Help please? Write the equation for the Red line.

The rate of decrease in the revenue reduces each year, resulting in an

approximate quadratic equation model that is concave upwards.

\(\mathrm{The \ quadratic \ equation \ models \ is}; \ \underline{y = 76.5 \cdot x^2 - 2264.8 \overline 3 \cdot x + 18769. \overline 6}\)

The difference between the actual and predicted values are;

\(\begin{array}{|c|c|c|c|}\underline{Year}& \underline{Difference \ in \ Values}\\2008&0\\2009&-143.\overline 6\\2010&-118.\overline 3\\2011&0\\2012& 62.\overline 3\\2013&71.\overline 6\\2014&0\end{array}\right]\)

Reasons:

The variables are;

x = Number of years since 2,000

y = Revenue for  physically recorded music in millions of dollars

Required:

To model the decline using a quadratic equation.

Solution:

The general form of the quadratic equation is; y = a·x² + b·x + c

When y = 5547, x = 8

We get;

5547 = a·8² + b·8 + c = 64·a + 8·b + c

5547 = 64·a + 8·b + c...(1)

When y = 3113, x = 11

We get;

3113 = a·11² + b·11 + c = 121·a + 11·b + c

3113 = 121·a + 11·b + c...(2)

When y = 2056, x = 14

We get;

2056 = a·14² + b·14 + c = 196·a + 14·b + c

2056 = 196·a + 14·b + c...(3)

Subtracting equation (2) from equation (1) gives;

5547 - 3113 = 64·a + 8·b + c - (121·a + 11·b + c) = -57·a - 3·b

2434 =  -57·a - 3·b...(4)

Subtracting equation (3) from equation (2) gives;

3113 - 2056 = 121·a + 11·b + c - (196·a + 14·b + c) = -75·a - 3·b

1057 = -75·a - 3·b...(5)

Subtracting equation (5) from equation (4) gives;

2434 - 1057 = -57·a - 3·b - (-75·a - 3·b) = 18·a

1377 = 18·a

\(a = \dfrac{1377}{18} = 76.5\)

a = 76.5

From, equation (4), 2434 =  -57·a - 3·b, we have;

2434 =  -57 × 76.5  - 3·b

Therefore;

\(b = \dfrac{2434 + 57 \times 76.5}{-3} = -\dfrac{13589}{6} = -2264.8 \overline{3}\)

b = -2264.8\(\mathbf{\overline 3}\)

From equation (1), we get;

5547 = 64 × 76.5 + 8×(-2264.8\(\overline 3\)) + c

Therefore;

c = 5547 - (64 × 76.5 + 8×(-2264.8\(\overline 3\))) = 18769.\(\overline 6\)

c = 18769.\(\mathbf{\overline 6}\)

Therefore, the quadratic model is; \(\underline{y = 76.5 \cdot x^2 - 2264.8 \overline 3 \cdot x + 18769. \overline 6}\)

Verifying, we have in year 2012, x = 12

y = 76.5×12² - 2264.8\(\overline 3\)×12 + 18769.\(\overline 6\) = 2607.74

The completed table and comparison of the predicted physical revenue

and actual values is presented as follows;

\(\begin{array}{|c|c|c|c|}Year&Actual \ Revenue&Predicted \ Revenue& Difference \\2008&5547&5547&0\\2009&4439&4582.\overline 6&-143.\overline 6\\2010&3653&3771.\overline 3&-118.\overline 3\\2011&3113&3113&0\\2012&2670&2607. \overline 6 & 62.\overline 3\\2013&2327&2255.\overline 3&71.\overline 6\\2014&2056&2056&0\end{array}\right]\)

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Answer:

y = 77.738x^2 - 2270.810x + 18661.929

Step-by-step explanation:

The sample of given data is Sample 1: 1, 2, 3, 4, 5 Sample 2: 6, 7, 8, 9, 10

b)Sample 1: 1, 2, 3, 4, 5 Sample 2: 6, 7, 8, 9, 10

(a) An example of data with SS(between) = 0 and SS(within) > 0 could be the following:

Sample 1: 1, 2, 3, 4, 5

Sample 2: 6, 7, 8, 9, 10

Sample 3: 11, 12, 13, 14, 15

In this example, the means of each sample are all different from each other, but the grand mean (8) is equal to the mean of each sample. Therefore, there is no variability between the means of the samples, resulting in SS(between) = 0. However, there is still variability within each sample, resulting in SS(within) > 0.

