Molly is verifying if the two functions are inverses of each other? Her answer is as follows:

f(g(x))=x+5 g(f(x))=x+5

She stated that they are not inverses of each other. Is she correct and why? Explain.

The probabilities, using the binomial distribution, are given as follows:

a. P(X = 2) = 0.2109.

b. P(X = 3) = 0.0469.

c. P(X ≥ 2) = 0.2617.

d. P(X < 3) = 0.9492.

The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure.

The mass probability formula is given by the equation presented as follows:

The parameters, and their meaning are listed as follows:

The parameter values for this problem are given as follows:

n = 4, p = 0.25.

Hence the relevant probabilities are given as follows:

Then:

P(x ≥ 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.2109 + 0.0469 + 0.0039 = 0.2617.

P(x < 3) = 1 - (P(X = 3) + P(X = 4)) = 1 - (0.0469 + 0.0039) = 0.9492.

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Answer:

144

Step-by-step explanation:

The man has 7 shirts in total, so he can take 3 of those shirts on his 3-day trip without repetition. This means that he can make 7 different combinations of shirts, since each shirt has only one choice. For example, he could take shirts A, B, and C; or he could take shirts D, E, and F; or he could take shirts G, A, and B. In total, he has 7 different combinations of shirts to choose from.
The number of combinations of shirts that the man can take without repetition can be found using the formula for combinations, which is:
C(n, r) = n! / (r! * (n-r)!)

In this case, n = 7 (the total number of shirts) and r = 3 (the number of shirts he will take with him).

Plugging in these values into the formula, we get:

C(7, 3) = 7! / (3! * (7-3)!)

C(7, 3) = 7! / (3! * 4!)

C(7, 3) = 5040 / (6 * 24)

C(7, 3) = 5040 / 144

C(7, 3) = 35

Therefore, the man can take 35 different combinations of shirts without repetition.

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To show that d/dx (csc(x)) = −csc(x)cot(x), we will use the chain rule and the derivative of the inverse function.

The chain rule states that the derivative of a composite function is the product of the derivatives of the individual functions. The derivative of the inverse function is the reciprocal of the derivative of the original function. Here are the steps:

1. Start with the given function: d/dx (csc(x))
2. Rewrite csc(x) as 1/sin(x): d/dx (1/sin(x))
3. Use the chain rule to find the derivative: (d/dx 1)(d/dx sin(x))
4. The derivative of 1 is 0, so the first term becomes 0: (0)(d/dx sin(x))
5. The derivative of sin(x) is cos(x), so the second term becomes cos(x): (0)(cos(x))
6. Simplify the expression: 0
7. Use the derivative of the inverse function to find the derivative of 1/sin(x): -1/sin^2(x)
8. Rewrite sin^2(x) as (sin(x))(sin(x)): -1/(sin(x))(sin(x))
9. Simplify the expression by canceling out one of the sin(x) terms: -1/sin(x)
10. Rewrite 1/sin(x) as csc(x): -csc(x)
11. Rewrite -1/sin(x) as -cot(x): -cot(x)
12. Combine the two terms to get the final answer: −csc(x)cot(x)

Therefore, d/dx (csc(x)) = −csc(x)cot(x).

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The equation -7t-6=-7t has no solution.

Because when we try to isolate the variable t on one side of the equation, we end up with an equation that is not true.

Here's how we can do this:
-7t-6=-7t

First, we can add 7t to both sides of the equation:
-6=0

This equation is not true, so there are no values of t that will make this equation true. Therefore, the equation has no solution.

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Answer:

1. Transitive

2. Reflexive

3. Symmetric

4. Reflexive

5. Symmetric

6. Transitive

The statements which can be assumed from the diagram are:

Parallel lines are coplanar infinite straight lines in geometry that never intersect. In the same three-dimensional space, parallel planes are any planes that never cross.

Parallel curves are curves that do not touch each other or intersect and preserve a predetermined minimum distance

In simple geometry, two geometric objects are perpendicular if the intersection at the point of junction known as a foot results in right angles.

From the given image, it can be seen that

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Answer:

C, E

Step-by-step explanation:

Answer choice A implies that [tex]42 +22 \geq 50 + 27[/tex], which is false

Answer choice B implies that 50 is half of the population, however the population is 200, so it is false

Answer choice C implies that [tex]50 + 27\geq[/tex] all other combinations, which is true.

