what is a polyhedron

we can draw in finite number circle from one point. so there are n number of possibility to draw circle from on given single point.

Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.

Area of circle =  

\(\pi r^2\\r = 10\\A = 3.14 X 20 X 20\\A = 628unit sq\\\)

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The scale factor of triangle PQR to triangle ABC is equal to 2/3.

Scale factor is the ratio between the scale of a given original object and a new object, which is its representation but of a different size either bigger or smaller.

The dilation of the triangle PQR implies it is expanded to the bigger triangle ABC, we shall evaluate for the scale factor as follows:

side PR corresponds to side AC and we derive the scale factor as follows:

scale factor = 12/18

by simplification;

scale factor = 2/3

Therefore, the scale factor of triangle PQR to triangle ABC is equal to 2/3.

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According to this, 3/10 of an inch on a map corresponds to 7/8 miles in actual distance.

In the case of a unit rate expressed as a fraction, the denominator is 1 unit. Divide the denominator by the denominator to represent a rate as a unit rate.

According to this, 3/10 of an inch on a map corresponds to 7/8 miles in actual distance.

Conversion Unit, This unit of conversion, also known as a rate, is utilized to help us map out greater numbers on a smaller piece of paper. Miles to Inches conversion factor is

Data provided 3/10 in equals 7/8 miles.

This suggests that we would depict the real 7/8 miles of distance on the map by 3/10 inches. Inevitably, this would result in a reduction in size or length.        

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Answer:

less than 90°

Step-by-step explanation:

Acute angles are less than 90°

Answer:

Less than 90 degree

Step-by-step explanation:

Because acute triangles are less than 90 degree.

And an acute triangle only include acute angles, no right angles (equal 90 degree) or obtuse angles (greater that 90 degree and less than 180 degree).

So... the answer is less than 90°! less than 90°! less than 90°! A! A! A!

Cheers! (￣▽￣)～■□～(￣▽￣)

The sentences are 4 = false, 5 = true and 6 = false.

4 = False: Measures of central tendency, such as the mean, median, and mode, actually show the center or average of a set of data.

They do not provide information about how the data tends to move away from the center.

Measures of dispersion, such as the standard deviation or range, are used to assess the spread or variability of the data.

5 = True: Measures of central tendency are used to determine the center or typical value of a dataset.

The mean, for example, calculates the average of all the data points, while the median represents the middle value when the data is arranged in ascending or descending order.

The mode identifies the most frequently occurring value.

6 = False: "Inferential" statistics involves making inferences or drawing conclusions about a population based on information obtained from a sample.

It uses probability theory and sampling techniques to generalize findings from a smaller group (sample) to a larger group (population).

In essence, inferential statistics allows researchers to make educated guesses or predictions about a larger population based on the information gathered from a representative sample.

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Answer:

d

Step-by-step explanation:

Answer:

I NEED HELP TO SO

Step-by-step explanation:

1+1

Answer:

1 ≤ x ≤ 5

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

if you roll a die and you want to get a 6, there are 6 sides on the cube, 5 that are not 6 and 1 that is. so the odds against you rolling a 6 are 5 to 1

Answer:

We can be 95% confident that wind speed decreases, on average, between 1.20 knots and 1.42 knots for each millibar increase in minimum pressure.

Step-by-step explanation:

The computed confidence interval for a certain statistical parameter gives a range of value represented by a minimum value and a maximum value. The α value upon which the value was calculated represents the probability of the estimated value containing the true value of the parameter in question.

The minimum and maximum values represents the range of possible slope parameters, the true value falls in between two negative values, thus we have a negative slope, depicting a decline in one variable and the as the other increases.

From the options above, the most appropriate option is ;

We can be 95% confident that wind speed decreases, on average, between 1.20 knots and 1.42 knots for each millibar increase in minimum pressure.

Answer:

-2/3 is the answer I believe

When President Dwight Eisenhower ordered the Arkansas National Guard into service to enforce court orders to desegregate schools, it was an example of a) executive orders.

Executive orders are directives issued by the President of the United States that have the force of law. They are used to manage and govern the operations of the federal government. In this case, President Eisenhower used his executive authority to deploy the Arkansas National Guard to enforce the desegregation of schools as mandated by the courts.

