consider a circle of radius 2 centered at the origin. find parameterizations of this curve under the following assumption. clearly state any restriction on the variable of parametrization

The integral of k*f(x) equals the integral of f(x) multiplied by k because the total of k*f(x) equals the sum of f(x) multiplied by k.

K*F(x) Integral = K*Fintegral (x). This is inferred from the description of a definite integral as the upper limit of a term sum. The area under the curve can be divided into a number of rectangles and their areas added if we are taking the integral of a function from a to b. The integral then equals the maximum value of this total. The result is identical to the original sum increased by k if we multiply each term of the sum by a constant called k. as a result, the maximum allowed f(x) multiplied by k because the total of k*f(x) equals the sum of f(x) multiplied by k.

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The correct orientation and location of triangle DEF is option B (as shown in the attachment to this answer).

Rotation is one of the types of solid transformation which involves turning a given object about a reference point or line at a certain required measure of angle. Other types of transformation are: dilation, translation and reflection.

Dilation: This is a process in which the dimensions of an object is either increased or decreased to produce its image.

Translation: This is a procedure that requires moving a given object a number of units in a specified direction.

Reflection: This requires flipping an object over a line to produce an image.

In the question, after rotating triangle ABC 90^o clockwise; the correct orientation and location of triangle DEF is option B.

A sketch of this is attached to this answer for clarity.

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Answer: x^3+3x^2+22x+66+234/x-3

Step-by-step explanation: I used synthetic division and this is what I got hope this helps

The ratio of rubies to diamonds is equal to 1:4.

In Mathematics, a ratio simply refers to a mathematical expression that is typically used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

In this scenario, we would assign variables to the number of rubies and number of diamonds as follows;

Since the number of rubies is four (4) times the number of diamonds, this can be represented as a ratio as follows;

R = 4D ⇒ R:D = 1:4.

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Answer:

6 divided by 2/3 = 9

Step-by-step explanation:

because it is mathematically correct (can check via calculator)

and the question includes the fact that S cut the rope into 9 sections from 6.

To the function u=I+6, for the output 20 input is 14.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

For the table 2, the rule is u=I+6

For output u=14, we get

14=I+6

I=8 (Input)

For output u=28, we get

28=I+6

I=22 (Input)

For input I=24, we get

u=24+6

u=30 (Output)

For output u=16

16=I+6

I=10 (Input)

For output u=20

20=I+6

I=14 (Input)

For input I=48

u=48+6

u=54 (Output)

Therefore, to the function u=I+6, for the output 20 input is 14.

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The number of arrivals who came in each day while this particular widget shop was open. Therefore, statement 2 is correct.

The process by which a sample of observations is selected from a population to assume the population is known as random sampling. This process ensures that the results we get from your sample should be close to what we would have gotten if we measured the complete population. So that all the units in the population have an equal chance of being chosen using the simplest random sample.

In the given scenario, the number of arrivals each day for the widget store should have equal chance. To be specific, we should only take into account the number of visitors on the days when the store is open.

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The dimension of the largest possible rectangular area that can be fenced for $4800 is 300 yard × 150 yard. The area, A of the rectangle as a function of its width, w is A = 300w - 1.5w².

Let the width of the rectangular area be "w" and its length be "l".

The cost of the east-west direction fencing is

2w * 12 = 24w

and the cost of the north-south direction fencing is

2l * 8 = 16l

Since the rancher wants to spend exactly $4800 on fencing, we can write an equation to represent the cost:

24w + 16l = 4800

Divide by 8

3w + 2l = 600

Therefore, l = 300 - 1.5w

The area of the rectangle is given by "lw", so

A = lw

Substituting the value of "l" from the first equation into this second equation:

A = (300 - 1.5w)w

A = 300w - 1.5w²

Thus, the area of the rectangle is a function of its width and can be expressed as Area = 300w - 1.5w².

To find value of w with maximum area, dA/ dw = 0

300 - 3w = 0

w = 100

Therefore, l = 300 - 1.5*100

l = 150

--The question is incomplete, answering to the question below--

"A rancher who wishes to fence off a rectangular area finds that the fencing in the east-west direction will require extra reinforcement due to strong prevailing winds. Because of this, the cost of fencing in the east-west direction will be $12 per (linear) yard, as opposed to a cost of $8 per yard for fencing in the north-south direction. Find the dimensions of the largest possible rectangular area that can be fenced for $4800, express the area of the rectangle as a function of its width."

