What are the domain and range of f(x) = (one-sixth) Superscript x + 2?

Her sales in order to earn at least $29,000 this year must be at least 60000

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

Using the above as a guide, we have the following:

Earnings = 20000 + 15% * x

Where x is sales

The earnings is atleast 29,000

So, we have

20000 + 15% * x ≥ 29,000

This gives

15% * x ≥ 9,000

So, we have

x ≥ 60000

Hence, her sales must be at least 60000

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Answer:

7.7cm to 1 decimal place

Step-by-step explanation:

for 1st circle, area of full circle = π r² = π (12)² = 144π

area of sector for 1st circle = (42/360) X 144π = 16.8π

for sector of 2nd circle, area = 16.8π

area of sector = (103/360) π r² = 16.8π

π r² = (16.8π) ÷ (103/360)

= 184.469.....

r² = 58.718.....

r = 7.7 cm to 1 decimal place

There are $18$ possible integers $n$ that can be formed using the digits $6,7,8,9$ where each digit is used no more than once and the resulting integer is a multiple of $3$.

To determine if a number is divisible by $3$, we can add up its digits and see if that sum is divisible by $3$. Since $6+7+8+9 = 30$ is divisible by $3$, any integer formed by these four digits will be divisible by $3$ if and only if it contains at least one $9$.

There are four ways to choose the location of the $9$ in the integer. Once we've chosen the location for the $9$, we can fill the remaining three spots with the digits $6,7,$ and $8$ in any order. Since there are $3! = 6$ ways to order three distinct elements, there are $4\times 6 = 24$ ways to form an integer using the digits $6,7,8,9$ with no repetition that is divisible by $3$. However, we've counted the integer $9876$ twice, so there are actually only $18$ possible integers.

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To represent the world population in billions t years after 2000, an exponential growth equation can be used.

Explanation:

Let y be the world population in billions t years after 2000. Let t be the time elapsed in years since 2000. Let y0 be the world population in billions in the year 2000. Let r be the annual growth rate of the world population as a decimal.

Using the exponential growth equation, we can write:

y = y0 * (1 + r)^t

To find the value of r, we can use the population data from 2000 and 2005. The population growth from 2000 to 2005 can be calculated as:

(6.515 - 6.124) / 6.124 = 0.0638

This means that the world population grew at an annual rate of 0.0638 or 6.38% per year. Therefore, the exponential growth equation for the world population in billions t years after 2000 is:

y = 6.124 * (1 + 0.0638)^t

This equation can be used to estimate the world population in any year t after 2000.

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The two opposite Interior angles of the triangle are y and 56°.

In a triangle, the sum of the measures of the interior angles is always 180°. the three interior angles of the triangle A, B, and C. The exterior angle, which is the angle formed by extending one of the sides of the triangle, is equal to the sum of the two non-adjacent interior angles.

So, if we call the two non-adjacent interior angles that form the exterior angle x and y, we can write:

x + y = 124°    (1)

The third interior angle, C, can be found by subtracting the sum of the other two interior angles from 180°:

C = 180° - (x + y)   (2)

We can use equation (1) to solve for one of the variables, say x, in terms of the other, y:

x = 124° - y

Substituting this into equation (2), we get:

C = 180° - (124° - y + y) = 56°

Therefore, the two opposite interior angles of the triangle are y and 56°.  that there are different possible values for y, depending on which exterior angle we are considering. However, once we know one of the opposite interior angles, we can always find the other one by subtracting it from 180°.

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The solution of the inequality is as follows:

y ≥ 8

Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.

Therefore, let's solve the inequality by finding the value of variable y in the inequality.

A variable is a number represented with letter in the inequality.

Therefore,

11 - 4y ≥ -21

subtract 11 from both sides of the inequality

11 - 4y ≥ -21

11 - 11 - 4y ≥ -21 - 11

-4y ≥ - 32

divide both sides of the inequality by -4

y ≥ - 32 / - 4

y ≥ 8

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Answer:

D. y ≤ 8

Step-by-step explanation:

Given inequality:

[tex]11-4y \geq -21[/tex]

To solve for y, begin by subtracting 11 from both sides of the inequality:

[tex]\begin{aligned}11-4y-11 &\geq -21-11\\\\-4y &\geq -32\end{aligned}[/tex]

To isolate y, divide both sides by -4.

As we are dividing by a negative number, we must reverse the direction of the inequality symbol.

