define a regular $n$-pointed star to be the union of $n$ line segments $p 1p 2, p 2p 3,\ldots, p np 1$ such that the points $p 1, p 2,\ldots, p n$ are coplanar and no three of them are collinear, each of the $n$ line segments intersects at least one of the other line segments at a point other than an endpoint, all of the angles at $p 1, p 2,\ldots, p n$ are congruent, all of the $n$ line segments $p 1p 2, p 2p 3,\ldots, p np 1$ are congruent, and the path $p 1p 2, p 2p 3,\ldots, p np 1$ turns counterclockwise at an angle of less than 180 degrees at each vertex. there are no regular 3-pointed, 4-pointed, or 6-pointed stars. all regular 5-pointed stars are similar, but there are two non-similar regular 7-pointed stars. how many non-similar regular 1000-pointed stars are there?

Answer:

Pete is 5

Step-by-step explanation:

Let Pete's age be x

Therefore Masha is 3x

since their age difference is 10,

3x - x = 10

2x = 10

x = 5

check:

3x = 15

x = 5

15 - 5 = 10

The actual height of the house is 0.910 feet.

When both the original dimensions and the new dimensions are known, the scale factor may be determined. When employing the scale factor, there are two terms that must be understood. When a figure's size is increased, we refer to this as scaling up, and when its size is decreased, we refer to this as scaling down.

Given:

Scale : 14 inch = 3 feet

So, 1 inch is represented by

= 3/14

So, 4.25 inch represented as

= 3/14 x 4.25

= 0.910 feet

Hence, the actual height is 0.910 feet.

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The units digit of an integer every square of an integer ends with (=has a units digit) 0, 1, 4, 5, 6, or 9.

This question can be answered in a variety of ways. Finding squares with the unit digits 0, 4, 5, and 6 is one way to demonstrate by means of elimination that the answer must be 2. The reason this method works is that you're presuming one of the answers to this specific multiple-choice question is true, but it's not actually that fulfilling.

A more effective method is to note that any number has the form (10m+i) such that 0i9. By squaring, you may determine exactly which numbers are feasible units digits in a square by getting 100m2+20mi+i2, etc. in turn.

Every square of an integer should have the units digit (0, 1, 4, 5, 6, or 9) as its final value.

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Jerome will have $3261.93 after 4 years

The formula for compound interest is A = P(1 + r/n)^(nt)

where:

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per year

t = the number of years the money is invested or borrowed for.

In this case, P = $3,000, n = 3, r =  2.1% = 0.021, t = 4 years. Thus:

A = P(1 + r/n)^(nt)

A = 3000(1 + 0.021/3)^(3×4)

A = 3000(1 + 0.021/3)^(12)

A = $3261.93

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No, it is not possible to construct a triangle with the sides 9.1cm ,8.3cm and 17.5cm because sum of the any two sides is not greater than the third side .

The side lengths are given as : 9.1cm ,8.3cm and 17.5cm  ;

we know that , the triangle is formed only when the sum of two sides of triangle is greater than third side .

applying this property , we get that ;

⇒ 9.1 + 8.3 = 17.4 > 17.5 ; False

⇒ 8.3 + 17.5 = 25.8 > 9.1 ; True

⇒ 9.1 + 17.5 = 26.6 > 8.3 ; True .

we can see that the sum of the sides 9.1 and 8.3 is 17.4 which is not greater than the third side (17.5) ,

Therefore , the triangle cannot be constructed .

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Therefore , the solution of the given problem of  surface area comes out to be  unused space is equal to 2π - (5π/6 + √3/2) m² .

Its surface area serves as a proxy for how much overall space it occupies. The whole environment of a three-dimensional shape is taken into account when calculating its surface area. The overall size of something is its surface area. The volume of water in a cuboid can be determined by summing the face on each of the six rectangular sides. To determine the box's measurements, apply the following formula: For 2lh, 2lw, & 2hw, the surface is exactly the same (SA). The region is represented by the surface area of the muti form.

Here,

Given:

AB = D = 4 m (R = 2 m)

The size of the AB semicircle is:

=> Area = πr²/2

=>A = 2π

The dimensions of the little semicircle are a=5/6 + 2/3/2 m2 and a=5/6 + 3/2 m2.

The remainder area is therefore equal to A- a.

= 2π - (5π/6 + √3/2) m²

The unused space is equal to 2π - (5π/6 + √3/2) m²

Therefore , the solution of the given problem of area comes out to be  unused space is equal to 2π - (5π/6 + √3/2) m² .

