The graphs of f(x) and g(x) are shown below:

Graph of function f of x open upward and has its vertex at negative 7, 0. Graph of function g of x opens upward and has its vertex at negative 9, 0.

If f(x) = (x + 7)2, which of the following is g(x), based on the translation? (1 point)

g(x) = (x + 9)2
g(x) = (x + 5)2
g(x) = (x − 9)2
g(x) = (x − 5)2

The pie chart for the information given are attached below.

Pie charts gives a graphical representation of related items , expenses as a fraction of a whole. Each slice represents a group in the data. The size of the slice also corresponds to the size or value assigned to the group in the data.

For the first pie chart, Food has the highest value in terms of expenses. This means the size of the food slice in pie chart would be the largest and saving being the smallest .

Similarly, Maths would have the biggest slice and Social science would have the smallest in the second pie chart.

Therefore, the pie charts are attached below .

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To analyze the data, Sabastian should follow the following steps:Define the research question,Collect the data,Organize the data,Analyze the data,Interpret the results and Communicate the results

1. Define the research question: He needs to clarify the research question, and identify the variables he is investigating.

2. Collect the data: He should obtain the data he needs through a survey, experiment, observation, or any other appropriate method.

3. Organize the data: He needs to sort and arrange the data in a meaningful way, such as using tables, graphs, or charts.

4. Analyze the data: He should use statistical techniques to explore the data and identify patterns, trends, and relationships among the variables.

5. Interpret the results: He should draw conclusions based on the data analysis, and assess the implications of the findings for the research question.

6. Communicate the results: He should present the findings in a clear and concise manner, using appropriate visuals and language, to effectively communicate the results to others.

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The probability in this problem is given as follows:

p = 10!/20!.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is then calculated as the division of the number of desired outcomes by the number of total outcomes.

For this problem, the desired outcomes are the arrangements of the 10 dolls from these countries, hence:

10!.

For the total outcomes, they are the arrangements of 20 dolls, hence:

20!.

Hence the probability is given as follows:

10!/20!.

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The area of triangle BCD is 12 square centimeters.

To find the area of triangle BCD, we need to determine the height of the triangle. Since rectangle ABDE shares side BD with triangle BCD, the length of BD is equal to the width of the rectangle, which is given as 9 centimeters.

The area of a triangle is given by the formula: Area = (base × height) / 2.

In this case, the base of the triangle is CD, which is given as 6 centimeters.

To find the height of the triangle, we can use the fact that the area of rectangle ABDE is 36 square centimeters. The area of a rectangle is given by the formula: Area = length × width.

Since the area of the rectangle is 36 square centimeters and the length of DE is 9 centimeters, we can determine the width of the rectangle: width = Area / length = 36 / 9 = 4 centimeters.

Since the width of the rectangle is equal to the length of BD, we can conclude that the height of the triangle, which is perpendicular to the base CD, is also 4 centimeters.

Now we can calculate the area of triangle BCD using the formula mentioned earlier:

Area = (base × height) / 2 = (6 × 4) / 2 = 24 / 2 = 12 square centimeters.

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Diego is making the mistake of not following the correct steps while solving a quadratic equation, which has led him to divide each side of the equation by 2 instead of square root(100). This mistake has occurred because he is trying to find a value instead of the actual answer to the problem.A)

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Answer:

  4.5 kWh

Step-by-step explanation:

You want an estimate of the mean of the solar panel output represented by the given histogram.

The mean of the output values can be estimated as the weighted average of the middle of each interval, weighted by the area of the histogram in that interval.

The computation looks like ...

  [tex]\dfrac{.5\times1+1.5\times1+2.5\times1+3.5\times4+4.5\times4+5.5\times3+6.5\times 2+7.5\times2}{1+1+1+4+4+3+2+2}\\\\\\=\dfrac{81}{18}=4.5[/tex]

The mean daily energy output of the solar panel is about 4.5 kWh.

