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For the given function  f(x) = ⁿ√p(x), The Domain depends on the value of n and The Domain is all real numbers if n is ODD.

What is the definition of a function?

In mathematics, a function is a relation between a set of inputs (also known as the domain) and a set of possible outputs (also known as the range) with the property that each input is associated with exactly one output.

In other words, a function takes an input value, performs a specific operation or set of operations on it, and produces an output value. It can be represented by a rule, formula, or graph that relates each input to its corresponding output.

Now,

The domain of the function f(x) = ⁿ√p(x) depends on the value of n.

If n is odd, then the function is defined for all real numbers, and the domain is all real numbers.

If n is even, then the function is defined only for non-negative real numbers, and the domain is all non-negative real numbers.

Therefore, the statement "The Domain is all real numbers" is not always true for the function f(x) = ⁿ√p(x). The correct statements are:

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The probability of rolling an odd product is 3/4 or 0.75.

The probability of rolling a product that is greater than or equal to 20 is 8/16 or 0.5.

The probability of rolling a product that is less than 10 is 1/4 or 0.25.

The probability of rolling a product that is a multiple of 10 is 3/16 or 0.1875.

Probability is the measure of the likelihood that an event will occur. It is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

The probability of rolling an odd product is 3/4 or 0.75. This is because there are 12 odd products on the grid out of a total of 16 products.

The probability of rolling a product that is greater than or equal to 20 is 8/16 or 0.5. This is because there are 8 products on the grid that are greater than or equal to 20 out of a total of 16 products.

The probability of rolling a product that is less than 10 is 1/4 or 0.25. This is because there are 4 products on the grid that are less than 10 out of a total of 16 products.

The probability of rolling a product that is a multiple of 10 is 3/16 or 0.1875. This is because there are 3 products on the grid that are a multiple of 10 out of a total of 16 products.

Krystal's game is an example of probability. In this case, Krystal is using the grid to calculate the probability of different outcomes when rolling the two number cubes. By understanding the probability of different outcomes, Krystal can make informed decisions and predict the likely outcome of her game.

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Because the function is one-to-one we know that it is invertible, from that we conclude:

If a function is one-to-one, then the function is invertible in its domain, if we define f⁻¹(x) as the inverse, then we can define two relations:

f( f⁻¹(x)) = x

And that if:

f(x)= y

then:

f⁻¹(y) = x

Here we know that:

f(0) = 7

Then the inverse evaluated in 7 must give 0, this is:

f⁻¹(7) = 0

And the second expression is:

( f(0) )⁻¹

This is not an inverse function, this is the inverse of the function evaluated in 0, then we will get:

( f(0) )⁻¹ = ( 7 )⁻¹ = 1/7.

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After solving the equations e know that Planet II is 35 million miles away from the sun.

The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.

An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.

As in 3x + 5 = 15, for example.

There are many different types of equations, including linear, quadratic, cubic, and others.

The three primary forms of linear equations are point-slope, standard, and slope-intercept.

So, let x be the separation between planet I and the sun.

Planet II's distance from the sun is x-30.2.

Planet iii's distance from the sun is equal to x+24.8.

x + x-30.2 + x+24.8 = 190.2

Mix related phrases to find x.

3x - 5.4 = 190.2

3x = 195.6

x = 65.2

65.2 million miles separate planet I from the sun.

Planet II is 35 million miles from the sun or 65.2-30.2.

Planet iii is 90 million miles from the sun (65.2 + 24.8 = miles).

Therefore, after solving the equations e know that Planet II is 35 million miles away from the sun.

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The measure of angle PQS is of 23º, hence the correct option is given by option C.

The angle addition postulate states that if two angles share a common vertex and a common angle, forming a combination, the measure of the larger angle will be given by the sum of the smaller angles.

In the context of this problem, the angle PQR is the combination of angles PQS and SQR, hence the equation is given as follows:

m < PQR = m < PQS + m < SQR.

Replacing the measures into the equation, the value of x is obtained as follows:

5x + 8 + 2x - 3 = 26

7x = 21

x = 3.

Then the measure of angle PQS is obtained as follows:

PQS = 5(3) + 8 = 15 + 8 = 23º.

