What is the formula for the arc length of the sector of a circle?

Check the picture below.

notice, it says that PT is perpendicular to SQ.

now onto the other one

well, a parallelogram with one right-angle and at least one pair of congruent sides, hell a rectangle is that, so is an square, so no dice.

a rhombus that has congruent diagonals, well, a square is that but so is a rectangle, no dice.

a parallelogram whose diagonals bisect each other, well, a square has that, sure, a rhombus too and a rectangle too, no dice.

a rectangle with perpendicular diagonals, well, a rhombus has perpendicular diagonals, however is not a rectangle, a square is a rectangle  also with perpendicular diagonals too.

Answer: -2

Step-by-step explanation:

change in y/ change in x.

-4/4 ---> slope is -1

plug x and y coordinates AND SLOPE into y=mx+b

-3= -4/4(1)+b

-3= -1 +b

-2=b

The value of the definite integral of f(x) over the interval [−1, 5] is estimated to be between 36 and 42.

A function is a mathematical concept that assigns a unique output value for each input value. It is a rule that takes in an input or set of inputs and maps it to a specific output. Functions are represented by symbols, usually denoted by a letter, such as "f".

In mathematical notation, a function is usually expressed as "f(x)" where "x" is the input and "f(x)" is the corresponding output. For example, a function could be defined as f(x) = x^2, which means that for any value of x, the function will calculate and return the square of that value.

Functions play a central role in mathematics and are used to model real-world phenomena and to study the relationships between variables. They are also used in computer programming to perform specific tasks, such as converting temperatures from Celsius to Fahrenheit or calculating the square root of a number.

Since 6≤f(x)≤7 for −1≤x≤5, we have a lower bound of 6 and an upper bound of 7 for the function over this interval. This means that, for any possible value of f(x) in the interval, we can use 6 as a lower estimate and 7 as an upper estimate for the definite integral. Hence, we have:

Lower estimate: ∫5−1 6 dx = 6(5 - (-1)) = 6(6) = 36

Upper estimate: ∫5−1 7 dx = 7(5 - (-1)) = 7(6) = 42

So, the value of the definite integral of f(x) over the interval [−1, 5] is estimated to be between 36 and 42.

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The mean of the given data be 0.17.

Variance is a measure of dispersion that considers the spread of all data points in a data collection, in contrast to range and interquartile range. The standard deviation, which is just the square root of the variance, is the other often used measure of dispersion.

A measure of variability is the variance. It is determined by averaging the squared deviations from the mean. Your data set's variability is shown by its variance. The variance is greater in respect to the mean when the data are more dispersed.

Since the data are stated in the question to be evenly distributed, the mean will be determined using the formula.

Mean = a + b /2

Where, a be the minimum value and b be the maximum value

for the data: 0.15,0.16,0.17,0.18, and 0.19

The value of a = 0.15 and b = 0.19

Substitute the values in the above equation, we get

Mean = (0.15 + 0.19) /2

simplifying the above equation, we get

Mean = 0.34/2

Mean = 0.17

Therefore, the mean of the given data be 0.17.

The complete question is:

Thickness measurements of a coating process are made to the nearest hundredth of a millimeter. The thickness measurements are uniformly distributed with values 0.15, 0.16, 0.17, 0.18, and 0.19. Determine the mean and variance of the coating thickness for this process.

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The sailor is 10 meters above the water and the lighthouse is 40 meters tall, so the total height between the two is 50 meters. Therefore, the sailor will first see the lighthouse from 50 meters away.

Assuming the lighthouse is directly in front of the sailor, the light from the lighthouse will reach the sailor first when the total distance between them is 50 meters. This means the sailor will first see the lighthouse from 50 meters away. In addition, the angle between the sailor and the lighthouse will be equal to the angle of the light when it reaches the sailor's eyes. The angle of the light will depend on the curvature of the earth, the height of the lighthouse, and the height of the sailor.

Assuming the lighthouse is at sea level, the angle of the light when it reaches the sailor's eyes can be calculated using the following equation:

Angle

= arcsin (50 / (2 * 6371))

Where 6371 is the radius of the earth in km.

This calculation gives an angle of 0.0058°. This means the light from the lighthouse will reach the sailor from a distance of 50 meters with an angle of 0.0058°.

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The x-intercept and y-intercept can find by using graphically and solving the equation.

What is the x-intercept?

A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed.

If we have an equation, then there are two ways to find x-intercepts and y-intercepts.

1) Graphically

2) Solving the equation

Graphically:

If we have a graph of an equation, then find the points where the graph cuts the x-axis. The points are known as x-intercepts. The graph that cuts the y-axis is the y-intercepts.

Solving the equation:

Putting x = 0 in the equation to find the value y-intercept.

Put y = 0  in the equation to find the value x-intercept.

