how many ways are there to seat six people around a circular table where two seating's are considered the same when everyone has the same two neighbors without regard to whether they are right or left neighbors? note: 6!

a. The 90% confidence interval to estimate of the percentage of yellow peas will be (34.04%, 41.58%).

b. The correct option will be Yes, the confidence interval does not include 0.25, so the true percentage could not equal 25%.

The bounds of a confidence interval of proportions is given according to the equation as follows:

p ± zα/2 * √(p(1-p)/n)

Here z is the critical value of the distribution, n is the sample size, from which the estimate was built

The confidence level is of 90%, thus the critical value is z = 1.645, using a z-distribution calculator.

The values of the sample size and of the estimate are:

0.260 ± 1.96 √(0.260(1-0.260)/593)

= 0.260 ± 0.037

= (0.223, 0.297)

Thus the interval is: (24.33%, 30.37%).

25% is part of the interval, hence the correct statement will be:

No, the confidence interval includes 0.25, so the true percentage might easily equal 25%.

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Answer:

5.5 in

Step-by-step explanation:

first set up an equation. 24 is your total, so put it on one end of the equal side, and x+2 on the other (24=x+2) then you subtract 2 from BOTH SIDES so that u get x by itself

24=x+2

-2       -2

22=x

since it is a square divide 22 by 4

22/4= 5.5

so 5.5 in is your answer.

Answer:6 FOR EACH OF THE SIDE

Step-by-step explanation:

Ok we know that a square has 4 equal sides and we know the total perimeter is 24, all we need to do is multiply 4*2 which is 8, so 4x+8 and all we need to do is circle move and divide so 4x+8=24, 4x=16, x=4 and now we know that each side has a total value of 6 since substitute x with 4 and get 6.

Using the line of best fit, it is found that the projected time for a man who is 166 cm tall is of 7.966 minutes.

It gives the project time in minutes to run the 3000 meters for a men of a height of x centimeters, according to the following function:

y = -0.081x + 21.412.

Hence, for a men of 166 centimeters, x = 166 and the projected time in minutes is given as follows.

y = -0.081(166) + 21.412 = 7.966.

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This figure begins with the sentence, “We substitute x equals 3 and y equals 2 into both equations.” The first equation reads 3 times x minus 7equals 7. Then, 3 times 3 minus 2 equals 7. Then 7 = 7 is true. The second equation reads x minus 2y equals 4. The n times 2 minus 2 times 2 = 4. Then negative 2 = 4 is false.

The ordered pair (3, 2) made one equation true, but it made the other equation false. Since it is not a solution to both equations, it is not a solution to this system.

Exercise  5.1.1

Determine whether the ordered pair is a solution to the system:  {x−y=−12x−y=−5

(−2,−1)

(−4,−3)

Answer

Exercise  5.1.2

Determine whether the ordered pair is a solution to the system:  {3x+y=0x+2y=−5

(1,−3)

(0,0)

Answer

Exercise  5.1.3

Determine whether the ordered pair is a solution to the system:  {x−3y=−8−3x−y=4

(2,−2)

(−2,2)

Answer

Solve a System of Linear Equations by Graphing

In this chapter we will use three methods to solve a system of linear equations. The first method we’ll use is graphing. The graph of a linear equation is a line. Each point on the line is a solution to the equation. For a system of two equations, we will graph two lines. Then we can see all the points that are solutions to each equation. And, by finding what the lines have in common, we’ll find the solution to the system.

Most linear equations in one variable have one solution, but we saw that some equations, called contradictions, have no solutions and for other equations, called identities, all numbers are solutions. Similarly, when we solve a system of two linear equations represented by a graph of two lines in the same plane, there are three possible cases, as shown in Figure  5.1.1 :

This figure shows three x y-coordinate planes. The first plane shows two lines which intersect at one point. Under the graph it says, “The lines intersect. Intersecting lines have one point in common. There is one solution to this system.” The second x y-coordinate plane shows two parallel lines. Under the graph it says, “The lines are parallel. Parallel lines have no points in common. There is no solution to this system.” The third x y-coordinate plane shows one line. Under the graph it says, “Both equations give the same line. Because we have just one line, there are infinitely many solutions.”

Figure  5.1.1

For the first example of solving a system of linear equations in this section and in the next two sections, we will solve the same system of two linear equations. But we’ll use a different method in each section. After seeing the third method, you’ll decide which method was the most convenient way to solve this system.