Answer choice D implies that [tex]33 + 22\leq 50[/tex], which is false

Answer choice E implies that [tex]42 \leq 22+22[/tex], which is true

So, C & E are correct

This statement means that the inverse cosine function, cos −1x, gives the angle y whose cosine is x, within the range of 0≤y≤π.

Complete the statement. y=cos −1x means that x=cos y, for 0≤y≤π

This statement means that the inverse cosine function, cos −1x, gives the angle y whose cosine is x, within the range of 0≤y≤π. In other words, if we know the value of x, we can use the inverse cosine function to find the angle y that has a cosine of x. This is useful for solving equations involving cosine, such as finding the angles of a triangle given the lengths of its sides.

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The Surface Area of Container is 954. 56 inch².

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. Square units are used to measure it as well.

For each three-dimensional geometrical shape, surface area and volume are determined. The area or region that an object's surface occupies is known as its surface area.

As, we Know the Surface Area of Cylinder

= 2πr² + 2πrh

Radius of the base = 8 inches

Height of the cylinder = 11 inches.

Now, putting the values we get

= 2πr² + 2πrh

= 2 x 3.14 x 8 x 8 + 2 x 3.14 x 8 x 11

= 401.92 + 552.64

= 954. 56 inch²

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x² - 7y - 4x²y + 8xy² is standard form of equation.

What are equations, and what different kinds are there?

Equations can be divided into two categories: identities and conditional equations. Any value of the variables results in an identity being true. Only certain values of the variables in a conditional equation result in truth.

                     When two expressions are joined together by the equals sign ("="), the result is an equation. A mathematical statement that demonstrates the equality of two mathematical expressions is the definition of an equation.

  8xy²+1x²-4x²y-7y

standard form = 8xy² + 1x² - 4x²y - 7y

                       =  x² - 7y - 4x²y + 8xy²

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Answer:

3

Step-by-step explanation:

by the help of Prashant chettri

The fraction of a day that the average fire burns is given as follows:

100%.

The fraction of a day that the average fire burns is obtained applying the proportions in the context of the problem.

For the log cabin, the fraction is given as follows:

1/4.

The average fire burns four times this length, hence the length is given as follows:

4 x 1/4 = 4/4 = 1 = 100% of a day.

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The coordinate of D is (0, - 2) if the points A, B and C are 3 corners of a parallelogram the answer would be (0, - 2).

In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.

It is given that:

the points A, B, and C are 3 corners of a parallelogram what are the coordinates of D.

Let D = (x, y)

Now, We know that;

The midpoint of AC = Mid-point of BD

(-2 + 5)/2 = (x + 3)/2

3 = x + 3

x = 0

(- 3+3)/2 = (y + 2)/2

y = - 2

Thus, the coordinate of D is (0, - 2) if the points A, B and C are 3 corners of a parallelogram the answer would be (0, - 2).

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Answer:

You must be really must to answer that paper yho

Answer: Your answer will be [tex]x=7[/tex]

If it's okay, I would like someone to talk to. My email address is jeremiah.mccrocklin06 at symbol g mail . com

(-3x + 2y + z = 0 )

The equation of the plane passing through the origin and containing the vectors \( \left[\begin{array}{c}1 \\ -1 \\ 1\end{array}\right] \) and \( \left[\begin{array}{l}1 \\ 0 \\ 3\end{array}\right] \) can be found by taking the cross product of the two vectors and using the resulting vector as the normal vector of the plane. The cross product of the two vectors is given by:

\( \left[\begin{array}{c}1 \\ -1 \\ 1\end{array}\right] \times \left[\begin{array}{l}1 \\ 0 \\ 3\end{array}\right] = \left[\begin{array}{c}(-1)(3) - (1)(0) \\ (1)(3) - (1)(1) \\ (1)(0) - (1)(-1)\end{array}\right] = \left[\begin{array}{c}-3 \\ 2 \\ 1\end{array}\right] \)

Therefore, the equation of the plane is given by:

\( -3x + 2y + z = 0 \)

This is the equation of the plane passing through the origin and containing the two given vectors.

