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The average rate of change of the function over the interval -2 ≤ x ≤ 4 is given as follows:

4.

The average rate of change of a function is given by the change in the output divided by the change in the input.

The two points in this problem are given as follows:

(-2, -3) and (4,21).

Hence the change in the output is of:

21 - (-3) = 24.

The change in the input is of:

4 - (-2) = 6.

Hence the rate is of:

24/6 = 4.

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Answer:

CD = 6.3

Step-by-step explanation:

triangles CFG and CDE are similar, so their side lengths are proportional

this means CD/CF = CE/CG

since we don't know CF, we need to first solve for CF in order to find CD

luckily, we know CD = CF + FD, and FD is given:

CD/CF = CE/CG -> (CF + FD) / (CF) = CE/CG

multiply both sides by CF to get CF + FD = CE * CF / CG

move the terms with CF to one side, and the constants to the other side:

CF - CF(CE/CG) = -FD

solve for CF:

CF(1-(CE/CG)) = -FD, CF = FD / ((CE/CG) - 1) = (1.8)/(((2.4+6)/(6)) - 1) = 4.5

Since CD = CF+FD, CD = 4.5 + 1.8 = 6.3

Answer: No Solution

Step-by-step explanation: When you use the elimination method on second equation by multiplying it by 2 you get two equations that add up to a different solution. Since the variable coefficients are the same on both, there will be no solution.

The number of bagels when you buy for $50 will be 120 bagels.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

A shop sells bagels for $5 per dozen.

Let 'x' be the number of bagels and 'y' be the total cost. Then the equation is given as,

y / x = 5 / 12

12y = 5x

The number of bagels when you buy for $50 will be given as,

12(50) = 5x

600 = 5x

5x = 600

x = 120

The number of bagels when you buy for $50 will be 120 bagels.

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The system is inconsistent.

The two lines are parallel and never intersect.

====================================================

Work Shown:

Solving the 1st equation for y.

3x-y=18

-y=18-3x

y = -(18-3x)

y = -18+3x

y = 3x-18

Plugging that into the other equation to solve for x.

-2y=-6x-120

-2(y)=-6x-120

-2(3x-18)=-6x-120

-6x+36=-6x-120

-6x+6x=-120-36

0x = -156

0 = -156

We arrive at a false statement.

Therefore, this system has no solutions

The system is inconsistent.

If you were to use a graphing tool like Desmos or GeoGebra, then you'll see the two lines are parallel. They never intersect to form a solution.

The equation that represents the whole scenario is 3.80 + 2.25(x) = 33.05  and the number of miles is 13.

Here we will use the linear equation concept to solve the problem. Since we don't know the number of miles represent it with a variable 'x' and form a Linear equation according to the given condition in the problem. Now solve the resultant equation for the value of variable 'x'  

Here we have  

The taxi company charged a pick-up fee of $3.80 plus $2.25 per mile. the total fare was $33.05, not including the tip.    

Let 'x' be the number of miles in the taxi ride

Total cost to travel 'x' mile = 3.80 + 2.25(x)  

From the given data, the total fare was $33.05

=> 3.80 + 2.25(x) = 33.05

=> 2.25x = 33.05 - 3.80

=> 2.25x = 29.25

=> x = 29.25/2.25

=> x = 13

Therefore,

The equation that represents the whole scenario is 3.80 + 2.25(x) = 33.05  and the number of miles is 13.

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Answer:

(x - 2) is not a factor of f(x)

Step-by-step explanation:

We can use the Remainder Theorem to check if (x - 2) is a factor of f(x) = x^3 - 2x^2 + 2x + 3.

The Remainder Theorem states that if we evaluate a polynomial at a specific value and the result is zero, then that value must be a root of the polynomial and therefore the polynomial can be divided by the corresponding linear factor.

So, if we plug in x = 2 into f(x), we get:

f(2) = 2^3 - 2 * 2^2 + 2 * 2 + 3

= 8 - 8 + 4 + 3

= 7

Since f(2) is not equal to zero, it follows that (x - 2) is not a factor of f(x).

Alternatively, we could use the Factor Theorem, which states that a polynomial is divisible by (x - a) if and only if f(a) = 0. Since f(2) is not equal to zero, (x - 2) is not a factor of f(x).