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Answer:

The average daily balance on Perry's credit card for the period beginning October 10 was $714, and the balance at the end of the cycle was $506. To calculate the balance due, we need to know the length of the billing cycle. Assuming a 30-day billing cycle, we can use the average daily balance method to calculate the interest charged. The formula for interest charged is: Average Daily Balance x APR x Days in Billing Cycle / 365. Plugging in the numbers, we get: $714 x 0.08 x 30 / 365 = $4.68. Adding this interest to the ending balance of $506, the total balance due is $510.68.

Answer:

Step-by-step explanation:

The equation for the cost of parking in Garage A for t hours is:

A = 3t + 7

The equation for the cost of parking in Garage B for t hours is:

B = 4t + 3

To find the number of hours parked, t, that would make the cost of each garage the same, we can set the two equations equal to each other and solve for t:

3t + 7 = 4t + 3

Subtracting 3t from both sides, we get:

7 = t + 3

Subtracting 3 from both sides, we get:

4 = t

Therefore, if Bella parks for 4 hours, the cost of parking in Garage A and Garage B will be the same.

To verify, we can substitute t = 4 into the two equations:

A = 3(4) + 7 = 19

B = 4(4) + 3 = 19

So, if Bella parks for 4 hours, the cost of parking in Garage A and Garage B will be $19.

Answer:

Bella is deciding between two parking garages. Garage A charges an initial fee of $7 to

park plus $3 per hour. Garage B charges an initial fee of $3 to park plus $4 per hour.

Let A represent the amount Garage A would charge if Bella parks for t hours, and let

B represent the amount Garage B would charge if Bella parks for t hours. Write an

equation for each situation, in terms of t, and determine the hours parked, t, that

would make the cost of each garage the same.

A = $7 + $3

B = $3 + $4

The Rational Expression (18x³yz)/(6xyz⁴) when simplified has its value to be 3x²/z³

Given that

(18x³yz)/(6xyz⁴)

To simplify the given rational expression, we can start by canceling out any common factors between the numerator and denominator.

In this case, we can simplify the expression as follows:

(18x³yz)/(6xyz⁴) = (3x * x * x * y)/(y * z * z * z) =

Evaluate the products

So, we  have

(18x³yz)/(6xyz⁴) = (3x²)/(z³)

Remove the brackets

(18x³yz)/(6xyz⁴) = 3x²/z³

Therefore, the simplified expression is 3x²/z³.

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Answer: The area of a rhombus can be calculated using the formula:

A = (base x height) / 2

Substituting the given values, we get:

A = (17 in x 14 in) / 2

A = 119 sq in

Therefore, the area of the rhombus is 119 square inches.

Hence, the answer is option B, 119 in2.

Step-by-step explanation:

The area of the rhombus is 238 square inches.

To find the area of a rhombus, you can use the formula: Area = base * height.

In this case, the base of the rhombus is 17 inches and the height is 14 inches. Plugging these values into the formula, we get Area = 17 * 14 = 238 square inches.

Therefore, the area of the rhombus is 238 square inches.

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The correct answer is B. 9 3/10. An improper fraction is a fraction where the numerator (the top number) is larger than the denominator (the bottom number).

A fraction is a number that represents a part of a whole. It is a number that is written as two numbers separated by a line, one above the other. The top number is called the numerator and it represents the number of parts being considered.

In the given example, 49/10 is an improper fraction. To convert this improper fraction into a whole number or a mixed number, you need to divide the numerator by the denominator. When you divide 49 by 10, the answer is 4 with a remainder of 9. This is how you get the mixed number 9 3/10 which is the same as 49/10.

9 3/10 is a mixed number which consists of a whole number and a fraction. The whole number is 9 and the fraction is 3/10. The fraction 3/10 can also be written as its simplest form of 1/10 by dividing the numerator and the denominator by 3.

To check if the answer is correct, you can multiply the whole number (9) and the denominator (10) of the mixed number first, and then add the numerator (3) to get the answer of 49. So, 9 x 10 + 3 = 90 + 3 = 93. The answer is 93, which is the same as the numerator of the given improper fraction (49).

