∈ b.

Since a ⊆ c, we know that x ∈ c because every element in set a is also in set c.
Similarly, since b ⊆ d, we know that y ∈ d because every element in set b is also in set d.

Now, we have x ∈ c and y ∈ d, so the ordered pair (x, y) belongs to c × d.

Step 4: Conclusion
Since any arbitrary ordered pair (x, y) in a × b also belongs to c × d, we can conclude that a × b ⊆ c × d.

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We can rewrite the expression as 3(x - 2)(x - 4). As we can see, the multiplication matches the original polynomial, so our factored form is correct.

To write the polynomial 3x² - 18x + 24 in factored form, we need to find the factors of the quadratic expression. First, we can look for a common factor among the coefficients. In this case, the common factor is 3. Factoring out 3, we get:

3(x² - 6x + 8)

Next, we need to factor the quadratic expression inside the parentheses. To do this, we can look for two numbers whose product is 8 and whose sum is -6. The numbers -2 and -4 satisfy these conditions.

To check if this is the correct factored form, we can multiply the factors:
3(x - 2)(x - 4) = 3(x² - 4x - 2x + 8)

= 3(x² - 6x + 8)

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The value of the ratio a:b is 2:1

Surds are values of a square roots that cannot be simplified as whole numbers or integers. They are usually called irrational numbers.

Example of some surds are the square root of prime numbers.

Analysis:

a + b\(\sqrt{3}\) = \(\frac{1}{2 - \sqrt{3} }\)

Rationalizing the right hand side by the conjugate surd which is 2 + \(\sqrt{3}\)

\(\frac{1}{2 - \sqrt{3} }\)  x \(\frac{2 + \sqrt{3} }{2 +\sqrt{3} }\) = \(\frac{2 + \sqrt{3} }{4 -2\sqrt{3} +2\sqrt{3} -3}\) = \(\frac{2 + \sqrt{3} }{1}\) = 2 + \(\sqrt{3}\)

Equating,

a + b\(\sqrt{3}\) = 2 + \(\sqrt{3}\)

Comparing the variables,

a = 2,   b\(\sqrt{3}\) = \(\sqrt{3}\), b = 1

The ratio, a: b = 2:1

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