help with this question please

The answer is cos(B/2) = 2√5 / 5

Half angle formula of cosine: cos B/2 = ±√[(1 + cos B) / 2]

Given: The positive value of cos 1/2 B in the simplest radical form with a rational denominator, if cos B = 3/5:

Regarding applying the cosine half-angle formula:

cos²(B/2) = (1 + cos B) / 2

put value of cos B =3/5 (given)

cos²(B/2) = (1 + 3/5) / 2

on simplifying

cos²(B/2) = (8/5) / 2

cos²(B/2) = 4/5

on taking under root we get

cos(B/2) = 2/√5

use a rational denominator and the simplest radical form hence, cos(B/2) = 2√5 / 5

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The value of the composite function f(g(-3) is -32

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

f(x) = x + 4. q(x) = 12x

The above are individual functions

This means that

f(g(x)) = 12x + 4

For f(g(-3)), we have

f(g(x)) = 12 * -3 + 4

Evaluate

f(g(x)) = -32

Hence, the value of the composite function is -32

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Answer:

60

Step-by-step explanation:

1=3

2=6

3=9

The relation is Y=3X

Y20 = 3X20=60

A car was worth $24,000 two years ago. The automobile is worth $23,160 this year. 3.5% of the value of the car has decreased.

24,000 - 23,160 = 840

840/24,000 = 0.035

Simplifying the above equation, we get,

0.035 = 3.5%

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The possible locations of point P are  (-7, -1) and (-7, -11)

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

M = (-7, -6)

Also, we have"

P = 5 units from M

And

P = same x coordinate as point m.

This means that

P = (-7, y)

5 units from (-7, -6) is calculated as

(-7, -6 + 5) and (-7, -6 - 5)

Evaluate

(-7, -1) and (-7, -11)

Hence, the possible location is (-7, -1) and (-7, -11)

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A matrix consisting entirely of zeros is called a zero matrix, or an all-zero matrix.

It is denoted with the symbol O and can be written in a matrix form, such as O = [0 0 0 0] where the number of columns and rows depends on the size of the matrix. A zero matrix is a matrix which has all its elements equal to zero. It has a number of special properties that make it useful in linear algebra. For instance, the sum of any two zero matrices is a zero matrix, and any scalar multiple of a zero matrix is a zero matrix. Additionally, the product of two zero matrices is a zero matrix, and the product of a zero matrix and an identity matrix is a zero matrix. These properties make it useful in solving systems of linear equations where all the coefficients are zero. Finally, the inverse of a zero matrix does not exist since its determinant is zero.

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The perimeter of the triangle which has a bisector that splits a triangle into 6 sides would be = 47½

A bisector is defined as the line that divides a shape into two equal parts.

The perimeter of triangle is the sum total of all the sides of the triangle. That is;

perimeter = a1 + a2 + b1 + b2 + c1 + c2

But the value of only 3 sides which is exactly half of the perimeter where given;

= 11/3+22/3+153/12

= 44+ 88+ 153/12

= 285/12

Therefore perimeter

= 285/12 + 285/12

= 570/12

= 47½

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At the four corners of an equilateral triangle are three point charges.

Due to the fact that three charges do not cancel one another out with Colombian force, the system can never reach equilibrium.

A subatomic particle's electric charge causes it to experience a force when it is in an electric and magnetic field.

Electric charge is the property of matter that causes it to experience a force when subjected to an electromagnetic field. Protons and electrons most typically carry positive and negative charges, which are the two forms of electric charges. Energy is created by charge movement.

The most frequent charge carriers for positive and negative electric charges, respectively, are protons and electrons. The coulomb (C) is the standard unit of electric charge used by the International System of Units (ISO) (SI).

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Complete question -

Three point charges are placed at the corners of an equilateral triangle. Assuming only electrostatic force are acting

Therefore , the solution of the given problem of percentage comes out to be 32 liters after 60% increased.

Any value that may be expressed as a fraction of 100 is referred to as a percentage in mathematics. The acronyms "pct.," "pct," or "pc" are also occasionally used. However, the "%" symbol is typically used to denote it. The proportional amount has no dimensions and is flat. Percentages can be viewed as fractions because their numerator is 100. To indicate that a number is a percent, it needs to be followed by the percent symbol (%).

Here,

Given:

=> 20 liters is the given volume

It is increased by 60% ,

then the final volume is :

=> 20 + 60/100 *20

=> 20 + 0.6*20

=> 20 + 12

=> 32 liters

Therefore , the solution of the given problem of percentage comes out to be 32 liters after 60% increased.