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QUESTION :Choose the whole number or mixed number that is equivalent to this improper fraction.

49/10

A. 4 9/10

B. 9 3/10

The value for x in the given triangle is 36.81. The solution has been obtained by using the concept of trigonometry.

What is trigonometry?

Right-angled triangles, including their sides, angles, and connections, are studied in the branch of mathematics known as trigonometry.

We are given a right angled triangle with perpendicular 32 and base x.

We know that tan θ is the ratio of triangle's perpendicular to its base.

Here, θ = 41°

So, we get

⇒ tan 41° = [tex]\frac{32}{x}[/tex]

⇒ 0.8693 = [tex]\frac{32}{x}[/tex]

⇒ 0.8693x = 32

⇒ x = 36.81

Hence, the value for x in the given triangle is 36.81.

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Guitar tabs are generally considered easier to read than regular musical notation because they are written in a language that most guitarists are familiar with.

Guitar is a stringed musical instrument played with the fingers or a pick. It is one of the most popular instruments in the world and is widely used in genres such as rock, jazz, blues, country, folk, and classical.

Unlike traditional notation, guitar tabs do not require any knowledge of music theory to understand. Instead, they are laid out in a straightforward format that conveys the pitch of a note and the timing of when it should be played. This makes it easier for most guitarists to quickly learn a new piece of music without having to spend time studying the complexities of traditional notation. Additionally, guitar tabs also offer an easy way to determine the fingering of certain chords or techniques.
While guitar tabs are easier to read than traditional notation, they do have some drawbacks. For one, guitar tabs cannot convey the same level of detail about a piece of music as traditional notation can. Additionally, it can be difficult for some to distinguish between rhythm and lead parts when reading guitar tabs. Finally, guitar tabs do not easily convey the dynamics or expression of a piece of music, which are important to consider when playing music.

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Step-by-step explanation:

To find out how many more people visited Canada than Mexico, we need to subtract the number of visitors to Mexico from the number of visitors to Canada:

12,968,000 - 9,807,000 = 3,161,000

Therefore, 3,161,000 more people visited Canada than Mexico in 2002.

Answer:

9 seconds

Step-by-step explanation:

right side of the graph touches the x axis at 9

The answer is C. 0.6 hours. They will play each game for 0.6 hours, or 36 minutes.

What are combinations ?

In mathematics, combinations are a way of selecting objects from a set without regard to their order. In other words, a combination is a selection of objects where the order of the selection does not matter.

To find out how long Gretchen and Nina will play each game, we need to divide the total time they will play by the number of games they will play.

Total time they will play = 3.6 hours

Number of games they will play = 6

So, the time they will play each game = Total time ÷ Number of games

= 3.6 hours ÷ 6 games

= 0.6 hours

Therefore, the answer is C. 0.6 hours. They will play each game for 0.6 hours, or 36 minutes.

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Answer:

Step-by-step explanation:

To determine how long your retirement savings will last when withdrawing R2 500 at the beginning of every month, we need to use a financial formula called the future value of an annuity formula, which calculates the future value of a series of equal withdrawals made at regular intervals over a fixed period of time.

In this case, we want to calculate how many months it will take for your retirement savings to be depleted, given that you will be withdrawing R2 500 at the beginning of every month. The formula is:

n = [log(PMT/(PMT - r*PV))]/[log(1+r)]

where:

PMT = R2 500 (the regular payment you will make every month)

r = 7,10%/12 (the monthly interest rate, which is the annual rate of 7,10% divided by 12)

PV = R411 016 (the present value of your retirement savings)

Using the above values in the formula, we get:

n = [log(2500/(2500-((7.10%/12)*411016))))]/[log(1+(7.10%/12))]

n = 182.1

Therefore, it will take approximately 182.1 months, or 15.2 years, until you run out of money, assuming all other factors remain constant, and you withdraw R2 500 at the beginning of each month.