Answer:

The minimum value of C is 14

Step-by-step explanation:

Sketch the graph of the constraints using

2x + y = 20

with intercepts (0, 20) and (10, 0)

2x + 3y = 36

with intercepts (0, 12) and (18, 0)

The solution to both are above the lines

Solve 2x + y = 20 and 2x + 3y = 36 to find the point of intersection at (6, 8)

Then the coordinates of the vertices of the region formed are

(0, 20), (6, 8) and (18, 0)

Evaluate the objective function at each vertex to determine minimum value

C = 0 + 20 = 20

C = 6 + 8 = 14

C = 18 + 0 = 18

Thus the minimum value of C is 14 when x = 6 and y = 8

Hope this helped to get you answer!

The solution of c(r) in 3D spherical coordinates behaves differently  because in 3D, there are radial and angular dimensions.

3D coordinates refers to the system of three-dimensional spatial representation of an object, where each point in 3D space is represented by a set of three values, also known as coordinates. These coordinates are typically written in the form (x, y, z), where x, y, and z represent the values along the three axes of a three-dimensional coordinate system.

3D coordinates are commonly used in computer graphics, engineering, and mathematics to describe the positions and orientations of objects in 3D space. In computer graphics, for example, objects are often represented using 3D coordinates to specify their position, orientation, and size in the virtual world. In engineering and mathematics, 3D coordinates are used to describe the positions of points in three-dimensional space and to perform transformations, such as rotations and translations, on these points.

The 3D coordinate system is a fundamental tool for visualizing, analyzing, and manipulating objects in three-dimensional space, and it provides a powerful way to describe complex 3D shapes, geometric relationships, and physical interactions.

The solution of c(r) in 3D spherical coordinates behaves differently than the solution of c(x) in 1D coordinates because in 3D, there are radial and angular dimensions to consider, which can affect the overall behavior of the solution. Additionally, the spherical coordinates take into account the spherical symmetry of the problem, while the 1D coordinates do not.

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Answer:

(-1,1)

Step-by-step explanation:

1.  Rearrange either equation to isolate one of the variables.   Lets use 6x - y = -7 :

6x - y = -7

-y = -7 - 6x

y = 7+6x

2.  Now use this definition of x in the second equation:

5x + y = -4

5x + (7+6x) = -4

11x  = -11

 x = -1

3.  Now use x = -1 in either equation to find y:

   6x - y = -7

  6 (-1) - y = -7

-y = -1

y = 1

The solution is  (-1,1)

See the attached graph.

Answer: How can you tell whether X and Y are proportional?

Step-by-step explanation: How can you tell whether X and Y are proportional?

To know if a relationship is proportional, you should look at the ratios between the two variables. If the ratio is always the same, the relationship is proportional. If the ratio changes, the relationship is not proportional. please select brainiest if right

Alex will not be able to complete his job. According to the measurement given for the coil, the electrician will not be able to complete the job.

The circumference of the coil of wiring can be calculated with

C= 2πr

where r is the radius and π= 3.14

The radius can be calculated by dividing the diameter by 2. Then:

r= 18 inches ÷ 2

r= 9 inches

Convert 9 inches to yards (1 yard= 36 inches)

(9 inches)(1 yard ÷ 36 inches) = 0.25 yard

Substitute this radius into the formula:

C= 2(3.14)(0.25 Yard)

C= 1.57 Yard

Since there are 21 circles of wire, we need to multiply C= 1.57 yards by 21

C = (1.57 Yard)(21) = 32.97 Yard

The coil has 32.97 yards of wire and Alex needs 34 yards, therefore, this coil will not be enough to complete the job.

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Based on the given time; the number the second hand points at are;

There are a total of 12 numbers on a clock starting from 1 and ending at 12

There are 60 strokes or lines with equal spaces on a clock

Each stroke or line represents a second

60 seconds = 1 minutes

1. 15 seconds after 1:00.

= The seconds hand points at 3

2. 30 seconds after 1:00.

The seconds hand points at 6

3. 1 minute after 1:00.

1 minutes = 60 seconds

The seconds hand points at 12

4. 5 minutes after 1:00

5 minutes = 300 seconds

The seconds hand points at 12

Therefore, the seconds hand of the given time points at 3, 6, 12 and 12 respectively.