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The sound intensity level should be decreased by 2 dB to carry the studio into consistency with the rules.

A decrease of 2 dB can be accomplished by one or the other by closing down a portion of the machines (since the sound intensity level declines by 6 dB for each splitting of the sound power) or by introducing sound-sealing materials.

Thus, to carry the studio consistent with the rules, 16 machines would need to be closed down.

It's vital to follow well-being and security rules in the working environment to guarantee the prosperity of representatives and forestall hearing harm. Decreasing the number of machines or introducing soundproofing materials can bring the studio into consistency.

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The quantities that are proportional to 8⁄12 are 24 / 36 and 2 / 3.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that the fraction is 8 / 12. The equivalent expression will be calculated as:-

8 / 12 = 2 / 3

16⁄36 = 4 / 9

12⁄16 = 3 / 4

24⁄36 = 2 / 3

2⁄3 = 2 / 3

18⁄24  = 3 / 4

The equivalent expressions will be 8 / 12 = 24 / 36 = 2 / 3.

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The equation that correctly solves the given equation for t is C) t = (100 - G) / 4

To solve for t in the equation G = -4t + 100, we need to isolate t on one side of the equation. To do this, we start by subtracting 100 from both sides:

G - 100 = -4t + 100 - 100

Simplifying the right side:

G - 100 = -4t

Finally, dividing both sides by -4:

t = (100 - G) / -4

So, option C) t = (100 - G) / 4 correctly represents the equation for t in terms of G.

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Your question is incomplete but most probably the full question was:

A swimming pool is being drained. The number of gallons of water in the pool changes with time t according to the equation G = -4t + 100.

Which equation correctly solves the given equation for t?

A) t = 4G - 100

B) t = -4G + 100

C) t =

100 - G

4

D) t =

G - 100

4

The functions that are solutions of the differential equation y" - 4y' -21y = 0 is -Option E: y(x) = [tex]e^{-3x}[/tex] Option F: y(x) = [tex]e^{7x}[/tex]

A differential equation is any equation that has one or more terms and one or more derivatives of the dependent variable with respect to the independent variable.

The given differential equation is y" - 4y' -21 = 0

This can be written as characteristic equation -

m² - 4m - 21 = 0

m² - 7m + 3m - 21 = 0

m(m - 7) + 3(m - 7) = 0

(m + 3)(m - 7) = 0

m = -3 and m = 7

The general solution is given by

[tex]y = (C1 + xC2)e^{-3x}[/tex]

[tex]y = C1 e^{-3x} + C2 xe^{-3x}[/tex]

[tex]y = (C1 + xC2)e^{7x}[/tex]

[tex]y = C1 e^{7x} + C2 xe^{7x}[/tex]

So, now the solutions are y = [tex]e^{-3x}[/tex], [tex]y = xe^{-3x}[/tex], [tex]y = e^{7x}[/tex]and [tex]y = xe^{7x}.[/tex]

Therefore, the solutions are y = [tex]e^{-3x}[/tex] and [tex]y = e^{7x}[/tex]

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The equation x - 3 = 2 when evaluated is x = 5

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

x - 3 equal to 2.

Express the equation properly

So, we have the following representation

x - 3 = 2

Add 3 to both sides of the equation

This gives

x - 3 + 3 = 2 + 3

Evaluate the like terms

x = 5

Hence, the solution is x = 5

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Complete question

What is x - 3 equal to 2.

Evaluate

The correct option representing the domain of the relation is given as follows:

{−3, −1, 0, 2, 4}

The domain of a function is the set that contains all the input values of the function, hence on the graph it is the values of x, representing the number of years.

The values of x are the values of x for which there is a dot, hence they are given as follows:

Meaning that the fourth option represents the correct option.

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The correct option is option D. That is, R'(4,1). The RST coordinates of the given point is: (4,1).

The midpoint is the spot that is in the center of a line that connects two locations. The two reference points that make up a line's endpoints are where it finds its middle. At the halfway point, the line that links these two locations is evenly divided in half. Additionally, if a line is drawn to split the line that links these two points, the midway point is achieved. The midpoint formula may be used to determine the midpoint between two locations when we know their coordinates. The midpoint formula may be used to determine the coordinates of the other endpoint if we know the midpoint's coordinates as well as those of the other endpoint. RST coordinate is (4,1).

