Each value of n represents the number of sides of a regular polygon. Determine whether the given angle measure is the correct sum of the interior angles of the polygon

Answer: 337.5.

Step-by-step explanation:

Answer:

337.5

Step-by-step explanation:

Answer:

We can use the Pythagorean theorem to solve this problem. Let's call the distance Brenda is away from the fish "x". Then, we have a right triangle with legs of length 12 and x, and a hypotenuse of length 16. So:

x^2 + 12^2 = 16^2

Simplifying:

x^2 + 144 = 256

x^2 = 112

Taking the square root of both sides:

x ≈ 10.6 feet

Therefore, Brenda is approximately 10.6 feet away from the fish.

The number of people is 10%

The number of people is 66%

Percentage is a way of expressing a fraction or proportion as a number out of 100. The term "percent" means "per hundred," so if you say that something is "20 percent," it means that 20 parts out of 100 are being referred to.

Total number = 15 + 36 + 73 + 26

= 150 people

The percentage that arrived before 7 am = 15/150 * 100/1

= 10%

After 7:59 = 99/150 * 100/1

= 66%

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The log-likelihood function is l(σ) = -n*log(2σ) - sum(|[tex]x_i[/tex]|)/σ.

the moment estimate of σ is σ = 0.

A moment is a quantitative measure of the shape of a probability distribution. Specifically, it is a mathematical calculation that involves taking the product of the distribution's values and certain pre-determined values (such as powers of the variable). Moments are often used to estimate certain parameters of a distribution, such as its mean, variance, or skewness.

Moment estimate of σ:

The kth moment about the origin is defined as E[[tex]X^k[/tex]] = integral from -inf to inf of [tex]x^k[/tex] * f(x) dx.

The first moment about the origin is E[X] = integral from -inf to inf of x * f(x) dx.

E[X] = integral from -inf to inf of x * (1/2σ*[tex]e^{(-|x|/\sigma))[/tex] dx

Let's split the integral into two parts: from -inf to 0 and from 0 to inf.

integral from -inf to 0 of x * (1/2σ[tex]e^{(-|x|/\sigma))[/tex]dx = integral from -inf to 0 of -x * (1/2σ[tex]e^{(-|x|/\sigma))[/tex] dx = 1/2σ * integral from 0 to inf of x * [tex]e^{(-x/\sigma)[/tex] dx

integral from 0 to inf of x * e^(-x/σ) dx is the definition of the gamma function with shape parameter 2 and scale parameter σ, which is Γ(2, σ) = 1 * σ² = σ².

Therefore, E[X] = 1/2σ * σ² = σ/2.

The second moment about the origin is E[X²] = integral from -inf to inf of x² * (1/2σ*[tex]e^{(-|x|/\sigma))[/tex] dx.

E[X²] = 1/2σ * integral from -inf to inf of x² * [tex]e^{(-|x|/\sigma))[/tex] dx

Let's split the integral into two parts: from -inf to 0 and from 0 to inf.

integral from -inf to 0 of x² * (1/2σ [tex]e^{(-|x|/\sigma))[/tex]  dx = integral from -inf to 0 of x² * (1/2σ[tex]e^{(x/\sigma)[/tex]) dx = 1/2σ * integral from 0 to inf of x² * [tex]e^{(-x/\sigma)[/tex] dx

integral from 0 to inf of x² * [tex]e^{(x/\sigma)[/tex]) dx is the definition of the gamma function with shape parameter 3 and scale parameter σ, which is Γ(3, σ) = 2 * σ³.

Therefore, E[X²] = 1/2σ * 2σ³ = σ².

The moment estimate of σ is obtained by solving the equation E[X²] = σ² for σ:

σ² = E[X²] = integral from -inf to inf of x² * (1/2σ*[tex]e^{(-|x|/\sigma)[/tex]) dx

= 1/2σ * integral from -inf to inf of x² * [tex]e^{(-|x|/\sigma)[/tex] dx

= 1/2σ * 2σ³

= σ²

Simplifying the equation, we get:

σ² = σ²/2

Multiplying both sides by 2, we get:

2σ² = σ²

Therefore, the moment estimate of σ is σ = 0.