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The costs for each item in this problem are given as follows:

The costs are obtained solving a system of equations, for which the variables are given as follows:

Seven hot dog(s) and four hamburger(s) cost $16.00, hence:

7x + 4y = 16

1.75x + y = 4

y = 4 - 1.75x.

Four hot dog(s) and seven hamburger(s) cost $19.75, hence:

4x + 7y = 19.75

x + 1.75y = 4.9375.

Replacing the first equation into the second, the value of x is given as follows:

x + 1.75(4 - 1.75x) = 4.9375

2.0625x = 2.0625

x = 1.

The value of y is given as follows:

y = 4 - 1.75

y = 2.25.

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The error is:

∠M and ∠N are supplementary.

m∠M + m∠N = 180

∠N and ∠0 are supplementary.

m∠N + m∠0 = 180

We have,

In a parallelogram, consecutive angles are supplementary.

A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length.

Since opposite sides are parallel, opposite angles in a parallelogram are congruent (equal in measure).

Consecutive angles are the pair of angles that share a side in the parallelogram.

The sum of the measures of these consecutive angles is always 180 degrees, making them supplementary.

Thus,

The error is:

∠M and ∠N are supplementary.

m∠M + m∠N = 180

∠N and ∠0 are supplementary.

m∠N + m∠0 = 180

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a) The function is vertically stretched and shifted parabola with translated horizontally to the right by 5 units, and vertically shifted upward by 2 units.

b) The function is vertically compressed and shifted parabola with translated horizontally to the left by 6 units, and vertically shifted downward by 4 units.

Given data,

a)

For the function g(x) = 3(x - 5)² + 2, the transformations of the graph of the parent function f(x) = x² can be described as follows:

Vertical Stretch: The coefficient 3 in front of the parent function causes a vertical stretch by a factor of 3. This means the graph of g(x) will be three times taller than the graph of f(x).

Horizontal Translation: The expression (x - 5) inside the square term indicates a horizontal translation to the right by 5 units. This means the graph of g(x) will be shifted horizontally to the right by 5 units compared to the graph of f(x).

Vertical Translation: The constant term 2 outside the square term causes a vertical translation upward by 2 units. This means the graph of g(x) will be shifted vertically upward by 2 units compared to the graph of f(x).

Therefore, the graph of g(x) = 3(x - 5)² + 2 will be a vertically stretched and shifted parabola, compared to the graph of the parent function f(x) = x². It will be taller, translated horizontally to the right by 5 units, and vertically shifted upward by 2 units.

b)

For the function g(x) = (1/3)(x + 6)² - 4, the transformations of the graph of the parent function f(x) = x² can be described as follows:

Vertical Compression: The coefficient 1/3 in front of the parent function causes a vertical compression by a factor of 1/3. This means the graph of g(x) will be one-third as tall as the graph of f(x).

Horizontal Translation: The expression (x + 6) inside the square term indicates a horizontal translation to the left by 6 units. This means the graph of g(x) will be shifted horizontally to the left by 6 units compared to the graph of f(x).

Vertical Translation: The constant term -4 outside the square term causes a vertical translation downward by 4 units. This means the graph of g(x) will be shifted vertically downward by 4 units compared to the graph of f(x).

Hence , the graph of g(x) = (1/3)(x + 6)² - 4 will be a vertically compressed and shifted parabola, compared to the graph of the parent function f(x) = x². It will be one-third as tall, translated horizontally to the left by 6 units, and vertically shifted downward by 4 units.

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Answer:

B. -√(3)/2

Step-by-step explanation:

Given:

We know that in the 2nd quadrant, sinθ is positive and cosθ is negative.

The Pythagorean identity states that sin²(θ) + cos²(θ) = 1.

Substituting sin(θ) = 1/2, we get:

(½)² + cos²(θ) = 1

cos²(θ) = ¾

cos(θ) = -√(3)/2

Therefore, the value of cos(θ) is -√(3)/2.

The graph for the circle equation (x-2)²+(y+1)²=9 is in option D.