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The percent of burger restaurants in that country in 2016​ was:

35.1%

To calculate the percentage of burger restaurants in a specific country in 2016, we can divide the number of burger restaurants in that country by the total number of burger restaurants worldwide, then multiply the result by 100.

Percentage of burger restaurants in a specific country

Percentage of burger restaurants in the specific country

So, in 2016 there were approximately 35.1% of all burger restaurants in the world located in that country.

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By separating the variables, the given differential equation will be cosy = -1/2 sin2x + C.

Differential equation definition

Differential equations are those that have derivatives of one variable with regard to another variable quantity.

Any arrangement of derivatives is possible, and certain words may include a derivatives-and-variable product or derivatives by themselves. They might also have several different variables.

The differential equation shown is

csc(y) dx = sec2(x) dy

The fact that

csc(y) = 1/ siny

1/cosx = sec(x)

We can also write it;

dy/cos2x = dx/siny

Cross multiplication with variable separation.

Cos2x dx = siny dy

In distinction;

cosy = -1/2 sin2x + C

Therefore, Cosy = -1/2 sin2x + C will be the supplied differential equation by separation of variables.

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Fraction of a tablespoon might Tamar use =  4 / 9

A ratio is used to show a relationship between two numbers or a comparison of

two items. The numbers are separated by a colon (:) as in x : y. For example, three

nurses and four medical assistants working a clinic shift can form a ratio. Ratios

may be presented in three formats that provide the set-up for solving proportions.

a. 3 : 4 (three nurses to four medical assistants)

b. 3

4

(three nurses to four medical assistants)

c. 3 is to 4 (three nurses to four medical assistants)

The relationship can represent something as simple as the 1 : 3 ratio commonly used

to mix frozen juices. We use one can of frozen juice concentrate to three cans of

water. Ratios are fractions that represent a part-to-whole relationship. Often when

we work with ratios, we use the fraction format to reduce the ratio to its simplest

form.

Ratios are always reduced to their lowest form

The ratio between the number of tablespoons of salt used and the liters of beans made is:

[tex]\frac{1/3}{3 / 4}[/tex]

=1/3 *4/ 3

=4 / 9

Fraction of a tablespoon might Tamar use =  4 / 9

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Answer:The motel clerk has 33 $1 bills and 18 $10 bills.

Step-by-step explanation:

Let the number of $1 bills = x, so then number of $10 bills is 51-x.From the problem description, you can write:x($1)+(51-x)($10) = $213 Simplify and solve for x.x+510-10x = 213-9x+510 = 213 Add 510 to both sides.-9x = -297 Divide both sides by -9x = 33 and 51-x = 51-33 = 18.

Answer: The answer will be 7b^3

Answer:

the answer is 7 root 3

Step-by-step explanation:

Answer:

22.0 cm

Step-by-step explanation:

Solution Given:

radius(r)= 3.5 cm

we know that

circumference of the circle =2 pi r= 2*π*3.5 =2*22/7*3.5=22.0 cm

you are right

Answer:

22.0

Step-by-step explanation:

3.5 is the radius=r. To find the circumference, we calculate [tex]2\pi r=2\pi\cdot3.5[/tex]That equals about 21.99... When we round it, that equals 22.

Hope that helped! Let me know if you have any further questions.

Answer:

Average speed = Total distance ÷ Total time

Average speed = 16250 km ÷ 10 days = 1625 km/day

1 km = 1000 m

1625 km = 1625 × 1000 m = 1,625,000 m

1 day = 24 hours = 24 × 60 minutes = 1440 minutes

10 days = 10 × 1440 minutes = 14400 minutes

Average speed = 1,625,000 m ÷ 14400 minutes = 113.19 m/min

1 minute = 60 seconds

Average speed = 113.19 m/min ÷ 60 seconds/min = 1.8865 m/s.

Step-by-step explanation:

The measures of the smallest and the largest possible integral lengths of the third side of the triangle is 21 and 1 respectively

What is Triangle?

A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.

A side of a triangle must be always less than or equal to the sum of other two sides and greater than the difference of other two sides.

Say the required side is x.

So x<9+11 and x>9-11

So 20<x<2

So the smallest integer is 21 and the largest integer is 1

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The measures of the smallest and the largest possible integral lengths of the third side of the triangle is 21 and 1 respectively

What is Triangle?

A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.

A side of a triangle must be always less than or equal to the sum of other two sides and greater than the difference between the other two sides.

Say the required side is x.

So x<9+11 and x>9-11

So 20<x<2

So the smallest integer is 21 and the largest integer is 1

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A relationship that has a zero slope include the following: A. A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 2, 2, 2, 2.

In Mathematics, the slope of a linear relationship can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following slope and data points on the line:

Substituting the given data points into the slope formula, we have the following;

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (2 - 2)/(-1 - (-3))

Slope, m = 0/2

Slope, m = 0.

