An arc is 70.7 meters long and is intercepted by a central angle 5pi/4 radians. Find the diameter of the circle

The value of h in terms of x when the volume of cylinder is equal to that of cone is h = 6x²

Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface. The unit of volume is in cubic units such as m3, cm3, in3 etc. Sometimes, volume is also termed capacity.

The volume of a cone is linked to the volume of a cylinder. A cone is one third of the volume of a cylinder. The volume of a cone is ¹/₃ × π × r² × l. To calculate the volume we multiply these values together.

The volume of cylinder = πr²h

and volume of cone = 1/3 πr²h

since the volume of the cone and cylinder are equal

πr²h = 1/3 πr²h

r in cylinder = x cm and h is 2x

r in cone = x cm

therefore πx²×2x = 1/3πxh

divide both side by πx

π2x³/πx = h/3

2x² = h/3

therefore h = 3×2x²

h = 6x²

therefore the value of h in terms of x is h = 6x²

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Answer:

A. False

B. False

C. False

D. False

E. False

Explanation:

A. The ratio of the number of gallons of red paint to the number of gallons of blue paint in shade B is 2:1, but this statement only holds true for the first set of values provided.

B. The statement is not true since the table does not provide information about the proportion of blue to red paint in shade A or B.

C. The statement is not true since the table does not provide information about the proportion of blue to red paint in shade A or B.

D. The statement is not true since the table does not provide information about the proportion of blue to red paint in shade A or B.

E. The statement is not true since there's no information about how the shade A is made.

Step-by-step explanation:

The equation 2 2r 8 3r 16 is a linear equation in two variables (r and 3r).

To solve for r, we can use the method of elimination. First, we subtract the second equation from the first equation:

2 2r 8 3r 16

-2 2r 8 3r 16

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

0 0 0

Since the equation is now equal to 0, this means that r is equal to 0. We can confirm this by substituting 0 in for r in both equations:

2 2(0) 8 3(0) 16

2(0) 8(0) 16

0 0 16

Since 0 = 16 is not true, this confirms that r = 0.

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Answer:

2.1

Step-by-step explanation:

σ total ^ 2 = σ randi ^2 + σ leah ^2 = 1.1^2 + 1.8^2 = 4.45

σ total = √4.45 = 2.1

Randi and Leah can expect the total number of hours spent studying to vary by approximately 2.1 hours from the mean.

The correct option is C.

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.

Given:

Randi and Leah are studying together for an exam.

Let X represent the number of hours Randi spends studying nightly, and let y represent the number of hours Leah spends studying nightly.

The mean of X is 4.5 hours with a standard deviation of 1.1 hours, and the mean of Y is 3.7 hours with a standard deviation of 1.8 hours.

Assuming these are independent random variables,

S = X + Y

σ²  = σ²(Randi)² + σ²(Leah)

    = (1.1)² + (1.8)²

    =√(4.45)

σ  = 2.1

Therefore, the sum is 2.1.

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Answer:

16 logs

because if 4 logs are burned  in 2 hours then in 8 hours it would be 16 because 2hrs times 4 is 8 hours

you do the same to the logs which is 4 x 4

then u get 16

hope this helps!

It is possible to construct a triangle whose sides are 2 cm 3 cm and 4 cm because the sum of two sides are greater than the third sides.

In the given question, we have to check that it is possible to construct a triangle whose sides are 2 cm 3 cm and 4 cm.

To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always greater than the third side.

To check this we firstly add the 2 and 3

2 + 3 > 4

5 > 4

Now we add 2 and 4

2 + 4 > 3

6 > 3

Now we add 3 and 4

4 + 3 > 2

7 > 2

It is possible to construct a triangle whose sides are 2 cm 3 cm and 4 cm because the sum of two sides are greater than the third sides.

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Answer:

y=8x+5

Step-by-step explanation:

y=mx+b is slope intercept form

m stands for Slope = 8

b is y intercept = +5

plug it in and you get y=8x+5

By dividing the width and height by the dpi, one may get the pixel size. Additionally, a digital camera will have pixel dimensions, which are the sum of its resolution's horizontal and vertical pixel counts (e.g., 2,048 by 3,072), this is the formula to calculate pixel.