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The expressions for (h - g)(x) and (h . g)(x) are -x - 8 and  (x - 5)(2x + 3)

While the function (h + g) (-1) is -5

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

g (x) = 2x+3

h(x) = x - 5

This means that

(h - g)(x) = x - 5 - 2x - 3

Evaluate

(h - g)(x) = -x - 8

Also, we have

(h . g)(x) = (x - 5)(2x + 3)

Lastly, we have

(h + g)(-1) = (x - 5) + (2x + 3)

So, we have the following equation

(h + g)(-1) = ((-1) - 5) + (2(-1) + 3)

Evaluate

(h + g)(-1) = -5

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Answer: 36.4

Step-by-step explanation:

27.3= (3/4)y

divide both sides by 3/4 to isolate the y

27.3/(3/4)= 36.4

To double-check, plug in 36.4 to y; should get you 27.3

An estimate of the real height of the lamp post is 9m.

The first step is to determine the scale of the drawing. The scale can be determined by dividing the height of the lamp post by the height of the car. The height of the lamp post when measured with a ruler is 10.8 cm and the height of the car is 1.8cm

here, we have,

Scale = length of the lamp post / height of the car

10.8 / 1.8 = 6

Now, multiply the scale by the width of the car.

The real height of the lamp post = 6 x 1.5 = 9m

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Here, we don't know the exact values for the speed or the lap length, so we need to use symbols in the equation  i.e., x= 8 / (5.5  / lap length × speed ).

There are a couple of ways to approach this problem, but one common method is to use the formula: distance = speed x time.

To find the time it took Andre to run each lap, we need to find the distance he covered in 8 minutes and then divide that by the number of laps. Here are the equations:

1. Distance = 5.5 laps x lap length

2. Distance = speed x 8 minutes

3.  x = (5.5 x lap length) / (speed x 8)

4.  x = 8 / (5.5 / lap length x speed)

Note that we don't know the exact values for the speed or the lap length, so we need to use symbols in the equations.

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Since 4.286766 is closer to 4 than it is to 8, we can write the final result as: 4.286766 ≈ 2²

We can start by evaluating each bracketed expression first:

{(67)3} = 67 * 67 * 67 = 42,949,769

{(67)2} = 67 * 67 = 4489

Next, we evaluate the first part of the expression:

(67)3 * 2 = 42,949,769 * 2 = 85,899,538

Next, we evaluate the second part of the expression:

(67)2 * (67)2 = 4489 * 4489 = 20,067,961

Finally, we divide the result of the first part by the result of the second part:

85,899,538 / 20,067,961 = 4.286766

To express this result as a power of 2, we find the nearest power of 2 and write it in exponential form:

2² = 4

Thus, Since 4.286766 is closer to 4 than it is to 8, we can write the final result as: 4.286766 ≈ 2²

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Since 4.286766 is closer to 4 than it is to 8, we can write the final result as: 4.286766 ≈ 2²

We can start by evaluating each bracketed expression first:

{(67)³} = 67 * 67 * 67 = 42,949,769

{(67)²} = 67 * 67 = 4489

Next, we evaluate the first part of the expression:

(67)³ * 2 = 42,949,769 * 2 = 85,899,538

Next, we evaluate the second part of the expression:

(67)² * (67)² = 4489 * 4489 = 20,067,961

Finally, we divide the result of the first part by the result of the second part:

85,899,538 / 20,067,961 = 4.286766

To express this result as a power of 2, we find the nearest power of 2 and write it in exponential form:

2² = 4

Thus, Since 4.286766 is closer to 4 than it is to 8, we can write the final result as: 4.286766 ≈ 2²

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Answer:

Below

Step-by-step explanation:

Her base salary (500) for the week PLUS her comission (.3 * 1575)

   totals 972.50 dollars

Answer: probably greater than 3 1/2 inches, since bumper stickers are usually wider than they are tall

Step-by-step explanation:

The sum of interior angle in 12-gon is 1800°, in 102-gon is 18000°, in 90-gon is 15840° and 36-gon is 6120° and measure of interior angle in 12-gon is 150°, in 102-gon is 176.5°, in 90-gon is 176° and 36-gon is 170°

A polygon is a two-dimensional geometric shape consisting of straight lines and having three or more sides. The sides of a polygon are line segments that connect its vertices, or corners, and the vertices are where the sides meet. The most common types of polyggon include triangles, squares, rectangles, and hexagons. There are also many types of irregular polygon, which have sides of different lengths or angles, as well as regular polygon, which have equal sides and equal interior angles.

The sum of the interior angles and the measure of the interior angle of a regular polygon can be found using the formula:

Sum of interior angles = (n-2) * 180°

Measure of interior angle = Sum of interior angles / n

Where n is the number of sides of the polygon.