[tex]\begin{aligned}\dfrac{-4y}{-4} &\geq \dfrac{-32}{-4}\\\\y&\leq8\end{aligned}[/tex]

Therefore, the solution to the given inequality is y ≤ 8.

If the area between the function and the -axis on the interval [a, b] is 10 and the function is continuous on and on, then the average value of the function on this interval is between m and M, where m and M are the lower and upper bounds for the function on the interval.

To find the average value of a continuous function on an interval, we need to use the following formula:
Average value = (1 / b-a) * ∫[a,b] f(x) dx
where a and b are the endpoints of the interval, and ∫[a,b] f(x) dx represents the definite integral of the function over the interval.
In this case, we are given that the area between the function and the -axis on the interval [a, b] is 10. This means that ∫[a,b] f(x) dx = 10.
We don't know the values of a and b, but we do know that the function is continuous on and on, which means that it is continuous on the entire interval [a, b]. Therefore, we can assume that the function is integrable on this interval.
To find the average value of the function, we need to know the length of the interval [a, b]. This is given by the difference between the endpoints: b-a.
We don't know the value of b-a, but we do know that the function is continuous on and on, which means that it is bounded on this interval. This means that there exist numbers M and m such that m ≤ f(x) ≤ M for all x in [a, b].
We can use this information to find an upper bound and a lower bound for the average value of the function:
Lower bound = (1 / (b-a)) * ∫[a,b] m dx = m
Upper bound = (1 / (b-a)) * ∫[a,b] M dx = M
Therefore, the average value of the function on the interval [a, b] is between m and M. We cannot determine the exact value of the average value without knowing more information about the function or the interval.
In summary, if the area between the function and the -axis on the interval [a, b] is 10 and the function is continuous on and on, then the average value of the function on this interval is between m and M, where m and M are the lower and upper bounds for the function on the interval. The length of the interval [a, b] and the exact value of the function would be needed to find the exact value of the average value.

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We get the following sine model for the vertical displacement y of a point on the blade at time t: y = 7.5 sin(2π(3t - 1)) + 40. This model gives the height above the ground of a point on the blade at time t, measured in minutes.

Assuming that the blades move in a circular motion, the vertical displacement of a point on a blade can be modeled using a sine function.

Let's start by finding the period of the function, which is the time it takes for the blade to complete one full rotation. Since the blade completes 3 rotations every minute, the period is:

T = 1/3 minutes

Next, we need to find the amplitude of the function, which is half the distance between the highest and lowest points of the blade's path. Since the blade is 15 feet long, the amplitude is:

A = 15/2 = 7.5 feet

Finally, we need to find the vertical displacement of the blade at time t, measured in minutes. Let's assume that t=0 corresponds to a blade pointing directly upwards. As the blade rotates, it moves in a circle with radius 15 feet, centered at a height of 40 feet above the ground. The vertical displacement of the blade is the y-coordinate of the point on the circle at angle θ, where θ is given by:

θ = 2π(3t - 1) (in radians)

This formula gives the angle in radians that the blade has rotated through at time t, taking into account the fact that the blade starts at a random angle at t=0. (The "-1" term ensures that the blade starts at the top at t=0.)

Putting it all together, we get the following sine model for the vertical displacement y of a point on the blade at time t:

y = 7.5 sin(2π(3t - 1)) + 40

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The relationships between the line segments in the diagrams are as follows:

a) Equal Length

b) Parallel

c) Perpendicular

d) Equal Length

Let's analyze each diagram and determine the relationships between the line segments.

a) Equal Length:

In this diagram, the two line segments appear to be of the same length. They do not appear to be parallel or perpendicular to each other. When the lengths of two line segments are equal and their orientation doesn't affect this equality, we say they are of equal length. In this case, both line segments simply share the same length without any specific angle relationship.

b) Parallel:

In this diagram, the two line segments run side by side in the same direction and do not intersect. When two lines follow this pattern, they are considered parallel. Parallel lines have the same slope, which means they maintain a constant distance between each other as they extend indefinitely.

c) Perpendicular:

In this diagram, the two line segments meet at a right angle, forming a perfect 90-degree angle where they intersect. When two lines intersect at a right angle, they are referred to as perpendicular. Perpendicular lines have slopes that are negative reciprocals of each other, meaning they intersect at right angles.

d) Equal Length:

Similar to the first diagram, in this case, the two line segments are of equal length. They are not parallel or perpendicular; they simply have the same length.

