Simplify fully:

Please help!!

by trigonometry the magnitude of the force P so that the resultant force exerted on the stake is vertical. The magnitude of the force is 196.6 N.

When a force system acts on an item, the difference between the forces is referred to as the Resultant force. When an item is under the influence of two or more forces, the combined force may be calculated by adding up the separate forces. The forces in all directions will be the same for all the forces if they are all acting in the same direction. The SI unit for resultant force is the Newton.

Given that,

α = 30°

Using the triangle rule, and the law of sines:

120 N / Sin 30° = P / Sin 25°

or, P =  (Sin 25° /  Sin 30°) × 120

or, P = 101.428 N

or, P = 101.4 N

and also, θ = 180 - 25 - 30

θ = 125°

the value of resultant is:

120 N / Sin 30° = R / Sin 25°

or, R = 196.6 N

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The terms, when sorted into groups of " like terms " gives:

Like terms :

Unlike terms :

To sort a set of algebraic terms into groups of like terms, you must look for terms that have identical variables and exponents. These terms can be combined and simplified using the rules of addition and subtraction. in this scenario, they include: - 7 y ² and y ², 0. 5 kt and - 10 kt, 6 and 9.

Terms that have different variables or exponents are considered unlike terms and cannot be combined in this way. They include : - 4 p and p ², 5 x and 5, 3 ad and 2 bd .

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Answer:

0.5236 radians per minute

or

0.00872665 radians per second

Step-by-step explanation:

Let's first define angular speed

Angular speed is the rate at which an object changes it angles which we measure in radians in a given time. Angular speed has a magnitude (a value only whereas velocity is a vector with speed and direction)

The angular speed, ω of an object is given by the formula
ω = θ/t

where  θ is the angle in radians
1 full revolution is 360° or 2π radians

t = time taken for completing θ radians of rotation

We are given that the Ferris wheel completes 1 full revolution in 12 minutes

1 full revolution = 2π radians

t = 12 minutes

Angular speed = ω = θ/t =  2π/12 radians/minute

ω = 0.5236 radians per minute

or in radians per second

ω = 0.5236/60 = 0.00872665 radians per second

Two triangles having two pairs of congruent sides and a pair of congruent angles do not necessarily meet the SAS congruence criterion, therefore Angie is incorrect.

The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one is congruent to the included angle and corresponding two sides of the other triangle.

An included angle is found between two sides that are under consideration.

In the image, the triangles are congruent to each other by the Side-Angle-Side Congruence Theorem (SAS).

Thus, two triangles having two pairs of corresponding sides and one pair of corresponding angles that are congruent to each other is not enough justification for proving that the two triangles are congruent based on the SAS Congruence Theorem.

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Answer:

The equation of the proportional relationship can be written as y = (2/3)x.

Step-by-step explanation:

This equation is derived by using the fact that the slope of the relationship between x and y is 2/3. The slope of a line can be expressed as the ratio of the change in y to the change in x, which is represented by (delta y) / (delta x).

Since the slope is 2/3, the change in y for a unit change in x can be expressed as 2/3 * x. This relationship can then be written in terms of x and y by solving for y:

y = (2/3) * x.

In this equation, y is directly proportional to x with a constant of proportionality equal to 2/3.

Answer:

Yes, Uncle Sonny is correct.

Step-by-step explanation:

If two figures are related by a dilation, then corresponding lines or line segments in the figures will be congruent. In a dilation, the ratio of the lengths of corresponding lines or line segments remains constant, which means they will have the same length. Therefore, they are congruent.

Answer:

5564+746655754673346

Answer: 1468.17

Step-by-step explanation:

Answer:

modal class is 70 - 79

Step-by-step explanation:

the modal class is the interval which occurs most often

in this case 70 - 79 occurs 6 times

then modal class is 70 - 79

The revenue function (Rx) when x is 1, 4, 8, 12,16, 20 are 72,252,468,432, and 300 respectively.

Revenue function is a formula or equation representing the way in which particular items of income behave when plotted on a graph. For example, the most common revenue function is that for total revenue in the equation y = bx, where y is the total revenue, b is the selling price per unit of sales, and x is the number of units sold.