For a 12-gon:

Sum of interior angles = (12-2) * 180° = 1800°

Measure of interior angle = 1800° / 12 = 150°

For a 102-gon:

Sum of interior angles = (102-2) * 180° = 18000°

Measure of interior angle = 18000° / 102 = 176.5°

For a 90-gon:

Sum of interior angles = (90-2) * 180° = 15840°

Measure of interior angle = 15840° / 90 = 176°

For a 36-gon:

Sum of interior angles = (36-2) * 180° = 6120°

Measure of interior angle = 6120° / 36 = 170°

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(b)  The value of f^(-1) is g.

(c)  The value of f ◦ f ◦ f = f ◦ (f ◦ f) is f((f ◦ f)(x)) = f((x * (x-1))*((x * (x-1)) - 1)).

According to the question

(a) To prove that f is bijective, we need to show that it is both injective (one-to-one) and surjective (onto).

Injectivity: Let x, y ∈ a such that f(x) = f(y). Then, x * (x-1) = y * (y-1). Multiplying both sides by x-1, we get x = y, meaning that f is injective.

Surjectivity: Let z ∈ a. Then, z = z * (z-1) / (z-1), which means that there exists an x ∈ a such that f(x) = z. This shows that f is surjective.

Therefore, f is bijective.

(b) To find the inverse of f, we need to find a function g: a → a such that f(g(x)) = x and g(f(x)) = x for all x ∈ a.

Consider the function g: a → a defined by g(x) = x / (x-1) for all x ∈ a.

Let x ∈ a. Then, f(g(x)) = f(x / (x-1)) = (x / (x-1)) * ((x / (x-1)) - 1) = x. Similarly, g(f(x)) = g(x * (x-1)) = x * (x-1) / (x * (x-1) - 1) = x. This shows that f and g are inverses.

Therefore, f^(-1) = g.

(c) To find f ◦ f ◦ f, we first evaluate f ◦ f and then evaluate f of the result.

Let x ∈ a. Then, (f ◦ f)(x) = f(f(x)) = f(x * (x-1)) = (x * (x-1)) * ((x * (x-1)) - 1). Hence, f ◦ f ◦ f = f ◦ (f ◦ f) = f((f ◦ f)(x)) = f((x * (x-1)) * ((x * (x-1)) - 1)).

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The values of the x component of d1 is 6.5, the y component of d1 is 23 the x component of d2 is 2.6 and the y component of d2 is 9.2

Given that,

d1 +d2 = 7.0d3,   (1)

d1-d2 = 3.0d3    (2)

and d3= 1.3i +4.6j         (3)

Adding equation 1 and equation 2

d1 +d2 +d1 -d2 = 7 d3 + 3 d3

2d1 = 10 d3

d1 = 5d3

and we also have that  d3= 1.3i +4.6j    

substitute the given d3 in  d1 = 5d3

therefore , d1 = 5(1.3i +4.6j)

d1 = 6.5i + 23 j

here the x component of d1 is 6.5

subtract 2 from 1

d1+d2-d1+d2 = 7d3-3d3

2d2 = 4d3

d2 = 2d3

d2 = 2(1.3i +4.6j)

     = 2.6 i + 9.2j

here the x component of d2 = 2.6

the y component of d2 = 9.2

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The value of the test statistic in this case is 75.00. This suggests that 75% of drivers under the age of 18 still use a cell phone while driving.

The value of the test statistic in this case is the percentage of drivers under the age of 18 who still use a cell phone while driving. The test statistic is calculated using the following formula:

Test Statistic = (Number of Drivers under 18 using Cell Phone)/ (Total Number of Drivers under 18) x 100

For this case, the test statistic is calculated as follows:

Test Statistic = (150/200) x 100 = 75.00

Therefore, the value of the test statistic in this case is 75.00. This suggests that 75% of drivers under the age of 18 still use a cell phone while driving.

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Answer:

The boat traveling at 30 miles per hour will travel 30 * (2/3600) = 0.05 miles in 2 seconds.

Step-by-step explanation:

Here's a step-by-step explanation to find the distance traveled by the boat in 2 seconds:

Start with the speed of the boat, which is given as 30 miles per hour.

To find the distance traveled in 2 seconds, we need to convert the speed from miles per hour to miles per second.

To convert from miles per hour to miles per second, divide the speed by 3600 (since there are 3600 seconds in an hour).

30 / 3600 = 0.008333333 (miles per second)

Multiply the speed in miles per second by the time in seconds to find the distance traveled.

0.008333333 * 2 = 0.016666666 miles

So the boat will travel 0.016666666 miles in 2 seconds, or approximately 0.05 miles.