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Whatever 18x+1 equals is what it equals

The exact length (in inches) of the arc of a circle formed by given angle (in radians) and radius  is 5.233 inches.

The radius of a circle and the central angle determine the length of an arc. We are aware that given an angle of 360 degrees, the arc length corresponds to the circumference. Thus, the arc length is determined by multiplying the radius by the Centre angle (in radians).

Arc length = radius x angle(in radians)

Radius = 2 inches

Angle = 5pi/6 radians

Arc length = 2 x (5pi/6)

                = 5.233

Hence, the arc length is 5.233 inches.

Correct question :

find the exact length (in inches) of the arc of a circle formed by an angle that measures 5pi/6 radians if the circle has radius 2 inches. (round you answer to two decimal places.)

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Answer:

No, these ratios are not equivalent.

Step-by-step explanation:

The value of x is 10.79

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

sin (tetha) = opp/ hyp

cos ( tetha) = adj/ hyp

tan ( tetha) = opp/ adj

tetha = 26

hyp = 12

adj = x

cos 26 = x/12

cos 26 × 12 = x

x = 0.899 × 12

x= 10.79

Therefore the value if x is 10.79

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Answer:

how would i know the closing price ...

The value of the expression 14.5 * 35 is 507.5

From the question, we have the following parameters that can be used in our computation:

14.5 * 35

The given expression is a simple expression that can be solved using a calculator

Using a calculator, we have the following solution

14.5 * 35 = 507.5

Hence, the solution is 507.5

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hash functions are mathematical functions that create a hash value, also known as a message digest, by converting variable-length messages into a single fixed-length value.

A hash function converts a given numeric or alphanumeric key into a practical and controllable integer value. The mapped integer value acts as an index in the hash table.

A hash function, in its simplest form, converts a significant number or string into a tiny integer that can be used as the index in the hash table. The pair has the form (key, value), and one can find a value for a given key by using a "function" that converts keys to values.

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By  polynomial equation, 7i , −7i this we get  1, y = x²  + 49 .

The x-axis and the graph's intersection points, or the places where y = 0, are known as the roots.

The roots of y equal 0

By figuring out what x is when x ( 7 I ) = y and y = 0 we can find the root at x = 7 i.

x 7 I is the factor.

By determining the value of x at the point where x ( 7 I ) = y and y = 0, the root at x = 7 I was discovered.

x + 7 I is the factor.

One equation can be created by combining all the variables.

y = ( x − 7 i ) ( x + 7 i)

To make the equation y = (x 7 I (x + 7 I easier to understand, multiply all the elements.

Use the FOIL Method to extend (x 7 I ) (x + 7 I

Put the distributive property to use.

y =  x ( x + 7 i ) − 7 i ( x + 7 i )

Put the distributive property to use.

y = x ⋅ x + x ( 7 i ) − 7 i ( x + 7 i )

Put the distributive property to use.

y = x ⋅ x + x ( 7 i ) − 7 i x − 7 i ( 7 i )

Clarify terminology.

x x + x ( 7 I ) x 7 I x ( 7 I ) is the result of combining the opposing terms.

y = x x + 7 I x + 7 I x 7 I ( 7 I ) Rearrange the elements in the terms x ( 7 I ) and 7 I x.

To get y = x x + 0 7 I ( 7 I ), subtract 7 I x from 7 I x.

y = x x 7 I ( 7 I ) is the result of adding x x and 0.

Condense each phrase.

Divide x by x to get y: x 2 7 I (7 I

7 I ( 7 I times itself..

Calculate y = x 2 49 I I by multiplying 7 by 7.

Raising I to the power of 1, y = x²- 49 ( I I

I must be raised to the strength of

1 . y = x 2 − 49 ( i i )

Raise I to the power of 1 and then find y as y = x 2 49 ( I I )

When combining exponents, use the power rule a m a n = a m + n.

y = x ² − 49 i1 + 1

To get y = x ²-  49 I ² ,add 1 and 1.

I ² should be rewritten as 1; y = x ² -  49. -  1

y = x ² + 49 multiplied by 49 by 1.

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Dion will make $16381.2 in a year.

What is simple interest?

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,

The formula for simple interest is:

S = p*t*r/100

where P is the principal amount of money, R is the interest rate as a decimal, T is the time.

Dion gave $12, 848 to his local church

which he calculated as 27.5 % of his yearly salary.