The given circle equation is (x-2)²+(y+1)²=9.

The equation of a circle is different from the formulas that are used to calculate the area or the circumference of a circle.

The standard equation of a circle with center at (x₁, y₁) and radius r is (x-x₁)²+(y-y₁)²=r².

From the given equation, we have

Center: (2, -1)

Radius: 3

Therefore, the correct option is D.

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We substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

The given system of equations are 2x-1/3y = -2...(1)

3x+y=1...(2)

We solve this system of equations by using substitution method.

Let us solve for x in equation to substitute it in equation (2).

2x=-2+1/3y

Divide both sides of equation by 2.

x=-1+1/6y

Now plug in the value of x in equation 2.

Hence, we substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

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Answer:

Let h be the number of hamburgers sold on Friday.

We know that the number of cheeseburgers sold was three times the number of hamburgers sold.

c = 3h

where c is the number of cheeseburgers sold.

We also know that the combined total of hamburgers and cheeseburgers sold was 584, so we can write:

h + c = 584

Substituting c = 3h into the second equation, we get:

h + 3h = 584

Simplifying:

4h = 584

Dividing both sides by 4, we get:

h = 146

Therefore, 146 hamburgers were sold on Friday.

For the expression [tex]x^{\frac{m}{n}}[/tex], m represents the power to which x is raised, and n represents the root that is being taken.

The general format of the exponential expression is given as follows:

[tex]x^{\frac{m}{n}}[/tex]

To obtain the radical form, we have that:

Hence the equivalent expression is given as follows:

[tex]x^{\frac{m}{n}} = \sqrt[n]{a^m}[/tex]

Hence m represents the power to which x is raised, and n represents the root that is being taken.

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Answer:

the correct answer is 193

Step-by-step explanation:

25×1-0=25

25×2-1=49

49×2-1=97

97×2-1=193

The period is approximately 4 seconds, as it takes about 4 seconds for the particle to complete one full oscillation.

The period of the graph represents the time taken for one complete oscillation. The graph shows a periodic motion, which is a repeated motion that occurs at regular intervals.

In this context, the graph represents the motion of a particle undergoing simple harmonic motion, which is a type of periodic motion.The graph shows displacement on the y-axis and time on the x-axis.

The amplitude of the motion is represented by the maximum displacement of the particle, which is 4 cm in this case. The period of the motion is the time taken for one complete oscillation,

In this case, the frequency is approximately 0.25 Hz, which means that the particle undergoes one complete oscillation every 4 seconds

which is the time it takes for the particle to move from one extreme point to the other extreme point and back again. In this graph,

The frequency of the motion is the number of complete oscillations per unit time, which is the inverse of the period.

Overall, the period of the graph represents the time taken for one complete oscillation in a periodic motion, and in this context, it represents the time it takes for a particle undergoing simple harmonic motion to move from one extreme point to the other extreme point and back again.

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The evaluated expression is none of them. The evaluated expression is 63/16.

The correct answer is option E.

To evaluate the expression (-2)^2(6)^0-(4)^-2[tex](-2)^2(6)^0-(4)^-2[/tex], let's break it down step by step.

First, let's simplify the terms within parentheses:

[tex](-2)^2[/tex] = 4 (squaring a negative number gives a positive result)

[tex](6)^0[/tex]= 1 (any number raised to the power of 0 is equal to 1)

[tex](4)^-2 = 1/(4^2) = 1/16[/tex] (negative exponent indicates taking the reciprocal)

Now, we substitute these simplified values back into the original expression:

4 * 1 - 1/16

Next, let's simplify the multiplication:

4 - 1/16

To subtract fractions, we need a common denominator:

4 = 64/16 (multiplying numerator and denominator by 4)

Now, we can subtract the fractions:

64/16 - 1/16 = (64 - 1)/16 = 63/16

Therefore, the evaluated expression is 63/16.

