The interior angle of a regular polygon with n sides is 150 degrees. Calculate the value of n

Answer:

(15/4)4^x

Step-by-step explanation:

Substituting the x and y values of the first point, we get:

y = ab

60 = ab^(2)

Substituting the x and y values of the second point, we get:

y = ab

960 = ab^(4)

Now we can solve for a and b by eliminating one of the variables. One way to do this is to divide the second equation by the first equation:

960/60 = (ab^(4))/(ab^(2))

16 = b^(2)

Taking the square root of both sides, we get:

b = ±4

Since an exponential function can only have positive values for b, we choose b = 4. Now we can solve for a by substituting b = 4 into one of the original equations:

60 = a(4^(2))

60 = 16a

a = 60/16

a = 15/4

Therefore, the values of a and b are a = 15/4 and b = 4, and the exponential function is y = (15/4)4^x.

The student's original statement has an issue in the way the "not" operator is used. The "not" operator (!) is negating the entire expression, including the variable 'x', rather than just the inequality. This leads to incorrect evaluation.

To correctly determine if x is not greater than 20, you should use the "less than or equal to" (<=) operator instead. Here is the corrected statement:

if (x <= 20)

This statement will be true if x is less than or equal to 20, which is the intended condition.

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Answer:

Diameter is equal to twice the radius. Given, radius is 4 cm. Diameter = 2(4) = 8 cm. Hence, diameter of the circle with radius as 4 cm is 8 cm.

Step-by-step explanation:

please

give brianliest

Answer: Area = 0

Step-by-step explanation:

((2*2)*3.14)-(4*3.14) = 0

The measure of angle ACD is approximately 109.5 degrees.

What are parallel lines ?

Parallel lines can be defined in which the lines which are equidistant to each other and they never intersect.

To solve for m<ACD, we can use the fact that the sum of the angles in a triangle is 180 degrees.

We can start by finding the measure of angle ACD, which is opposite to the known side length of 10 units. Using the Law of Cosines, we have:

cos(ACD) = (AD * AD + CD * CD - 100) / (2 * AD * CD)

We know that AD = 8 units and CD = 6 units, so plugging in these values, we get:

cos(ACD) = (64 + 36 - 100) / (2 * 8 * 6) = -1/3

Since -1/3 is negative, we know that angle ACD is obtuse, meaning it measures between 90 and 180 degrees. Therefore, we can take the inverse cosine of -1/3 to find its measure:

cos(ACD) = (-1/3) ≈ 109.5 degrees

Therefore, the measure of angle ACD is approximately 109.5 degrees.

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Answer:

£164.50

Step-by-step explanation:

If the discount is 6%, then the discounted price is 94% of the original price.

95% of £175 = 0.94 × £175 = £164.50

The missing dimension of the cone is its height, which is approximately 2.5 m when rounded to the nearest tenth.

We can use the formula for the volume of a cone, which is:

Volume = (1/3)πr²h

where r is the radius of the base and h is the height of the cone.

We are given the volume of the cone as 13.4 m³ and the radius as 3.2 m. Substituting these values into the formula, we get:

13.4 = (1/3)π(3.2)²h

Multiplying both sides by 3 and dividing by π(3.2)², we get:

h = 3 × 13.4 / π(3.2)²

h ≈ 2.5 m

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Answer:

The answer should be 20,365.714 but I am not sure

Step-by-step explanation:

Answer:

8;-2

Step-by-step explanation:

8 is the x axis and -2 is the y axis

Answer:

Step-by-step explanation:

As per the combination concept, there are 735,471 ways to choose 16 shows from a set of 24.

To find the number of ways to choose 16 shows from a set of 24, we can use the formula for combinations, which is:

ⁿCₓ = n! / x!(n-x)!

Where n is the total number of objects in the set (in this case, 24), and x is the number of objects we want to choose (in this case, 16). The exclamation mark (!) denotes the factorial function, which means multiplying the number by all positive integers less than itself.