S = 12, 848 * 1*27.5 /100 = 3533.2

Total = 3533.2+12, 848 = $16381.2

Hence Dion will make $16381.2 in a year.

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In a case whereby One number is 11 less than another ,If their sum is increased by eight, the result is 81 the numbers will be 42.

The concept that will be used here is summation. A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There are always an even number of terms in a summation. There could be only two terms, or there could be one hundred, thousand, or a million. There are summations with an infinite number of terms.

Let the first number be wriiten as = x

second number = x-11

The we can add up as :

(x + x -11 + 8) =81

2x -3 =81

2x =84

x = 42

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Answer:  To find the surface area of the figure, we need to add up the areas of all the individual faces. The triangular prism has three rectangular faces and three triangular faces, and the rectangular prism has six rectangular faces.

The triangular prism:

The area of one of the rectangular faces is (x * z)/2 = (5 * 8.75)/2 = 21.875 inches^2

The area of one of the triangular faces is (x * W)/2 = (5 * 6.2)/2 = 15.5 inches^2

The rectangular prism:

The area of one of the rectangular faces is x * y = 5 * 20 = 100 inches^2

So, the total surface area of the figure is

(3 * 21.875) + (3 * 15.5) + (6 * 100) = 65.625 + 46.5 + 600 = 712.125 inches^2

So the surface area of the figure is 712.125 inches^2

Step-by-step explanation:

To find the football field's area in square yards, we need to multiply the length by the width, both of which are given in different units of measurement (yards and feet).

Steps:

1. Convert the width of the field from feet to yards: 160 feet / 3 feet/yard = 53.33 yards

2. Multiply the length and width of the field to find its area: 100 yards * 53.33 yards = 5,333 square yards. Therefore, the area of the football field is 5333.33 square yards.

The room is square since the length and range of the room are the same. Hence, we can apply the area of the square formula to cipher the area of the given carpet demanded to cover the room. Hence, the answer is 16 square yards.

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The area of the field in square yards will be 16 sq. yards.

To calculate the size of a football field in square yards, multiply the length by the width, which are both given in separate units of measurement (yards and feet).

First, we'll convert the field's width from feet to square yards.

There are 3 feet in 1 yard,

So 160 feet is the same as 160 / 3 = 53.333 yards.

Then we'll multiply the length by the width: 100 * 53.333 = 5333.33 square yards.

Therefore, the area of the football field is 5333.33 square yards.

The room is square since its length and width are equal.

As a result, we can use the area of the square formula to calculate the area of the provided carpet required to cover the room.

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The measure of angle K and L in the first figure is ∠L = 23 degrees and ∠K = 157. Second figure, the measure of ∠K = ∠L = 70 degrees.

A polygon's interior angle is the angle created between its two adjacent sides. Alternately, we may state that the internal angle of a polygon refers to the angle measured at the interior portion of a polygon.

For figure 2 the two lines are parallel to each other, and the line that meets the parallel line at points at M and L are from two equal lines.

Hence, the angle suspended by both are equal, that is:

∠L = ∠M

∠L = 23 degrees.

Now, the ∠K and ∠J are created by two parallel lines; hence they are equal:

∠K = ∠J = x

The sum of interior angles of a quadrilateral is 360, so:

∠L + ∠M + ∠J + ∠K = 360

23 + 23 + x + x = 360

46 + 2x = 360

2x = 360 - 46

x = 157

Hence, the measure of angle K and L is 157 and 23 respectively.

For the second figure, the angle K and L are created by equal length of segments.

∠K = ∠L = x

The sum of interior angles of a quadrilateral is 360, so:

∠L + ∠M + ∠J + ∠K = 360

x + 90 + 130 + x = 360

2x + 220 = 360

2x= 360 - 220

x = 70

Hence, the angle of K and L is 70 degrees.

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The statement is true about the home appliances sales is "Home appliances sales increased profits by 8 percentage points".

Given that ,

The right answer is that 90% of all random samples of 50 students from this high school would produce a 90% confidence interval that contains the actual mean amount of money students spend on lunch.

an appliance store manager noted that the sales of home appliances contributed

74 % of the store profits in the year 2010, and 82 % in the year 2011.

Thus, the profit in the year 2010 is 74 %.

The profit in the year 2011 is 82 %.

The increased profit from year 2010 to 2011 is ( 82-74 ) % = 8%

Hence, the statement true about the home appliances sales is "Home appliances sales increased profits by 8 percentage points".

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The value of sin(0) should be considered as the  [tex]\frac{\sqrt5}{5}[/tex] in second quadrant.