Exercise  5.1.4 : How to Solve a System of Linear Equations by Graphing

Solve the system by graphing:  {2x+y=7x−2y=6

Answer

Exercise  5.1.5

Solve each system by graphing:  {x−3y=−3x+y=5

Answer

Exercise  5.1.6

Solve each system by graphing:  {−x+y=13x+2y=12

Answer

The steps to use to solve a system of linear equations by graphing are shown below.

TO SOLVE A SYSTEM OF LINEAR EQUATIONS BY GRAPHING.

Graph the first equation.

Graph the second equation on the same rectangular coordinate system.

Determine whether the lines intersect, are parallel, or are the same line.

Identify the solution to the system.

If the lines intersect, identify the point of intersection. Check to make sure it is a solution to both equations. This is the solution to the system.

If the lines are parallel, the system has no solution.

If the lines are the same, the system has an infinite number of solutions.

Exercise  5.1.7

Solve the system by graphing:  {y=2x+1y=4x−1

Answer

Exercise  5.1.8

Solve the system by graphing:  {y=2x+2y=−x−4

Answer

Exercise  5.1.9

Solve the system by graphing:  {y=3x+3y=−x+7

Answer

Both equations in Exercise  5.1.7  were given in slope–intercept form. This made it easy for us to quickly graph the lines. In the next example, we’ll first re-write the equations into slope–intercept form.

Exercise  5.1.10

Solve the system by graphing:  {3x+y=−12x+y=0

Answer

Exercise  5.1.11

Solve each system by graphing:  {−x+y=12x+y=10

Answer

Exercise  5.1.12

Solve each system by graphing:  {2x+y=6x+y=1

Answer

Usually when equations are given in standard form, the most convenient way to graph them is by using the intercepts. We’ll do this in Exercise  5.1.13 .

Exercise  5.1.13

Sopt form.y=12x−3m=12,b=−3{y=12x−3x−2y=4 If we solve the second equation for y, we get x−2y=4x−2y=−x+4y=12x−2m=12,b=−2

The two lines have the same slope but different y-intercepts. They are parallel lines.

Figure  5.1.3  shows how to determine the number of solutions of a linear system by looking at the slopes and intercepts.

The scale factor used in the dilation is -2

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

Figure with vertices at L(1, 1)

Image with vertices at L'(-2, -2)

The scale factor is calculated as

Scale factor  = L'/L

Substitute the known values in the above equation, so, we have the following representation

Scale factor  = (-2, -2)'/(1, 1)

Evaluate

Scale factor  = -2

Hence, the scale factor is -2

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The rate of return on the stocks over the eight-year period, rounded to the nearest whole percent, is approximately 184%.

To calculate the rate of return, we can use the formula:

Rate of Return = (Final Value - Initial Value) / Initial Value

In this case, the initial value of the investment was $1,000, and the final value is $2,839.42. Plugging these values into the formula, we get:

Rate of Return = ($2,839.42 - $1,000) / $1,000 = $1,839.42 / $1,000 ≈ 1.83942

To convert this decimal to a percentage, we multiply it by 100:

Rate of Return ≈ 1.83942 * 100 ≈ 183.942

Rounding this to the nearest whole percent, we get 184%. Therefore, the rate of return on the stocks is approximately 184%.

It's important to note that there seems to be a discrepancy between the given final value of $2,839.42 and the expected result of 184%. The correct calculation of the rate of return should yield a result closer to 184% rather than 156%.

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Using trigonometric identities in terns of sinθ,  tan²θsin²θ = sin⁴θ/(1 - sin²θ)

Trigonometric identities are mathematical equations that contain trigonometric ratios.

Given the trigonometric identity tan²θsin²θ, we desire to write it in terms of sinθ, we proceed as follows.

Since we have tan²θsin²θ  (1)

Using the trigonometic identity 1 + tan²θ = sec²θ = 1/cos²θ

Making tan²θ subect of the formula, we have that

tan²θ = sec²θ - 1

= 1/cos²θ - 1

So, substituting this into the given equation, we have that

tan²θsin²θ = (1/cos²θ - 1)sin²θ

Now using the trigonometric identity sin²θ + cos²θ = 1

⇒ cos²θ = 1 - sin²θ

So, we have that

tan²θsin²θ = (1/cos²θ - 1)sin²θ

= (1/(1 - sin²θ) - 1)sin²θ

= [1 - (1 - sin²θ )]sin²θ/(1 - sin²θ)

= [1 - 1 + sin²θ )]sin²θ/(1 - sin²θ)

= [0 + sin²θ )]sin²θ/(1 - sin²θ)

= [sin²θ]sin²θ/(1 - sin²θ)

= sin⁴θ/(1 - sin²θ)

So, tan²θsin²θ = sin⁴θ/(1 - sin²θ)

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150 students scored between 42 and 56 on the district geometry test.