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Answer:

IT IS C!!! ITS RIGHTTTTTTT

The length of the diagonal of the rectangle is 41 units.

To find the length of a diagonal of a rectangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse).

In this case, the rectangle is the right triangle, and the lengths of the two shorter sides are 9 and 40 units. So we can write the equation:

9² + 40² = d²

Expanding both sides:

81 + 1600 = d²

Adding the two sides:

1681 = d²

Taking the square root of both sides:

d = 41 units

So the length of the diagonal of the rectangle is 41 units.

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The length of the diagonal of the rectangle is 41 units.

To find the length of a diagonal of a rectangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse).

In this case, the rectangle is the right triangle, and the lengths of the two shorter sides are 9 and 40 units. So we can write the equation:

9² + 40² = d²

Expanding both sides:

81 + 1600 = d²

Adding the two sides:

1681 = d²

Taking the square root of both sides:

d = 41 units

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Thus, the response is: B) The pavement becomes the new surface (and Earth).

The law of conservation of momentum states that an object's momentum may only be transferred, not created or destroyed, and is equal to its mass times its velocity.

The momentum the car (and its contents) had before braking must go somewhere when it skids to a halt. The friction force between the tyres and the road in this instance causes it to be transferred to the pavement (and Earth). The friction force slows the car down until it comes to a stop by acting in the opposite direction of the car's speed.

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A contradiction in logic that arises when assertions of the form "This statement is false" are taken into account. If a statement is untrue, it is true if it is true; the opposite is true if a statement is false.

What is the paradox theory?

Ontologies of dualism, which consist of two seemingly incompatible components that when combined create a dynamic unity and continual change, are the basis of the paradox theory.

                      According to academic definitions, a paradox is a set of tensions that are at odds with one another, dependent upon one another, and persistent.

What is an example of a paradox?

Despite the fact that all creatures are equal, some are more equal than others. The pigs in George Orwell's Animal Farm came up with this saying, which they later used.

                         This claim is contradictory since no two things can be equally equal to one another.

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The number of students is the cost of the trip the same at each museum is 25

When we write expressions for the total cost of each field visit and set them equal, we find the solution to be the ratio of the difference in fixed cost to the difference in variable cost.

 y = 75 +7x . . . . . cost for x students to visit the science center

 y = 50 +8x . . . . cost for x students to visit the natural history museum

Subtracting the first equation from the second, we get

 0 = -25 +x

 25 = x . . . . . add 25; the number of students such that costs are equal

The cost will be the same either place for 25 students.

Here, the fixed cost difference is 75-50=25, and the variable cost difference is 8-7=1. The ratio of these costs is

 $25/($1 /student) = 25 students.

This relationship only holds when the higher fixed cost is associated with the lower variable cost. Charges are such that one place caters to larger numbers of students (science center), and one prefers fewer students (natural history museum).

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Using mathematical expressions, for the cost of the trip to be the same at each museum, the number of students must be 5.

Mathematical expressions combine variables, constants or numbers, and mathematical operators., without the equation or inequality symbols.

                          Science Center   History Museum

Cost per student       $8                           $5

Fixed cost                  $5                         $20

Let the number of students = x

The total cost at the Science Center = 5 + 8x

The total cost at the History Museum = 20 + 5x

For the cost to be the same at either center:

5 + 8x = 20 + 5x

3x = 15

x = 5

Thus, when the number of students attending either museum is 5, the cost is the same.

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Kylie is far from luthor by 20 feet.

What is pythagoras theorem?

The Pythagorean Theorem, often known as Pythagoras Theorem, is a crucial concept in mathematics that describes how the sides of a right-angled triangle relate to one another. Pythagorean triples are another name for the sides of the right triangle.

We have these segment lengths of 12 feet and 16 feet.

The goal is to find the length between kylie and luthore, . This is the hypotenuse of the right triangle.

Use the pythagorean theorem to get the following:

12²+16²=hypo²

144+256=hypo²

400=hypo²

hypo=[tex]\sqrt{400}[/tex]

hypo=20 feet .

kylie is far from luthor by 20 feet.

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The trigonometric ratios are

tan J = (10√35 / 37 )

cot J = 37/ (10√35)

What is the trigonometric ratio?

Trigonometric ratios are the ratios of a right triangle's sides. The sine (sin), cosine (cos), and tangent (tan) are three often used trigonometric ratios. There are other trigonometric ratios which are reciprocals of these ratios.