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Answer:

B. A radioactive compound decays at a rate of 19% per hour.

Step-by-step explanation:

We can eliminate C. (A town's population grows at a rate of 9.2% every year.) and D. (Money invested in a savings account grows at an annual rate of 4.2%.) since both of the options show growth, not decay. That leaves us with A. and B. The problem speaks of exponential, not linear, so B. would be the answer. If they asked for the linear decline or decay, A. would be the answer.

The contexts that represents exponential decline or decay is A radioactive compound decays at a rate of 19% per hour.

Exponential Decay is a reduction or decrease in the value of the quantity compared to the value of the previous quantity. Examples of phenomena that are classified as decay are a decrease in the price of goods and the decay of radioactive substances.

Based on the question above, option C and Option D Both options increase, It shows no decrease, so it can be ruled out.

While option B: the problem is exponential rather than linear.

If ask about linear decay, the answer is A.  

A.  radioactive compound decays at a rate of 19% per hour.

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Common theorems, properties, or strategies to the proof of the Triangle Proportionality Theorem and its converse include using similarity and congruence, angle-angle criterion, and transitive property of equality.

The Triangle Proportionality Theorem states that if a line is drawn parallel to one side of a triangle to intersect the other two sides, then the ratio of the lengths of the intersecting lines is equal to the ratio of the lengths of the corresponding sides of the triangle.

The converse of the Triangle Proportionality Theorem states that if two pairs of corresponding sides in two triangles are proportional, then the two triangles are similar.

Overall, these theorems, properties, and strategies form the basis for proving both the Triangle Proportionality Theorem and its converse, and they are used to establish the relationships between the lengths of sides and angles in triangles.

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The domain of the function is all real numbers , except x = 0

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.

Given data ,

Let the domain of the function be represented as D

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

When the value of the x of function approaches zero from the positive direction , the function f ( x ) gets larger

And , when the value of the x of function approaches zero from the negative direction , the function f ( x ) gets larger in the negative direction

Now , the domain of the function will be all the real numbers except 0

Hence , the domain of the function is all real numbers except 0

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The exponential function of the family f(x) = 2^x with a vertical shrink and a translation down 5 units is given as follows:

A. f(x) = 0.5(2)^x - 5.

The parent function is defined as follows:

f(x) = 2^x.

For the vertical shrink, the function is multiplied by a constant that has an absolute value less than one, hence:

f(x) = 0.5(2)^x.

For the translation down 5 units, the number 5 is subtracted from the definition of the function, hence:

A. f(x) = 0.5(2)^x - 5.

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Step 1: Calculate the length of one platter. To calculate the length of one platter, multiply 0.4 meters by 4 sides, which gives us a total of 1.6 meters.

Step 2: Calculate the length of the row of platters. To calculate the length of the row of platters, multiply the length of one platter (1.6 meters) by the number of platters (7), which gives us a total of 11.2 meters.

Therefore, the row of platters is 11.2 meters long.

What exactly are algebraic word issues? The process of converting phrases into equations and then solving those equations is known as solving algebraic word problems. a single variable, and. In a real-world situation, the variable typically stands for an unknowable quantity.

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Answer:

Step-by-step explanation:

Since ∠S and ∠Y are complementary, we have:

∠S + ∠Y = 90°

We also know that:

m∠S = 2(m∠Y) − 30°

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

2(m∠Y) − 30° + ∠Y = 90°

Combining like terms:

3(m∠Y) = 120°

Dividing both sides by 3:

m∠Y = 40°

Therefore, m∠Y is 40 degrees.

The total kilotons of carbon dioxide would the country emits over the course of the 11-year period will be 2.23 x 10 ⁻¹⁵ kilotons.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a small country emits 115,000 kilotons of carbon dioxide per year. in a recent global agreement, the country agreed to cut its carbon emissions by 1.6% per year for the next 11 years.

The total kilotons of carbon dioxide would the country emits over the course of the 11-year period will be calculated as:-

Amount = 115000 x ( 0.016)¹¹

Amount = 2.23 x 10 ⁻¹⁵ kilotons.