Box whisker plots are used to abstract a collection of data that has been approximated using an interval scale. Just a box plot is another name for it. They are mostly employed while interpreting data. It is one of the graphical approaches that shows how the dataset's data varies from one another. The histogram may be used to display the data as well. Yet a histogram offers a useful presentation. Box and whisker plots are preferable to histograms because they may exhibit numerous sets of data on a single graph, which adds more information.

From the box whisker plot we see that the lower quartile is 42 and the median is 56.

The median represents the 50th percentile whereas lower quartile is 75%.

The difference is:

75 - 50 = 25%.

Now, for 600 scores we have:

25% of 600

= 25/100 (600) = 150

Hence, 150 students scored between 42 and 56 on the district geometry test.

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The congruency of triangle ABC and triangle AED is based on SAS ( Side Angle Side )

The term congruent triangles refer to triangles that are equal in size of sides as well as size of the angles corresponding to each side or angle.

The congruent triangle theorem are of some basic theorems which include

As regards the question the theorem used is the Side Angle Side -  SAS. This has it that the two sides and the included angle are equal.

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Answer: AAS

Hope this helps!

Answer:

2.9 meters.

Step-by-step explanation:

First we multiply the length, 3.8, by the width, 1.5, to get the base, 5.7 (this step is not entirely necessary, but makes it much easier).  Then we divide the volume, 16.53, by the base, 5.7, to get the height, 2.9 meters.

Answer:

i think its 21.83 i may be wrong but im pretty sure its 21.83

Step-by-step explanation:

Answer:

Its B and E

Step-by-step explanation:

PLS MAKE ME BRAINLIEST

To simplify the expression (cos θ / (1 - csc θ)) * ((1 + csc θ) / (1 + csc θ)), we can use the property of reciprocals, using which we get the  simplified expression: (cos θ * sin θ) / ((sin θ - 1) * (sin θ + 1))

Recall that csc θ is the reciprocal of sin θ, so csc θ = 1/sin θ.

Let's simplify the expression step by step:

(cos θ / (1 - csc θ)) * ((1 + csc θ) / (1 + csc θ))

Since csc θ = 1/sin θ, we can substitute it in the expression:

(cos θ / (1 - (1/sin θ))) * ((1 + (1/sin θ)) / (1 + (1/sin θ)))

Now, let's simplify the expression further:

(cos θ / ((sin θ - 1)/sin θ)) * (((sin θ + 1)/sin θ) / ((sin θ + 1)/sin θ))

To divide by a fraction, we can multiply by its reciprocal:

(cos θ / ((sin θ - 1)/sin θ)) * ((sin θ / (sin θ + 1)) * (sin θ / (sin θ + 1)))

Now, let's simplify the expression:

(cos θ * sin θ) / ((sin θ - 1) * (sin θ + 1))

The expression is now simplified, and we cannot simplify it any further.

Final simplified expression: (cos θ * sin θ) / ((sin θ - 1) * (sin θ + 1))

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The given differential equation is y(6) - y'' = 0. To find the general solution, we need to solve the differential equation and express the solution in terms of a general form with arbitrary constants is  y(x)  = c1e^x + c2e^(-x)

The general solution of the differential equation y(6) - y'' = 0 is y(x) = c1e^x + c2e^(-x), where c1 and c2 are arbitrary constants.
Explanation: We start by assuming a solution of the form y(x) = e^(rx), where r is a constant. Taking the first and second derivatives of y(x), we have y' = re^(rx) and y'' = r^2e^(rx). Substituting these derivatives into the differential equation, we get:
e^(6r) - r^2e^(rx) = 0
Since e^(rx) is never zero, we can divide both sides by e^(rx):
1 - r^2 = 0
Solving for r, we have two possible solutions: r = 1 and r = -1. Therefore, the general solution of the differential equation is:y

   y(x)  = c1e^x + c2e^(-x),
where c1 and c2 are arbitrary constants that can be determined from initial conditions or additional information. This general solution represents the set of all possible solutions to the given differential equation.

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Answer: 336 papers

Step-by-step explanation:

A week except Sunday = 6 days

56 newspapers * 6 days = 336 newspapers in all

Answer:

336

Step-by-step explanation:

Given That:

Days : 7 - 1 = 6

Number of papers per day : 56

SO,

all papers: 56 x 6 = 336

Hope this helps.