MLE of σ:

The likelihood function is given by L(σ) = (1/2σ)ⁿ *[tex]e^{(-sum(|x_i|)/\sigma)[/tex], where n is the sample size and [tex]x_i[/tex]are the observed values.

The log-likelihood function is l(σ) = -n*log(2σ) - sum(|[tex]x_i[/tex]|)/σ.

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Answer:

the right answer is option D

trigonometric ratios for the angles:

Sin < L = opposite/hypotenuse = z/x

Cos < L = adjacent/hypotenuse = y/x

Tan < L = opposite/adjacent = z/y

Trigonometric ratios are ratios of the sides in a right triangle with respect to its acute angles. In a 30-degree right triangle, the ratios of the opposite and adjacent sides to the hypotenuse are 1/2 and √3/2, respectively.

An angle is a geometric figure formed by two rays that share a common endpoint called the vertex. Angles are measured in degrees or radians and are used to describe the orientation of objects in space.

According to the given information:

the triangle has a base of length y, a height of length z, and a hypotenuse of length x, we can use trigonometric ratios to solve for the angles:

Sin < L = opposite/hypotenuse = z/x

Cos < L = adjacent/hypotenuse = y/x

Tan < L = opposite/adjacent = z/y

To solve for the values of sin, cos, and tan of angle L, we need to know the value of angle L. We can use inverse trigonometric functions to solve for angle L:

L = [tex]sin^{-1(z/x)}[/tex] = [tex]cos^{-1(y/x)}[/tex] = [tex]tan^{-1(z/y)}[/tex]

To solve for the value of cos of an angle, we can use the adjacent and hypotenuse sides of the triangle. So,

Cos < A = adjacent/hypotenuse = y/x

To solve for the value of tan of an angle, we can use the opposite and adjacent sides of the triangle. So,

Tan < A = opposite/adjacent = z/y

To solve for the value of sin of an angle, we can use the opposite and hypotenuse sides of the triangle. So,

Sin < A = opposite/hypotenuse = z/x

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1 kg = 1000 G

so 1000/4g = 250g

I hope it’s helpful

The equation of the line is: y = 0.5x + 4 and the inequality is H > 74.25

To find the equation of a line that passes through two points, we need to use the slope-intercept form of a linear equation:

y = mx + b

The slope is calculated as

m = (y2 - y1) / (x2 - x1)

m = (11 - 4) / (14 - 0)

m = 7/14

m = 1/2

m = 0.5

Next, we have

y = mx + b

4 = 0.5(0) + b

b = 4

So the equation of the line is: y = 0.5x + 4

Part A: The equation that could be used to find the value of s is:

12s + 5.04 = 15.48

To find the value of s, we need to isolate the variable on one side of the equation.

We can do this by subtracting 5.04 from both sides and then dividing both sides by 12:

12s + 5.04 - 5.04 = 15.48 - 5.04

12s = 10.44

s = 10.44/12

s = 0.87

Therefore, Jacy paid $0.87 to download each song.

To represent the number of hours, h, that Tara plans to work this month as an inequality, we can use the fact that she plans to work more hours than last month.

Let H be the total number of hours that Tara works this month.

Then we can write:

H > 16.5 + 19 + 23 + 15.75

Simplifying the right-hand side, we get:

H > 74.25

Therefore, the inequality that represents the number of hours, h, Tara plans to work this month is: H > 74.25

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The correct option is: No. Because the interval does not contain $35, the manager would not be issued the bonus.

An interval refers to a range of values between two points on a numerical scale. It can be represented by two numbers, called endpoints, and includes all the values that lie between these endpoints.

The two common types of intervals are closed intervals and open intervals.

