Find the length of the arc on a circle of radius r intercepted by a central angle θ. (Round your answer to two decimal places.) Radius r Central Angle θ 16 inches 240°Find the length of the arc on a circle of radius r intercepted by a central angle θ. (Round your answer to two decimal places.)Radius r Central Angle θ
16 inches 240°

Answer:

(1, -7)

Step-by-step explanation:

(x,y)  ⇒ (y, x)

(1,-7) ⇒(-7,1)

Answer:3

Step-by-step explanation:

Answer: the answer is 3

Step-by-step explanation:I  did the dividing on paper  and the answer is 3

Answer:

Step-by-step explanation:

This problem can be solved using a technique called the Pigeonhole Principle. The Pigeonhole Principle states that if n+1 or more objects are placed into n pigeonholes, then at least one pigeonhole will contain two or more objects.

In this problem, we have 1600 delegates divided into 16000 committees of 80 persons each. We can think of each delegate as an object and each committee as a pigeonhole. Since 1600 delegates are placed into 16000 pigeonholes, we know that by the Pigeonhole Principle, at least one pigeonhole will contain two or more delegates.

In other words, there must be at least one committee that has at least two delegates in common with another committee. We can prove that there will be at least four common members by assuming the worse scenario where each committee is formed by different people, and noting that there are more delegates than the number of committees, so it's impossible that all committees have different members, and therefore there will be at least four common members.

Therefore, it is possible to find two committees having at least four common members.

If Csc(θ) =  1.7894 then θ = 34°.

Equations using trigonometric functions that hold true for all possible values of the variables are known as trigonometric identities.

Given:

Csc(θ) =  1.7894

To find the value of θ:

θ = Csc⁻¹(1.7894)

By the Cosecant calculator,

θ = 34°

Therefore, the value of θ = 34°.

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The size of a television screen that is 21.6 inches wide and 16.2 inches high is approximately 27 inches (measured diagonally).

What is the Pythagorean theorem?

It's a relation in Euclidean geometry among the three sides of a right triangle. In it, the square of the hypotenuse is equal to the sum of the squares of the other 2 sides.

The size of a television screen can be found by using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the length of the diagonal of the screen is the hypotenuse, the width is 21.6 inches, and the height is 16.2 inches. We can use the theorem to find the length of the diagonal:

diagonal²= width² + height²

diagonal² = 21.6² + 16.2²

diagonal² = 467.76 + 262.44

diagonal² = 730.2

diagonal = √730.2

diagonal ≈ 27 inches

Hence, the size of a television screen that is 21.6 inches wide and 16.2 inches high is approximately 27 inches (measured diagonally).

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On solving the provided question, we can say that by equation  it cost to buy the material assuming you can buy a piece exactly the right size = $350.

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.

the floor costs  =  3.50 per square foot

assuming we can buy a piece exactly the right size = x

then cost =

x * 3.50

let x be 100

cost = $350

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a. Media usage is categorical and Tiredness is quantitative. The effect of media is the explanatory variable and Tiredness is the response variable.

b. Yes, this is an observational study.

This research was done via observation. The researchers are not modifying or controlling any variables; instead, they are watching and assessing the correlation between media use and fatigue. By visiting randomly chosen households and interviewing the adult household member with the closest birthday, they are gathering data.

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the answer is just D

One of the most popular dance types of the sixteenth century was the pavane, another one are galliard and allemande.

Instruments in math are tools or processes used to perform mathematical operations and calculations. Examples of instruments in math include calculators, rulers, compasses, protractors, and computers. These instruments can be used to solve problems, analyze data, and understand mathematical concepts. Additionally, instruments in math can be used to teach students about problem-solving and allow them to gain a deeper understanding of mathematics.

This was a slow, stately dance, usually in duple meter, that was popular in courts and societies across Europe. It was usually accompanied by lute or harpsichord and sometimes with viols. The pavane was often used as a ceremonial dance in courts and was usually performed by couples.

Another popular dance type of the sixteenth century was the galliard. This was a lively, energetic dance, usually in triple meter, that was popular in courts and societies across Europe. It was usually accompanied by lute or harpsichord and sometimes with viols. The galliard was often used as a dance for entertainment and was usually performed by couples.