The Supreme Court's landmark decision in Brown v. Board of Education in 1954 declared that segregation in public schools was unconstitutional. However, resistance to desegregation persisted in some areas of the country, including Arkansas. To ensure compliance with the court's ruling, President Eisenhower exercised his executive power and deployed the National Guard to Little Rock, Arkansas, to protect and enforce the rights of African American students seeking to attend previously all-white schools.

Therefore, President Eisenhower's action of ordering the Arkansas National Guard to enforce court orders to desegregate schools falls under the category of a) executive orders, as he used his executive authority to implement a policy decision.

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Answer:

1) x = 12.2

3) x = 21.7

5) x = 17.9

7) x = 31.8

Step-by-step explanation:

Use Pythagorean Theorem (a^2 + b^2 = c^2 where a and b are bases and c is hypotenuse)

1) 10^2 + 7^2 = x^2

100 + 49 = x^2

149 = x^2

x = sqrt 149 which is about 12.2

3) 16^2 + x^2 = 27^2

256 + x^2 = 729

x^2 = 473

x = sqrt 473 which is about 21.7

5) 9^2 + x^2 = 20^2

(we know the other base is 9 because in an isosceles triangle, the altitude (the height) is the same as the median (which divides the base into half)

81 + x^2 = 400

x = sqrt 319 which is about 17.9

7) 16^2 + y^2 = 22^2 (y is the height of the triangle)

256 + y^2 = 484

x = sqrt 228

(sqrt 228)^2 + (44-16)^2 = x^2

228 + 784 = x^2

x^2 = sqrt 1012 which is about 31.8

Step B in the proof of de Moivre's theorem is justified by the factoring property, which simplifies the expression by separating the real and imaginary parts.

The justification for step B in the proof of de Moivre's theorem is the factoring property. In this step, the expression [cos(kθ) + i sin(kθ)] ∙ [cos(θ) + i sin(θ)] is factored to simplify the expression.

By applying the distributive property (step A), the product of the real parts and the product of the imaginary parts are calculated separately. The result is expressed as:

C = (cos(kθ)cos(θ) - sin(kθ)sin(θ)) + i(sin(kθ)cos(θ) + cos(kθ)sin(θ))

Step B involves factoring out the common terms from the real and imaginary parts of the expression C, resulting in:

C = cos(kθ + θ) + i sin(kθ + θ)

The factoring step B allows us to simplify the expression and bring it closer to the desired form, which is to prove that [cos(θ) + i sin(θ)]k + 1 is equal to cos[(k + 1)θ] + i sin[(k + 1)θ] (step E).

Therefore, the justification for step B in the proof is the factoring property, which helps simplify the expression and move closer to the desired form.

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Complete Question:

What is the justification for step B?

Review the proof of de Moivre’s theorem.

Proof of de Moivre's Theorem

[cos(θ) + i sin(θ)]k + 1

A = [cos(θ) + i sin(θ)]k ∙ [cos(θ) + i sin(θ)]1

B = [cos(kθ) + i sin(kθ)] ∙ [cos(θ) + i sin(θ)]

C = cos(kθ)cos(θ) − sin(kθ)sin(θ) + i [sin(kθ)cos(θ) + cos(kθ) sin(θ)]

D = cos(kθ + θ) + i sin(kθ + θ)

E = cos[(k + 1)θ] + i sin[(k + 1)θ]

A) distributive property

B) factoring

C) multiplication rule

D) assumption (for n = k step)

Answer: It’s D

Step-by-step explanation:

Convert it to a decimal and multiply is the best way to describe rate in simple interest formula.

The real yearly cost of funds over the course of a loan is the annual rate that is charged for borrowing (or made by investing), expressed as a single percentage number. An interest rate indicates how expensive borrowing is or how lucrative saving is. Therefore, if you are a borrower, the interest rate is the sum you pay for borrowing money and is expressed as a percentage of the overall loan amount.

Given

The r in the simple interest formula stands for rate.

Convert it to a decimal and multiply is the best way to describe rate in formula.

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Answer: 36 is 4% of 90

Step-by-step explanation: create a fraction of 36/90 then divide both numbers by 18.