The smallest component of a visual display or digital image is a pixel, also known as a picture element. A grid of pixels is used to create computer screens. Red, blue, and green illumination components make up each pixel, which may produce millions of distinct colors by combining them in various ways and at various intensities.

For instance, a computer with a display resolution of 1280 x 768 will create up to 98,3040 pixels on a display screen. The number of pixels per inch of the monitor screen affects image quality; more pixels per inch produce better images.

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Therefore , the solution of the given problem of combination comes out to be 6,500,000.

Combinations are mathematical operations that count the variety of configurations that can be made from a set of objects, where the direction of the selection is irrelevant. You can choose any combination of the components in any order. Combinations and permutations can be confused.

Here,

Berry, we'd like to estimate the amount of potential student IDs.

among the available figures are;

Ten numbers: 0 1 2 3 4 5 6 7 8

26 alphabets, as well

There are 10 options for the first digit.

Ten alternatives for the second digits

Three digits, 10 options

10 options for the fourth digit

26 options for the first alphabet

Second Alphabet: There are 25 options available if we choose all the other alphabets outside the one we first chose.

the number of potential student IDs will therefore be;

=>10 * 10 * 10 * 10 * 25 * 26 = 6,500,000

Therefore , the solution of the given problem of combination comes out to be 6,500,000.

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Answer:

The first number is 4, the second is 3

Step-by-step explanation:

We can make 2 equations, let x be the first number, and y be the second number.

x = 3y - 5

4x - 2y = 10

We sub x = 3y - 5

=> 4(3y - 5) - 2y = 10

=> 12y - 20 - 2y = 10

=> 10y - 20 = 10

=> 10y = 30

=> y = 3

Sub y = 3 into x = 3y - 5

x = 3(3) - 5

x = 4

Therefore, the first number is 4, and the second is 3

Therefore , the solution of the given problem of tables comes out to be  to recall multiplication tables without just repeating the numbers is by using skip counting.

A mathematical list is a list of numbers that represents the results of a calculation with several inputs. organized in rows and columns, data consists of numbers and descriptions. It is simple to recall the table and the 10 pattern. 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30 are the numerals in numerical order. Value mapping are used to illustrate the connections between various data elements.

Here,

One of the most effective techniques to recall multiplication tables without just repeating the numbers is by using skip counting.

When counting by skips, you always start with the integer you're counting by and keep adding it.

For instance, if you skip count by 2, you would get 2, 4, 6, 8, 10, etcetera.

Therefore , the solution of the given problem of tables comes out to be  to recall multiplication tables without just repeating the numbers is by using skip counting.

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The expression that gives the town's population 555 years from now can be calculated using the following formula:

Population (t) = Population (0)×[tex](1+growth rate)^{t}[/tex]

Where t is the time period, in this case 555 years, Population (0) is the initial population, and Growth Rate is the rate of growth, in this case 2.3%.

Plugging in the values, the expression giving the town's population 555 years from now is:

990099009900 × [tex](1+0.023)^{555}[/tex]

This expression gives a population of 236793241036.6 people, which is the estimated population of the town of Springfield, USA 555 years from now.

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On solving the provided question we can say that the radius of circle is 2.1415 cm.

Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. At every angle, it is also rotationally symmetric about the center. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.

We know, Central angle (θ) = (length arc)/radius ….(1)

Convert angle in radian:

Angle in radians = Angle in degrees x π/180° = 197° x π/180 = 1.09

From (1),

Radius = (length arc)/Central angle

= 8/3.1415 =2.1415cm

Therefore radius is 2.1415 cm.

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There are infinitely many solutions and thus infinitely many values for x and y in the first system of equations. There are no solution for the second system of equations.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side

The first system of equations are,

y = 1/2 x + 1

-2x + 4y = 4

Multiplying throughout the first equation by 4, we get

4y = 2x + 4

and the second equation is 4y = 2x + 4

Both the equations are same and so the lines coincide.

They have infinitely many solutions.