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The equation is true, the point (-1,6) does indeed lie on the line (-3,5).

The equation of a line is typically written in the form y = mx + b, where m is the slope and b is the y-intercept. In order to determine whether or not the point (-1,6) lies on the line (-3,5), we need to plug in the x and y values of the point into the equation of the line and see if the equation is true.

First, we need to find the slope of the line. The slope is the difference in the y values divided by the difference in the x values:

m = (5 - 6)/(-3 - (-1)) = -1/-2 = 1/2

Next, we need to find the y-intercept of the line. We can do this by plugging in one of the points and solving for b:

5 = (1/2)(-3) + b

b = 5 + (3/2) = 13/2

Now we have the equation of the line: y = (1/2)x + 13/2

Finally, we can plug in the x and y values of the point (-1,6) to see if the equation is true:

6 = (1/2)(-1) + 13/2

6 = -1/2 + 13/2

6 = 12/2

6 = 6

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Therefore , the solution of the given problem of arithmetic mean comes out to be  option A an=3+2(n-1).

The usual values of a list are determined by adding up every single integer one of the items on the list, which are frequently referred to as the organization's objectives. The number of list items with the highest abundance is then used to adjust these average values. Mathematical growth trends are similar. The number 21 turns into seven by adding three to the true means of the digits 5, 7, and 9, which is 4.

Here,

The following is the formula for the general word "an" in an arithmetic sequence:

=> a = a1 + (n - 1)d

where the first term is denoted by a1, the term number is n, and the common difference is d.

A1 = 3 and A11 = 23 are provided. To determine the common difference, we can use the method for the eleventh term:

=> a11 = a1 + (11 - 1)d

=> 23 = 3 + 10d

=>  d = 2

Inputting this number of d into the general term's formula yields the following results:

=> a = 3 + (n - 1)2

The right response is therefore: an=3+2(n-1).

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The function that generates the sequence 1, 2, 4, 8, ... is:

Of(x) = 2^(x-1)

We can check this by plugging in the first few values of x:

Of(1) = 2^(1-1) = 1

Of(2) = 2^(2-1) = 2

Of(3) = 2^(3-1) = 4

Of(4) = 2^(4-1) = 8

Therefore, the answer is option B.

The solutions to the given trigonometric equation on the interval [0,2π) are θ = 2π/3 and θ = 4π/3. These values can also be expressed in decimal form as θ = 2.09 and θ = 4.19, rounded to two decimal places

To solve the given trigonometric equation on the interval [0,2π), we need to use the quadratic formula.

First, let us rewrite the equation in terms of x:
2x^2 + 5x + 2 = 0

Next, we can apply the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)

Plugging in the values from the equation:
x = (-(5) ± √((5)^2 - 4(2)(2)))/(2(2))

Simplifying:
x = (-5 ± √(25 - 16))/4
x = (-5 ± √9)/4
x = (-5 ± 3)/4

This gives us two possible values for x:
x = (-5 + 3)/4 = -2/4 = -0.5
x = (-5 - 3)/4 = -8/4 = -2

Now we need to convert these values back to θ by using the inverse cosine function:
θ = cos^-1(-0.5)
θ = cos^-1(-2)

The first value, θ = cos^-1(-0.5), gives us two solutions on the interval [0,2π):
θ = 2π/3 and θ = 4π/3

The second value, θ = cos^-1(-2), does not give us any solutions on the interval [0,2π) because the cosine function only takes on values between -1 and 1.

Therefore, the solutions to the given trigonometric equation on the interval [0,2π) are θ = 2π/3 and θ = 4π/3. These values can also be expressed in decimal form as θ = 2.09 and θ = 4.19, rounded to two decimal places.

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Answer:

The second answer is correct

Step-by-step explanation:

The first image shows nuclear fusion, combining two lighter nuclei to make a helium and a heavy nucleus, and the second image shows nuclear fission, taking a large unstable nucleus and turning it into two lighter nuclei.

Answer:

c(t) = $85 × (1.09)^t

Step-by-step explanation:

Assuming that the inflation rate remains constant at 9% per year, the cost of the athletic shoes after t years can be determined by multiplying the original cost by the inflation factor for t years, which is given by (1 + 0.09)^t, or 1.09^t. Therefore, the algebraic rule to determine the cost, c(t), of the shoes after t years is:

c(t) = $85 × 1.09^t

Simplifying the expression, we get:

c(t) = $85 × (1.09)^t

where t is the number of years after the original purchase.