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The percent is easily represented as a fraction (e.g., 25% as 1/4 or 50% as 1/2). Using the fraction form can make calculations easier to understand and perform, especially when dealing with whole numbers.

You might want to use the fraction form of a percent instead of the decimal form when working with fractions or when it is easier to simplify a problem using fractions. For example, if you are trying to find 25% of a number and the number can be easily divided by 4, it may be simpler to write 25% as 1/4 rather than 0.25. Additionally, if you are working with ratios or proportions, it may be more useful to use fractions rather than decimals to keep the numbers in the same format.
In finding the percent of a number, you might want to use the fraction form of the percent instead of the decimal form when working with ratios, simplifying calculations, or when the percent is easily represented as a fraction (e.g., 25% as 1/4 or 50% as 1/2). Using the fraction form can make calculations easier to understand and perform, especially when dealing with whole numbers.

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The translation of the triangle, 2 units up and 3 units to the left, followed by a dilation by a scale factor of 4 about the origin, indicates;

The coordinates of the vertex B is; (-20, 0)

A dilation transformation is one in which the size of the pre-image is transformed to produce the image, which may be smaller or increased in size.

The coordinates of the vertices of the triangles are;

A(3, 3), B(-2, -2), and C(4, -4)

The translation applied to the triangle are;

Vertical translation = 2 units up

Horizontal translation = 3 units to the left

The scale factor of the dilation = 4

The center of dilation = The origin

Therefore, we get;

The transformation applied to the vertices are as follows;

A(3 - 3, 3 + 2), B(-2 - 3, -2 + 2), and C(4 - 3, -4 + 2), which produces the coordinate points;

A(0, 5), B(-5, 0), and C(1, -2)

The dilation by a scale factor of 4, with the center of dilation at the origin, therefore, produces;

4 × (0, 5) ⇒ A'(0, 20)

4 × (-5, 0) ⇒ B'(-20, 0)

4 × (1, -2) ⇒ C'(4, -8)

The vertex of the coordinate B are therefore; (-20, 0)

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The margin of error is approximately $43.51. The 98% confidence interval for the mean amount of mortgage paid per month by all homeowners in this area is ($1466.49, $1553.51). The banker should use a sample size of at least 285.

a) We want to find the margin of error for a 98% confidence interval. The critical value for a 98% confidence interval with 97 degrees of freedom is 2.326. The margin of error is then:

margin of error = critical value * (standard deviation / sqrt(sample size))

= 2.326 * (194 / sqrt(98))

≈ 43.51

So the margin of error is approximately $43.51.

b) The 98% confidence interval is given by:

sample mean ± margin of error

= $1510 ± 43.51

= ($1466.49, $1553.51)

So the 98% confidence interval for the mean amount of mortgage paid per month by all homeowners in this area is ($1466.49, $1553.51).

c) We want to find the sample size required to have a margin of error of $25. Solving the margin of error formula for sample size, we get:

sample size = (critical value * standard deviation / margin of error)^2

Since we want a 98% confidence interval, the critical value is 2.326. The standard deviation is still $194. Plugging in $25 for the margin of error, we get:

sample size = (2.326 * 194 / 25)^2

≈ 284.87

So the banker should use a sample size of at least 285.

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cos(C) = (4.12^2 + 4^2 - 5^2) / (2(4.12)(4)) ≈ 0.8197

C ≈ 36.99°

To find 2C, we simply multiply C by 2:

2C ≈ 73.98°

Therefore, the correct answer is D. 73.98.

Answer: The required equation of the straight line is: y = -5x+3

Step-by-step explanation:

we know, the equation of a straight line is :

y = mx + c ----(i)

where y = y coordinate, x = x coordinate, m = slope of the straight line, and c = intercept of the straight line.

Slope, m = tan theta = y2 - y1 / x2 - x1,

In this question, c = 3,

m = y2 - y1 / x2 - x1  

Here, taking y2 = 3, y1 = -2, x2 = 0, x1 = -1 , we have,

=> m = 3 - (-2) / 0 -1

=> m = -5

Now, putting the values of m and c in equation (i) we get,

y = -5x + 3, which is the required solution.

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To solve for the equation of a straight line, we calculate the slope 'm' and y-intercept 'b' from the graph and substitute these values into the standard line equation y=mx+b.

To work out the equation of the straight line we usually use the standard form of a linear equation which is y=mx+b, where 'm' is the slope of the line and 'b' is the y-intercept. The slope 'm' can be found by identifying two points on the line and applying the formula (y2 - y1) / (x2 - x1). The y-intercept 'b' is where the line crosses the y-axis. Once 'm' and 'b' have been calculated, they can be substituted into the equation format to find the equation of the line.