The third popular dance type of the sixteenth century was the allemande. This was a slow, stately dance, usually in duple meter, that was popular in courts and societies across Europe. It was usually accompanied by lute or harpsichord and sometimes with viols. The allemande was often used as a ceremonial dance and was usually performed by couples. It was usually danced in a line or circle formation, with each dancer taking the lead in turn.

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The length of the side of the smaller square is 7 inches.

Let x be the length of the side of the smaller square.

The length of each side of a square is 3 inches more than the length of each side of a smaller square. Thus the length of the side of the larger square is

(x + 3) inches.

The area of the smaller square is

x^2 square inches.

The area of the larger square is

(x + 3)^2 square inches.

We can set up the equation:

x^2 + (x + 3)^2 = 149

Expanding and simplifying the equation gives:

x^2 + x^2 + 6x + 9 = 149

Combining like terms:

2x^2 + 6x - 140 = 0

Using the quadratic formula, we can solve for x:

x = (-b ± √(b^2 - 4ac)) / 2a

x = (-6 ± √(6^2 - 4 * 2 * (-140))) / 2 * 2

x = (-6 ± √(36 + 1120)) / 4

x = (-6 ± √(1156)) / 4

x = (-6 ± √(596)) / 4

x = (-6 ± 34) / 4

x = -10 or x = 7

The side length of the smaller square can't be negative, so x = 7 inches.

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Converting 46.1031 to 4 significant figures, we have 46.10.

Rounding off numbers implies reducing the number of digits in a given number to a preferred length. The two modes are significant figures, or decimal places.

Decimal places requires reducing the numbers of digits in a given number to a required number but considering the position of the decimal point. In significant figures, the length of the given number is reduced to a required number by not considering the position of the decimal.

In the given question, we are to convert 46.1031 to 4 significant figures.

This can be done by counting four digits, and rounding off the digits after.

So that we have;

46.1031 = 46.10 (4 sf)

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The conversation of 46.1031 to 4 significant figures would be = 46.10

A four significant figures are those figures that shows that all zeros to the right of the last significant zero after the decimal point.

From the given figure such as 46.1031, to convert to four significant figures, 46.10

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The following are the valid bases for an exponential function:

An exponential function has the form f(x) = ab^x, where a and b are constants, and b is greater than 0 but not equal to 1. In this case, C, D, E, F, and G all have the correct form of an exponential function.

Options A, B and H are incorrect because:

The options C, D, E, F, and G are valid exponential functions because they have the correct form of f(x) = ab^x, where a and b are constants, and b is greater than 0 but not equal to 1.

The base can be negative or fractional, but as long as it's a constant, it's still a valid exponential function.

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Answer: Otis should borrow the money for 60 months (5 years) so he can afford his monthly payment of $200.

Step-by-step explanation: To calculate the duration of the loan, we can use the formula:

Duration (in months) = Loan amount / Monthly payment

In this case, the loan amount is $10,000, and the monthly payment is $200. So by substituting the values, we get:

Duration (in months) = 10000 / 200 = 50

The duration of the loan is 50 months, however, the bank offers him a rate of 7.5%.

To calculate the total interest, we can use the formula:

Total Interest = Loan amount * Interest Rate * Duration (in months) / 12

The total interest is = 100007.5/10050/12 = 3750

So the Otis will have to pay an additional $3750 in interest over the course of the loan.

So, the total amount he will have to pay is 10000+3750 = 13750

And the time duration to pay this amount is 60 months ( 5 years)

Note: As per the information provided, the interest rate is not annual, it is monthly. So, it is not necessary to divide it by 12 in the interest formula. The equation should be Total Interest = Loan amount * Interest Rate * Duration (in months)

Therefore , the solution of the given problem of average comes out to be the box is the population for selecting 8 cables from that box.

The exact number in the mean of an ordered dataset is known as the median value. A maximum likelihood measure, often known as an average, is the difference between the min and max 50% of the data. The median and mode are calculated using various formulae depending on whether there are an odd or perhaps even number of data points.

Here,

Since every member of the population has a newspaper subscription, all but 8% of them make up the sample.

A sample is (B)

4, where the population to be sampled is one box chosen from the available 4. C) The one of the four boxes that was randomly selected.

The population for choosing a box seems to be of size 4, and the box is the population for selecting 8 cables from that box.