Answer:

1935.2 ft

Step-by-step explanation:

Picture a right triangle with distance from tower to the bus (x)  as the base, and height of the tower 986 ft as the height (y).  Find distance from tower to bus using tan27 = y/x =986/x.  Solve for x:

x = 986/tan27 = 1935.2 ft

A ratio that can be used to determine the slope of this line include the following: D. [tex]\frac{7\;+\;2}{-5\;+\;-8}[/tex]

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the slope formula, we have the following;

Slope (m) = (7 - (-2))/(-5 - 8)

Slope (m) = (7 + 2)/(-5 - 8) ⇒ (Required ratio)

Slope (m) = 9/-13

Slope (m) = -0.6923.

In this context, we can reasonably infer and logically deduce that the slope of this line is equal to -9/13 or -0.6923.

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Step-by-step explanation:

there is something severely wrong with the problem definition.

when the Hypotenuse = 9, there is no 30-60-90 triangle with a leg = 6.

and when we are just focusing that this is a right-angled triangle with the Hypotenuse = 9, then 6 cannot be the longer leg.

it is also not clear what the solution is supposed to be. the 2nd leg ? the area ? the perimeter ? the height(s) ? ...

what ?

so, all I can do here is to show you why I said what I said :

30-60-90 triangle with Hypotenuse = 9

then the longer leg is opposite of the 60° angle and therefore sin(60)×9 = 7.794228634...

the shorter leg is opposite of the 30° angle and therefore sin(30)×9 = 0.5×9 = 4.5

a right-angled triangle with Hypotenuse = 9, one leg = 6 gives us per Pythagoras for the other leg

9² = 6² + leg²

81 = 36 + leg²

45 = leg²

leg = sqrt(45) = 6.708203932...

so, you see, as stated above, there is no leg with the length 6 in such a 30-60-90 triangle.

and in a more general right-angled triangle, if one leg = 6, then the other leg is actually longer.

therefore, there is everything wrong with the problem definition.

Answer:

To find an appropriate trigonometric substitution of the form x = f(t) to simplify the integral, we need to look for expressions involving square roots of the form:

sqrt(a^2-x^2)

sqrt(a^2+x^2)

sqrt(x^2-a^2)

If we have sqrt(a^2-x^2), we can use the substitution x = a sin(t) or x = a cos(t) depending on which one of them makes the expression simpler.

If we have sqrt(a^2+x^2), we can use the substitution x = a tan(t) or x = a sec(t).

If we have sqrt(x^2-a^2), we can use the substitution x = a sec(t) or x = a tan(t).

It is important to keep in mind the trigonometric identities and the Pythagorean theorem to simplify the integrals after substituting.

Step-by-step explanation:

hope its help <:

Y = 5 cos(0.3185x) + 10 is the volume of oxygen as a function of time can be modeled by this cosine function.

What is  cosine function ?

The cosine function is a mathematical function that relates the ratio of the sides of a right triangle. In a right triangle, the cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. In trigonometry, the cosine function is defined as the ratio of the adjacent side to the hypotenuse in a right triangle. The cosine function is periodic, meaning it repeats itself at regular intervals, and has a range of values between -1 and 1. It is commonly used in mathematics, physics, and engineering to model periodic phenomena such as sound waves, electromagnetic waves, and oscillations.

According to the question:
To find the equation of the cosine function, we need to identify the amplitude, period, phase shift, and vertical shift of the function based on the given information.

Since point M is the minimum value of the function, the vertical shift is 10. This means that the equation of the function is of the form:

Y = A cos(Bx - C) + D

where D = 10.

To find the amplitude, we need to find the distance between the maximum and minimum values of the function. Since the graph of a cosine function oscillates between its maximum and minimum values, the amplitude is half the distance between these values.

From the graph, we can see that the maximum value of the function is 20, so the distance between the maximum and minimum values is:

20 - M = 20 - 10 = 10

Therefore, the amplitude is:

A = 10/2 = 5

To find the period, we need to find the distance between two consecutive peaks or troughs of the function. From the graph, we can see that the distance between two consecutive peaks is approximately 6.28 units. This means that the period is:

P = 6.28

To find the phase shift, we need to find the horizontal shift of the function from its standard form. Since the minimum value of the function occurs at x = 0, the phase shift is:

C =

Therefore, the equation of the cosine function is:

Y = 5 cos((2π/P)x - C) + D

Y = 5 cos((2π/6.28)x) + 10

Simplifying,

Y = 5 cos(0.3185x) + 10

So, the volume of oxygen as a function of time can be modeled by this cosine function.