Sin J =opposite/hypotenuse

Sin J  = √35/ 7

=> J = sin^-1( √35/ 7 )

=> J= 57.68 degrees

tan J = opposite/adjacent = √35/IJ

=> tan (57.68) = √35/IJ  

=> 1.5806 = √35/IJ  

=> IJ = √35 / 1.5806 = 3.74

=> IJ = 37/10

tan J =  √35 / (37/10 ) = (10√35 / 37 )

cot J = 1/tan J = 1/(10√35 / 37 ) = 37/ (10√35)

The trigonometric ratios are

tan J = (10√35 / 37 )

cot J = 37/ (10√35)

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The inequality equation is -4 < x < 6

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the modulus function be represented as A

Now , the equation will be

| x - 1 | < 5   be equation (1)

Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.The value of the modulus function is always non-negative.

So , -5 < x - 1 < 5

On simplifying the equation , we get

Adding 1 on both sides of the equation , we get

-5 + 1 < x - 1 + 1 < 5 + 1

-4 < x < 6

Hence , the number line will denote the inequality having x more than -4 and less than 6

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The wide of the street from building a to building b is 18.32m

The Pythagoras theorem states that if a triangle is right-angled then the square of the hypotenuse is equal to the sum of the squares of the other two sides.

The three sides of a triangle are collectively called Pythagoras triples.

The formula is measured as:

c²= a²+ b²

Where

'c' = hypotenuse of the right triangle

'a' and 'b' are the other two legs.

First, let's consider △ADC,

AD²+AC²=CD²

12²+AC²=16²

AC²=256−144

AC=10.58 m

Again consider △BEC,

EC²=BC²+BE²

16²=14²+BC²

256−196=BC²

BC=7.745m

Width of the road= AC+BC = 10.58+7.74=18.32m

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Answer:

Simon used the distributive property to get from step 3 to step 4. This is because in step 3, he multiplied both sides of the equation by -8, which is an example of the distributive property.

Step-by-step explanation:

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The equation for d, the distance in meters that Martin covers per second, is d × 15 = 100

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Martin runs 100 meters in 15 seconds, we need to find the equation for d, the distance in meters that Martin covers per second

Since, Martin run 100 m in 15 sec

Therefore,

In 1 sec = 100 / 15

Therefore, d = 100 / 15

d × 15 = 100

Hence, the equation for d, the distance in meters that Martin covers per second is d × 15 = 100

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. side is inches long, side is inches

long,and side is inches long

Here is the complete question. Please find

attached a diagram showing the scaled and real

drawing

Use the given and the of

the scale drawing to determine the side lengths

of the real object

. side a is 7 inches long, side b is 6 inches

long,and side c is 3 inches long

. side a is 30 inches long, side b is 25 inches

long, and side c is 20 inches long

. side a is 40 inches long, side b is 35 inches

long,and side c is 20 inches long

. side a is 175 inches long,side b is 150 inches

long, and side c is inches long

A scale drawing is a reduced form in terms of

of an original image / building / object

the scale drawing is usually reduced at a constant

dimension

= original dimensions /

dimensions of the scale drawing

The scaled drawing is an enlarged image of the

original triangle.

It is enlarged at a ratio of :

original dimensions

a = 35/5 =

b = 30/5=

c = 15/5 =

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The side lengths of the real object will be 175 in, 150 in, and 75 in, respectively.

To determine the side lengths of the real object, we need to use the given scale factor and the side lengths of the scale drawing. The scale factor given is 5:1, which tells us that the scale drawing is 5 times smaller than the real object. Therefore, we can use this ratio to determine the side lengths of the real object. For example, if the side length of the scale drawing is 35 in, then the side length of the real object will be 5 times larger, which is 175 in. We can use this same ratio for the other side lengths of the scale drawing. The side length of the scale drawing is 30 in, so the side length of the real object will be 150 in. The side length of the scale drawing is 15 in, so the side length of the real object will be 75 in. Therefore, the side lengths of the real object will be 175 in, 150 in, and 75 in, respectively.

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The confidence interval can be expressed as (27.4%, 38.0%).

This confidence interval can be calculated using the formula (X ± z*σ/√n), where X is the sample mean, z is the z-score that corresponds to the desired confidence level (in this case, 95%), σ is the population standard deviation, and n is the sample size.

This is calculated using the formula:

lower bound = point estimate - margin of error and

upper bound = point estimate + margin of error.

In this case, the point estimate is 33.2% and the margin of error is 5.8%.

Therefore, lower bound = 33.2% - 5.8% = 27.4% and

upper bound = 33.2% + 5.8% = 38.0%.

This means that we are 95% confidence interval that the true population proportion lies between 27.4% and 38.0%.

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The equation for the number of bouquets is 12B = 75 - 3 and the number of bouquets is 6.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a florist has 75 tulips with which to make bouquets. She will use 12 tulips in each bouquet. If the florist ends up with 3 tulips left.

The equation can be written as:-

12B = 75 - 3

12B = 72

B = 72 / 12

B = 6

Hence, the number of bouquets is 6, and the equation for the number of bouquets is 12B = 75 - 3.

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