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Answer:

2

Step-by-step explanation:

F^-1 IS AN INVERSE, SO F(2)=3 THEREFORE F^-1(3) = 2

Answer:

[tex]\frac{w^{6} }{9}[/tex]

Step-by-step explanation:

To divide powers that have the same base, subtract the denominator's exponent from the numerator's exponent.

Doing so leaves us with [tex]3^{-2}[/tex] [tex]k^{0}[/tex][tex]w^{6}[/tex].

Next, you need to calculate 3 to the power of −2 to get  [tex]\frac{1}{9}[/tex].

Then, calculate k to the power of 0 to get 1.

Multiply  [tex]\frac{1}{9}[/tex] and 1 to get [tex]\frac{1}{9}[/tex].

This leaves us with [tex]\frac{1}{9} w^{6}[/tex], which is equivalent to our final answer.

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Answer: The laborer charges $100.00 for a day's weeding contract and was paid $1500.00 for weeding 5 acres of land. This means he received $1500.00 - $100.00 = $1400.00 for weeding 5 acres of land.

The amount he received per acre is $1400.00 / 5 acres = $280.00 per acre.

So the answer is 280

Answer:93.3884%

Step-by-step explanation:

Based on the given conditions, formulate:(121-8)%121

Calculate the sum or difference:113/121 

Rewrite a fraction as a decimal:0.933884

Multiply a number to both the numerator and the denominator: 0.933884* 100/100 

Calculate the product or quotient: 93.3884/100

Rewrite a fraction with denominator equals 100 to a percentage: 93.3884%

Answer:

Step-by-step explanation:

(x+8)(x−8)x2+13 is the answer

The given expression is:

x+8x+2⋅(x+2)(x−8)x2+13

To simplify this expression, you can start by simplifying the denominator:

2⋅(x+2)(x−8)x2+13 = 2(x2-6x-16)x2+13 = 2(x2-6x-16)x2 + 26x - 26x + 13

= 2(x2-6x-16)x2 + 26x + (-26x + 13)

Now you can rewrite the original expression as:

x+8x+(2(x2-6x-16)x2 + 26x + (-26x + 13))

= x(1 + 8x2(x2-6x-16)x2 + 26x + (-26x + 13))

x(2(x^2-6x-16)x^2 + 13)

We can simplify the expression inside the parenthesis first:

2(x^2-6x-16)x^2 = 2x^4 - 12x^3 - 32x^2

Substituting this back into the original expression, we get:

x(2x^4 - 12x^3 - 32x^2 + 13)

Multiplying out the brackets, we get:

2x^5 - 12x^4 - 32x^3 + 13x

Now, we can factor out a common factor of x:

x(2x^4 - 12x^3 - 32x^2 + 13)

= x(2x^4/x - 12x^3/x - 32x^2/x + 13/x)

= x(2x^3 - 12x^2 - 32x + 13/x)

Finally, we can factor the expression inside the brackets:

= x(2x^3 - 16x^2 + 4x^2 - 32x + 8x - 8 + 13/x)

= x(2x^2(x-8) + 4x(x-8) + 8(x-8) + 13/x)

= x(x-8)(2x^2+4x+8) + 13(x-8)/x

= (x-8)(x^3+2x^2+4x+13)/x

Now we can see that the expression can be written as:

(x-8)(x^3+2x^2+4x+13)/x

To simplify further, we can divide x into the numerator to get:

(x+8)(x−8)x^2+13

Therefore, the expression is equal to (x+8)(x−8)x2+13.

The measure of arc BED is 218 degree.

We know,

The total measure of a circle is 360°

Now, from the figure let us consider the Centre of circle at O.

Then, <DOL + <LOB +< BOD= 360

90 + 52 + <BOD= 360

142 + <BOD= 360

<BOD = 360- 142

<BOD = 218

Thus, the measure of arc BED is 218 degree.

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If you save 20% of your paycheck each week, you would save $44.80 if you made $224 in a week. In a month (4 weeks), you would save a total of $179.20.

To determine how much you would save each week, you need to multiply your paycheck by the percentage you want to save:

$224 x 20% = $44.80

Therefore, you would save $44.80 each week if you made $224 and saved 20% of your paycheck.

