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2 years ago

7

For questions 5-6, find the regression equation that best models the data shown in the table.

1 answer:

navik [9.2K]2 years ago

7 0

Answer:

$\large \boxed{\mathbf{y = 2.538e^{0.6699x}}}$

Step-by-step explanation:

x 0 1 2 3 4 5 6 7

y 2 6 12 17 36 72 138 275

The points appear to follow an exponential growth curve.

The regression equation is

$\large \boxed{\mathbf{y = 2.538e^{0.6699x}}}$

The figure below shows the graph of your points and the regression line.

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Find the standard form of the equation of the ellipse with the given characteristics. Vertices: (4, 0), (4, 14); endpoints of th

saul85 [17]

Answer:

The standard form of the ellipse is $\frac{(x-4)^{2}}{9} + \frac{(y-7)^{2}}{49} = 1$ .

Step-by-step explanation:

The major axis of the ellipse is located in the y axis, whereas the minor axis is in the x axis. The center of the ellipse is the midpoint of the line segment between vertices, this is:

$(h, k) =\frac{1}{2}\cdot V_{1} (x,y) + \frac{1}{2}\cdot V_{2} (x,y)$ (1)

If we know that $V_{1} (x,y) = (4,0)$ and $V_{2}(x,y) = (4, 14)$ , then the coordinates of the center are, respectively:

$(h,k) = \frac{1}{2}\cdot (4, 0) + \frac{1}{2}\cdot (4,14)$

$(h,k) = (2,0) + (2, 7)$

$(h, k) = (4, 7)$

The length of each semiaxis is, respectively:

$a = \sqrt{(1 - 4)^{2}+(7-7)^{2}}$

$a = 3$

$b = \sqrt{(4-4)^{2}+(0-7)^{2}}$

$b = 7$

The standard equation of the ellipse is described by the following formula:

$\frac{(x-h)^{2}}{a^{2}}+ \frac{(y-k)^{2}}{b^{2}} = 1$

Where:

$h$ , $k$ - Coordinates of the center of the ellipse.

$a$ , $b$ - Length of the orthogonal semiaxes.

If we know that $h = 4$ , $k = 7$ , $a = 3$ and $b = 7$ , then the standard form of the ellipse is:

$\frac{(x-4)^{2}}{9} + \frac{(y-7)^{2}}{49} = 1$

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2 years ago

According to the National Oceanic and Atmospheric Administration, the blue whale is the largest animal on Earth. Blue whales wei

never [62]

Answer: The blue whale's weight is 150 times heavier than the narwhal's weight.

Step-by-step explanation:

Given: Weight of Blue whale = $3\times10^5\text{ pounds}$

Weight of Narwhal = $2\times10^3\text{ pounds}$

Number of times blue whale's weight is heavier than the narwhal's weight = $=\dfrac{\text{Weight of Blue whale}}{\text{Weight of Narwhal }}$

$=\dfrac{3\times10^5}{2\times10^3}\\\\=1.5\times10^{5-3}\ \ \ [\dfrac{a^m}{a^n}=a^{m-n}]\\\\=1.5\times10^2\\\\=1.5\times100=150$

Hence, the blue whale's weight is 150 times heavier than the narwhal's weight.

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cestrela7 [59]

Answer: B

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answer:

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