The mapping F and G are defined on R, the set of real numbers by F(x)=x^2+3 and G(x)=x-2. Find: a) (G composition of F)(x), b) (F composition of G)(x), c) is the composition of F and y commutative. Using Brainly.in app.​

The Cadbury Report is a document that was produced by "The Committee on the Financial Aspects of Corporate Governance

The Cadbury Report, also known as Financial Aspects of Corporate Governance, is a document that was produced by "The Committee on the Financial Aspects of Corporate Governance," which was led by Sir Adrian Cadbury, the chairman of Cadbury.

It contains recommendations on how company boards and accounting systems should be set up to reduce the risks and failures associated with poor corporate governance. The Cadbury committee was established by the London Stock Exchange in 1991, and a draft of the report was released in May 1992. In December of that same year, it was released in its altered and complete form.

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The formula is: f(x) = 2 * sin(x * 5 / 2π) + 5

A = 5 - 3 = 2, the amplitude of the function.

Since (0,3) is the minimum, the midline is at y = 3 + 2 = 5, the average value of the maximum and minimum.

Let "c" be the shift, so the equation of the midline is y = 5 + c.

At x = 5, the function intersects its midline, so 5 = 5 + c.

Therefore, c = 0.

The period of the function is 2π / b, where b is the number of radians for one complete cycle.

Since the function intersects its midline at (5,5), b = 5.

Therefore, the period of the function is 2π / 5.

The formula of the sinusoidal function is:

f(x) = A * sin(b * (x - c)) + d,

where d = 5, the equation of the midline.

Therefore, the formula is:

f(x) = 2 * sin(x * 5 / 2π) + 5

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The number of miles that the business person can travel  on the $110 is; 290.68 miles

The general form of the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

The daily rate of $37.33 can be said to be the  y-intercept.

While 25 cents or $0.25 can be said to be the slope.

Thus, the equation of the line formed is;

y = 0.25x + 37.33

At a cost of $110, the number of miles is;

110 = 0.25x + 37.33

0.25x = 110 - 37.33

0.25x = 72.67

x = 72.67/0.25

x = 290.68 miles

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According to the problem the volume of the solid generated by revolving the region is .

The amount of space a thing occupies is its volume, which is expressed in cubic units. It is a three-dimensional measure of an object's size, as opposed to its length and width, which are considered two-dimensional measures. Volume is commonly used to measure the capacity of containers, such as barrels, tanks, and boxes.

This is a solid of revolution generated by revolving the region bounded by the curves y=[tex]e^{(x-9)}[/tex] and y=0 and the lines x=9 and x=10 about the x-axis. To find the volume of this solid, we can use the method of washers.

The formula for the volume of a solid of revolution generated by revolving a region bounded by two curves about the x-axis is given by:

V = π∫[tex]b a [((f(x))^{2} - (g(x))^{2}] dx[/tex]

In this problem, f(x) = [tex]e^{(x-9)}[/tex] and g(x) = 0. Thus,

V = π∫10 9 [tex]e^{(2x-18)} dx[/tex]

Integrating, we get

V = π [tex][\frac{e^{(2x-18)}}{2}] 10^{9}[/tex]

V = π(157.087 - 1.1102)/2

V = 78.488π [tex]cm^{3}[/tex] equal to the integral of the area of the region over the interval [9, 10] with respect to x.

The area of the region is equal to the integral of y from 9 to 10. Thus, the volume of the solid generated by revolving the region is equal to the double integral:

V = ∫[tex]9^{10}[/tex] ∫[tex]0^{e^{(x-9)} } dy dx[/tex]

Evaluating the integral yields:

V =∫ [tex]9^{10} e^{(x-9)} dx[/tex]

[tex]= \frac{e^{(x-9)} }{9^{10} }\\ =e^{1} -1\\ =2.718-1 =1.718[/tex]

Therefore, the volume of the solid generated by revolving the region is 1.718.

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The value of vector (2u + v) is -5i +8k +5j and the value of u.v is -7.

Geometrical objects with magnitude and direction are called vectors. A line with an arrow pointing in its direction can be used to represent a vector, and the length of the line corresponds to the vector's magnitude.

As a result, vectors are depicted as arrows and have starting and ending points.