(b) An example of data with SS(between) > 0 and SS(within) = 0 could be the following:

Sample 1: 1, 2, 3, 4, 5

Sample 2: 6, 7, 8, 9, 10

Sample 3: 11, 12, 13, 14, 15

In this example, the means of each sample are all the same (8), but the values within each sample are all different from each other. Therefore, there is variability between the means of the samples, resulting in SS(between) > 0. However, there is no variability within each sample, resulting in SS(within) = 0.

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The values of a and b from the logarithmic function are a = -2 and b = 3

The parent function of the logarithmic function is f(x) = log(x), which has the domain (0, +∞) and the range (-∞, +∞).

To transform the parent function h(x) = log(x + a) + b, we can use the following steps:

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

a = -2 i.e. 2 units right

b = 3 i.e. 3 units up

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The set of all months that contains less than 31 days is; {February, April, June, September, November}.

It follows from the task content that the set whose elements are to be determined is characterized by containing less than 31 days.

On this note, it follows that the elements of the set are; February (28/29 days), April (30 days), September (30 days), June (30 days) and November (30 days).

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Answer:

centre = (5, - 6 ) , radius = 7

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

given

x² + y² - 10x + 12y + 12 = 0 ( subtract 12 from both sides )

x² + y² - 10x + 12y = - 12 ( collect terms in x/ y )

x² - 10x + y² + 12y = - 12

using the method of completing the square

add ( half the coefficient of the x/ y terms )² to both sides

x² + 2(- 5)x + 25 + y² + 2(6)y + 36 = - 12 + 25 + 36

(x - 5)² + (y + 6)² = 49 = 7² ← in standard form

with centre (5, - 6 ) and radius = 7

Answer:

Center = (5, -6)

Radius = 7

Step-by-step explanation:

To find the center and the radius of the circle represented by the given equation, rewrite the equation in standard form by completing the square.

To complete the square, begin by moving the constant to the right side of the equation and collecting like terms on the left side of the equation:

\(x^2-10x+y^2+12y=-12\)

Add the square of half the coefficient of the term in x and the term in y to both sides of the equation:

\(x^2-10x+\left(\dfrac{-10}{2}\right)^2+y^2+12y+\left(\dfrac{12}{2}\right)^2=-12+\left(\dfrac{-10}{2}\right)^2+\left(\dfrac{12}{2}\right)^2\)

Simplify:

\(x^2-10x+(-5)^2+y^2+12y+(6)^2=-12+(-5)^2+(6)^2\)

       \(x^2-10x+25+y^2+12y+36=-12+25+36\)

       \(x^2-10x+25+y^2+12y+36=49\)

Factor the perfect square trinomials on the left side:

\((x-5)^2+(y+6)^2=49\)

The standard equation of a circle is:

\(\boxed{(x-h)^2+(y-k)^2=r^2}\)

where:

Comparing this with the rewritten given equation, we get

Therefore, the center of the circle is (5, -6) and its radius is r = 7.

(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

To solve the exercise using Polya's four-step problem-solving strategy, we will apply the procedures presented in the lesson.

(a) For the series 1+2+3+4+...+392:

Using the arithmetic series formula Sn = (n/2)(a + l), where n is the number of terms, a is the first term, and l is the last term, we can substitute the values: Sn = (392/2)(1 + 392) = 196(393) = 77,028.

(b) For the series 1+2+3+4...x:

To find the sum of this series, we need to know the number of terms (n) based on the value of x. Since the series follows a consecutive pattern, the number of terms will be equal to x itself. Thus, the sum of the series would be Sn = (x/2)(1 + x).

(c) For the series 546 + 547 + 548 + 549:

Using the arithmetic series formula Sn = (n/2)(a + l), we can determine the number of terms (n) by subtracting 546 from 549 and then adding 1: n = 549 - 546 + 1 = 4. Substituting the values into the formula: Sn = (4/2)(546 + 549) = 2(1095) = 2,190.