Plugging in the numbers, we get:

²⁴C₁₆ = 24! / 16!(24-16)! = 735471

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Answer:

i don't know i haven't done integers in a long time

Step-by-step explanation:

If the cycle time is 2 minutes per customer, 30 customers can be served per hour.

The given cycle time is 2 minutes per customer. To calculate how many customers can be served per hour, we need to calculate the number of minutes in an hour as follows: 60 minutes = 1 hour.

The time taken for each customer is 2 minutes. Therefore, the number of customers that can be served per hour can be calculated as follows:

Number of customers per hour = (60 minutes/hour) ÷ (2 minutes/customer)
Number of customers per hour = 30 customers.

Therefore, the number of customers that can be served per hour is 30, according to the given cycle time of 2 minutes per customer.

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The first inequality -4 ≤ x ≤ 3 represents the values of x that fall between the two vertical lines, while the second inequality 1 ≤ y ≤ 6 represents the values of y that fall between the two horizontal lines.

An inequality is a mathematical statement that compares two quantities or expressions using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to).

Inequalities can involve variables or constants, and can be expressed in one variable or multiple variables. The solution to an inequality is the set of values that satisfy the inequality.

For example, the inequality 2x + 3 > 7 is true for values of x that are greater than 2, since if we substitute x = 2, we get 2(2) + 3 = 7, which is not greater than 7. On the other hand, if we substitute x = 3, we get 2(3) + 3 = 9, which is greater than 7, so the inequality is true for x > 2.

Inequalities have many applications in mathematics and other fields, such as economics, physics, and engineering. They are used to represent constraints in optimization problems, to model relationships between variables, and to describe ranges of possible values for a quantity or variable.

To determine the double inequalities that define the shaded region, we need to find the equations of the two boundary lines that form the sides of the shaded region.

The two vertical lines are x=-4 and x=3. The two horizontal lines are y=1 and y=6.

The shaded region is enclosed by these four lines, so the double inequalities that define it are:

-4 ≤ x ≤ 3 and 1 ≤ y ≤ 6

The first inequality -4 ≤ x ≤ 3 represents the values of x that fall between the two vertical lines, while the second inequality 1 ≤ y ≤ 6 represents the values of y that fall between the two horizontal lines. Together, they define the rectangular shaded region with vertices (-4,1), (-4,6), (3,6), and (3,1).

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Answer:

I attached your answer along with an explanation

Step-by-step explanation:

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The probability that the proportion of persons with a retirement account in a random sample of size 555 differs from the population proportion by less than 5% is approximately 0.8327.

We need to make some assumptions about the population proportion of persons with a retirement account and the standard deviation of the sampling distribution of sample proportions. Let's assume that the population proportion is p = 0.5 (i.e., half of the population has a retirement account) and that the standard deviation of the sampling distribution is given by:

σ = sqrt((p*(1-p))/n)

where n is the sample size.

Substituting the values given in the question, we have:

σ = sqrt((0.5*(1-0.5))/555) = 0.0258

To find the probability that the sample proportion differs from the population proportion by less than 5%, we need to find the probability that the absolute difference between the sample proportion and the population proportion is less than 0.05. This can be written as:

P(|p_hat - p| < 0.05)

where p_hat is the sample proportion.

We can standardize this expression by subtracting the population proportion from both sides and dividing by the standard deviation:

P(|p_hat - p|/σ < 0.05/σ)

P(-0.97 < Z < 0.97)

where Z is a standard normal variable. We can find this probability using a standard normal table or a calculator:

P(-0.97 < Z < 0.97) = 0.8327

Rounding to four decimal places, we have:

P(|p_hat - p| < 0.05) = 0.8327

Therefore, the probability that the proportion of persons with a retirement account in a random sample of size 555 differs from the population proportion by less than 5% is approximately 0.8327.

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The value of angle x in the given figure is 79°.

The highest and lοwest walls οf a skew are used tο split the curved lines that make up its ends using Cartesian measurements. A cοllisiοn between twο pοles at an intersectiοn is a pοtential. Angle is anοther οutcοme οf twο things interacting. They resemble dihedral fοrms the mοst clοsely. A twο-dimensiοnal curve can be created by placing twο line beams in variοus cοnfiguratiοns between their ends.