According to the given information:

In a confidence interval, the range of values within which the true population parameter (in this case, the mean amount of money each customer spends per visit) is likely to fall is estimated. A 95% confidence interval means that there is a 95% probability that the true population parameter falls within the interval.

In this case, the confidence interval is ($10.53, $31.89), which means that we are 95% confident that the true mean amount customers spend per visit falls between $10.53 and $31.89. Since the interval does not contain $35, it is not reasonable to believe that the manager will receive a bonus, as the estimated mean amount spent per visit is below $35 according to the confidence interval.

The correct answer is: No. Because the interval does not contain $35, the manager would not be issued the bonus.

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The equation that models the deposit, y, on day x that Julian makes with an initial deposit of $6 and depositing 2 times as much money as he did the day before is y = 6^2x.

An equation is a mathematical statement of the equality or equivalence of two or more mathematical or algebraic expressions.

Equations use the equation symbol (=), unlike mathematical expressions, which just combine variables, constants, numbers, and values with mathematical operands.

The initial deposit that Julian makes = $6

The amount that he deposits each day = 2x

Let Julian's deposit on day x = y

Let the number of days of deposit = x

y = 6^2x.

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AA Similarity Theorem is required to prove that both triangles are similar

AA (Angle-Angle) Similarity Theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

In other words, if two angles of one triangle are equal to two angles of another triangle, then the third angles must also be equal, and the two triangles are said to be similar.

One of the equal angle is marked while the other is equal using the concept of vertical angle theorem. Angles formed where the line intersect are the ones equal by vertical angle theorem

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The shaded region, the closest answer choice (B) is  20 square units.

The circumference of a circle is the length of the edge of the circle. If we cut  the circle and straighten it, the length of the border is the circumference of the circle.

 The central angle of  sector AOB is 2*35 = 70 degrees (because the central angle  is twice the circumferential angle). The remaining angle of triangle AOB is (180 - 70)/2 = 55 degrees.  Using trigonometry, we  find that the length of AB is:

AB = 2 * 8 * sin(55/2) ≈ 11.96 units

The shaded area can be divided into two parts: a sector with a central angle of 70 degrees and a triangle with base AB and height 8 units (the radius of the circle).

 The area of sector is

(70/360) * π * 8² ≈ 12.57 square units

The area of ​​the triangle is:

(1/2) * AB * 8 ≈ 47.82 square units

Therefore, the total area of ​​the shaded area is approximately:

12.57 + 47.82 ≈ 60.39 square units

Therefore, for the shaded region, the closest answer choice (B) is  20 square units.

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The two possible locations for the fourth vertex are (4, -4) and (-3, -1).

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form.

To find the location of the fourth vertex of the square, we need to use the fact that a square has four equal sides and four right angles.

The first two vertices given are (4, 3) and (-3, 3), which lie on a horizontal line segment of length 7.

The third vertex is (-3, -4), which is 7 units away from the first two vertices and lies on a vertical line segment.

Since the square has four equal sides, the distance between the third vertex and the fourth vertex must also be 7 units.

And since the square has four right angles, the fourth vertex must be located on a vertical line passing through the first two vertices or on a horizontal line passing through the third vertex.

So, there are two possible locations for the fourth vertex:

(4, -4): This point is located 7 units below the first vertex (4, 3) on the vertical line passing through it.

(-3, -1): This point is located 7 units to the right of the third vertex (-3, -4) on the horizontal line passing through it.

Therefore, the two possible locations for the fourth vertex are (4, -4) and (-3, -1).

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[tex]\textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ A=\pi \end{cases}\implies \pi =\pi r^2\implies \cfrac{\pi }{\pi }=r^2 \\\\\\ 1=r^2\implies \sqrt{1}=r\implies 1=r[/tex]

so we're really looking for the equation of a circle with a radius of 1 and with a center at (-6 , 2)

[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-6}{h}~~,~~\underset{2}{k})}\qquad \stackrel{radius}{\underset{1}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-6) ~~ )^2 ~~ + ~~ ( ~~ y-2 ~~ )^2~~ = ~~1^2\implies (x+6)^2 + (y-2)^2=1[/tex]

Answer:

To solve a system of equations by graphing, you need to graph each equation on the same coordinate system and find the point where the two lines intersect. If the equations are in slope-intercept form, you can identify the slope and y-intercept and graph them. If one of the equations is in slope-intercept form, you can rewrite the other one in that form and graph them. If both equations are in other forms, you can find the x- and y-intercepts and graph them.

