Find a line of best fit to represent the data. Let y = ticket price and x = the number of years since
1980 (1980 is year zero, 1981 is year one). Approximate a line to represent the data, a slope, a yintercept and equation that models your line of best fit.

It takes 4 weeks at minimum for each pair to hug at least once if they sit in random order.

Analyzing the Given Information

As per the given information,

Number of people = 8

It is given that they sit in random order every week.

W e assume that the order is not repeated.

There are 4 pairs and since a person hugs both the persons on his immediate left and right.

Determining the Number of Weeks

Total number of people to be hugged by each person = 7

Number of people hugged by a person in one week = 2

So, number of weeks taken by each to huge every other person = 7/2

⇒ It will take (3 +1) for every pair to hug.

It takes 4 weeks at a minimum for every pair to hug if we assume that  their order is not repeated.

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The matricial equation of the degenerate parabola is [tex]\left[\begin{array}{c}x'\\y'\end{array}\right] = \left[\begin{array}{c}\frac{ \sqrt{2} }{2}\cdot x + \frac{1}{8}\cdot x^{2}+1 \\\-\frac{\sqrt{2}}{2}\cdot x + \frac{1}{8}\cdot x^{2} + 1 \end{array}\right][/tex].

A parabola is degenerated when its axis of symmetry is not parallel to any orthogonal axis (i.e. x, y). First, we have to find an "equivalent" parabola whose axis of symmetry is parallel to the y-axis and whose vertex is along that axis.

Direction of the degenerate parabola

[tex]\tan \theta = \frac{2 - 1}{2 - 1}[/tex]

tan θ = 1

θ = 45°

This means that the degenerate parabola must be rotated 45° clockwise (- 45°) around the origin with respect to the "equivalent" parabola.

Distance from the vertex to the focus

[tex]p = \sqrt{(2 - 1)^{2}+(2 - 1)^{2}}[/tex]

[tex]p = \sqrt{2}[/tex]

Vertex of the "equivalent" parabola

[tex](h', k') = (0, \sqrt{2})[/tex]

Equation of the "equivalent" parabola

[tex]y = \frac{1}{4\cdot p}\cdot x^{2} + k'[/tex]

[tex]y = \frac{1}{4\sqrt{2}}\cdot x^{2}+\sqrt{2}[/tex]

Now we apply following rotation formula:

[tex]\left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{cc}\cos (-45^{\circ})&-\sin (-45^{\circ})\\\sin (-45^{\circ})&\cos (-45^{\circ})\end{array}\right] \cdot \left[\begin{array}{c}x\\\frac{1}{4\sqrt{2}}\cdot x^{2}+\sqrt{2}} \end{array}\right][/tex]

[tex]\left[\begin{array}{c}x'\\y'\end{array}\right] = \left[\begin{array}{c}\frac{ \sqrt{2} }{2}\cdot x + \frac{1}{8}\cdot x^{2}+1 \\\-\frac{\sqrt{2}}{2}\cdot x + \frac{1}{8}\cdot x^{2} + 1 \end{array}\right][/tex]

A representation of the degenerate parabola is shown in the figure attached below.

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Yes, (3, -2) is a solution for the linear system y = 2x - 8 and 2x + 4y = -2

In mathematics, the theory of linear systems is the foundation and core part of linear algebra, a subject that is used in most parts of modern mathematics. When the number of equations is the same as the number of variables, there is likely to be a solution. Not guaranteed, but likely.

If there is no solution, the equations are called "inconsistent".

One or infinitely many solutions are called "consistent"

In mathematics, a system of linear equations is a set of one or more linear equations involving the same variables

We need to find whether (3, -2) is a solution for the linear system y = 2x - 8 and 2x + 4y = -2 or not

Let y = 2x - 8.......(1)

From equation (1) we get, y - 2x = -8.....(2)

2x + 4y = -2.........(3)

Put (3,-2) in equation (2) , we get

-2 - 2(3) = -2 -6 = -8

LHS = RHS

Put (3,-2) in equation (3) , we get

2(3) + 4(-2) = 6 - 8 = -2

LHS = RHS

Hence,(3, -2) is a solution for the linear system y = 2x - 8 and 2x + 4y = -2

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The equation that can be used to represent total tickets sales is 2170 = 5s + 2f + 10a

let

Expression for number of students tickets sold;

s = f + 15

Expression for number of faculty tickets sold;

f = 2a

Expression for number of alumni tickets sold;

f = 2a

a = f/2

2170 = 5s + 2f + 10a

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#6

Yes

Direct variation because Time increases cupcakes increases and vice versa

#B

Constant of proportionality represents the amount of time required per cupcakes

#7

Yes we can find it

We have to check the x and y values of the ordered pairs (x,y)

If y is decreasing with respect to increase in x then it's inverse variation

Answer:

Step-by-step explanation:jneke

There is no such value of 'a' such that f(x) = 9x² + 4 and g(x) = (3x - a)² are equivalent.

Two polynomials are said to be equivalent only when the coefficients of all powers of x are equal for both the polynomials.

In the question, we are asked is there a value of 'a' such that f(x) = 9x² + 4 and g(x) = (3x - a)² are equivalent.

We know that two polynomials are said to be equivalent only when the coefficients of all powers of x are equal for both the polynomials.

Thus to check, we expand g(x), using the formula (p - q)² = p² + q² - 2pq.

g(x) = (3x - a)²,

or, g(x) = (3x)² + (a)² - 2(3x)(a),

or, g(x) = 9x² + a² - 6ax.

For f(x) = 9x² - 4, and g(x) = (3x - a)² to be equivalent,

As we need two different values of, 'a' at the same time, which ain't possible, thus we can say that there is no such value of 'a' such that f(x) = 9x² + 4 and g(x) = (3x - a)² are equivalent.

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The statement which is true about the end behaviour of the graphed function is; As the x-values go to positive infinity, the function’s values go to positive infinity.

The graph given according to the task content is described to have its first minimum at (-2,0), and then a maximum at; (-0.5, 5) and finally a minimum at; (1.05, -41).

Additionally, since the graph has 3 zeroes as given, it follows that the graph is that of a cubic function which takes the w-form.

Consequently, it can be inferred from the statements above that; As the x-values go to positive infinity, the function’s values go to positive infinity.

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Answer:

A

Step-by-step explanation:

edge 23

Because we have a vertical asymptote at x = 0 and a horizontal asymptote at y = -1, we conclude that the correct option is the last one.

Here we have the function:

[tex]f(x) = \frac{1}{x} - 1[/tex]

First notice that we have a vertical asymptote at x = 0, because we can't divide by zero.

Now, notice that when x tends to infinity or negative infinity, the first term becomes zero, then we have a horizontal asymptote at y = -1.

Then the correct option is the last one:

"On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 0, and the horizontal asymptote is at y = negative 1."

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Answer:

Last option

Step-by-step explanation:

Answer:

x=1/3

Step-by-step explanation:

(2/x)+4=3^3+1

(2/x)+4=10

(2/x)=6

2=6x

1/3=x

x=1/3

There is also a possibility that you meant to write 2/(x+4)=3^2+1

2/(x+4)=3^2+1

2/(x+4)=10

2=10x+40

-38=10x

x=-3.8

Answer: -35/16

Step-by-step explanation:

i just took the test:)

Answer:

True

Step-by-step explanation:

We got the formula for that:

F=ma

now if you replace the given data, it's gonna be

F=5 kg×3m/s²====> F=15kg.m/s²

Answer:

Step-by-step explanation:

I'm not entirely sure that this is correct, but it seems so to me from what I've  read.

The Coordinate system uses N,S,E,W to denote plus and minus. N (north) and E (east) are plus, and S (south) and W (west) are minus. North is + y and S is - y. E (east is plus x W is minus x)

(4,-7) = 4 east 7 south is what I would use as my answer.

Answer:

see image

Step-by-step explanation:

see image. We can use the given info and definition of isosceles (congruent sides) and reflexive property (something is congruent to itself) to prove (i) by SSS.

The using "Corresponding Parts of Congruent Triangles are Conguent" (CPCTC) to get more info to prove (ii) by SAS

The NBA league exhibits more competitive balance.

The chance that each team in a league has of winning the title is referred to as competitive balance. The championship would be won by each team on a regular basis in an ideal competitive environment. In contrast, if there was no balance between the two types of competition, the same team would consistently prevail.

Competitive balance is often regarded as a desirable trait because too much predictability makes fans of the lesser franchises angry and fans of the defending champions complacent, which lowers interest in the sport as a whole.

The "Noll-Scully" measure is the competitive balancing metric that is most frequently used in sports. The winning percentage of each league team's standard deviation (SD) is used to compute it. The SD is then divided by what it would be if all teams had equal talent and the outcomes were entirely random.

For NBA team, competitive balance = 0.134/32*82 = 0.343

For EPL team, competitive balance = 0.158/20*38 = 0.30

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The probability that one would have selected 2 five-dollar bills is; 1/4.

It follows from the task content that the piggy bank contains; 4 one-dollar bills and 4 five-dollar bills to make a total of 8 bills.

Hence, provided the probability events are carried out with replacement, the probability to have selected 2 five-dollar bills is;

= 4/8 × 4/8

= 1/4.

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Answer:

1/4

Step-by-step explanation:

Initially, as x increases, y decreases.

The slope of the graph is equal to 1 for all x between x=0 and x=3.

Starting at x=3, the function value y increases as x increases.

The slope of the graph is equal to 3 for x between x=3 and x=5.

For x between x=0 and x=4, the function value y decreases then increases to 0.

For x between x=4 and x=8, the function value y increases and decreases to 0.

From the graph, initially the it goes down when x increases up-to the x value 3. After that from x value 3 to 5, the graphs goes up. After that from the x value 5 it goes down to zero.

The slope of the line is the measurement of inclination of that line from the positive x-axis. It can be calculated by the following formula.

[tex]Slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

The slope of the graph between x=0 to x=3

[tex]Slope=\frac{-3-0}{3-0}=-1[/tex]

The slope of the graph between x=3 to x=5

[tex]Slope=\frac{3-(-3)}{5-3}=3[/tex]

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Applying the distance formula, to calculate the coordinates of B, use: 3 =√[(x-4)² + (y-2)²]  

The distance formula, [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex], is used to find the distance between two points on a coordinate plane.

We are given one point A(4, 2), let:

B (x, y) = (x2, y2)

A(4, 2) = (x1, y1)

d = 3 units

Plug in the values into the distance formula to find how to calculate the coordinates of B:

3 =√[(x-4)² + (y-2)²]  

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The value of x is 3. The correct option is the third option- 3

The width of the backyard is 9 yards. The correct option is the first option-  9 yards

From the question, we are to determine the value of x

13.

Perimeter of a rectangle = 2 (l + w)

Where l is the length

and w is the width

From the given information,

Perimeter = 24 cm

In the given diagram,

l = 3x cm

w = 3 cm

Thus,

24 = 2(3x + 3)

24 = 6x + 6

6x = 24 - 6

6x = 18

x = 18/6

x = 3

Hence, the value of x is 3. The correct option is the third option- 3

14.

From the given information,

The width of the yard is 3 less than 4 times the length

That is,

w = 4l - 3 --------- (1)

Also,

Perimeter = 24 yards

∴ 24 = 2(l + w) ---------- (2)

Put equation (1) into (2)

24 = 2(l + w)

24 = 2(l + 4l - 3)

24 = 2(5l - 3)

24 = 10l - 6

10l = 24 + 6

10l = 30

l = 30/10

l = 3 yards

Substitute the value of l into equation (1) to get w

w = 4l - 3

w = 4(3) - 3

w = 12 - 3

w = 9 yards

Hence, the width of the backyard is 9 yards. The correct option is the first option-  9 yards

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The record that represents an outlier in this data set is John's weight.

An outlier is a data point that differs significantly from other observations.

In other words, an outlier is a value or point that differs substantially from the rest of the data.

Therefore, the record that represents an outlier in this data set is  John's weight. This is because it is on the

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The answer to the question isit has only one solution  x = 0

The equation that Kate is solving is given as

2/3(6x - 3) = 1/2(6x - 4)

Then we have to factorize the equations

Such that we would have

[tex]\frac{2(6x-3)}{3} =\frac{2(3x-2)}{2}[/tex]

The next step of the equation would have to do with opening the equation

Then we would have 4x - 2 = 3x - 2

then 4x - 3x = 0

Then x = 0

Hence the solution of the equation is that it only has one solution x = 0

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Answer:

B. The equation has one solution: x = 0.

Step-by-step explanation:

The statements which summarize each student's conjecture are:

Trey and Serena are both trying to find the number of stones that were in the original arch or vault. Thus, when they identify the number of stones and its main features, they would be able to determine the type of arch or vault that was built there.

The statements which summarize each student's conjecture are:

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Complete Question:

The Students' Conjectures: During an archeological dig, the students found a voussoir from a semicircular stone arch. A voussoir is a trapezoidal (wedge-shaped) stone used to build an arch or vault.

1. What are the students trying to find out? (1 point)

2. Complete the table to summarize each student's conjecture: (2 points: 1 point for each row)

Answer:

Step-by-step explanation:

The piecewise defined function is formed by the following three functions: y = 40, for 0 ≤ x < 15, y = 0.0425 · x² - 3.8 · x + 87.438, for 15 ≤ x < 65 and y = 0.4 · x - 6, for x ≥ 65.

In this problem we have a piecewise defined function formed by three functions: (i) Linear equation, (ii) Quadratic equation, (iii) Linear equation. The first function is y = 40, for 0 ≤ x < 15.

The second function can be found based on the knowledge of three points:

y = a · x² + b · x + c

(x₁, y₁) = (15, 40)

40 = 225 · a + 15 · b + c

(x₂, y₂) = (45, 2.5)

2.5 = 2025 · a + 45 · b + c

(x₃, y₃) = (65, 20)

20 = 4225 · a + 65 · b + c

And the quadratic equation is y = 0.0425 · x² - 3.8 · x + 87.438, for 15 ≤ x < 65.

And the latter linear equation is:

y = m · x + b

m = (30 - 20)/(90 - 65)

m = 0.4

And the x-intercept is:

b = y - m · x

b = 20 - 0.4 · 65

b = - 6

The linear equation is y = 0.4 · x - 6, for x ≥ 65.

The piecewise defined function is formed by the following three functions: y = 40, for 0 ≤ x < 15, y = 0.0425 · x² - 3.8 · x + 87.438, for 15 ≤ x < 65 and y = 0.4 · x - 6, for x ≥ 65.

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Comparing with the original expression, the value that will go into the green box is 5

Given the indices expression below;

[tex]\frac{4^{-5}}{4^4}[/tex]

Since 4^-5 is equivalent to 1/4^5, hence the given expression will be equivalent to;

[tex]\frac{1}{4^5\times4^4}[/tex]

Comparing with the original expression, the value that will go into the green box is 5

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A and B are independent events if the probability of getting a red convertible is 0.08

The given parameters are:

P(A) = 0.20

P(B) = 0.40

The events are independent, if

P(A and B) = P(A) * P(B)

So, we have:

P(A and B) = 0.20 * 0.40

Evaluate

P(A and B) = 0.08

Hence, A and B are independent events if the probability of getting a red convertible is 0.08

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Complete question

A video game randomly chooses your car color and type. The probability of getting a red car is 0.20, and the probability of getting a convertible is 0.40.

Event A = You get a red car.

Event B = You get a convertible.

A and B are independent events if _____.

A.The probability of getting a red car or a convertible is 0.60.

B.The probability of getting a red car or a convertible is 0.08.

C.The probability of getting a red convertible is 0

D.The probability of getting a red convertible is 0.08

Between 95% confidence interval and 80% confidence interval, 95% confidence interval is wider than 80% confidence interval.

Given two confidence interval 95% and 80%.

For a given sample data, each confidence interval have different width.

This is because the critical value associated with the confidence level becomes larger as the confidence level is increased which results in an increased interval.

Confidence interval is the range of estimate.

The confidence interval for a population proportion can be found by the following formula:

p±[tex]\sqrt{(pq)/n}[/tex]

The value of z will be wider if the value of p,q are greater.

Hence 95% confidence interval will be wider than 80% confidence interval.

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Answer:

3/5

Step-by-step explanation:

the chance of landing on an even number (2 or 4) is 2/5

the chance of landing on the unshaded section (3) is 1/5

add the 2 together since the problem said "or" to get 3/5

The equation of a trend line that passes through the points (7, 450) and (14, 401) is y = -7x+99.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

More than one variable may be present in a linear equation. An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.

Points are: (7, 450) and (14, 401)

Slope(m)=(401-450)/(14-7)

              = -49/7

              = -7

Equation of trend line:

(y-450)= -7(x-7)

y-450= -7x+49

y= -7x+49+450

y= -7x+499

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A is proportional.

Lets simplify the problem,

← divide numerator/ denominator by 4

= 4/20= 1/5

Thus A form a proportion

≠ 1/5

Thus B is not a proportion

← divide numerator/ denominator by 4

=  2/5 ≠ 1/5

Thus C is not a proportion

5/1 ≠ 1/5

Thus D is not a proportion

A is proportional.

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The value of the expression ((-3)^4)^2 when simplified is 6561

Expressions are mathematical statements represented by numbers, arithmetic operations and variables

The expression is given as:

((-3)^4)^2

Start by expanding the inner bracket

((-3)^4)^2 = ((-3)*(-3)*(-3)*(-3))^2

Next, we evaluate the product (-3)*(-3)*(-3)*(-3)

This gives

((-3)^4)^2 = (81)^2

Next, expand the exponent

((-3)^4)^2 = (81) * 81

Next, we evaluate the product

This gives

((-3)^4)^2 = 6561

Hence, the value of the expression ((-3)^4)^2 when simplified is 6561

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Answer:

50000

Step-by-step explanation:

Using

[tex]P(percentage) \times CP(cost \: price) = Sales \: Tax[/tex]

Putting the given values

P × 25000 = 1750

[tex]P = \frac{1750}{25000} [/tex]

[tex]P = 0.07 \times 100[/tex]

[tex]P = 7\%[/tex]

Now

For purchase price of a new car.

[tex]P \times CP=Sales \: Tax[/tex]

[tex]7 \times CP = 3500[/tex]

[tex]CP = 50000[/tex]

Hope it helps you, any confusions you may ask!