The values of all trigonometric functions' dependent on the value of the ratio of sides of a right-angled triangle are known as trigonometric ratios. The trigonometric ratios of a right-angled triangle's sides about any of its acute angles are known as that angle's trigonometric ratios.

Calculation of the value of sin(0):

Since the equation is [tex]cos(o)=\frac{-2\sqrt{5}}{5}[/tex]

by the Pythagorean theorem -

[tex]h^2=p^2+b^2[/tex]

value of perpendicular is = [tex]\sqrt5[/tex].

The trigonometry ratios for a specific angle ‘θ’ is given below:

Trigonometric Ratios:

Sin θ = Perpendicular/Hypotenuse

Cos θ = Base/Hypotenuse

Also in the case when 0 is an angle in quadrant II

So based on this, we can say that value of sin(0) should be considered

as the    [tex]\frac{\sqrt5}{5}[/tex].

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Event A has the highest probability, which is "at least one 6 appears when 6 fair dice are rolled.

Event A: At least one 6 appears when 6 fair dice are rolled has the highest probability. The probability of rolling at least one 6 with a fair die is 5/6, and the probability of rolling at least one 6 with 6 fair dice is (5/6)^6.

Event B: At least two 6's appear when 12 fair dice are rolled has a lower probability than A.

Event C: At least three 6's appear when 18 fair dice are rolled has a lower probability than B.

So among these three events, this is event A with the highest probability.

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Answer:

9 cm

Step-by-step explanation:

cos B = adj/hyp

cos B = BC/AB

cos 25° = 8 m / AB

AB = 8 m / cos 25°

AB = 9 cm

You can only convert 1/6 to a decimal probability and round to 2 decimal places if you include the percentage sign (%) at the end.

When converting fractions to decimal probabilities, it is important to include the percentage sign (%) at the end. This is because when converting a fraction to a decimal, the result is not a whole number, but a decimal probability. For example, 1/6 can be written as a decimal probability of 0.17, but it is usually written as 0.17% to indicate the probability of an event occurring. The percentage sign is essential for students to understand that the decimal is a probability, rather than an incorrect answer. Percentage sign also allows the decimal to be rounded to two decimal places, giving a more precise answer. Without the percentage sign, the decimal will appear to be a whole number, which is not the correct answer.

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The number of hours that Alonso would have to work to earn $ 554. 40, given the same hourly wage, is 37.9 hours

To find the number of hours that Alonso needs to work in the week to make $ 554. 40, you first need to find the hourly wage :

= Amount earned / Hours worked

= 204. 40 / 14

= $ 14. 60 per hour

If Alonso wants to earn $ 554 .40 then the number of hours he would need to work is:

= Amount to be earned / Hourly wage

= 554. 40 / 14. 60

= 37.9 hours

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A possible equation to express the situation described is 2x + 4y = 110.

The word equation can be defined as a mathematical expression that uses numbers, symbols, and even letters to mathematically represent a situation.

Consider the variables:

Now relate these variables using letters and symbols

2x (number of tables that can fit two people) + 4y (number of tables that can fit four people) = 110

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If an oil change at city auto is regularly $30 Mr. Allen has a coupon for 15% off. The  equation that can be used to find the sale price, S, of an oil change is: 3. s=0.85(30).

First step is to find the percentage left if he has a coupon for 15% off.

Percentage left = ( 1- 0.15)

Percentage left  = 0.85 or 85%

Now let find the sales price

Sales price = 0.85(30)

Sales price = $25.50

Therefore the  equation that can be used to find the sale price, S, of an oil change is: 3. s=0.85(30).

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The complete question is:

An oil change at city auto is regularly $30 Mr. Allen has a coupon for 15% off. Which equation can be used to find the sale price, S, of an oil change?

1. s=0.85 divided by 30

2. s=85 divided by 30

3. s=0.85(30)

4. s=85•30

The exponential function [tex]Y=21{(1.44)}^x[/tex] represents growth when x ∈ N.

The formula for exponential growth is [tex]y = y_0.e^{(kt)}.[/tex]

The formula for exponential decay is [tex]y = y_0.e^{(-kt)}.[/tex].

Given, An exponential function [tex]Y=21{(1.44)}^x[/tex].

Now, This function can represent growth or decay depending upon the values of 'x'.

If x ∈ N, Then this exponential function [tex]Y=21{(1.44)}^x[/tex] represents growth.

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