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Step-by-step explanation:

what is the question ?

solve for x and y ?

multiply the second equation by 3 and add that result to the first equation. then solve for x. then pick any original equation and solve for y.

-2x - 3y = 8

15x + 3y = 18

-----------------------

13x 0 = 26

x = 26/13 = 2

5×2 + y = 6

10 + y = 6

y = -4

Therefore , the solution to the given problem of percentage comes out to be  total number of student  = 182 (approx).

In mathematics, a percentage is a number or ratios that is expressed as a portion of 100. Occasionally, the acronyms "pct.," "percent growth," & "pc" are also used. But it is commonly indicated by the percent sign, "%." The % amount has no dimensions. Percentages are essentially fractions when the denominator is 100. Use the percent sign (%) to indicate that a quantity is a percentage by placing it next to it.

Here,

Given :  22% of x is 40

thus,

To find the value of x , where x is the total number of students in that class.

=>  22/100* x = 40

=> x = 40 * 100 /22

=> x = 4000/22

=> x =181.81

So, x = 182 (approx)

Therefore , the solution to the given problem of percentage comes out to be   total number of student  = 182 (approx).

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The probability of having a 2 on first roll, 3 on second roll and 4 on third roll is 1 / 216

A fair dice is a dice that is equally likely to land on any of its faces, meaning that each face has the same probability of facing up after a roll. The probability of getting a specific face on a fair dice is represented by the number of ways that face can appear divided by the total number of possible outcomes.

For a standard six-sided fair dice, the total number of possible outcomes is 6, since there are six faces on the dice. The probability of getting a specific face (for example, the number 4) is 1/6, because there is only one way to get that number out of the six possible outcomes.

The probability of landing 2 on first roll, 3 on second roll and 4 on third roll is given as;

P = (1/6 * 1/6 * 1/6)

P = 1 / 216

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[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{5}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{0}}} \implies \cfrac{ 1 }{ 2 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{ \cfrac{ 1 }{ 2 }}(x-\stackrel{x_1}{0})\implies y=\cfrac{1}{2}x+\text{\LARGE 4}~\hfill \stackrel{y-intercept}{(0,\text{\LARGE 4})}[/tex]

The data points to use is based on two companies knowledge to accomplice.

Here in this question we have been given an example of our time in a school team in which you have to realize on data to convince a group about the recommendation.

Here we also know that when we were making any recommendation to convince a group we have to keep its positive wherever we response to a question about the time you had to convince someone to do something your way.

Here we have also know that you may be tempted so may be tempted to put a negative spin on situation.

So, in order to accomplish the we have to accomplice and will have knowledge two companies knowledge to accomplice

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In accordance with the above assertion, the offered differential equation by variable separation is P = 1/ (k*e^t +1).

A differential equation in mathematics is one that has one or more negatively influencing variables. Dy/dx provides the function's derivative. The phrase describes an equation with several ways to connect the dependent variable to one or more regressors.

dP/dt = P - P^2

1/(P - P^2)dP = dt

∫1/(P - P^2)dP = ∫dt

t + c = 1/(P - P2)dP, where c would be a constant

Use the partial fractions method to calculate the integrated on the left. We wish to rewrite 1/(P-P2) in the pattern A/P+B/(1-P) for those constants A and B since P-P2 factors to P(1-P). We therefore have:

1/[P(1-P)] = A/P + B/(1-P)

A(1-P) + BP = 1

When P is 1, we have A(1-1)+B(1)=1, or B=1.

When P is 0, we have A(1-0)+B(0)=1, or A=1.

So, we can rewrite 1/(P-P^2) as 1/P+1/(1-P).

Whilst doing the entire on the ODE's left side, we have:

∫1/(P - P^2)dP

∫[1/P + 1/(1-P)]dP

∫(1/P)dP + ∫1/(1-P)dP

ln(P) + ∫1/(1-P)dP

Make a u-substitution to perform the second integral:

u = 1-P, du = -dP

ln(P) - ∫(1/u)du

ln(P) - ln(u)

ln(P) - ln(1-P)

ln[P/(1-P)]

Reconnecting that to the ODE yields the following:

ln[P/(1-P)] = t + c

e^ln[P/(1-P)] = e^(t + c)

P/(1-P) = e^t * e^c

P/(1-P) = ke^t, where k is a constant equal to e^c

P = (1-P)ke^t

P = ke^t - Pke^t

P + Pke^t = ke^t

P(1 + ke^t) = ke^t

P = ke^t / (1 + ke^t)

P = e^t / (1/k + e^t)

P = e^t / (d + e^t), where d is a constant equal to 1/k

So, the general solution to the ODE is P = e^t / (d + e^t), where d is a constant.

p*(1-p) = k*e^t ( we say that e^k is a constant)

1-p/p = k*e^t

P = 1/ (k*e^t +1)

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The complete question is-

Solve the given differential equation by separation of variables.

dP/dt = P - P²

False. Solving a system of linear equations requires solving for multiple variables.