Answer:

\(a^3-b^3+4a-4b:\:\left(a-b\right)\left(a^2+ab+b^2+4\right)\)

Step-by-step explanation:

Given the expression

\(a^3-b^3+4a-4b\)

solving the expression

\(a^3-b^3+4a-4b\)

as

\(\mathrm{Apply\:Difference\:of\:Cubes\:Formula:\:}x^3-y^3=\left(x-y\right)\left(x^2+xy+y^2\right)\)

\(a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)\)

also

\(\mathrm{Factor\:out\:common\:term\:}4\)

\(=4\left(a-b\right)\)

so the expression becomes

\(=\left(a-b\right)\left(a^2+ab+b^2\right)+4\left(a-b\right)\)

\(\mathrm{Factor\:out\:common\:term\:}\left(a-b\right)\)

\(=\left(a-b\right)\left(a^2+ab+b^2+4\right)\)

Therefore,

\(a^3-b^3+4a-4b:\:\left(a-b\right)\left(a^2+ab+b^2+4\right)\)

The value of x is the sum of angle ABO and angle CDO because they are the acute angles made out of parallel lines.

Parallel lines are lines that are always the same distance apart and never intersect. They maintain a constant distance from each other as they extend indefinitely in both directions

Recall one of the theorem:

- Alternate angles made by 2 parallel lines are always equal.

Applying this theorem,

angle ABO + angle CDO = angle BOD

50° + 30° = x°

x° = 80°

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When parking downhill next to a curb, you should turn your front wheels into the curb.

This means you should steer the wheels towards the curb or to the right if you are in a country where vehicles drive on the right side of the road.

By turning the wheels into the curb, it provides an extra measure of safety in case the vehicle rolls downhill. If the brakes fail, the curb will act as a barrier, preventing the car from rolling into traffic.

Turning the wheels away from the curb leaves the vehicle vulnerable to rolling freely downhill and potentially causing an accident.

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Answer:

=2016x5

Step-by-step explanation:

(x+y)n=∞∑r=0~nCrxn−ryr is given by

Tr+1=~nCrxn−ryr.

Hence T5=T4+1=~9C4x9−4⋅24

=9!(9−4)!4!⋅x5⋅16

=2016x5

We have shown that if zo is a zero of a linear phase filter, then zo¹ = zo + Δz is also a zero. This holds true because the linear phase property ensures that the filter's phase response varies linearly with frequency, and hence, any frequency offset from zo will yield a corresponding zero in the transfer function.

For a linear phase filter, the phase response is linearly proportional to the frequency. Let's consider a linear phase filter with a zero at frequency zo. The transfer function of the filter can be expressed as H(z) = A(z - zo), where A is a constant and z represents the complex frequency variable.

To find the zero at zo¹, we need to analyze the filter's transfer function at a frequency offset from zo. Let's substitute z with (z - Δz) in the transfer function, where Δz represents a small frequency offset. The new transfer function becomes H(z - Δz) = A((z - Δz) - zo).

Now, let's evaluate the new transfer function at the frequency zo¹ = zo + Δz. Substituting zo¹ into the transfer function, we have H(zo¹ - Δz) = A((zo¹ - Δz) - zo).

Expanding the equation, we get H(zo¹ - Δz) = A(zo¹ - Δz - zo) = A(zo - zo + Δz - Δz) = A(0) = 0.

Therefore, we have shown that if zo is a zero of a linear phase filter, then zo¹ = zo + Δz is also a zero. This holds true because the linear phase property ensures that the filter's phase response varies linearly with frequency, and hence, any frequency offset from zo will yield a corresponding zero in the transfer function.

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Answer:

Step-by-step explanation:

Triangle MNP is a right triangle with the following values:

Interior angles of a triangle sum to 180°. Therefore:

m∠M + m∠N + m∠P = 180°

m∠M + 58° + 90° = 180°

m∠M + 148° = 180°

m∠M = 32°

To find the measures of sides MN and NP, use the Law of Sines:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Substitute the values into the formula:

\(\dfrac{MN}{\sin P}=\dfrac{NP}{\sin M}=\dfrac{PM}{\sin N}\)

\(\dfrac{MN}{\sin 90^{\circ}}=\dfrac{NP}{\sin 32^{\circ}}=\dfrac{8}{\sin 58^{\circ}}\)

Therefore:

\(MN=\dfrac{8\sin 90^{\circ}}{\sin 58^{\circ}}=9.43342722...\)

\(NP=\dfrac{8\sin 32^{\circ}}{\sin 58^{\circ}}=4.99895481...\)

To find the perimeter of triangle MNP, sum the lengths of the sides.