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Answer:

Step-by-step explanation: 5.) Circular shape.

     6.) Feet.

     7.) Circle.

     8.) The circumference is 9 and the radius is 18.

     9.)  By the way we would need to use The Circumference as 2 and the radius to be 9 to equal 18 for the radius circle.

By rewritting the exponential equation, we can see that the correct options are B and C.

We know that the balance is modeled by the exponential equation below:

[tex]A = 328.23\times e^{0.045*(t - 2)}[/tex]

Now we want to see which of the other equations are equivalent to this one, so we need to rewrite this equation, so let's do that.

First we can rewrite the second part to get:

[tex]A = 328.23\times e^{0.045\times(t - 2)}\\\\A = 328.23\times(e^{-2*0.045*}\times e^{0.045\times t})\\\\A = 300\times e^{0.045\times t}[/tex]

So that is an equivalent equation.

We also can keep rewritting this to get:

[tex]A = 300\times e^{0.045\times t}\\\\A = 300\times(e^{0.045})^t\\\\A = 300\times(1.046)^t[/tex]

The correct options are B and C.

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Answer:

f(-x) = 8^-x

Step-by-step explanation:

y = 1 arctan(1/2(x-0)) - [tex]\frac{\pi }{3}[/tex], which simplifies to y = arctan(1/2(x-[tex]\frac{\pi }{3}[/tex])). So correct option is B.

An equation is a mathematical statement that uses symbols and mathematical operations to show that two quantities are equal. Equations are used to represent a wide range of relationships and can be used to solve problems and make predictions.

The original equation is y = arctan x. To horizontally compress the graph by 1/2, we need to replace x with 2x. The equation becomes y = arctan(2x).

To translate the graph down by [tex]\frac{\pi }{3}[/tex] units, we need to subtract [tex]\frac{\pi }{3}[/tex] from y. The equation becomes y = arctan(2x) - [tex]\frac{\pi }{3}[/tex].

So far, we have y = arctan(2x) - [tex]\frac{\pi }{3}[/tex]. To match the form y = a arctan(b(x-c)) + d, we need to further transform the equation.

We can write 2x as 1/2(4x), so the equation becomes y = arctan(1/2(4x)) - [tex]\frac{\pi }{3}[/tex].

Comparing this with y = a arctan(b(x-c)) + d, we have a = 1, b = 1/2, c = 0, and d = -[tex]\frac{\pi }{3}[/tex].

Substituting these values, we get y = 1 arctan(1/2(x-0)) - [tex]\frac{\pi }{3}[/tex], which simplifies to y = arctan(1/2(x-[tex]\frac{\pi }{3}[/tex])).

Therefore, the answer is B. y= arctan(1/2(x-[tex]\frac{\pi }{3}[/tex])).

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The complete question is:

The equation y = 1 arctan(1/2(x-0)) -π/3 can be written as y = arctan(1/2(x-π/3)).

What is equation ?

An equation is a mathematical statement that proves the equality of two quantities by using symbols and mathematical procedures. Equations can be used to express a wide variety of relationships, solve issues, and generate predictions.

The first formula is y = arctan x. We must swap out x for 2x in order to horizontally compress the graph by half. y = arctan is the new formula.(2x).

We must deduct π/3  from y in order to scale the graph downward by π/3 units. Y = arctan(2x) -π/3 is the new equation.

y = arctan(2x)-π/3  is what we now have. We need to further alter the equation so that it has the form y = an arctan(b(x-c)) + d.

Since 2x can be written as 1/2(4x), the equation changes to y = arctan(1/2(4x)) -π/3.

We have a = 1, b = 1/2, c = 0, and d = π/3- when y = an arctan(b(x-c)) + d is compared to this.

The result of substituting these numbers is y = 1 arctan(1/2(x-0)) -π/3, which may be written as y = arctan(1/2(x-π/3)).

y= arctan(1/2(x-π/3)), hence the solution is B.

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Answer:

$16

Step-by-step explanation:

12C + 28 = 22012C = 220 - 2812C = 192C = 192÷12C = 16

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