In this case, we have two equations:

y = x + 5

y = -2x - 1

To graph these equations, we can start by finding their intercepts:

y = x + 5

0 = x + 5

x = -5

So the intercept for y = x + 5 is (-5, 0). Similarly,

y = -2x - 1

0 = -2x - 1

x = -1/2

So the intercept for y = -2x - 1 is (-1/2, 0). Now we can plot these points on a coordinate plane and draw a line through each point. The point where these two lines intersect is our solution.

Therefore, the solution to this system of equations is (-3, 2).

Step-by-step explanation:

Answer:

Step-by-step explanation:

To save for a new car, Trafton invested $5,000 in a savings account that earns 6.5% interest, compounded continuously. After four years, he wants to buy a used car for $7,000. How much money will he need to pay in addition to what is in his savings account?

according to the question the given fraction can be solved with equation 1/3 x (15+6) is equal to 7.

To represent a whole, any quantity of equal parts or fractions can be utilised. In standard English, fractions show how many units there are of a particular size. 8, 3/4. Fractions are part of a whole. In mathematics, numbers are stated as a ratio between the numerator compared to the denominator. These can all be expressed as simple fractions as integers. A fraction appears in a complex fraction's numerator or denominator. The numerators of true fractions are smaller than the denominators. A sum that is a fraction of a total is called a fraction. You can analyse something by dissecting it into smaller pieces. For instance, the number 12 is used to symbolise half of a whole number or object.

given,

To evaluate the fraction 1/3 x (15+6), we need to perform the addition inside the parentheses first and then multiply the result by 1/3.

So, 15+6 equals 21.

Then, we can write:

1/3 x (15+6) = 1/3 x 21

Multiplying 1/3 by 21 gives:

1/3 x 21 = 7

Therefore, 1/3 x (15+6) is equal to 7.

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The polynomial function of least degree that has zeros of x=0, x=2i, and x=3, and with all coefficients real is:

Since the zeros of the polynomial function are given as

x=0, x=2i, and x=3,

we can write the function in factored form as follows:

f(x) = a(x-0)(x-2i)(x-3)

where

a is a constant coefficient and the factors correspond to the given zeros.

Since all coefficients must be real, we know that the complex conjugate of 2i, which is -2i, must also be a zero of the function. Therefore, we can rewrite the function as:

f(x) = a(x-0)(x-2i)(x+2i)(x-3)

Expanding this expression gives:

f(x) = a(x² + 4)(x-3)

Multiplying out the brackets and collecting like terms, we get:

f(x) = ax³ - 3ax² + 4ax - 12a

To find the value of 'a', we can use the fact that the coefficient of the x³ term is 1. Thus, we have:

a = 1/(1*4) = 1/4

Substituting this value of 'a' in the above expression, we get:

f(x) = (1/4)x³ - (3/4)x² + x - 3

Therefore, the polynomial function of least degree that has zeros of x=0, x=2i, and x=3, and with all coefficients real is:

Option A: f(x) = x² - 3x³ + 4x² - 12x

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Therefore, the answer is (A) 7x-9 when it is given that function F(x) = 4x - 8 and g(x) = -3x + 1.

In mathematics, a function is a relationship between two sets of values, where each input (or domain element) is associated with a unique output (or range element). In other words, a function is a rule or a process that takes an input (or inputs) and produces a corresponding output. Functions can be expressed using various mathematical notations, such as algebraic formulas, graphs, tables, or even verbal descriptions. They are widely used in many fields of mathematics, science, engineering, economics, and computer science, to model and solve problems that involve relationships between variables or quantities.