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Step-by-step explanation:

The difference in elevation between the bottom of the canyon and the bird's nest is 504 1/2 - (-62 2/5) = 504 1/2 + 62 2/5 = 566 5/5 = 566 feet

Answer:

Step-by-step explanation:

Say sea level is 0.

Bottom of the canyon is -62.4ft and bird's nest is 504.5ft

Subtract.

504.5 - 62.4 = 442.1ft

Answer:

  12/37

Step-by-step explanation:

Given right triangle ABC with sides AB=37, BC=12, and CA=35, you want the cosine of angle B.

The cosine of an angle in a right triangle is ...

  Cos = Adjacent/Hypotenuse

The leg adjacent to angle B is BC=12. The hypotenuse is AB=37.

Using these values, the cosine of B is ...

  cos(B) = BC/BA

  cos(B) = 12/37

The correct option regarding the number of solutions of the sustem of equations is given as follows:

No solution.

We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.

The line going through points (0,4) and (3,3) is given as follows:

y = -0.33x + 4.

The line going through points (0,-1) and (3,-2) is given as follows:

y = -0.33x - 1.

The two functions have the same slope, hence they are parallel lines, and thus the number of solutions is of zero.

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Answer:

3x+5y = -13

Step-by-step explanation:

Since there are two variables, you must solve for one of them first. One way we can do that is through elimination.

X seems the easiest to eliminate.

We can subtract the two equations.

 x - 4y = -10
- 2x+9y = -3

If we subtract it like this, it wouldn't eliminate any variables. So, let's multiply the first equation by 2 so both equations have 2x.

 2x - 8y = -20
- 2x+9y = -3
Now, subtract the equations.

-17y = -17

We can solve for y now.

y = 1

Since we have y's value, we can solve for x. Plug y back into one of the equations.

x - 4(1) = -10

x - 4 = -10

x = -6

Now that we have both the x and y values, simply plug it into 3x+5y.

3(-6) + 5(1)

-18 + 5
-13

So the answer is -13

Yes, Ernesto has enough oil to make both recipes. Each recipe calls for 1/3 cup of oil, and he has one cup of oil. Therefore, he has enough oil to make both recipes with some oil left over.

Answer:

The Value of R is 20%.

Step-by-step explanation:

Let R be the interest rate (in percentage) per year. The interest earned after one year would be R% of £8,500, which is (R/100) * £8,500 = £(R * 85)/100.

After paying tax, the amount Nick receives would be (R * 85)/100 * (100 - 30)/100 = £(R * 85 * 70)/10000.

Since Nick receives £166.60 after paying tax, we have:

£(R * 85 * 70)/10000 = 166.60

Solving for R, we get:

R = (10000 * 166.60) / (85 * 70) = 20.0.

Therefore, the interest rate R is 20%.

A polynomial regression model is a good choice for this data, as it can fit the trend of increasing population growth over time.

A function is a mathematical concept that assigns a unique output value for each input value.

In mathematical notation, a function is usually expressed as "f(x)" where "x" is the input and "f(x)" is the corresponding output. For example, a function could be defined as f(x) = x^2, which means that for any value of x, the function will calculate and return the square of that value.

To model the world population data, we can use a mathematical function to fit the data points. A polynomial regression model is a good choice for this data, as it can fit the trend of increasing population growth over time.

To find the expected world population in 2017, we would need to estimate the polynomial regression model using the data points provided and then evaluate the model at the year 2017.

Research shows that the actual world population in 2017 was approximately 7.5 billion, which is higher than our estimated value based on the limited data points provided. This highlights the importance of considering additional factors and data when making predictions about the world population.

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The complete question is

The mean (expected value) of X is 3.48, and the standard deviation of X is 1.27.

The mean or expected value of X, representing the number of games the team might win, can be calculated using the formula:

E(X) = n * p

where:

n = number of games (6)

p = probability of winning each game (0.58)

So, E(X) = 6 * 0.58 = 3.48

The standard deviation of X, representing the spread of the distribution, can be calculated using the formula:

SD(X) = √(n * p * (1 - p))

where:

n = number of games (6)

p = probability of winning each game (0.58)

So, SD(X) = √(6 * 0.58 * (1 - 0.58)) = 1.27

Therefore, the mean of X is 3.48, and the standard deviation of X is 1.27.

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