The estimated regression equation by least squares method minimizes the sum of the.

Planets around other stars can be detected by carefully measuring the "brightness" or "light intensity" of stars.

When a planet orbits a star, it causes a slight change in the brightness or light intensity of the star. This is known as the transit method of planet detection. As the planet passes in front of the star from our line of sight, it blocks a small portion of the star's light, causing a temporary decrease in its brightness. By carefully measuring these changes in brightness over time, scientists can infer the presence and characteristics of planets orbiting the star. This method has been instrumental in the discovery of numerous exoplanets in recent years.

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The price vectors a. p₁ = 3 and p₂ = 2, Mary will consume only good 1.

Here we have the Utility function as

U(x₁ , x₂) = 3x₁ + x₂

From the given utility function we can clearly see that these goods are substitutes for each other

Now,

δU/δx₁ = 3

δU/δx₂ = 1

Hence we get the Marginal Rate of Substitution or MRS

\(=- \frac{\delta U/ \delta x_1 }{\delta U/ \delta x_2}\)

= -3

The MRS signifies that for every additional unit of 1, Mary is willing to give up 3 units of good 2

|MRS| = 3

For Mary to only consume good 1, |MRS| > p₁/p₂

Hence here we get the p/p ratio for the 4 price vectors to be

a. 3/2 = 1.5

b. 10/3 = 3.33

c. 4

d. 15.4 = 3.75

Hence we can clearly say that for the price vectors p₁ = 3 and p₂ = 2, Mary will consume only good 1.

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Answer:-4.6

Step-by-step explanation:

Answer: hey good morning, 12/30 simplified is 2/5 hope this helped :))

Step-by-step explanation:

Step-by-step explanation:

what is the difference between the x- values ?

and what is the difference between the y- values ?

a transformation means a simple shift. so, addition of subtraction. no multiplication or such.

1 to -1 ? -2

-1 to -3 ? -2

5 to 3 ? -2

6 to 6 ? 0

3 to 3 ? 0

-2 to -2 ? 0

so, the transformation is (-2, 0)

The yc(x) is the complementary solution, and yp1(x) and yp2(x) are the particular solutions for the 2x² and 5cos(7x) terms

using the method of undetermined coefficients, we first identify the complementary and particular solutions.
The complementary solution comes from the homogeneous equation

\( y'' + 49y = 0.\)

This has the characteristic equation r² + 49 = 0, giving us r = ±7i. So, the complementary solution is

\(yc(x) = C1cos(7x) + C2sin(7x).\)
For the particular solution, we have two terms:

\( 2x² and 5cos(7x)\). For the 2x² term, we assume\( yp1(x) = Ax² + Bx + C.\) Plugging into the equation, we find the coefficients A, B, and C.

For the 5cos(7x) term, the assumed particular solution is

\( yp2(x) = Dcos(7x) + Esin(7x).\)

Since this overlaps with the complementary solution, we must multiply by x, so

\(yp2(x) = x(Dcos(7x) + Esin(7x)).\)

Plug it into the equation to determine D and E.
Finally, the general solution is \(y(x) = yc(x) + yp1(x) + yp2(x)\),

where yc(x) is the complementary solution, and yp1(x) and yp2(x) are the particular solutions for the 2x² and 5cos(7x) terms, respectively.

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Answer:

Hi there!

Your answer is:

It will take 171 minutes and approximately 43 seconds to use 400 and 2/3rds gallons of water! If you need it in decimal format, your answer is 171.71!

Step-by-step explanation:

2 & 1/3 gals per 1 minute

Divide by 2 & 1/3 to determine mins per 1 gal

1gal per 3/7ths of a minute

× 400 & 2/3

400 & 2/3 gals per 171 & 5/7ths minutes

I hope this makes sense!

Answer:

2

Step-by-step explanation:

Rise is 10 run is 5 Rate of Change is rise over run.

An example of a linear equation that represents a horizontal line is expressed as: y = 1.

The linear equation that represents a horizontal line is expressed as y = b, where the value of b is the point on the x-axis where the line intercepts the y-axis horizontal line. The point is on the line is (0, b).

An example of a graph that shows a horizontal line is attached below where the line cuts the y-axis at (0, 1).  Thus, the linear equation is expressed as y = 1.

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The required scale factor between the building and toy model is given as 900.

The scale factor is defined as the ratio of the modified change in length to the original length.

Here,
The area of the front side of the toy building is 1 square foot.
The real building's front side has an area of 900 square feet.
The real buildings as a dilation of the toy,
Scale factor = 900 /1
Scale factor = 900

Thus, the required scale factor between the building and the toy model is given as 900.

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Answer:

35 and 37

Step-by-step explanation:

consecutive ODD numbers, 35 then 37.. 35+37 = 72

Answer:

11 hours

Step-by-step explanation:

$386.25 - (35 x $7.50) = $123.75 <--- overtime

$7.50 x 1.5 = $11.25

$123.75 / $11.25 = 11 hours overtime

Answer:

75+325=400/25=16

13 more

16weeks total

And

Step-by-step explanation:

Answer: 10

Step-by-step explanation:

9.457

Above 5= change of # before decimal point

Answer:

9

Step-by-step explanation:

9.4 rounds down to 9, if it were 9.5 it would round up to 10

Answer:

1/12

Step-by-step explanation:

because because you have one choice out of 12 choices and that gives you 112

A linear system with 3 equations and 4 variables by representing it with an augmented matrix and bringing the matrix to reduced row-echelon form can be solved.