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The question probable may be:

Evaluate the following expression:[tex](-2)^2(6)^0-(4)^-2[/tex]

A.0

B.1

C.1

D. 1/2

E. None of the above

Thus, the mass is increasing at a rate of 0.15625 kg per hour, and the mass on this day is 4.5 kg.

Let's consider a general formula for finding the rate of increase:Rate of increase = k x original valueHere, k is a constant that represents the rate of increase per unit of time, and the original value is the initial value of the quantity being measured.

For example, if the original value is 3.2 kg and the rate of increase is 0.5 kg per hour, we can use the formula to calculate the mass at any time t as follows: Mass at

time t = 3.2 + (0.5 x t)

where t is the time elapsed in hours.In order to find k, we need to know the rate of increase and the original value.

Once we have these values, we can rearrange the formula to solve for

k:k = rate of increase / original value

For example, if the mass is increasing at a rate of 0.5 kg per hour and the original value is 3.2 kg, we can calculate k as follows:

k = 0.5 / 3.2k = 0.15625

To find the rate of increase on a specific day, we need to know how much time has elapsed since the original value was measured. Once we have this information, we can plug it into the formula we derived earlier:Mass at time t = 3.2 + (k x t)For example, if 8 hours have elapsed since the original value was measured, we can calculate the mass on that day as follows:

Mass at time t = 3.2 + (0.15625 x 8)

Mass at time t = 4.5 kg

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The solution as an ordered pair (x, y), of the system of equations on the given graph is: (4, 1).

The solution to a system of equations with a given graph is found by identifying the point or points where the graphs of the equations intersect. These points represent the values that satisfy both equations simultaneously.

The graph given shows that the two lines intersect at the point whose coordinates are (4, 1). Therefore, the solution is (4, 1).

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The surface area of the pentagonal pyramid is 261.8 cm²

A pyramid is a three-dimensional shape. A pyramid has a polygonal base and flat triangular faces.

The area occupied by a three-dimensional object by its outer surface is called the surface area.

A pentagonal pyramid will have 5 equal lateral faces. This lateral face s are triangles.

The area of a triangle is expressed as;

A = 1/2 bh

where b is the base and h is the height.

A = 1/2 × 7 × 9

A = 63/2

A = 31.5 cm

For 5 triangles

= 5 × 31.5

= 177.5 cm²

The total surface area = area of base + lateral area

= 177.5 + 84.3

= 261.8 cm²

Therefore the surface area of the pentagonal pyramid is 261.8cm²

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Answer:

Step-by-step explanation:

I and II

Pages in a book and leaves on a tree can be counted precisely. They are discrete.

The height of a person cannot be measured exactly. We can get very good

approximations (to a lot of decimal places) but never exact. This is continuous.

One role of plants in the carbon cycle is the process of carbon dioxide (CO2) absorption during photosynthesis. Plants are able to take in atmospheric CO2 and convert it into organic carbon compounds through the process of photosynthesis.

During photosynthesis, plants utilize sunlight, water, and CO2 to produce carbohydrates and release oxygen as a byproduct.This absorption of CO2 by plants helps in reducing the concentration of greenhouse gases in the atmosphere, thus playing a crucial role in mitigating climate change.

By capturing carbon from the atmosphere, plants act as natural carbon sinks, storing carbon in their tissues, including leaves, stems, roots, and woody structures. Some carbon is stored temporarily, such as in leaves or as plant biomass, while other carbon can be stored for longer periods when plants die and decay, leading to the formation of fossil fuels over millions of years.

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The sample size of 300  would most likely be closest to the actual parameter value of the population.

We have to find the a sample of which of the sizes which would

most likely be closest to the actual parameter value of a population.

In general, as the sample size increases, the estimate obtained from the sample is more likely to be closer to the actual parameter value of the population.

This is because a larger sample size provides more information and reduces the impact of sampling variability.

Therefore, among the given options, the estimate obtained from a sample size of 300  would most likely be closest to the actual parameter value of the population.

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Domain of the function represented by the graph of a quadratic function y = [tex]x^2[/tex] – 4 with a minimum value at the point (0,-4) is all real numbers.