The second system of equations are,

y = -x - 3

y + x = 2 ⇒ y = -x + 2

Both are in the form of y = mx +c, which is the equation of the line in slope intercept form.

Here m is the slope.

Given lines have the coefficient of x same, and so slopes are same.

So the lines are parallel.

Two parallel lines does not have a solution.

Hence the first system of equations have infinitely many solutions and second system of equations does not have any solution.

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The ratio of a circle can be found through the formula A = πr2, where A is the area of the circle and r is the radius of the circle.

To find the ratio of a circle, you must first calculate the area of the circle. To calculate the area, multiply the value of π (3.14159) by the square of the radius (r2). For example, if the radius of the circle is 4, the area of the circle would be 3.14159 x 42, which is equal to 50.2653. The ratio of a given circle can then be found by dividing the area of the circle (50.2653) by the square of the radius (42), which gives 1.273.

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The majority of the data is split to the right and left of the mean.

The data is mostly divided to the right and left of the mean. The normal distribution is symmetric and continuous. Positively skewed data will have a higher mean than the median. If the data distribution is tilted to the left, the mean is less than the median, which is frequently less than the mode. A probability function that defines how the values of a variable are distributed is known as the normal distribution. The mean, median, and mode values in a normal distribution are all equal. So, in the context of a normal distribution curve, point (ii) is valid.

Here,

The data is mostly divided to the right and left of the mean. The normal distribution is symmetric and continuous. Positively skewed data will have a higher mean than the median.

The data is mostly divided to the right and left of the mean.

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On solving the provided question, we can say that - There exist 333 integers smaller than 1000 that are evenly divisibility test by 3 if you divide 1000 by 3, which results in 333 with a residual of 1.

The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.

here,

1000/3

remainder = 1

divisor = 333

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On solving the provided question, we can say that in the rectangle L = 6 units and B = 2 units, Perimeter, P = 2(L+B) => P = 2(6+2) => P = 16 units

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

here,

in the rectangle

L = 6 units

B = 2 units

Perimeter, P = 2(L+B)

P = 2(6+2)

P = 16 units

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Both aviv and marco were correct about the expression

given that

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context. Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Many authors distinguish an expression from a formula, the former denoting a mathematical object, and the latter denoting a statement about mathematical objects

Aviv and Marco were trying to describe the parts of the expression 5a/2a+3.

Aviv said, "The entire expression is the quotient of 5a and 2a+3"

Marco said, "On it's own, 2a+3 is a sum with 2 terms."

now , we need to find who is correct

according to aviv The expression 5a/2a+3 is the quotient of the terms as it can be written as 5a ÷ ( 2a+3 ).

according to marco the expression 2a+3 is sum of two terms

Therefore both aviv and marco are correct

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Mark the sides BC and DF as congruent.

A triangle in geometry is a three-sided polygon with three edges and three vertices.

The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic.

This characteristic is known as the triangle's angle sum property.

If ABC is a triangle, it is written as ABC, where A, B, and C represent the triangle's vertices.

In Euclidean geometry, a triangle is a two-dimensional shape that is represented by three non-collinear points in a single plane.

A closed, two-dimensional shape is a triangle. It is a polygon with three sides. Straight lines make up all of the sides.

The vertex is the intersection of two straight lines. The triangle therefore has three vertices.

According to our question-

We are given a side and an adjacent angle, and we must figure out which side or angle is needed in order for SAS to provide proof.

SAS stands for side-angle-side and calls for the congruency of two sides and the included angle on both triangles.

The side of the designated angle B and D that is missing is as follows:

side DF or BC.

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The simple interest earned by Edin after 3 years is $45.

The formula for the simple interest is-

SI = PRT/100

The interest which would be earned in 3 years:

SI = 300*5*3 / 100

SI = 45

Thus, the interest earned by Edin after 3 years is $45.

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Answer:

its c

Step-by-step explanation:

2 x 12= 24, 3 x 8=24 and 4 x 6=24

A chord is the line segment that the two points determine, i.e., the interval on the secant with the two points as its ends.