The final answer for each part is:

(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

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If there is no solution to the system of equations, it signifies that the equations describe two parallel lines in the two-dimensional plane. This indicates that the lines will never meet because they have the same slope but separate y-intercepts. This signifies that the two lines are geometrically distinct and will never intersect.

A geometric significance is a geometric aspect or quality of a form or item. This encompasses the object's size and orientation, as well as its symmetry and proportions. Several areas, including architecture, engineering, graphic design, and mathematics, rely on geometric importance. In architecture, for example, the size and direction of a structure may be utilised to decide how much light it receives and how much shade it casts. The geometry of an item can be used to determine its strength, stiffness, and durability in engineering. The symmetry and dimensions of an object may be employed in graphic design to produce an appealing and balanced design.

The given question states that when there are no solutions to a system of K equations in two variables, it means that the lines associated with those equations are either parallel or coincident. Geometrically, this means that the lines are not intersecting, which implies that the two variables cannot simultaneously satisfy all of the equations.

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Answer:

a

Step-by-step explanation:

it the only one with an area of 17 square inches

Answer: Polygon A is 17 Square units

Answer:

ano yan ang tanong mo

Step-by-step explanation:

ano yan

Answer:

6

Step-by-step explanation:

The two triangles are similar which means the the two length is parallel

.°., the Length of the smaller triangle=6

Answer:

-5

Step-by-step explanation:

We just have to calculate (-1/2) / (1/10) = (-1/2) * 10 = -5.

Answer:

(0.5,1)

Step-by-step explanation:

The midpoint formula is \((\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})\)

Let's do x first

-1+2=1

1 ÷2=0.5

y

5+-3=2

2÷2=1

(0.5,1)

Hope this helps :-)

Each friend had originally 13 action figures before buying 11 more.

Given that there are 5 friends and each of them has x action figures in his or her collection. When they buy 11 more action figures, the total number of action figures they will have is 120.

a) We need to find an equation that models the problem. Let x be the original number of action figures that each friend had.

Therefore, the total number of action figures that each friend will have after purchasing 11 more is x + 11.

The total number of action figures will be 5(x + 11) = 5x + 55.

Now, according to the problem,5x + 55 = 120

This is our equation that models the problem.

b) We have to solve the equation 5x + 55 = 120 to find the original number of action figures, x, that each friend had before buying 11 more action figures.

5x + 55 = 120

5x = 120 - 55 (subtract 55 from both sides)

5x = 65x = 13

Therefore, each friend had originally 13 action figures before buying 11 more.

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Answer:

x<4

Step-by-step explanation:

3x < 12

Divide with 3 on each side

x< 4

In words x has all the real numbers that are less than 4 or x belongs to any number from -ve infinity to 4.

The graph of the inequality 3x < 12 on a number line would consist of an open circle at 4, followed by a shaded region to the left of 4 and extending indefinitely in that direction.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =

Greater than and equal=

We have,

To graph the inequality 3x < 12 on a number line, we can follow these steps:

- Start by isolating x by dividing both sides of the inequality by 3, which gives us x < 4.

- Draw a number line and mark a point at 4, which is the boundary between the values of x that satisfy the inequality and those that don't.

- Since the inequality is strict (i.e., "less than" and not "less than or equal to"), we need to indicate that the point x = 4 is not included in the solution set.

We can do this by making an open circle (or "unfilled dot") at 4 on the number line.

- Shade the portion of the number line to the left of the point x = 4, since these are the values of x that satisfy the inequality 3x < 12.

We can use an arrow pointing to the left to indicate that the shaded region extends indefinitely in that direction.

Thus,

The graph of the inequality 3x < 12 on a number line would consist of an open circle at 4, followed by a shaded region to the left of 4 and extending indefinitely in that direction.

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Answer:

a

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

I might be wrong but i'm pretty sure it's right

Answer:

I am assuming you mean the smallest decimal so it is 4.125

Step-by-step explanation:

you said quick so

Answer: 4.25

Step-by-step explanation: if you make all of these into a whole number the biggest number comes out to be 20 and its 4.25

Answer:

88.88% or 8/9 of the yard is mowed

Step-by-step explanation:

First step is to get the denominator to the same number. Both denominators have a least common multiple of 12.