To solve for a single variable, you would only need to solve one equation.

To solve a system of linear equations, you need to use methods such as elimination, substitution, or graphing. For example, consider the system of equations:

3x + y = 7

2x - y = 4

To solve this system, you could use elimination by adding the equations together. This would give you the equation 5x = 11. To solve for x, you would then divide both sides by 5, giving you x = 11/5.

Once you have solved for x, you can substitute this value into either of the original equations to solve for y. In this example, substituting 11/5 for x into the first equation would give you 3(11/5) + y = 7. Simplifying this equation gives you y = -2/5.

Therefore, the solution to this system of linear equations is x = 11/5 and y = -2/5.

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The line's x value at the x-axis intersection is referred to as the x intercept, and the line's y value at the y axis junction as the y intercept.

Because they are located on the horizontal and vertical axes, respectively, the x and y-intercepts are also known as the horizontal intercept and vertical intercepts.

The equation is a non-function

solve f(x)=6^x

Here are some points we can plug in. We should try to use full numbers:

(-2,1/36)

(-1,1/6)

(0,1)

(1,6)

This is the graph:

graph{6^x [-10, 10, -2, 40]}

Make sure the line approaches, but never touches, the x-axis. Even though the line sweeps up until it reaches infinity, it will never be vertical because that would render the equation useless.

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Answer: C - The statement is false.

Step-by-step explanation: Rhombuses also have perpendicular diagonals.

We can use the incenter to find the best location, because the point that is equidistant to all sides of a triangle is called the incenter.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, We know that;

The incenter is equidistant from the sides of the triangle and the point that is equidistant to all sides of a triangle.

Hence, We can use the incenter to find the best location, to place a streetlight so it was equidistant from three sidewalks.

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On solving the provided question we can say that equation of pendulum traces an arc, s, that is roughly 4.61 inches long.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

6° = 6°  X [tex]\pi /180 = \pi /30[/tex]

s = r∅

s = 44 X  [tex]\pi /30[/tex]

s = 4.61

Hence, The pendulum traces an arc, s, that is roughly 4.61 inches long.

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The number of revolutions per minute made by the wheel of a car with a diameter of 50 cm travelling at an average speed of 36 km/hr is 226.7 revolutions per minute.

Number of revolutions per minute = (36 x 1000) / (50 x 3.14) = 226.7 revolutions per minute

1. Convert the speed from kilometers to meters per hour

36 km/hr = 36 x 1000 m/hr

2. Calculate the circumference of the wheel

Circumference of wheel = Diameter x π

Circumference of wheel = 50 cm x 3.14 = 157 cm

3. Calculate the number of revolutions per minute

Number of revolutions per minute = (Speed in m/hr) / (Circumference of wheel in cm)

Number of revolutions per minute = (36 x 1000) / (50 x 3.14) = 226.7 revolutions per minute

The number of revolutions per minute made by the wheel of a car with a diameter of 50 cm travelling at an average speed of 36 km/hr is 226.7 revolutions per minute.

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Mathematics focuses on geometry, numbers, and form. For such, axioms and definitions are needed to describe the study's subjects. On the basis of those definitions and axioms, properties are proved using logic.

Mathematical logic help you in using a phone, sending a fax, or operating a vehicle and many other things.

Logic models are composed of mathematical constructs. When it comes to supporting its conclusions, mathematics employs logic. The "science" of reasoning is logic. It deals with arguments, hence learning what constitutes a strong argument is a need for becoming a logician.

Logic can also be applied in everyday conversation about non-mathematical subjects. The amount of reasoning required is typically much more for mathematical inquiries than for non-mathematical ones.

Therefore, logic is a technique that mathematicians (as well as other individuals) employ when it comes to supporting their claims. Proof involves logic.

Mathematical logic has a direct impact on our daily life now more than ever. I'm not only referring to the marks pupils receive or the number of required mathematical subjects. I'm referring to using a phone, sending a fax, or operating a vehicle. I'm referring to making a home, purchasing medication for your family, and enjoying music.

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The probability of getting 1st even and second odd is 9/36 = 1/4

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a certain event will occur.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty. For pupils in Class 10, probability is a crucial subject since it teaches all the fundamental ideas of the subject. One is the sum of the probabilities of all the events in a sample space.