Therefore , the solution of the given problem of average comes out to be the box is the population for selecting 8 cables from that box.

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We can also check if the function's equation is in the form y = mx + b.

What is function's equation ?

A function's equation is a mathematical statement that defines the relation between the input (also known as independent variable) and output (also known as dependent variable) of a function. The equation is typically represented by the letter "y" for the output, and one or more letters for the input (usually "x").

To determine whether a function has a constant or variable rate of change, we need to find the slope or rate of change between two points on the function. If the slope remains the same no matter what two points we choose, the function has a constant rate of change and is linear. If the slope changes depending on the two points we choose, the function has a variable rate of change and is nonlinear.

To determine whether a function is linear or nonlinear, we can also check if the function's equation is in the form y = mx + b, where m and b are constants. If it is, the function is linear, otherwise it is nonlinear.

It's important to mention that, in order to have a definitive answer, we need the function to be defined.

We can also check if the function's equation is in the form y = mx + b.

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On solving the provided question, we can say that since an equilateral triangle so, each angle will be 60

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

since an equilateral triangle has a side measure of 10 in.

and it is a equilateral triangle

so, all sides will be 10

so, each angle will be 60

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Answer:

A,B,D

Step-by-step explanation:

(A) is correct because 5*900+15*300>4000

(B) is correct because 15*900+5*300>4000

(D) is correct because C+P must be less than or equal to 25

The amount of time after which the employee will be earning $10 is 9 years.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

We have,

The raise per year = 3%

The amount received per hour = $7.54

The equation for the hourly wage after t years.

y = 7.54 x [tex]1.03^t[/tex]

Now,

For t = 9,

y = 7.54 x [tex]1.03^9[/tex]

y = 7.54 x 1.326

y = $10

Thus,

After 9 years the hourly earning is $10.

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you were in the garden, there are 34 people in the yard. 30 people left. 35 people are in the garden. This can be solved using addition.

Mathematically, addition is the process of merging several numbers together. The numbers that are being added are known as addends, and the outcome of the addition process, or the answer we ultimately obtain, is known as the sum. It is a fundamental mathematical operation that we employ on a daily basis. We add numbers in many different contexts. In arithmetic sums, the plus sign (+) is used to indicate addition.

The combination of at least two integers constitutes basic addition. Once a student has mastered counting, they may begin to study basic addition. By locating the addend at the top of the chart and tracing down to the row of the second addend, they may utilize an addition chart as a learning tool.

Given that,

there are 34 people in the yard.

Among them 30 people left.

Thus, (30 dead + 4 living + you ) = 35 people are in the garden.

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Therefore , the solution of the given problem of unitary method comes out to be the cost of soap after 2005 is $ 2.6145.

To finish a work using the unitary strategy, multiply the quantity with two after determining the size of a small slice. The unit variable technique, to put it simply, works to isolate a coded object from a specific group or sets of sets. For instance, 40 pens would cost 400 pounds (expression $1.01) = Rs. There is a chance that one nation will have complete control over the technique used to do this. Almost all living things have a unique trait..

Here,

Given :

=> Cost of soap $2.49 in 2003

=> Cost of soap in 2005

=> 2.49 + 5/100 * 2.49

=> 2.49 + 0.1245

=> 2.6145

Therefore , the solution of the given problem of unitary method comes out to be the cost of soap after 2005 is $ 2.6145.

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The probability of the 6th order being the order with the free appetizer is 0.0417 (approx).

The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not. In general, probability has many wonderful uses in games, in business to make forecasts based on likelihood, and in this emerging branch of artificial intelligence.

The probability of getting a free appetizer is 1/18.

The probability of not getting a free appetizer is 17/18.

If the restaurant gives away an appetizer on the 6th order, then there must have been 5 orders before the 6th one that had no free appetizer, followed by the one with the free appetizer.

[tex]P (X = 6) = P(N N N N N F)[/tex]

= 17/18 x 17/18 x 17/18 x 17/18 x 17/18 x 1/18

[tex]= \frac{17^4}{18^5}[/tex]  ≈ 0.0417

Thus, the probability of the 6th order being the order with the free appetizer is 0.0417 (approx).