R(x) = x × P(x)

When x = 1

R(x) = 1(75-3)

R(x) = 72

when x = 4

R(x) = 4( 75-12)

= 252

when x = 12

R(x) = 12(75-36)

R(x) = 468

when x = 16

R(x) = 16( 75-48)

= 432

when x = 20

R(x) = 20( 75-60)

= 300

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Step-by-step explanation:

(n+1)! = (n+1)n(n-1)(n-2)...×3×2

16n! = 16n(n-1)(n-2)...×3×2

16(n-1)! = 16(n-1)(n-2)...×3×2

we can now divide both sides by (n-1)! and get

(n+1)n = 16n + 16

n² + n = 16n + 16

n² - 15n - 16 = 0

1×n² - 15n - 16 = 0

we try to bring this into a form

(n + a)(n - b)

one factor has to contain "-", because we have "-16".

and because -15 = 1 - 16, we see that

a = 1

b = 16

n² - 15n - 16 = (n + 1)(n - 16)

and that is 0, when at least one of the factors is 0, because 0×... = 0.

so, the solutions are

n = -1

n = 16

n = -1 does not make any sense for n!

so, n = 16 is the solution.

Answer:

C = 5x+6

Step-by-step explanation:

one of the properties of triangle is the supplemental angle of B = sum of the other 2 angles

so 11x+1=6x-5+c

C = 5x+6

Answer:

a= 4

Step-by-step explanation:

Rearrange terms

Multiply all terms by the same value to eliminate fraction denominators

Cancel multiplied terms that are in the denominator

Multiply the numbers

than subastraract form both by 25

Simplify the expression

Subtract the numbers

Subtract the numbers

You will find the solution

The correct option on this statistics topic is (c) To determine if a significant X-Y relationship exists.

Statistics is a science and perhaps also the art of learning from data. As a discipline, it deals with the collection, analysis, and interpretation of data, and the effective communication and presentation of data-based results. 

In statistics correlation coefficient is a single number that represents the strength and direction of the relationship between variables.

Different types of correlation coefficients may be appropriate for your data, depending on the measurement level and distribution. Pearson's product-moment correlation coefficient (Pearson's r) is commonly used to assess the linear relationship between two quantitative variables. 

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the total area of the figure will be 53.13 unit square.

The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.

Given a figure that we will transform into three parts A, B, and C as shown in the attached figure

Where A is a semicircle with a radius of 3 unit

b is a triangle with a height of 6 and a base of 3 units

and C is a rectangle with a length of 6 and a width of 5 units

From the general formulas of area,

area of semicircle = pi/2 radius * radius

Area of rectangle = length * width

Area of triangle = 1/2 height * base

in our case,

area of semicircle = pi/2 3* 3

Area of semicircle = 14. 13 unit square

Area of rectangle = 6* 5

Area of rectangle = 30 unit square

Area of triangle = 1/2 6* 3

Area of triangle = 9

Thus, the total area of the figure will be = 14. 13 + 30 +9

Therefore, the total area of the figure will be 53.13 unit square.

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The coordinates of the image of quadrilateral DEFG after being reflected about the origin include the following:

D' = (9, 5).

E' = (-5, -4).

F' = (6, 2).

G' = (-4, -2).

In Geometry, a reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.

Generally speaking, reflecting a point about the origin is a a type of transformation which causes both the x-coordinate and the y-coordinate to become negated (the signs are changed);

(x, y)                              →               (-x, -y)

Ordered pair D  = (-9, -5) →   Ordered pair D' = (9, 5).

Ordered pair E  = (5, 4) →   Ordered pair E' = (-5, -4).

Ordered pair F  = (-6, -2) →   Ordered pair F' = (6, 2).

Ordered pair G  = (4, 2) →   Ordered pair G' = (-4, -2).

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The percentage error by calculating by differentials to approximate value of sqrt(99.4) = 0.00045 percentage.

For   percentage error Here first we have to find the value of sqrt(99.4) by  normal calculation and second we will calculate it by differential method then we will find the percentage error .

To approximate sqrt(99.4)  we will  use formula for linear approximation as given below  

f(x) = f(c) + f′(c)(x−c)

and we are dealing with square root so we have to find the f(x) ad here

f(x) = √x

and we will calculate  f'(x)  and here it is

f'(x) = 1/(2√x)

Here, x=99.4 and we choose c =100 because that’s the closest perfect square number to 99.4. so

f(c) = f(100) = √100 = 10

f'(c) = f'(100) =1/(2√100) = 1/20

f(x) =f(c) + f′(c)(x−c)

f(x) = f(99.4)=f(100)+f'(100)(99.4-100)

=10+1/20*(-0.6)

=9.97

Here we find the value by differential = 9.97

and by simple calculation the value is = 9.96995486

ans percentage error = (real value - differential value)/100

= (9.96995486-9.97)/100 = 0.00045 percentage

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Answer: $ 5.90 is the the cost of 2 panes of glass

In order to solve this we must divide the number of panes, by the cost spent on the panes. 20.65 divided by 7 is 2.95. This means that each pane is $ 2.95. If there are two panes that were also broken, we have to add 2.95 twice, which is $5.90. This means that the nursey owner must spend another $5.90 on two panes.