Number of outcomes with 1st even and second odd is 9

Total number of outcomes = 36

So, the probability of getting 1st even and second odd is 9/36 = 1/4

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The mean and standard deviation of the sampling distribution of the difference in sample means for 8 female and 8 male students who participated in the 2-mile run is -1.5 minutes and 2.413 minutes, respectively.

The mean of the sampling distribution of the difference in sample means is calculated by subtracting the mean of the female students from the mean of the male students, which is 7.3 - 8.8 = -1.5 minutes.

The standard deviation of the sampling distribution of the difference in sample means is calculated by taking the square root of the sum of the squares of the standard deviations of the two populations, which is sqrt(3.3^2 + 2.9^2) = 2.413 minutes.

Therefore, the mean and standard deviation of the sampling distribution of the difference in sample means is -1.5 minutes and 2.413 minutes, respectively.

The mean and standard deviation of the sampling distribution of the difference in sample means for 8 female and 8 male students who participated in the 2-mile run is -1.5 minutes and 2.413 minutes, respectively.

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40% first you turn it into a decimal, then u multiply it by 100 to get your percent.

For solving this question we will use the Unitary method

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The term "unitary method" refers to a process where the value of one item is initially determined before determining the values of any other items.

The unitary method's formula is to identify the value of a single unit, then multiply that value by the number of units to obtain the required value.

2/5 = 0.4

0.4 x 100 = 40% first u turn it into a decimal, then u multiply it by 100 to get ur percent

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The full question will be

Tyrone is converting StartFraction 45 Over 50 EndFraction to a percent. Which method should he use to find the percentage?

The total amount of time Martina spent doing these two assignments will be 13/20 Hr.

Total time taken by Martina to complete her chemistry assignment = (2/5) Hr.

Total time taken by the Martina to complete her maths assignment = (1/4) Hr.

One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division. The entire amount or sum of the two whole numbers is obtained by adding them.

So, for determining the total amount of time martina spent doing these two assignment, we need to add the value of time taken by her in completing both the assignment.

So, the value of total amount of time taken by Martina for completing both the assignment will be = (2/5)+)1/4) Hr.

=(8+5)(20)=13/20 Hr.

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So, theta = arctan(sqrt(500^2-d^2) / d) would give us the angle between the ground and the ladder where d is distance from the base of the ladder to the building.

The angle between the ground and the ladder can be found using the inverse tangent function (also known as arctan) and the Pythagorean theorem.

First, we need to find the ratio of the height of the ladder to the distance from the base of the ladder to the building. This ratio is known as the tangent of the angle between the ground and the ladder.

Let h be the height of the ladder and d be the distance from the base of the ladder to the building.

tan(theta) = h/d

Next, we can use the Pythagorean theorem to find the value of h:

d^2 + h^2 = 500^2

Now we can substitute the value of h in the first equation.

tan(theta) = sqrt(500^2-d^2) / d

To find the angle between the ladder and the ground, you can use the inverse tangent function on the above equation.

theta = arctan(sqrt(500^2-d^2) / d)

To find the exact value of the angle, you would need to know the value of d (distance from the base of the ladder to the building).

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Answer:

r=-7

Step-by-step explanation:

Let (x1,y1) be (1,r)and (x2,y2) be (5,1)

Slope m=2

[tex]slope = \frac{rise}{run} = \frac{y2 - y1}{ x2 - x1 } \\ = \frac{1 - r}{5 - 1} = 2 \\ 1 - r = 8 \\ r = - 7[/tex]

The value of x is 85°

A circular sector, also known as circle sector or disk sector is the portion of a disk enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the major sector

A sector is a region bounded by two radii of a circle and the intercepted arc of the circle. The angle formed by the two radii is called a central angle. A sector with a central angle less than 180° is called a minor sector. A sector with a central angle greater than 180° is called a major sector.

The sector where x is the minor sector

The angular distance is x and it is measured in degrees (°)

Therefore the value of x is 85°

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Yes, all requirements have been satisfied for drawing conclusions from statistics. would note a reduction in stress. whether the prerequisites for inference are present.

It is common practice to start with a statistical population or a statistical model that needs to be investigated when applying statistics to a problem in science, business, or society. The field of statistics is concerned with the collection, arrangement, organization, analysis, interpretation, and presentation of data.

The conditions for making judgments about a single proportion are Random: A random experiment or sample must have produced the data. For the sample distribution of pp with hat on top to be considered normal, there must be nearly equal numbers of expected successes and failures.

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