The correct answer is option D.

To determine the domain of the quadratic function y = [tex]x^2[/tex] - 4, we need to consider the x-values for which the function is defined. Since a quadratic function is defined for all real numbers, the domain of this function is "all real numbers."

Let's analyze the given function and its graph to understand why the domain is "all real numbers."

The function y =  [tex]x^2[/tex] - 4 represents a parabola that opens upward, which means it extends infinitely in both positive and negative x-directions. The vertex of the parabola is at the point (0, -4), indicating that the minimum value of the function occurs at x = 0.

Since there are no restrictions or limitations on the x-values for which the function is defined, the domain is unrestricted and encompasses all real numbers. In other words, the function can be evaluated and calculated for any real value of x, whether it is a negative number, zero, or a positive number.

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The angle opposite the hypotenuse is always 90 degrees, as a result, angle C in the given triangle is a right angle.

In the triangle given below, angle C is a right angle: To prove that this triangle is a right-angled triangle,

we must first confirm that it meets the Pythagorean Theorem's requirements, which states that the sum of the squares of the legs equals the square of the hypotenuse.

In other words, if the Pythagorean Theorem holds for the given triangle, it is a right-angled triangle, and if not, it is not a right-angled triangle.

Given the triangle's lengths: Leg AB measures 15 units. Leg BC measures 20 units.

Therefore, AC's length can be determined as follows: AC2 = AB2 + BC2AC2 = 15^2 + 20^2AC2 = 225 + 400AC2 = 625AC = √625AC = 25We can now confirm that the Pythagorean Theorem holds for this triangle

since AC2 = AB2 + BC2AC2 = 15^2 + 20^2AC2 = 225 + 400AC2 = 625AC = √625AC = 25

Since the Pythagorean Theorem holds for the given triangle, we can conclude that it is a right-angled triangle.

The angle opposite the hypotenuse is always 90 degrees, as a result, angle C in the given triangle is a right angle.

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Answer: 60

Step-by-step explanation:

You may need to finish the question, but I'm assuming they are asking for the number of combinations.

That is 5*4*3 or 60.

The percentage of the annual income spent on food by the family is 19.98 %.

The percentage of the annual income spent on food by the family is calculated as follows;

The given parameters include;

yearly income of the family = $29,850.00.

amount spent on food = $5963.00

The percentage of the annual income spent on food by the family is calculated as;

percentage of the annual amount on food = ( amount spent on food / total annual income) x 100%

percentage of the annual amount on food = ( $5963.00 /  $29,850.00) x 100%

percentage of the annual amount on food = 19.98 %

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A training field is formed by joining a rectangle and a semicircle as shown below. The rectangle is 8 m long and 5 m wide. Find the length of the training track. Use 3.14 for pi and do not round it off. So, the length of the training track is 28.56 meters.

Solution: The figure given below shows the field formed by a rectangle and a semicircle.In the above figure, `ABCD` is a rectangle of length 8 m and width 5 m. `AC` is the diameter of the semicircle. Let's find out the length of the training track. 

Length of the training track = (circumference of semicircle `+ 2AB`) metersCircumference of semicircle = `(1/2) × 3.14 × AC` meters  [Formula of circumference of circle = `2πr` where `r` is the radius and `π` is pi.

For semicircle, we need to take half of this circumference]Length of diameter `AC` = Length of rectangle `ABCD` = 8 m.[Given] Length of circumference of semicircle = `(1/2) × 3.14 × AC` = `(1/2) × 3.14 × 8` meters = 12.56 meters.

Perimeter of rectangle `ABCD` = `2(AB + BC)` meters  [Formula of perimeter of rectangle]                              

= `2(8 + 5)` meters.

= 26 metersLength of the training track = (circumference of semicircle `+ 2AB`) meters.            

= 12.56 m + 2 × 8 m meters.

= 28.56 meters.

Thus, the length of the training track is 28.56 meters.

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