\(\begin{aligned}\textsf{Perimeter}&=MN+NP+PM\\&=9.43342722...+4.99895481...+8\\&=22.4323820...\\&=22.43\; \sf units\; (2\;d.p.)\end{aligned}\)

the radius of convergence (R) is ∞, and the interval of convergence (I) is (-∞, ∞).

To find the radius of convergence (R) and the interval of convergence (I) of the series given by:

∑ 7(-1)^(n-1) n^n x^n

We can apply the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is L as n approaches infinity, then the series converges absolutely if L < 1, diverges if L > 1, and the test is inconclusive if L = 1.

Let's apply the ratio test to the given series:

L = lim(n→∞) |(7(-1)^(n-1) (n+1)^(n+1) x^(n+1)) / (7(-1)^(n) n^n x^n)|

Simplifying and canceling out common factors:

L = lim(n→∞) |(7(n+1) x) / (n^n)|

Taking the absolute value:

L = lim(n→∞) |7(n+1) x / n^n|

Now, let's evaluate the limit:

L = |7x| lim(n→∞) (n+1) / n^n

The limit can be further simplified by applying the ratio test for the sequence:

lim(n→∞) (n+1) / n^n = 0

Therefore, the limit L simplifies to:

L = |7x| * 0 = 0

Since L = 0, which is less than 1, the ratio test indicates that the series converges absolutely for all values of x. Thus, the series converges for all x.

For a series that converges for all x, the radius of convergence (R) is infinite (∞), and the interval of convergence (I) is the entire real number line (-∞, ∞).

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Answer:

Step-by-step explanation:

V= π(8)^2(12/3)

V= 64(4)π

V= 256π

V= 804.3 cm^3

Answer:

<abd+<dbc=<Abc

50+40=90

triangle abc is a right angled triangle being one angle 90 degree

Answer:

Step-by-step explanation:

Answer:

<abd+<dbc=<Abc

50+40=90

triangle abc is a right angled triangle being one angle 90 degree

Answer:

Step-by-step explanation:

For angle C,

cos(∠C) = \(\frac{\text{Adjacent side}}{\text{Hypotenuse}}\) = 0.97

sin(∠C) = \(\frac{\text{Opposite side}}{\text{Hypotenuse}}\) = 0.26

tan(∠C) = \(\frac{\text{Adjacent side}}{\text{Adjacent side}}\) = 0.27

Therefore, from the triangle ABC,

cos(∠A) = cos(90° - ∠C)

             = sin(∠C)

             = 0.26

sin(∠A) = sin(90 - ∠A)

            = cos(∠A)

            = 0.97

tan(∠A) = \(\frac{\text{sinA}}{\text{cosA}}=\frac{0.97}{0.26}\)

            = 3.73

Angle        \(\frac{\text{Adjacent side}}{\text{Hypotenuse}}\)                 \(\frac{\text{Opposite side}}{\text{Hypotenuse}}\)                    \(\frac{\text{Opposite side}}{\text{Adjacent side}}\)

  A                    0.26                       0.97                             3.73

Answer:

3 OR 8  hope this helps!

Step-by-step explanation:

The equation for the volume of the prism will be given as  V=x^3+3x^2

The volume of the prism is given by the following formula

\(\rm Volume = Width\times Length\times hieght\)

Here we have a condition in the question that

The height of a right rectangular prism is 3 units greater than the length

\(h=x+3\)

length will be l = x

The width will be w=x

now by putting the value in the formula we get

\(\rm Volume = w\times L\times h\)

\(\rm Volume = x \times x \times (x+3)\)

\(\rm Volume = x^3+3x^2\)

Thus the equation for the volume of the prism will be given as  \(V=x^3+3x^2\)

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Answer:

-1

Step-by-step explanation:

-5+4=5-4=1

-1 this is the answer

To find dw/dt using the chain rule, we need to differentiate w = x + y with respect to t. We are given that x = e^t, y = 2 + sin(2t), and z = 2 + cos(5t).

Using the chain rule, the derivative of w with respect to t, dw/dt, can be found as follows:

dw/dt = dx/dt + dy/dt

Now, let's find the derivatives of x and y with respect to t:

dx/dt = d/dt(e^t) = e^t

dy/dt = d/dt(2 + sin(2t)) = 2cos(2t)

Substituting these derivatives into the expression for dw/dt, we have:

dw/dt = dx/dt + dy/dt

     = e^t + 2cos(2t)

Therefore, dw/dt = e^t + 2cos(2t).

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