In the plane, a circle is created by each point that is a specific distance from another point (center). Therefore, it is a curve made up of points that are spaced out from one another in the plane in a fixed manner. It rotates symmetrically around the center at all angles. Every pair of points in the plane of a circle, which is a closed two-dimensional object, are evenly distanced from the "center." Specular symmetry is produced by a line that traverses the circle. It rotates symmetrically around the center at all angles.

given

The Latin verb secare, which means to cut, is where the word secant originates.

A secant crosses a circle at precisely two points in the case of a circle. A chord is the line segment that the two points determine, i.e., the interval on the secant with the two points as its ends.

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The correct option for the area of the circle is B. 3,419.46 cm².

The area of a circle is π multiplied by the square of the radius. The area of a circle(A) when the radius 'r' is given is πr².

Area of circle = πr²

π = 3.14

radius = diameter/2

radius of the circle = 66 cm/2

radius of the circle = 33 cm

Area of the circle = 3.14 × (33 cm)²

Area of the circle = 3.14 × 1089 cm²

Area of the circle = 3419.46 cm²

Therefore, the area of the circle measured by Jon and Becky is equal to 3,419.46 cm².

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For the given quadratic equation, the solutions are x = -3 and x = -3.

What is the completing square method?

The completing the square method is a technique used to solve quadratic equations of the form y = ax² + bx + c. The goal of this method is to convert the equation into the standard form of a quadratic equation, which is y = a(x + h)² + k, where a, h and k are constants.

To solve y = x² + 6x + 8 by completing the square, we need to add and subtract a value to the equation so that the x-term (x² + 6x) is a perfect square. In this case, we need to add and subtract (6/2)² = 9 to the equation, which gives us:

y = x² + 6x + 8

y = (x² + 6x + 9) - 1

Now, we can take the square root of the x-term, which is (x + 3)², and we get:

y = (x + 3)² - 1

The equation is now in the standard form of a quadratic equation, with y = (x + 3)² - 1. We can now solve for x by taking the square root of both sides of the equation and getting x = -3, -3 .

Alternatively, We can also solve for x by factoring the expression inside the square, which would give (x + 3) (x + 3) = 0 and x = -3, -3

Hence, for the given quadratic equation, the solutions are x = -3 and x = -3.

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100% percent of the espressos were single-shot.

What is the percentage?

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios, proportions, and rates. It is denoted by the symbol "%". For example, if you have 25 out of 100 items, you can express this as 25% to represent the proportion of items that you have.

The total number of espressos sold yesterday afternoon was 5. If 5 of them were single-shot, then 100% * 5 / 5 = 100% of the espressos were single-shot.

Hence, 100% percent of the espressos were single-shot.

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y equals the quantity negative 3 times x plus 7 end quantity over 4.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given a linear equation in two variables.

3x+ 4y = 7

We have to find an expression to calculate y from the equation.

Subtracting both sides of the equation with 3x, we get,

3x + 4y - 3x = 7 - 3x

4y = 7 - 3x

Dividing throughout by 4,

4y/4 = (7 - 3x)/4

y = (7 - 3x) / 4

Hence the value of y is the quantity negative 3 times x plus 7 end quantity over 4.

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Answer:

1

Step-by-step explanation:

X= -3-2=-5

y= -2-3=-5

-5/-5=1

The profit of the owner is $2204, if her payment is twice the sum of the

other employees' weekly wages.

A wage is the payment made to employees for the time they put in working for their employer. Always based on a specific period of time, wages are paid. On an hourly basis, typically. This is the origin of the phrase hourly worker. Salary and commissions are some additional types of payment.

Pay for lower level employees is determined by the number of hours worked. To record the number of hours worked each week, these employees typically use a time sheet or time card. To keep track of hourly employee hours, the majority of modern employers use computerised systems.

To enter their hours worked, employees must log in and out of the system. These workers are then paid either weekly or biweekly, depending on the state.

Given that the owner pays herself twice the sum of the other employees' weekly wages.

Sum wage of the employees =  $157.50 + $189.00 + $220.50+ $252.00+ $283.50

= $1102.5

She pays herself twice the sum

2 × $1102

= $2204

Thus, the profit of the owner is $2204.

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