To calculate how much you would save in a month, you need to multiply your weekly savings by the number of weeks in a month:

$44.80 x 4 = $179.20

Therefore, if you made $224 per week and saved 20% of your paycheck, you would save $44.80 each week and a total of $179.20 in a month.

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The function f(x) and g(x) have the same behavior for all real values except x = -1/4, as f(x) is not defined at x = -1/4.

The function f(x) is defined as follows:

f(x) = [(4x + 1)(x - 5)]/(4x + 1).

The denominator cannot be zero, hence the value that is outside the domain is given as follows:

4x + 1 = 0

4x = -1

x = -1/4.

For the other values, the 4x + 1 terms can be simplified, hence f(x) = g(x) = x - 5, meaning that they are equal.

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Answer:Therefore, the scale of the drawing is 1 inch : 3.166 feet.

Step-by-step explanation:

To find the scale of the drawing, we need to determine the ratio of the size of the porch in the drawing to its actual size.

First, we need to convert 38 inches to feet:

38 inches ÷ 12 inches/foot = 3.1667 feet

Next, we can set up a proportion:

drawing size / actual size = scale factor

Let x be the scale factor. Then:

x / 20 feet = 3.1667 feet / 20 feet

Simplifying the right side:

3.1667 feet / 20 feet = 0.1583

Multiplying both sides by 20 feet:

x = 0.1583 × 20 feet

x = 3.166 feet

Therefore, the scale of the drawing is 1 inch : 3.166 feet.

Based on the information, we can infer that the surface area of the rectangular prism is 485.5 in²

To calculate the surface area of the rectangular prism we must calculate the area of all the faces of the prism:

Now we must multiply each result by 2 because each of the faces is repeated 2 times.

Finally, we must add the values to find the total surface area of the rectangular prism:

Note: This question is incomplete. Here is the complete information.

Attached Image

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The value of BD is 6

Similar triangles are triangles that have the same shape, but their sizes may vary. The corresponding angles of similar triangles are equal.

Also the ratio of corresponding sides of similar triangles are equal.

Therefore;

12/x = x/3

x² = 12 × 3

x² = 36

x = √36

x = 6

Therefore the value of BD is 6

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Based on the evaluation of the conditions, the output "x < 0 and z > 0" will be printed. Therefore, the correct answer is B. x < 0 and z > 0.

The correct indentation of the statement would be as follows:

if (x > 0)

if (y > 0)

System.out.println("x > 0 and y > 0");

else if (z > 0)

System.out.println("x < 0 and z > 0");

Given that x = 1, y = -1, and z = 1, let's evaluate the conditions:

The first if statement checks if x > 0, which is true since x = 1.

Since the condition in the first if statement is true, we move to the inner if statement, which checks if y > 0. However, y = -1, so this condition is false.

The inner if statement is followed by an else if statement that checks if z > 0. Since z = 1, this condition is true.

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The value of x is given as follows:

x = 5.4.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For the angle of 60º, we have that:

Hence we apply the tangent ratio to obtain the value of x as follows:

tan(60º) = 9.3/x

x = 9.3/tangent of 60 degrees

x = 5.4.

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Answer:

---------------------

Use the formula:

where θ is the central angle in degrees, r is the radius

We have:

Substituting the given values, we get:

Therefore, the length of the arc is 14π cm.

All the conic section are,

1) Parabola

2) Hyperbola

3) Ellipse

4) Circle

We have to given that;

We have to find the conic section for each condition.

1) when a plane crosses the generating line at the intersection of a single cone from a double-napped cone.

Then, We get Parabola is formed.

2) We know when a plane intersects on one nape of a double napped cone and then the cross section that is obtained is either a parabola, ellipse or a circle.

But if it passes through both the napes of a double napped cone then the cross-section obtained is a hyperbola.

Hence, the answer is Hyperbola.

3) When, A plane intersects at one cone of a double-napped cone for that the plane is neither parallel to the generating line nor perpendicular to the axis,

Then, Ellipse is formed.

4) When plane intersect at one cone of a double napped cone such that the plane is perpendicular for the generating line.

Then, We get Circle is formed.

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Answer: -4 and 28

Step-by-step explanation:

    First, we will list factors of -112. Since we are multiplying to a negative number, we know that one number will be negative and one number will be positive.

    ±1, ±2, ±4, ±7, ±8, ±14, ±16, ±28, ±56 and ±112

    Looking at this list of factors, we see 28 and 4. We know that 28 - 4 = 24, and 28 * -4 = -112. This means the answer to our question is:

                   -4 and 28