In ΔBFG, ∠FBG = 46°

So according to angle sum property

46° + ∠BFG + BGF = 180°

Here ΔBFG is an isosceles triangle

46° + 2∠BFG = 180°

2∠BFG = 180° - 46°

2∠BFG  = 134

∠BFG = 134/2

∠BFG = 67° = ∠BGF

Using Vertically opposite angle

∠AFJ =  67°

With that in mind ∠BFA = ∠JFG

2∠JFG + 2∠AFJ = 360°

2∠JFG  = 360° - 2∠AFJ

2∠JFG  = 360° - 2(67)

2∠JFG  = 360° - 134

2∠JFG  = 226

∠JFG  = 226/2

∠JFG = 113°

In ΔFDC, ∠JFG  + ∠JDI + ∠HCG = 180°

113° + 33° + ∠HCG = 180°

∠HCG = 180° - (113° + 33°)

∠HCG = 34°

Also, ∠HGC = ∠BGF = 67°

Now, In ΔCGH, ∠HGC + ∠HCG + x = 180°

67° + 34° + x = 180°

x = 180° - (67° + 34°)

x = 79°

Thus, the value of angle x in the given figure is 79°.

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The three classifications of fundamental skull shapes are: +

The number of degrees of angulation (formed by the petrous pyramids and the midsagittal plane) for each classification is 45, 30, and 15 degrees, respectively.

The skull is a bony structure that supports the face and protects the brain. There are several different skull shapes, which can be classified into three main categories based on their length and width: brachycephalic, mesocephalic, and dolichocephalic.

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The new length of the rectangle is approximately 2.29 units. We use the formula for the area of a rectangle to solve for the new length, given the new width.

If the width and length of a rectangle are 3 and 8, respectively, and the width is increased to 10.5, we can calculate the new length of the rectangle using the formula for the area of a rectangle, which is length multiplied by width.

The original area of the rectangle is 3 x 8 = 24 square units. If we increase the width to 10.5, the new area of the rectangle becomes: 10.5 x length = 24 Solving for the length, we get: length = 24/10.5 = 2.29 (rounded to two decimal places)

It's important to note that changing one dimension of a rectangle can affect the other dimension, especially if we want to maintain the same area.

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However, it is important to note that without additional information about the function and the windmill itself, further conclusions about its design and performance cannot be made.

Hi! I'd be happy to help you describe the windmill based on the provided graph.The graph of the function represents the relationship between the height (y) of the tip of a windmill blade and the angle of rotation (Θ) made by the blade. This function is periodic, indicating that the windmill blade follows a repetitive motion as it rotates.

The height of the blade tip varies sinusoidally with respect to the angle of rotation, suggesting that the windmill has a circular or rotational motion. The amplitude of the function gives the length of the windmill blade, while the period of the function represents a full rotation (360 degrees) of the windmill blade.

In summary, the windmill has a rotational motion, with the height of the blade tip following a sinusoidal pattern. The length of the windmill blade and the time it takes to complete a full rotation can be determined by analyzing the amplitude and period of the function.

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The speed of the particle is 8 m/s, the force of resistance is [tex]0.3(8)^2[/tex], or 19.2 N.

A particle of mass 1.2 kg is moving with a speed of 8 m/s in a straight line on a horizontal table. A resistance force is applied to the particle in the direction of the motion. The magnitude of the force is proportional to the square of the speed, such that [tex]F=0.3v^2[/tex]

The force of resistance is an opposing force that acts to reduce the speed of the particle. As the particle moves faster, the resistance force increases. The force is proportional to the square of the speed, meaning that if the speed doubles, the force is multiplied by four. The force is also in the same direction as the motion, meaning that it will reduce the speed of the particle.