3/4 * 3/3 = 9/12

2/3 * 4/4 = 8/12

9/12 hours is how long it takes Evan to mow his backyard. He has 8/12 hours of work already done. If we divide the time already passed by the time still needed to mow the backyard, we can get how much of the yard is already mowed.

(8/12) / (9/12)

8/12 * 12/9  

96/108 = 88.88

\(x^3 y^4 \cdot x^5 y^{-5}\\\\=x^{5+3} \cdot y^{4-5}~~~~~~~~~~~~~~~~~~~~~~~;[a^m \cdot a^n = a^{m+n}]\\\\=x^8 y^{-1}\\\\=\dfrac{x^8}{y}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;\left[a^{-n} = \dfrac 1{a^n},~~~ a \neq 0\right]\)

2x<15

Step-by-step explanation:

2×15=30 if he spends less than he would have to be below 15 please give brainliest

Each liter is equivalent to exactly: 4.22675 cups.

I hope this helps!

The length of the unknown side length, |AB|, is 6.97

From the question, we are to determine the value of the unknown side length

The unknown side length is the hypotenuse

Using SOH CAH TOA

We can write that

sin 35° = 4/|AB|

∴ |AB| = 4 /sin35°

|AB| = 4 /sin35°

|AB| = 6.97

Hence, the length of the unknown side length, |AB|, is 6.97

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Answer: 16 - C

Step-by-step explanation:

So basicly, what it is asking is to solve this problem. I would like to call it a puzzle because there is a missing part that we have to find. Let's get this started!

Here is the equaiton: 2 x (8 - C)

First, we will multiply 8 by 2.

8 x 2 = 16

Now the equation is: 16 - C

We don't know what C is, so this equation is as done as we can do it.

The z-statistic test was conducted to determine the Deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

Report on the Analysis of American Airlines (Domestic) PerformanceThe quantitative analysis focused on three variables- load factors, revenue passenger miles, and available seat miles for American Airlines.

The Bureau of Transportation Statistics data for domestic flights from January 2006 to December 2012 was retrieved for the analysis. The quantitative analysis also focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. The results of the data are summarized in Table 2. Revenue Passenger Miles (RPM) mean is 6,624,897, the median is 6,522,230, and mode is NONE. The minimum is 5,208,159 and the maximum is 8,277,155. The standard deviation is 720,158.571, and the variance is 518,628,367,282.42.

Load Factors (LF) mean is 82.934, the median is 83.355, and mode is 84.56. The minimum is 74.91, and the maximum is 89.94. The standard deviation is 3.972, and the variance is 15.762. The Available Seat Miles (ASM) mean is 7,984,735, the median is 7,753,372, and mode is NONE. The minimum is 6,734,620, and the maximum is 9,424,489. The standard deviation is 744,469.8849, and the variance is 554,235,409,510.06.Figure 1 above displays the performance of American Airlines (Domestic).

The mean RPM is 7,984,735, and the linear regression line is y = 50584x - 2.53E+8. The linear regression line indicates a positive relationship between RPM and year, with a coefficient of determination, R² = 0.6806. A coefficient of determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variable. Therefore, 68.06% of the variance in RPM is predictable from the year. A one-way ANOVA analysis of variance test was conducted to determine the equality of means of three groups of variables; RPM, ASM, and LF. The null hypothesis is that the means of RPM, ASM, and LF are equal.

The alternative hypothesis is that the means of RPM, ASM, and LF are not equal. The level of significance is 0.05. The ANOVA results indicate that there is a significant difference in means of RPM, ASM, and LF (F = 17335.276, p < 0.05). Furthermore, a post-hoc Tukey's test was conducted to determine which variable means differ significantly. The test indicates that RPM, ASM, and LF means differ significantly.

The skewness test was conducted to determine the symmetry of the distribution of RPM, ASM, and LF. The test indicates that the distribution of RPM, ASM, and LF is not symmetrical (Skewness > 0).