The value of the vector (2u + v) is calculated as:-

E = (2u + v)

E = 2 ( -i + 5k) +( -3i + 5j -2k)

E = -2i +10k -3i +5j -2k

E = -5i + 5j + 8k

The value of u.v will be:-

u.v = ( -i +oj + 5k).(-3i +5j -2k)

u.v = 3 - 10

u.v = -7

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Complementary angles add up to 90°, write an equation using this knowledge and the information provided in the question:

66°+x° = 90°

Subtract 66° from both sides:

x° = 24°

Answer: The acceleration of the stuntman is given by the second derivative of the height function, which is:

h''(t) = d²h/dt² = (-2 * 2 * t * 1000 + 1000 * -2) = -4000t + 1000

So, the acceleration is -4000t + 1000 ft/sec².

Step-by-step explanation:

The value of H^ prime (17) will be 17

At H'(t) = 0 time t, for 9 ≤ t ≤ 23, the model predicts that the number of people in the park is a maximum.

a) To find the number of people who have entered the park by 5:00 P.M. (t = 17),

we need to find the definite integral of the function E(t) from 0 to 17.

b) The total amount of money collected from admissions to the park on the given day is the sum of the money collected before 5:00 P.M. and the money collected after 5:00 P.M.

We can find this by finding the definite integral of the function 15600/(t^2 - 24t + 160) for t from 0 to 17,

Now finding the definite integral of the function

11*9890/(t^2 - 38t + 370) for t from 17 to 23.

c) H(t) represents the number of people in the park at time t. H'(t) represents the rate at which the number of people in the park is changing at time t.

H(17) = 3725 means that at 5:00 P.M. there are 3725 people in the park.

H'(17) can be found by finding the derivative of the function H(t) at t = 17.

d) To find the time t at which the model predicts that the number of people in the park is a maximum, we need to find the maximum value of H(t) for 9 ≤ t ≤ 23.

This can be done by finding the derivative of H(t), setting it equal to 0, and solving for t.

The value of t at which H'(t) = 0 will correspond to the maximum value of H(t).

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Answer:

Step-by-step explanation: it just graph of y=-x

y+x=

4x+4y4y=

The pattern in the following expressions is of square of numbers.

what are expressions?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

Now,

In given expressions, In divisor the numerator and denominator are square of numerator and denominator in the dividend.

e.g. in (3/5)/(9/25)       9=3^2 and 25=^2

Hence,

            The pattern in the following expressions is of square of numbers.

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Answer:

$2.88

Step-by-step explanation:

formula → 3.6 × (1 - 20%)

→ 3.6 × (1 - 0.2)

calculate sum or difference

→ 3.6 × 0.8

→ = 2.88

The random variable's pdf is f(x) = (3/8) x^2 , x ∈ [0, 2].

Finding the normalizing constant that equals the integral of the pdf over the support of the random variable yields the constant in the pdf (probability density function).

The random variable's support is the interval [0, 2]. The normalizing constant can be calculated as follows:

∫_0^2 x^2 dx = [x^3/3]

_0^2 = (8/3) - (0) = 8/3

So, in the pdf, the constant is 1/(8/3) = 3/8, rounded to the second decimal place.

As a result, the random variable's pdf is:

f(x) = (3/8) x^2 , x ∈ [0, 2].

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Answer:

1st blank = 45

2nd blank = 90

Step-by-step explanation:

this is an quadratic sequence. (an^2 + bn + c)

use of the formulas

2a = (_)

3a + b = (_)

a + b + c = (_)

Answer:The probability of a female client choosing health insurance is 65%, and 60% of the company's clients are female, so the probability of choosing health insurance is:

P(health insurance) = 0.65 * 0.60 = 0.39

Therefore, the probability that a health insurance contract is chosen is 0.39.

Step-by-step explanation:

The probability of a female client choosing health insurance is 65%, and 60% of the company's clients are female, so the probability of choosing health insurance is:

P(health insurance) = 0.65 * 0.60 = 0.39

Therefore, the probability that a health insurance contract is chosen is 0.39.

5 STAR AND THANK ME PLS :))

Answer: 4

Step-by-step explanation:

The probability that fewer than 10 cans in a sample of 60 contain less than 499 ml of juice is approximately 0.5949 (rounded off to third decimal place).

To find the probability that fewer than 10 cans in a sample of 60 contain less than 499 ml of juice, we need to find the cumulative distribution function (CDF) of a normal distribution with a mean of 500 and standard deviation 4.

Using the Z-score formula, we can calculate the Z-score for 499 ml of juice: (499-500)/4 = -0.25

Next, we use a standard normal table to find the probability of a Z-score less than -0.25, which is 0.4051.