The equation for the force of resistance is [tex]F=0.3v^2[/tex], where v is the speed of the particle. Therefore, if the speed of the particle is 8 m/s, the force of resistance is [tex]0.3(8)^2,[/tex] or 19.2 N. This means that the force of resistance acting on the particle is 19.2 N.

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The inverse function for the given function F(x)=1/x² -3x +1  is given by

f⁻¹(x) =(3 ± √(9 + 4/(x - 1))) /2.

Function f(x) is equals to,

F(x)=1/x² -3x +1

Inverse of a function, we need to swap the positions of the x and y variables and then solve for y.

Let's start with the original function

f(x) = 1/x^2 - 3x + 1

Now we will swap x and y,

⇒ x = 1/y^2 - 3y + 1

Next, Solve for y in terms of x

⇒ x = 1/y^2 - 3y + 1

⇒ x - 1 = 1/y^2 - 3y

⇒ 1/(x - 1) = y^2 - 3y

⇒ 1/(x - 1) = y(y - 3)

⇒ y(y - 3) = 1/(x - 1)

⇒ y^2 - 3y - 1/(x - 1) = 0

Using the quadratic formula, solve for y to get inverse function we have,

y = (3 ± √(9 + 4/(x - 1))) / 2

Therefore, the inverse function of f(x) is equal to f⁻¹(x) =(3 ± √(9 + 4/(x - 1))) /2.

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The above question is incomplete, the complete question is:

F(x)=1/x squared -3x +1 then Find the inverse

Using fraction, the total number of cupcakes is obtained to be 5.

What is fraction?

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

If 4 cupcakes represent 80% of the order, then we can use proportional reasoning to find the total number of cupcakes.

Specifically, if x is the total number of cupcakes, then we can write -

4/x = 80/100

where the left-hand side represents the fraction of the order that is Nom-Nom-Nom cupcakes, and the right-hand side represents the percentage of the order that is Nom-Nom-Nom cupcakes.

Solving for x, we get -

x = 4 / (80/100) = 5

So the total number of cupcakes is 5. Since 4 of them are Nom-Nom-Nom cupcakes, the remaining 1 cupcake must be a Wow cupcake.

Therefore, in total there are 5 cupcakes.

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I've been waiting to order your cupcakes all day! I'll have 4 Nom-Nom-Nom cupcakes -- that's 80% of my order. The rest of the order are Wow.
Find the total number of cupcakes.

The value 1.106 represents the slope of the regression line or the rate of change of y with respect to x.

In the given regression equation y = 3.915(1.106)x:

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If you want each character to be approximately one inch in size, you would use a point size of 72 pts.

Point size is a unit of measurement used to determine the size of typefaces. It represents the height of the characters in a font. One point is equal to 1/72 of an inch, which means there are 72 points in one inch.

Therefore, if you want each character to be approximately one inch in size, you would need to use a font size of 72 points. This would ensure that the characters are roughly one inch tall, assuming that the font is designed to be proportional and not condensed or expanded.

Choosing a smaller point size, such as 1 pt or 24 pts, would result in characters that are much smaller than one inch. Choosing a larger point size, such as 36 pts, would result in characters that are larger than one inch.

Therefore the correct answer is option b.) 72 pts.

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Answer:

m = 50 + 6

m= 56

lol easy ques

This one is easy. All you have to do is add 6 to both sides to get the value of m

m-6=50

m=50+6

m=56

There are a total of 32 different possible footwear choices that we can make.

Given, The number of pairs of socks = 4

The number of pairs of shoes = 4

We are to find out the number of possible footwear choices we can make if we can wear any combination of socks and shoes, including mismatched pairs.

So, We can wear any pair of socks with any pair of shoes including a mismatch.

Thus, for each pair of socks, there are 4 possible pairs of shoes.

And for each pair of shoes, there are 4 possible pairs of socks.

Therefore, we can form,

Total number of possible footwear choices = 4 pairs of socks * 4 pairs of shoes * 2 (considering the case of mismatched pairs) = 32 pairs.

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Alexis has 12 quarters and 8 dimes.