I hope this helps & Good Luck <3 !!!

The answers to each part is given below.

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.

Given is a charitable organization.

{ a } -

Assume that the annual salary of the baseball player is ${x}. The amount donated would be -

10% of {x} = ${x/10}

In $120, you can send 1 child to school.

In $1, you can send (1/120) childrens to school.

In ${x/10}, you can send {x/1200} childrens to school.

{ b } -

Same answer as in the case of part {a}.

Therefore, the answers to each part is given above.

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Answer:

706.86

Step-by-step explanation:

The area of the sign will be found with the formula πr^2

r = 15 since the radius is half of the diameter

π(15)^2 = 706.86

Answer:

707 square inches.

Step-by-step explanation:

The area of a circle can be found using the formula A = πr^2, where r is the radius of the circle. The diameter of a circle is equal to twice the radius, so we can find the radius by dividing the diameter by 2.

In this case, the diameter of the circular railroad-crossing sign is 30 inches, so the radius is 30/2 = 15 inches.

So, the area of the sign is A = π * 15^2 = π * 225 = 706.86 square inches.

Rounding to the nearest whole number, the area of the sign is 707 square inches.

The value for differential equation is found as -

[tex]\frac{dP}{dt} =\frac{d}{dt} (\frac{c_1e^t}{1+c_1e^t})\\[/tex]

[tex]\frac{dP}{dt} - (\frac{c_1e^t}{(1+c_1e^t)} )(1-\frac{c_1e^t}{(1+c_1e^t)^2})\\ =(\frac{c_1e^t}{(1+c_1e^t)^2} )-(\frac{c_1e^t}{1+c_1e^t})(1-\frac{c_1e^t}{1+c_1e^t})=0[/tex]

What is differential equation?

Any equation with one or more terms and one or more derivatives of the dependent variable with respect to the independent variable is referred to as a differential equation.

The equation given is - [tex]P=\frac{c_1e^t}{1+c_1e^t}[/tex]

Take derivative with respect to t -

[tex]\frac{dP}{dt} =\frac{d}{dt} (\frac{c_1e^t}{1+c_1e^t})\\\frac{dP}{dt} =\frac{d}{dt}c_1 (\frac{e^t}{1+c_1e^t})[/tex]

By Quotient rule [tex]\frac{d}{dt} \frac{u}{v} =\frac{v\frac{du}{dt}- u\frac{dv}{dt}}{v^2}[/tex] -

[tex]\frac{dP}{dt} =c_1 (\frac{(1+c_1e^t)\frac{d}{dt}(e^t)-(e^t)\frac{d}{dt}(1+c_1e^t)}{(1+c_1e^t)} )\\\frac{dP}{dt} =c_1 (\frac{(1+c_1e^t)(e^t)-(e^t)(0+c_1e^t)}{(1+c_1e^t)} )[/tex]

([tex]\frac{d}{dx} e^t=e^t[/tex] and [tex]\frac{d}{dx} c_1=0[/tex] here [tex]c_1=[/tex]constant)

[tex]\frac{dP}{dt} =c_1e^t (\frac{(1+c_1e^t-c_1e^t)}{(1+c_1e^t)^2} )\\\frac{dP}{dt} = (\frac{(c_1e^t)}{(1+c_1e^t)^2} )[/tex]

Now, [tex]\frac{dP}{dt} =P(1-P)[/tex] -

[tex]\frac{dP}{dt} - (\frac{c_1e^t}{(1+c_1e^t)} )(1-\frac{c_1e^t}{(1+c_1e^t)^2})\\ =(\frac{c_1e^t}{(1+c_1e^t)^2} )-(\frac{c_1e^t}{1+c_1e^t})(1-\frac{c_1e^t}{1+c_1e^t})\\\frac{dP}{dt} =(\frac{c_1e^t}{(1+c_1e^t)} )(\frac{1}{1+c_1e^t}-1+\frac{c_1e^t}{1+c_1e^t})\\\frac{dP}{dt} =(\frac{c_1e^t}{(1+c_1e^t)} )(\frac{1-(1+c_1e^t)+c_1e^t}{1+c_1e^t})\\\frac{dP}{dt} =(\frac{c_1e^t}{(1+c_1e^t)} )(\frac{1-1-c_1e^t+c_1e^t}{1+c_1e^t})\\[/tex]

[tex]\frac{dP}{dt} =(\frac{c_1e^t}{(1+c_1e^t)} )(\frac{0}{1+c_1e^t})\\\frac{dP}{dt} =(\frac{c_1e^t}{(1+c_1e^t)} )(0)\\\frac{dP}{dt} =0[/tex]

Therefore, the value is [tex]\frac{dP}{dt} =0[/tex].