Additionally, the z-statistic test was conducted to determine the deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

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Applying the formula, it is found that the SP for both numbers is of 7.

The first step is finding the mean for both sets, hence:

\(M_x = \frac{4 + 0 + 1 + 3}{4} = 2\)

\(M_y = \frac{5 + 2 + 1 + 4}{4} = 3\)

Then, the SP(sum of products of deviations) is the sum of the multiplications between each value x and the mean, with each respective value of y(same index) and the mean, hence:

\(SP = (4 - 2)(5 - 3) + (0 - 2)(2 - 3) + (1 - 2)(1 - 3) + (3 - 2)(3 - 4) = 7\)

The SP for both numbers is of 7.

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Answer:

Value of the test statistic for this problem = -3.74

Step-by-step explanation:

Here

the sample size n = 1263

and the x = 565

So, the p' -value = 565/1263 = 0.4473

As per the test statistics formula, z value will be evaluated

z = (0.4473-p)/sqrt {p(1-p)/n}

Let us say that p = 0.5

Substituting the given value in above equation, we get -

z = (0.4473-0.5)/sqrt {0.5(1-0.5)/1263}

z = -3.74

The test statistic of the question is; z = -3.74

We are given;

Sample size; n = 1263

Number of people that said yes; x = 565

Sample proportion is; p'= 565/1263 = 0.4473

Formula for the test statistic of proportion is;

z = (p' - p)/(√(p(1 - p)/n)

We will assume that population proportion p = 0.5. Thus;

z = (0.4473 - 0.5)/(√(0.5(1 - 0.5)/1263)

z = -3.74

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Answer:

13.5

Step-by-step explanation:

9 a week so they reduced it by 50% wich would be 4.5 then they add 50% do the math its 13.5

Answer:

its the thrid one i think i might be wrong srry

Step-by-step explanation:

Answer:

20/53

Answer number 4

Step-by-step explanation:

There are 20 brown, 16 orange, 4 navy, and 13 purple marbles. A marble is drawn at random. What is the probability the marble is brown?

Let's first add the marbles together.

20+16+4+13=53

there are 53 marbles altogether.

20 of the marbles are brown.

So the probability of drawing a brown marble is 20/53

True, While "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

The statement "-1000 2/3 is not a real fraction" is true. A real fraction is a mathematical expression that represents a ratio of two real numbers. In a fraction, the numerator and denominator are both real numbers, and they can be positive, negative, or zero.

In the given statement, "-1000 2/3" is not a valid representation of a fraction. The presence of a space between "-1000" and "2/3" suggests that they are separate entities rather than being part of a single fraction.

To represent a mixed number (a whole number combined with a fraction), a space or a plus sign is typically used between the whole number and the fraction. For example, a valid representation of a mixed number would be "-1000 2/3" or "-1000 + 2/3". However, without the proper formatting, "-1000 2/3" is not considered a real fraction.

It's important to note that "-1000 2/3" can still be expressed as an improper fraction. To convert it into an improper fraction, we multiply the whole number (-1000) by the denominator of the fraction (3) and add the numerator (2). The result would be (-1000 * 3 + 2) / 3 = (-3000 + 2) / 3 = -2998/3.

In conclusion, while "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

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Similar triangles may or may not have equal side lengths

The true statement is (a) the slope of DF is equal to the slope of CD

The similar triangles are given as:

Triangle DEF and triangle CBD

The above means that the corresponding lines DF and CD have equal slope

The slope of segment DF is calculated as:

\(m =\frac{7 - (-2)}{1 - (-2)}\)

While the slope of segment CD is:

\(m =\frac{-2 - 4}{-2 - 0}\)

Hence, the true statement is (a)

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Answer: 39 ft2

Step-by-step explanation:

The area of the trapezoid is 39 square feet.

To find the area of a trapezoid, you can use the formula:

Area = (1/2) × (base1 + base2) × height

Given that the bases of the trapezoid are 16 feet and 10 feet, and the height is 3 feet, we can substitute these values into the formula:

Area = (1/2) × (16 + 10) × 3

Area = (1/2) × 26 × 3

Area = (1/2) × 78

Area = 39 ft^2

Therefore, the area of the trapezoid is 39 square feet.

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