Finally, we use the CDF formula for a normal distribution to find the probability that fewer than 10 cans in a sample of 60 contain less than 499 ml of juice:

P(X < 499) = 1 - P(X >= 499) = 1 - 0.4051 = 0.5949

Therefore, the probability that fewer than 10 cans in a sample of 60 contain less than 499 ml of juice is approximately 0.5949 (rounded off to the third decimal place).

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Answer:

This is the equation of the normal line at the point (2, 1) on the ellipse (x^2)/4 + y^2 = 2.

Step-by-step explanation:

The equation of the ellipse is (x^2)/4 + y^2 = 2. To find the equation of the normal line at the point (2, 1), we first need to find the slope of the tangent line at that point. To do this, we can use the formula for the slope of a tangent line:

slope = -(d/dx)(f(x)) / (d/dy)(f(y))

Where f(x) and f(y) are the equations of the ellipse.

So,

slope = -(x/2)/y = -x/2y

Now we can substitute the point (2, 1) into the equation for the slope:

slope = -(2/2)/1 = -1

We know that the slope of the normal line is the negative reciprocal of the slope of the tangent line, so the slope of the normal line is 1.

To find the equation of the normal line, we can use the point-slope form of a line:

y - y1 = m(x - x1)

Where (x1, y1) is the point on the line and m is the slope.

So,

y - 1 = 1(x - 2)

Simplifying, we get:

y = x - 1

This is the equation of the normal line at the point (2, 1) on the ellipse (x^2)/4 + y^2 = 2.

$150 each month

Step-by-step explanation:

1 year=12 months

$1800/12

= $150 each month

Answer:

$150 each month

Step-by-step explanation:

Step 1: take the amount of money she donates in a year and divide it by 12, because there are 12 months in a year. Dividing 1,800 by 12 will tell you how much money she donates each month.

[tex]\frac{1,800}{12}= 150[/tex]

The required distance between the two given cities using the distance formula is 93 miles.

Distance is the sum of an object's movements, regardless of direction.

The distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

Learn how to apply the Pythagorean theorem to find the distance between two points using the distance formula.

The Pythagorean theorem can be rewritten as d=(((x 2-x 1)2+(y 2-y 1)2) to calculate the separation between any two locations.

So, we have the points:

(53, 17) and (123, 78)

Distance formula:

d = √(x2-x1)² + (y2-y1)²

Now, calculate as follows:

d = √(x2-x1)² + (y2-y1)²

d = √(123-53)² + (78-17)²

d = √(70)² + (61)²

d = √(4,900) + (3,721)

d = √8,621

d = 92.84

Rounding off: 93 miles

Therefore, the required distance between the two given cities using the distance formula is 93 miles.

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The correct answer is d. dp/dt = 1/1200 P (500-P).

Rate of change is a major of house quickly one quantity change in relation to another it is parisu of the changing 122 the changing another quantity over specified time period it is commonly used mathematics physics economic and other discipline to make operate of vijay process is a caring rate of changing also known as velocity, derivative or slope.

This differential equation describes the rate of change of the number of people entering a movie theater. It states that the rate of change (dp/dt) is equal to the product of 1/1200 and the current number of people (p) in the theater, multiplied by the difference between the capacity of the theater (500) and the current number of people (p). This equation indicates that the rate of change of people entering the theater is proportional to the difference between the capacity and the current number of people.

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Using the permitted $110 for travel, the businessperson can cover 291 miles.

We need to deduct the daily rate of $37.33 from the permitted money, then divide the sum by the per-mile rate of 25 cents to get how many miles a businessperson can travel with $110.

$110 - $37.33 = $72.67

$72.67 ÷ $0.25 = 291 miles

It's crucial to remember that, regardless of how many kilometres the businessperson drives, the daily charge includes a fixed sum for the rental automobile. Each mile driven results in an additional fee known as the per-mile tariff. We may calculate the maximum number of miles the business person can travel without incurring additional costs by subtracting the daily rate from the permitted amount and dividing by the per-mile rate.

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Reversed Alternate Interior Angles.The theorem states that j || k.J and K converse different internal angles.

j and k angles.The Converse of Corresponding Angles Postulate leads to the expression j || k.

2Angles 2 and 5 make up the alternating inner angles of the lines j and k.Angle 2 equals Angle 5 if

Reversed Alternate Interior Angles.The theorem states that j || k.

J and K converse different internal angles.