A mathematical representation of a system based on the application of a linear operator is known as a "linear system" in systems theory. Ordinarily, compared to nonlinear systems, linear systems display much simpler features and properties. The automatic control theory, signal processing, and telecommunications all heavily rely on linear systems as a mathematical abstraction or idealisation.

Linear systems, for instance, are frequently used to model the propagation medium for wireless communication systems. An operator, H, that converts an input, x(t), into an output, y(t), a kind of black box description, can be used to describe a general deterministic system.

The superposition principle, or alternatively both the additivity and homogeneity properties, must be satisfied by a system to be considered linear, and only then.

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Step-by-step explanation:

The -5   makes the waveform amplitude of 5  the wave goes down to -5  and up to +5   BUT the -10 shifts the whole wave down 10

so it goes from -15  to -5    and the midline is then   y =  -10

The Taylor series for f(x) = x^(2/3) centered at x = 1 has the first four nonzero terms: 1 + (2/3)(x - 1) + (2/9)(x - 1)^2 + (4/81)(x - 1)^3.

To find the Taylor series for f(x) = x^(2/3) centered at x = 1, we need to calculate its derivatives at x = 1. Taking the first four nonzero derivatives, we have f'(x) = (2/3)x^(-1/3), f''(x) = (-2/9)x^(-4/3), and f'''(x) = (8/81)x^(-7/3).

Evaluating these derivatives at x = 1, we obtain f'(1) = 2/3, f''(1) = -2/9, and f'''(1) = 8/81. Using these values and the general formula for the Taylor series, we can write the first four nonzero terms as 1 + (2/3)(x - 1) + (2/9)(x - 1)^2 + (4/81)(x - 1)^3. To find the first three nonzero terms, we simply omit the last term from the series.

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The expression V − E + F is an illustration of the Euler's formula.

The expression V − E + F is always 2

The equation is given as:

V - E + F = 2

Where:

According to the Euler's formula, the relationship between V, E and F is:

V + F = 2 + E

Subtract E from both sides

V - E + F = 2

Hence, the expression V − E + F is always 2

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Answer:

\(\frac{4}{3}\)

Step-by-step explanation:

The area of a regular octahedron is given by:

area = \(2\sqrt{3}\ *edge^2\). Let a is the length of the edge (diagonal).

area = \(2\sqrt{3}\ *a^2\)

Given that the diagonal of the octahedron is equal to height (h) of the tetrahedron i.e.

a = h, where h is the height of the tetrahedron and a is the diagonal of the octahedron. Let the edge of the tetrrahedron be e. To find the edge of the tetrahedron, we use:

\(h=\sqrt{\frac{2}{3} } e\\but\ h=a\\a=\sqrt{\frac{2}{3} } e\\e=\sqrt{\frac{3}{2} }a\)

The area of a tetrahedron is given by:

area = \(\sqrt{3}\ *edge^2\) = \(\sqrt{3} *(\sqrt{\frac{3}{2} }a)^2=\frac{3}{2}\sqrt{3} *a^2\)

The ratio of area of regular octahedron to area tetrahedron regular is given as:

Ratio = \(\frac{2\sqrt{3}\ *a^2}{\frac{3}{2} \sqrt{3}*a^2} =\frac{4}{3}\)

Answer:

3/4

Step-by-step explanation:

Answer:

2 ÷ 8/3 is 0.75 !!

there you go!

The four-digit number that satisfies all the given clues is 5284.

In the given clues, we can analyze each condition to find the number.

Clue 1 states that all digits are different. Therefore, we can deduce that the digits are 5, 2, 8, and 4.

Clue 2 states that the product of digits R and S equals digit P. Looking at the available digits, the only combination that satisfies this condition is 8 and 4, as 8 * 4 = 32, and digit P can only be 3.

Clue 3 states that digit Q is one more than P. Since P is 3, Q must be 4.

Clue 4 states that the sum of all digits is 18. Adding up the digits 5 + 2 + 8 + 4 gives us 19, which does not meet the condition. Hence, we can conclude that Clue 4 is not valid or that there may be a mistake in the clues.

Finally, Clue 5 states that the four-digit number is divisible by 11. By checking the divisibility rule for 11, we find that 5284 is divisible by 11.

Therefore, the number that satisfies all the given clues is 5284.

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Answer:

The p=3    I think the area is 13 if im wrong srry

Step-by-step explanation:

Answer:

Step-by-step explanation:

There are no statements here

Answer:

Step-by-step explanation:

6hr(55mi/hr)

330mi

Answer:

140

Step-by-step explanation:

cause alternate interior angles

Answer: 29

Step-by-step explanation:

4y + 4 + 60 = 180

4y = 116

y = 29

well, since the y-intercept is at -5, or namely when the line hits the y-axis is at -5, that's when x = 0, so the point is really (0 , -5), and we also know another point on the line, that is (-1 ,6), to get the equation of any straight line, we simply need two points off of it, so let's use those two

\(\stackrel{y-intercept}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{-5})}\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{0}}} \implies \cfrac{6 +5}{-1} \implies \cfrac{ 11 }{ -1 } \implies - 11\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{- 11}(x-\stackrel{x_1}{0}) \implies y +5 = - 11 ( x -0) \\\\\\ y+5=-11x\implies {\Large \begin{array}{llll} y=-11x-5 \end{array}}\)