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The solution is, EF = 4√3

Area of a rectangle (A) is the product of its length (l) and width (w).

A= l. w

here, we have,

In rectangle ABCD, AB = 6, BC = 8, and DE = DF.

ΔDEF is one-fourth the area of rectangle ABCD.

We want to determine the length of EF.

First, we can find the area of the rectangle. Since the length AB and width BC measures 6 by 8, the area of the rectangle is:

A = 48 cm^2

The area of the triangle is 1/4 of this. Therefore:

A = 12 cm^2

The area of a triangle is half of its base times its height. The base and height of the triangle is DE and DF. Therefore:

12 = 1/2 * DF *DE

Since DE = DF:

24 = DF^2

Thus:

DF = 2√6 = DE

Since ABCD is a rectangle, ∠D is a right angle. Then by the Pythagorean Theorem:

DF^2 + DE^2 = EF^2

Therefore:

now, Squaring & Adding , we get,

FE^2 = 48

And finally, we can take the square root of both sides:

EF =  4√3

Hence, The solution is, EF = 4√3

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The Area of the given triangle is 1146.27 sq. units.

An important plane geometry theorem also referred to as Hero's formula.

By dividing the quadrilateral into two triangles along its diagonal, this formula is also used to determine the quadrilateral's surface area.

Given the semiperimeter and the lengths of the sides a, b, and c

[tex]p=\frac{a+b+c}{2}[/tex]

of a triangle, Heron's formula gives the area of the triangle as

[tex]A=\sqrt{p(p-a)(p-b)(p-c)}[/tex].

Now in the given question,

a = 57

b = 43

c = 58

Hence, the semi-perimeter,

[tex]p=\frac{a+b+c}{2}[/tex]

[tex]p=\frac{57+43+58}{2} =79[/tex]

Now we calculate the area,

[tex]A=\sqrt{p(p-a)(p-b)(p-c)} \\A=\sqrt{79(79-47)(79-43)(79-58)} \\A=\sqrt{79(22*36*21)} \\A=\sqrt{79*16632} \\A=\sqrt{1313928} \\A=1146.266[/tex]

Hence, the area of triangle is 1146.27 sq. units.

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It should be noted that the area model method is based on the simple equation that is used to find the area of a rectangle:

the length times the width equals the total area (LxW=A).

The area of a shape simply means the total space that is taken by the shape. It simply expresses the extent of the region on a particular plane as well as a curved surface.

For example, the area of a rectangle with the length of 48 units and a width of 21 units can be measured by multiplying 48 by 21. This will be 1008 units².

A overview was given as your information is incomplete

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linear function

x=5+n

given:

height of tree = 5ft

growth per month = 1ft

Find:

equation:

Computation:

asume:

New height of x

number of month = n

x=5+1(n)

x=5+n

hope this helped.

Answer:

Exact Form:

x=15/8

Decimal Form:

x=1.875

Mixed Number Form:

x=1 7/8

Step-by-step explanation:

Answer:

Step-by-step explanation:

divide $43.74 by 6 = 7.29 per pair

Answer:

x = 17.2 oz of substance A and C

x = 3.7 oz of substance B

Step-by-step explanation:

This is a word problem in mathematical optimization, which involves finding the values that maximize or minimize some objective function. To solve this problem, we need to find the optimal number of ounces of each substance to provide 100% of the required nutrition.

Let x be the number of ounces of substance A and C. Then the amount of substance B is 1 1/5 times either of these, or 1 1/5 x.

Since each ounce of substance A supplies 3% of the nutrition, the total contribution from A is 3x%. Similarly, the total contribution from B is 10 * 1 1/5 x = 11 x/5% and from C is 15x%.

The objective is to find x such that the total contribution from all three substances is 100%, or 3x + 11 x/5 + 15x = 100.

Solving for x, we have

29x/5 = 100

x = 100 * 5 / 29 = 17.24 oz

So, 17.24 oz of substance A and C, and 1 1/5 * 17.24 oz = 3.65 oz of substance B should be in the meal. Rounding to the nearest tenth, we have:

x = 17.2 oz of substance A and C

x = 3.7 oz of substance B