3. Angle 3 also equals Angle 10.

The exterior angles of the lines l and m are, respectively, Angle 3 and

Angle 10.

The Converse of Alternate Exterior Angles Theorem states that angle 3 equals angle 10, so l || m.

Reversed Alternate Interior Angles.The theorem states that j || k.J and K converse different internal angles.

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Answer:

300

Step-by-step explanation:

do 20 times 15 and you get 300 length times width = area

Answer:

300

Step-by-step explanation:

First of all, a square's side lengths must be the same for it to be correctly labeled as a square.

The quadrilateral we need to find the area for here is a rectangle.

The area of a rectangle is defined as length × width. So, to answer this question, all we need to do is multiply the given dimensions.

20 × 15

= (2 + 10) × 15

= (2 × 15) + (10 × 15)

= 30 + 150

= 300

Probability is a measure of the likelihood that a specific event will occur in a random experiment.

What is the Probability?

The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.

In other words, the probability is a number that represents the chance or chance of an event occurring out of all possible outcomes.

It is expressed as a fraction, decimal, or percentage.

For example, if there is a 50% chance of rain, this means that the probability of rain is 0.5 or 1/2.

Probability is important in decision-making, risk assessment, and mathematical modeling. It helps to quantify uncertainty and provides a way to assess the likelihood of different outcomes.

Hence, Probability is a measure of the likelihood that a specific event will occur in a random experiment.

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In the year 1998, the total average credit card debt for a U.S. household was approximately 6920 dollars.

As per the data given in the questions,

We have,

The expression for calculating the approximate value of the total average credit card debt in a u.s. household (in dollars) t years after 1995 is: 410t+5690

So, first we will calculate the value of t

As we have in the year 1998, t = 1998 - 1995 = 3.

So, for determining the value of the total average credit card debt in a u.s. household, we will simply plug in this value into the expression,

Thus, will get it as

410 * 3 + 5690

= 1230 + 5690

= 6920

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At the beginning of 2072 B.S., the population of the town was X.

Assuming the population growth rate is 10%, the population at the end of 2074 B.S. will be (X + 10% of X) + (X + 10% of X + 10% of X) = 1.1X + 1.1(1.1X) = 2.21X.

Therefore, the population of the town at the end of 2074 B.S. will be 2.21X. This is based on a linear population growth rate of 10% over two years. It is possible that the growth rate may not be constant, so the actual population may be slightly different.

In order to get a better estimate of the population at the end of 2074 B.S., it is important to consider other factors such as birth and death rates, migration, and economic and social factors.

For example, if the town is experiencing an influx of migrants, then the population growth rate may be higher than the estimated 10%. On the other hand, if the town faces an economic recession or job losses, then the population growth rate may be lower than the estimated 10%.

Overall, the population of the town at the end of 2074 B.S. is estimated to be 2.21X, based on a linear population growth rate of 10% over two years. However, this estimate may be slightly different depending on the other factors mentioned above.

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The output voltage, in millivolts (mV), for the circuit would be = 1,350 millivolts.

An amplifier is defined as the electronic device that can be used to increase the electrical signal of a power source.

The output voltage of an amplifier= input voltage × gains.

Where;

input voltage = 45 mV

The gain = 30

Therefore the output voltage= 45×30 = 1350millivolts.

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Answer:

x = 4cm

Step-by-step explanation:

If the triangle is equilateral, then we already know one of the sides has a length of 3+5 (8).

This, therefore, means the 2 other sides' lengths are also equal to eight, which means all we need to do to find x is subtract 4 from 8, which gives us 4.

Hope this helps

Answer:

[tex]x=\dfrac{20}{3}\; \sf cm[/tex]

Step-by-step explanation:

If a line is parallel to a side of a triangle and intersects the other two sides, then this line divides those two sides proportionally.

Applying the side-splitter theorem:

[tex]\implies \dfrac{3}{5}=\dfrac{4}{x}[/tex]

Cross multiply:

[tex]\implies 3 \cdot x=4 \cdot 5[/tex]

[tex]\implies 3x=20[/tex]

Divide both sides by 3:

[tex]\implies \dfrac{3x}{3}=\dfrac{20}{3}[/tex]

[tex]\implies x=\dfrac{20}{3}[/tex]

Therefore, the value of x is ²⁰/₃ cm

Answer:

22 in

Step-by-step explanation:

It travels 35/60 ths of the complete circumference of a circle with r =6 in

diameter = 12     circumference = pi * d

35/ 60  * pi * 12 =  ~22 inches