Mariam will have purchased 3.5 pounds of fruit if she purchases 3 pounds of apples and 0.5 pounds of strawberries.

Mariam will purchase a total of (x + y) pounds of fruit if she purchases x pounds of strawberries and y pounds of apples.

The arithmetic operations were used to arrive at the answer.

The four basic operations—often referred to as "arithmetic operations"—are thought to be able to describe all real numbers. Divide, multiply, add, and subtract are the four mathematical operations that result in the quotient, product, sum, and difference.

We are given that Mariam buys 0.5 pounds of strawberries and 3 pounds of apples.

So, the total pounds of fruit bought = 0.5 + 3 = 3.5

Similarly, if she buys x pounds of strawberries and y pounds of apples, then the total amount of pound of fruits  = (x + y)

Hence, the required solution has been obtained.

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As a result, the equation system has the following solution: x = -24/5, y = -9/5.

A mathematical assertion known as an equation is composed of a pair of expressions joined together by the equal symbol. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of a quantity x is 7.

One of the best methods to solve the given system of equations is the elimination method.

To apply the elimination method, we need to multiply one or both equations by a suitable constant so that when we add or subtract the two equations, one of the variables is eliminated. In this case, if we multiply the first equation by 3, we get:

9x + 21y = -57

Now we can add this equation to the second equation to eliminate the x variable:

9x + 21y = -57

-3x + 4y = 12

25y = -45

Dividing both sides by 25, we get:

y = -45/25 = -9/5

Now we can substitute this value of y into one of the original equations to solve for x. Let's use the second equation:

-3x + 4y = 12

-3x + 4(-9/5) = 12

-3x - 36/5 = 12

-3x = 12 + 36/5

-3x = 72/5

x = -24/5

As a result, the following is the system of equations' solution:

x = -24/5, y = -9/5

So the best method to solve this system of equations is the elimination method.

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The exact length of segment AB is equal to: D. √13 units.

Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represents the data points (coordinates) on a cartesian coordinate.

Substituting the given points into the distance formula, we have the following;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(4 - 2)² + (5 - 2)²]

Distance = √[(2)² + (3)²]

Distance = √(4 + 9)

Distance = √13 units.

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The lengths of the two legs are 2 centimeters and 9 centimeters.

Let's call the shorter leg of the right triangle x and the other leg y. According to the given information, we can create the following equation:

x = y - 7

Since we know that the hypothenuse is 13 centimeters, we can use the Pythagorean theorem to create another equation:

x^2 + y^2 = 13^2

Substituting the first equation into the second equation, we get:

(y - 7)^2 + y^2 = 13^2

Simplifying and rearranging terms, we get:

2y^2 - 14y - 72 = 0

Using the quadratic formula, we can solve for y:

y = (14 ± √(14^2 - 4(2)(-72))) / (2(2))

y = (14 ± √484) / 4

y = (14 ± 22) / 4

y = 9 or y = -2

Since the length of a leg cannot be negative, we reject the negative solution and take y = 9 centimeters as the length of the other leg. Then, we can use the first equation to find the length of the shorter leg:

x = 9 - 7

x = 2 centimeters

Therefore, the lengths of the two legs are 2 centimeters and 9 centimeters.

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Answer:

2400

Step-by-step explanation:

144 are seated

94% yet to arrive

6% = 144

Easy method Find the value of 1%

144/6 will be 1%

If 1% =24 then 100% will be 24x 100

Total tickets sold will be 2400

Check: 6% of 2400 is 144

The equivalent percent of 1/5 is 20%.  

To find this answer, we can convert the fraction to a decimal and then multiply by 100 to find the percent. Here are the steps:

1. Convert the fraction to a decimal: 1/5 = 0.2
2. Multiply the decimal by 100 to find the percent: 0.2 * 100 = 20%

Therefore, 1/5 is equivalent to 20%.

In terms of the shaded grid, if we were to shade 1 out of 5 squares, we would be shading 20% of the grid.

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Answer:

B

Step-by-step explanation: