find a power series representation centered at the origin for the function f(x) = 1 (7 − x) 2

Answer:

See below ↓

Step-by-step explanation:

a. Graph shown Below.

b.

domain : x ≥ 0

range : f(x) ≥ 0

c.

rate of waves:

\(\sf f(x) = 3.13\sqrt{x}\)

the wave is 10 m above the sea

\(\sf f(x) = 3.13\sqrt{10}\)

\(\sf f(x) = 9.9 \ m/s\)

Let the number be "x"

\(3x + 9 = 2x - 4\)

\(3x + 9= 2x - 4 \\ \\ \implies 3x - 2x = - 4 - 9 \\ \\ \implies x = - 13\)

\( \therefore \text{the required number is = - 13}\)

Answer:

- 35

Step-by-step explanation:

let the number be n then increased by 9 is n + 9 and decreased by 4 is n - 4 , so

3(n + 9) = 2(n - 4) ← distribute parenthesis on both sides

3n + 27 = 2n - 8 ( subtract 2n from both sides )

n + 27 = - 8 ( subtract 27 from both sides )

n = - 35

that is the number is - 35

Answer: 4

Step-by-step explanation:

Answer:

17.1 in2

Step-by-step explanation:

The actual cost to see the game is $150, as that is the amount you paid for the ticket. The cost in this scenario can be considered an opportunity cost. By choosing to attend the game instead of selling the ticket for $400, you forgo the opportunity to earn that additional $400.

In this scenario, the cost of attending the game refers to the actual amount of money you spent on the ticket, which is $150. This is the out-of-pocket expense that directly affects your financial resources.

On the other hand, the opportunity cost is the potential benefit or value that you give up by choosing one option over another. In this case, if you had sold the ticket for $400, you would have received a higher amount of money, which represents the opportunity cost of attending the game. By deciding to go to the game, you forego the opportunity to earn that additional $400.

Opportunity cost is a concept in economics that emphasizes the value of the next best alternative forgone when making a decision. It helps assess the trade-offs involved in different choices and helps in evaluating the true cost of a decision beyond the immediate financial expenses.

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Answer:

(0, 2).

Step-by-step explanation:

To find the y-intercept of the graph of the equation 3x + 3y = 6, we can set x = 0 and solve for y.

When x = 0, the equation becomes:

3(0) + 3y = 6

Simplifying, we get:

3y = 6

Dividing both sides by 3, we get:

y = 2

Therefore, the y-intercept of the graph is (0, 2).

Answer:  2

Step-by-step explanation: To find the y intersect, first make y the subject of the formula.

3x +3y = 6

3y = -3x + 6

Divide each term by 3

3y/3  =  -3x/3  + 6/3

y = -x + 2

Comparing with the general equation: y = ax^2 + bx + c

where c is the y intersect,

c = 2

Therefore the y intersect is at 2

Converting 1. 50μm²  to square meters gives 1. 5 × 10 ^-11

Conversion of units is defined as the conversion of different units of measurement for the same quantity, mostly through multiplicative conversion factors.

From the information given, we are to convert micrometers to square meters

Note that:

1 micrometer ( μm²) = 10^-12m²

Given 1. 50μm² =  xm²

cross multiply

x = 1. 50 × 10^-12

x = 1. 50 × 10^-12

x = 1. 50 × 10^-12

x = 1. 5 × 10 ^-11 square meters

Thus, converting 1. 50μm²  to square meters gives 1. 5 × 10 ^-11

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Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

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1. In the context of spacetime, the locus of points equidistant from the origin of a spacetime plane is a hyperbola.

In Euclidean space, the distance between two points is given by the Pythagorean theorem, which only considers spatial dimensions. However, in spacetime, the concept of distance is extended to include both spatial and temporal components. The spacetime distance, also known as the interval, is given by the Minkowski metric:

ds^2 = -c^2*dt^2 + dx^2 + dy^2 + dz^2,

where c is the speed of light, dt represents the temporal component, and dx, dy, dz represent the spatial components.

To determine the locus of points equidistant from the origin, we need to find the set of points where the spacetime interval from the origin is constant. Setting ds^2 equal to a constant value, say k^2, we have:

-c^2*dt^2 + dx^2 + dy^2 + dz^2 = k^2.

If we focus on a spacetime plane where dy = dz = 0, the equation simplifies to:

-c^2*dt^2 + dx^2 = k^2.

This equation represents a hyperbola in the spacetime plane. It differs from a circle in Euclidean space due to the presence of the negative sign in front of the temporal component, which introduces a difference in the geometry.

Therefore, the locus of points equidistant from the origin in a spacetime plane is a hyperbola.

(Note: The explanation provided assumes a flat spacetime geometry described by the Minkowski metric. In the case of a curved spacetime, such as that described by general relativity, the shape of the locus of equidistant points would be more complex and depend on the specific curvature of spacetime.)

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The actual dimensions of Abigail's house are 18 ft by 20 ft.

Abigail's house is represented by a scale drawing with dimensions of 9 cm by 10 cm. We are told that 6 cm on the scale drawing equals 12 ft. To find the actual dimensions of Abigail's house, we need to determine the scale factor.

First, we calculate the scale factor by dividing the actual length (12 ft) by the corresponding length on the scale drawing (6 cm). The scale factor is 12 ft / 6 cm = 2 ft/cm.

Next, we can use the scale factor to find the actual dimensions of Abigail's house. We multiply each dimension on the scale drawing by the scale factor.

The actual length of Abigail's house is 9 cm * 2 ft/cm = 18 ft.
The actual width of Abigail's house is 10 cm * 2 ft/cm = 20 ft.

Therefore, the actual dimensions of Abigail's house are 18 ft by 20 ft.

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The weighted average of the given data set is 33.

To find the weighted average of a data set, we need to multiply each data value by its corresponding weight, sum up the products, and divide by the total weight.

Given the data set with weights:

Data: 20, 40, 50

Weights: 5, 2, 3

To calculate the weighted average, we follow these steps:

1. Multiply each data value by its weight:

  (20 * 5) + (40 * 2) + (50 * 3)

2. Sum up the products:

  100 + 80 + 150 = 330

3. Calculate the total weight:

  5 + 2 + 3 = 10

4. Divide the sum of the products by the total weight:

  330 / 10 = 33

Therefore, the weighted average of the given data set is 33.

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Answer:

we have to see question 1 to help with number two

Answer:

Explanation:

Let the speed of the first person be x mph and the speed of the second person be y mph

Since one person's speed is faster than the other, we can have:

Mathematically, distance equals the product of speed and time

The time traveled by each person is 1.5 hours

The distance traveled by each of them is:

The sum of the two equals 18 miles

Thus:

Recall;

This means that the first person was walking 5 mph while the second was walking 7 mph

La cantidad total de veces que se utiliza el número 4 en las cifras desde 128 hasta 567 es 55 veces.

Considerando los números desde 128 hasta 567, la cantidad de veces que se utiliza el número 4 en las cifras es la siguiente:

En la posición de las centenas, el 4 aparece 1 vez: en el número 400.

En la posición de las decenas, el 4 aparece en 10 números: 140-149, 240-249, ..., 540-549.

En la posición de las unidades, el 4 aparece 5 veces en cada grupo de 10 números (por ejemplo, 134, 144, 154, ..., 564).

Hay 44 grupos de 10 números entre 128 y 567, así que el 4 aparece 44 veces en total.

Entonces, la cantidad total de veces que se utiliza el número 4 en las cifras desde 128 hasta 567 es:

1 (centenas) + 10 (decenas) + 44 (unidades) = 55 veces.

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Answer:

\( \frac{x}{4} + \frac{1}{2} = \frac{1}{8} \)

\( \frac{x}{4} = - \frac{3}{8} \)

\(x = - \frac{3}{2} = - 1 \frac{1}{2} \)

The solution to the equation x/4 + 1/2 = 1/8 is x = -3/2.

Consider the equation, we have only one x term, so taking all the terms without x to the other side and terms with x on one side.

x/4 + 1/2 = 1/8

Take the 1/2 term on the other side,

x/4=1/8 - 1/2

Taking the LCM on the Right side,

x/4 = (1-4) / 8

x/4 = -3/8

Now, we have x/4 so what we can do is, shift the 4 to the other side too, we get,

x = ( -3/8) * 4

x = -3/2

The solution to the equation x/4 + 1/2 = 1/8 is x = -3/2.

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Answer:

-2

Step-by-step explanation:

3( x+ 2)=2(x+2)​

=>3x+6=2x+4

=>3x-2x=4-6

=>x=-2

-2  is the value of x

Answer:

The answer is

Step-by-step explanation:

3( x+ 2)=2(x+2)

First expand the terms in the bracket

That's

3x + 6 = 2x + 4

Group like terms

Send the constants to the right side of the equation and those with variables to the left side

3x - 2x = 4 - 6

Simplify

We have the final answer as

Hope this helps you

The abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).

Given the equation x^2 = 2y.

The coordinates of the point are (4,1).We have to find the abscissa on the curve that is nearest to this point.So, let's solve this question:

To find the abscissa on the curve x2 = 2y which is nearest to the point (4,1), we need to apply the distance formula.In terms of x, the formula for the distance between a point on the curve and (4,1) can be written as:√[(x - 4)^2 + (y - 1)^2]But since x^2 = 2y, we can substitute 2x^2 for y:√[(x - 4)^2 + (2x^2 - 1)^2].

Now we need to find the value of x that will minimize this expression.

We can do this by finding the critical point of the function: f(x) = √[(x - 4)^2 + (2x^2 - 1)^2]To do this, we take the derivative of f(x) and set it equal to zero: f '(x) = (x - 4) / √[(x - 4)^2 + (2x^2 - 1)^2] + 4x(2x^2 - 1) / √[(x - 4)^2 + (2x^2 - 1)^2] = 0.

Now we can solve for x by simplifying this equation: (x - 4) + 4x(2x^2 - 1) = 0x - 4 + 8x^3 - 4x = 0x (8x^2 - 3) = 4x = √(3/8)The abscissa on the curve x^2 = 2y that is nearest to the point (4,1) is x = √(3/8).T

he main answer is that the abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).

The abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).

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Answer:

Sysem A has 2 real solutions (both the positive and negative form of a number can be squared to get a positive square)

System B has 0 real solutions (you can't square root a negative number and get a real number)

System C has 2 real solutions (same explanation as System A)

To estimate the percentage of people who weigh more than 180 pounds in a population with a mean of 152 pounds and a standard deviation of 26 pounds.

In order to estimate the percentage of individuals in a certain population who weigh more than 180 pounds, it is necessary to determine an appropriate sample size. Using statistical methods, it has been determined that a sample size of 890 people is required to achieve a 96% confidence level with an error no greater than 3 percentage points.

This means that data can be gathered from this number of participants to estimate the percentage of people who weigh more than 180 pounds in the population with a greater degree of accuracy and confidence. Understanding the appropriate sample size necessary for statistical analysis is important in ensuring the reliability and validity of research findings.

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Answer: 1,000 times longer

Step-by-step explanation: Dino have been extinct for about 60 million years ago, and Neanderthals have been extinct for about 40,000 years.

60,000,000 divided by 40,000 is 1500 so 1000 times longer (sorry if im wrong i'm new)

The perimeter is 32 inches.

How to find the perimeter of a figure?

The perimeter of a figure is the sum of the whole sides of the figure.

Therefore, the perimeter of the entire shape can be calculated as follows:

The shape is made of one half-circle attached to an equilateral triangle

Therefore,

circumference of the semi-circle = πr

r = 7 / 2 = 3.5 inches

circumference of the semi-circle = 3.5π

Hence,

perimeter of the shape = 7 + 7 + 7 + 3.5π

perimeter of the shape = 21 + 3.5(3.14)

perimeter of the shape = 21 + 10.99 = 31.99

Therefore, perimeter of the shape = 32 inches (approx)

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Answer:

the temp dropped about 10. degrees to -6

The correct option is D. x = 2, y = -5. The values of x and y of the solution to the system of equations are 2, -5.

When solving a set of equations in mathematics, a matrix is a collection of integers or expressions.

The matrix A is

[A]=[4 -6 8 -2]

The matrix Ax is

[Ax]=[38 -6 26 -2]

The matrix Ay is

[Ay]=[4 38 8 26]

All of the matrices' determinant is

|A| = 40

|Ax| = 80

|Ay| = -200

The value of x is (|Ax|) /(|A|) = 80/(40) = 2

The value of y is ( |Ay|)/(|A|) = -200/(40) = -5

Therefore, the value of x and y is 2, -5. The correct option is D

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Answer:

0.45

Step-by-step explanation:

You divided 2.25 by 5

this equation is only valid at the point (a, b) where we found the slope of the normal line. To find the equation of the normal line at a different point, we would need to repeat this process with new values of a and b.

To find the equation of the line normal (perpendicular) to the graph of y = x^3 + 3x^2 + 7x - 1 at a point (a, b), we need to determine the slope of the normal line at that point.

The slope of the tangent line to the curve at (a, b) is given by the derivative:

f'(x) = 3x^2 + 6x + 7

So the slope of the tangent line at x = a is:

m = f'(a) = 3a^2 + 6a + 7

The slope of the normal line is the negative reciprocal of the slope of the tangent line, so:

m_n = -1/m = -1/(3a^2 + 6a + 7)

Now we have the slope of the normal line at (a, b), and we just need to find the equation of the line in point-slope form, using the point (a, b):

y - b = m_n(x - a)

Substituting the expression for m_n, we get:

y - b = (-1)/(3a^2 + 6a + 7)(x - a)

Multiplying both sides by 3a^2 + 6a + 7 to eliminate the fraction, we get:

(3a^2 + 6a + 7)(y - b) = -(x - a)

Expanding and rearranging, we get the equation of the line normal to the graph of y = x^3 + 3x^2 + 7x - 1 at (a, b):

(3a^2 + 6a + 7)y = -x + (3a^2 + 6a + 7)b + a

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The value of the total area of the shaded region are,

⇒ 42 units²

We have to given that;

Sides of rectangle are,

AB = 9

BC = 6

Hence, The area of rectangle is,

⇒ 9 x 6

⇒ 54 units²

And, Area of triangle is,

A = 1/2 × 4 × 6

A = 12 units²

Thus, The value of the total area of the shaded region are,

⇒ 54 - 12

⇒ 42 units²

So, The value of the total area of the shaded region are,

⇒ 42 units²

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Answer:

\( - 5 = 0.5x \\ \frac{ - 5}{0.5} = x \\ - 10 = x\)

Step-by-step explanation:

this is the step

Answer:

Between 0 and 3: decreasing

Between 3 and 4: constant (stays the same)

Between 4 and 8: decreasing

Step-by-step explanation:

The probability of being served immediately in a three-server model is 0.2143 or approximately 21.43%.

Consider that the arrivals follow a Poisson distribution and the service times follow an exponential distribution, the probability of being served immediately in a three-server model can be calculated using the Erlang-C formula.

The Erlang-C formula is given by:

\(P0 = 1/[1 + (A1/A)^1 + (A2/(A*A1))^2/2 + (A3/(A*A1*A2))^3/3! + ... + (Ak/(A*A1*...*Ak-1))^k/k! + ...]\)

A = total traffic intensity for the system

The traffic intensity for each server is given by:

\(Ak = (A^k/k!) * P0\)

Where k = number of servers.

LEt A = λ/3μ

where 3 is the number of servers.

Using these formulas,

\(P0 = 1/[1 + ((λ/3μ)/1)^1 + ((λ/3μ)/(λ/3μ))^2/2 + ((λ/3μ)/(λ/3μ)^2)^3/3!]\)

Simplifying the expression, we get:

\(P0 = 1/[1 + 1/3 + (1/9)(1/3)^2 + (1/27)(1/3)^3]\)

P0 = 0.2143

Therefore, the probability of being served immediately in a three-server model is 0.2143

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Answer:

If the null hypothesis is rejected at a 1% significance level, then Multiple Choice the alternative hypothesis will be rejected at a 5% significance level

Step-by-step explanation:

The null hypothesis will not be rejected at a 5% significance level the alternative hypothesis will not be rejected at a 5% significance level O the null hypothesis will be rejected at a 5% significance level