Answer:

(17^1/7)^7 SIMPLIFIED is 498.26016735

The value of x is 20.

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

\(log_{10}(5x)= 2\)

(If no base is given with log function, the default base is 10 )

=> 5x=10²  

=> 5x = 100

=> x=100/5 =20

The value of x is 20.

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Answer:

Distance C from A =5km

Step-by-step explanation:

use the Pythagoras theorem's

{AC}^{2} = {BC}^{2} + {AB}^{2}

AC=✓3^2 + 4^2

AC = ✓9+16

AC = ✓25

AC = 5 km

therefore, C from A = 5 km

Answer:

lol i don't know this

Step-by-step explanation:

lol= laugh out loud

Answer:

about 440 balls

Step-by-step explanation:

The volume of the container is first calculated

\(v=\pi (5)^{2} (14)=1099.6 cu.in\)

It is now divided by the volume of the golf ball

\(#balls=\frac{1099.6}{2.5} =439.8\)

Hope this helps

Answer:

x: C

y: A

z:

Step-by-step explanation:

In a 45-45-90 triangle, the hypotenuse is larger than either of the legs by a factor of \(\sqrt{2}\). The length of x is therefore:

\(12\cdot \sqrt{2}=12\sqrt{2}\)

In a 30-60-90 triangle, the longer leg is larger than the shorter leg by a factor of \(\sqrt{3}\). Therefore:

\(y=\dfrac{12}{\sqrt{3}}=\dfrac{12\sqrt{3}}{3}=4\sqrt{3}\)

The hypotenuse of the 30-60-90 triangle is twice larger than the smallest leg, so it has a length of \(8\sqrt{3}\).

By the pythagorean theorem, you can find z+y:

\(z+y=\sqrt{(12\sqrt{2})^2-12^2}=\sqrt{288-144}=12\\\\4\sqrt{3}+z=12 \\\\z=12-4\sqrt{3}\)

Hope this helps!

Answer:

Step-by-step explanation:

z - some integer

then the consecutive integer would be:

z+1,  (or z-1)

the sum is 69 so:

z + z+1 = 96

2z = 68

z = 34

z+1 = 34 + 1 = 35

(or:

z + z-1 = 69

2z = 70

z = 35

z-1 = 35 - 1 = 34)

Answer: C

Step-by-step explanation:

The costs of a pack of pasta, a pack of noodles, and a pack of split peas are Pasta: $0.99 per pack, Noodles: $0.25 per pack, Split peas: $1.47 per pack

Answer:

Nope

Step-by-step explanation:

Rigid transformations don't change the area or perimeter of a shape.

Answer:

24.95-6.95= 18

18 divided by 8 = 2.25

So each tube of paint cost 2.25 dollars

Step-by-step explanation:

for the first equation we are subtracting the cost of the canvas from the total cost to find the cost of 8 tubes of paint and we get that 8 tubes of paint cost 18 dollars. Next we divide 18 by 8 to get the cost of a single tube of paint and we get 2.25.

Answer:

$2450

Step-by-step explanation:

One week = 7 days

$350 = 1 day

$ 2450 = 7 days(1 week)

350 * 7 = 2450

Writing linear equations given two points can be a useful skill when graphing linear equations.

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The horizontal asymptote of the function f(x) = (x - 2)/(x - 3)^2 is y = 0.

To determine the horizontal asymptote of a function, we need to examine the behavior of the function as x approaches positive or negative infinity. In this case, as x becomes very large or very small, the terms involving x-2 and x-3 become insignificant compared to the higher power of (x-3) squared in the denominator.

As x approaches positive or negative infinity, the (x - 2) term in the numerator does not affect the overall behavior of the function. However, the (x - 3)^2 term in the denominator becomes dominant.

Since (x - 3)^2 will always be positive, the function is always positive or zero. Therefore, as x approaches positive or negative infinity, the function approaches zero or a positive value but never crosses the horizontal line y = 0. Hence, the horizontal asymptote of the function f(x) = (x - 2)/(x - 3)^2 is y = 0.

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The values of a through e that make these two relations inverses of each other. a = b = c = d = e = are:

This refers to the function of a function f that undoes the operation of f. The inverse of f exists if and only if f is bijective. It is also known as reciprocals.

Now, if we assume that y = g(x) and y = h(x) are inverse of each other, where g(x) and h(x) are two different functions.

Then if a = g(b) then b = h(a).

Now, in the given table from the complete question, we would have

a = - 3.8, b = - 2.6, c = 1.7, d = 4.4 and e = 1.0 as the values of the function in inverse.

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