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3 years ago

What is the quadratic regression equation for the data set? PLEASEE HELP ME

Mathematics

1 answer:

Soloha48 [4]3 years ago

8 0

You're trying to find constants $a_0,a_1,a_2$ such that $\hat y=a_0+a_1\hat x+a_2{\hat x}^2$ . Equivalently, you're looking for the least-square solution to the following matrix equation.

$\underbrace{\begin{bmatrix}1&6&6^2\\1&3&3^2\\\vdots&\vdots&\vdots\\1&9&9^2\end{bmatrix}}_{\mathbf A}\underbrace{\begin{bmatrix}a_0\\a_1\\a_2\end{bmatrix}}_{\mathbf x}=\underbrace{\begin{bmatrix}100\\110\\\vdots\\70\end{bmatrix}}_{\mathbf b}$

To solve $\mathbf{Ax}=\mathbf b$ , multiply both sides by the transpose of $\mathbf A$ , which introduces an invertible square matrix on the LHS.

$\mathbf{Ax}=\mathbf b\implies\mathbf A^\top\mathbf{Ax}=\mathbf A^\top\mathbf b\implies\mathbf x=(\mathbf A^\top\mathbf A)^{-1}\mathbf A^\top\mathbf b$

Computing this, you'd find that

$\mathbf x=\begin{bmatrix}a_0\\a_1\\a_2\end{bmatrix}\approx\begin{bmatrix}121.119\\-3.786\\-0.175\end{bmatrix}$

which means the first choice is correct.

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2 years ago

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2 years ago

A gym allows members to attend two free strength-building classes each month as part of their $40 monthly membership fee. If the

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2 years ago

When rolling two six-sided number cubes, what is the probability of getting a sum of at least 5? 5/18 1/3 13/18 5/6

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The sample space for two six sided cubes =

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

Now the favourable events are those where the sum is greater than or equal to 5.

It means

(1,4) (1,5) (1,6)

(2,3) (2,4) (2,5) (2,6)

(3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

It means

favourable events = 30

and total possible events = 36

So probability = 30/36 = 5/6

Hence 4th option is the correct one.

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3 years ago

Micah is writing a function that models the height a dolphin reaches when it propels itself from underwater to the surface, leap

stepladder [879]

Answer:

The dolphin will be above the surface of the water for 2 seconds.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}$

$\Delta = b^{2} - 4ac$

The height of the dolphin after t seconds is given by:

$h(t) = -16t^2 + 96t - 128$

According to Micha's model, how long will the dolphin be above the surface of the water?

It stays above the surface of the water between the first and the second root. Initially, it is below water, when the first time for which $h(t) = 0$ it crosses the surface upwards, and then the second time for which $h(t) = 0$ it crosses the surface downwards.