Let's use d to represent the number of dimes and q to represent the number of quarters. We know that Alexis has a total of 20 coins, so d + q = 20.

We also know that the value of these coins is $3.80. Since dimes are worth $0.10 and quarters are worth $0.25, we can write an equation for the total value in cents:

10d + 25q = 380

To make things easier, let's divide both sides of the equation by 5:

2d + 5q = 76

Now we can use the first equation to solve for d in terms of q:

d + q = 20

d = 20 - q

Substituting this into the second equation gives:

2(20 - q) + 5q = 76

Expanding the parentheses and simplifying, we get:

40 - 2q + 5q = 76

3q = 36

q = 12

Therefore, Alexis has 12 quarters. We can check this by plugging q back into the first equation to find that she has 8 dimes as well:

d + q = 20

d + 12 = 20

d = 8

The total value of 12 quarters and 8 dimes is:

12 quarters x $0.25 per quarter + 8 dimes x $0.10 per dime = $3.00 + $0.80 = $3.80


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The twο pοssible values οf ∠R tο the nearest 10th οf a degree are 33.6° and 326.4°.

A triangle is a clοsed twο-dimensiοnal geοmetric shape with three straight sides and three angles. It is the simplest pοlygοn, which is a flat shape cοnsisting οf straight lines.

We can use the Law οf Cοsines tο find the length οf side QR:

[tex]c^2 = a^2 + b^2 - 2ab[/tex] cοs(C)

where c is the length οf side QR, a is the length οf side PQ (which is unknοwn), b is the length οf side PR (which is 7.8 cm), and C is the angle οppοsite side c (which is 30°). Substituting the given values, we get:

[tex]QR^2 = PQ^2 + 7.8^2 - 2(PQ)(7.8)cos(30^\circ )[/tex]

[tex]QR^2 = PQ^2 + 60.84 - 7.8PQ[/tex]

Next, we can use the Law οf Sines tο relate the length οf side PQ tο the angle οppοsite it, ∠P:

PQ/sin(30°) = QR/sin(P)

PQ = QR(sin(30°)/sin(P))

Substituting this expressiοn fοr PQ intο the equatiοn fοr [tex]QR^2[/tex] abοve, we get:

[tex]QR^2 = [QR(sin(30^\circ)/sin(P))]^2 + 60.84 - 7.8[QR(sin(30^\circ)/sin(P))][/tex]

Simplifying and rearranging, we get a quadratic equatiοn in terms οf QR:

[tex]QR^2 - 3.9QR + 28.99 = 0[/tex]

Using the quadratic fοrmula, we find that:

QR ≈ 7.466 cm οr QR ≈ 3.866 cm

Since we knοw that QR < PQ + PR = 6 + 7.8 = 13.8, the οnly valid sοlutiοn is QR ≈ 7.466 cm. Therefοre, we have:

[tex]cos(R) = (PQ^2 + QR^2 - PR^2)/(2PQQR)[/tex]

[tex]cos(R) = (PQ^2 + 7.466^2 - 7.8^2)/(2PQ(7.466))[/tex]

[tex]cos(R) = (PQ^2 - 4.928)/[2PQ(7.466)][/tex]

Since cοs(R) ≤ 1, we have:

[tex]PQ^2 - 4.928 ≤ 2PQ(7.466)[/tex]

Sοlving fοr PQ using the quadratic fοrmula, we get:

PQ ≤ 5.474 cm οr PQ ≥ 20.032 cm

Since PQ < PR, the οnly valid sοlutiοn is:

PQ ≈ 5.474 cm

Nοw we can use the Law οf Cοsines again tο find ∠R:

[tex]cos(R) = (PQ^2 + PR^2 - QR^2)/(2PQPR)[/tex]

[tex]cos(R) = (5.474^2 + 7.8^2 - 7.466^2)/(2(5.474)(7.8))[/tex]

cοs(R) ≈ 0.828

R ≈ 33.6° οr R ≈ 326.4°

Therefοre, the twο pοssible values οf ∠R tο the nearest 10th οf a degree are 33.6° and 326.4°.

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