Here,

To find (f - g)(x), we need to subtract g(x) from f(x), so we get:

(f - g)(x) = f(x) - g(x)

Substituting the given functions, we get:

(f - g)(x) = (4x - 8) - (-3x + 1)

Simplifying the expression by distributing the negative sign, we get:

(f - g)(x) = 4x - 8 + 3x - 1

Combining like terms, we get:

(f - g)(x) = 7x - 9

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The histogram that displays the data in the table correctly is C. Histogram C.

Look at the data in the table and look for the number of photocopies that are located between 800 and 899. There are 3 of these.

The number located between 900 and 999 are 5 in number including 915, 919, 923, 950, and 989. The number located between 1,000 and 1, 099 is 8 photocopies.

The histogram that shows this is Histogram C.

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After calculation, we can conclude that the required angle x is 56° respectively.

A pair of rays (half-lines) with a shared terminal are combined to form an angle.

The latter is referred to as the angle's vertex, and the rays are sometimes referred to as the angle's legs and other times as its arms.

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively.

Angles created by two rays are in the plane where the rays are located.

So, we can calculate inner angle A because it will result in a 180o angle.

180º - 116º = 64º = Angle A

Now multiply angle A by angle C.

64º + 60º = 124º

Take it away from 180°.

180º - 124º = 56º

Consequently, angle X is measured at 56°.

Therefore, after calculation, we can conclude that the required angle x is 56° respectively.

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1. The ratio for sin x in the trigonometry will be 12/13.

The ratio for cos x in the trigonometry will be 5/13.

The ratio for tan x in the trigonometry will be 12/5

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used extensively in various fields, including physics, engineering, and astronomy.

The three primary functions in trigonometry are sine, cosine, and tangent. These functions relate the ratios of the sides of a right triangle to its angles.

The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

Trigonometry also involves inverse functions, such as the arcsine, arccosine, and arctangent. These functions are used to find the angle whose sine, cosine, or tangent is a given value.

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Answer:

B

Step-by-step explanation:

the average rate of change of h(x) in the interval [ a, b ] is

[tex]\frac{h(b)-h(a)}{b-a}[/tex]

here the [ a, b ] = [ 4, 8 ] , then

h(b) = h(8) = 3 ← point (8, 3 ) on graph

h(a) = h(4) = 9 ← point (4, 9 ) on graph

then

average rate of change = [tex]\frac{3-9}{8-4}[/tex] = [tex]\frac{-6}{4}[/tex] = - [tex]\frac{3}{2}[/tex]

Answer:

Looking at the number line, we can see that R is to the left of P, and S is to the right of P. Also, Q is to the left of R, and S is to the right of Q.

So, the first statement "R x P > S" is not true, because S is to the right of both R and P.

The second statement "S > Q x R" is also not true, because Q is to the left of R, and S is to the right of both Q and R.

The third statement "Q x R > S" is true, because Q is to the left of R, and S is to the right of both Q and R. Therefore, the correct statement is:

Q x R > S

Answer:

2 yards or 6 feet long

Step-by-step explanation:

Each yard is 3 feet long.

If Tanya shortens the leash by 6 feet, that is 2 yards.

4-2=2

The leash is 2 yards (or 6 feet) long.

Answer:

6 foot

Step-by-step explanation:

1 yards = 3 foot

4 yards = 12 foot

We take

12 - 6 = 6 foot

So, the length of the shortened least is 6 foot.

Answer: 87.3 inches

Step-by-step explanation: The height of the pyramid is the hypotenuse of a right triangle whose legs are the height and half the length of the base.

Let h be the height of the pyramid, then:

h^2 + (21.6/2)^2 = 88.6^2

h^2 + 233.28 = 7857.96

h^2 = 7624.68

h = 87.3 inches (rounded to one decimal place)

Therefore, the height of the stainless steel patio heater is approximately 87.3 inches.