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As per the given standard deviation, the y intercept of the equation is 2.78 and the slope of the equation is 0.11 and the mean of the equation is 24.08

The term standard deviation in math is known as a quantity expressing by how much the members of a group differ from the mean value for the group

Here we have random sample of 142 high school students was asked how many meals per week their families ate together. And their responses produced a mean of 3.78 meals per week, with a standard deviation of 2.2.

And the equation of the line was written as,

=> GPA = 2.73 + 0.11 Meals.

Here let us consider that x meals and y refers the GPA.

Then the equation is rewritten as,

=> y = 0.11x + 2.73

While we compare this one with the standard form of the equation, then we get

the value of the slope as 0.11 and the intercept as 2.73

Then the value of the mean is calculated as,

=> 144/ (3.78 + 2.2)

=.> 24.08

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Answer:

x^2 +xy+3x+2y+2

Step-by-step explanation:

(x+2)(x+y+1)

Apply the distributive property by multiplying each term of x+2 by each term of x+y+1.

x^2+xy+x+2x+2y+2

Combine x and 2x to get 3x

x^2 +xy+3x+2y+2

Answer: x^2+xy+3x+2y+2

Step-by-step explanation:

Expand and simplify

The shortest segment in the given figure is EF

When two rays are united at a common point, then an angle is created. The two rays are referred to as the arms of the angle, while the common point is referred to as the vertex.

The geometric relationship between sides and interior angles is defined by the angle-side relationship theorem.

According to the angle-side relation theorem,

1. The lowest angle in each triangle lies opposite the shortest side.

2. The largest side is located across from the largest angle.    

3. The opposite of the second-largest side is the second-largest angle.          

Here we have    

EFGH is a quadrilateral and the given angles are

∠HEG = 68°, ∠EFG = 65°, ∠EGF = 55°, and ∠HGE = 71°    

The smallest angle in the given figure is ∠EGF = 55° which is opposite to the line segment EF

Therefore,

The shortest segment in the given figure is EF

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On solving the provided question we can say that by equation we have

remain = x+y = 5/8 + 1/8 = 6/8 3/4

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.

six whole pizzas, as well as  = 5/8 of another pizza

another one = 1/8 of a whole pizza

Remain -by forming equation

let x = 5/8 of another pizza

and y = 1/8 of a whole pizza

remain = x+y = 5/8 + 1/8 = 6/8 3/4

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The population of each country will become double in 47 years.

Given that,

The population of the Dominican republic is, n = 10.7 million.

The growth rate of the Dominican republic is, p = 1.5 %.

The population of Paraguay is, n' = 6.0 million.

The growth rate of Paraguay is p' = 1.5 %.

The doubling time of population growth depends on the rate of population growth.

Here,

n is the final population and n0 is the initial population and doubling the value in the future, n= 2*n0.

Solving this, we get:

t= ln (2*n0/n0)/(1.5/100) = 47 years.

Thus, we can conclude the population of each country will become double in 47 years.

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Yes, we can multiply everything on one side of an equation if you are only multiplying a fractionating that's adding.

Multiplicative Property:

The multiplicative nature of the equation dictates that both sides of the equation can be multiplied or divided by the same nonzero fraction or Gebraic Equation without changing the solution.

if a, b, and c are any three fractions

if a = b and c ≠ 0

1. a × c = b × c

2. a ÷ c = b ÷ c

Multiplicative property for Fraction:

When multiplying two fractions, the numerator and denominator are multiplied separately. The first numerator is multiplied by his second numerator, and the first denominator is multiplied by his second denominator. Finally, reduce the fraction to its lowest term. A fraction has the smallest form if 1 is the only common divisor between the numerator and denominator.

Properties of Multiplying Fractions

1. Multiplying a non-zero fraction by 1 yields the exact fraction

Example: 38 × 1 = 38

2. Multiplying 0 by a non-zero fraction yields zero.

Example: 38 × 1 = 38

3. The product of a fraction and its reciprocal is always 1.

Example: 25×52 = 2×55×2 =1010 =1

(the reciprocal of 25 is 52)

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Answer:

it should be 8 years and at 8 years they will both be 31 ft tall

Step-by-step explanation:

Answer:

Step-by-step explanation:

3x² + 2 * 3x * 5 - 5²

= 3x^2 +2 * 3x * 5 - 25 ( then do 2*3x*5 = 30x)

=3x^2+30x-25