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3 years ago

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Company X tried selling widgets at various prices to see how much profit they would make. The following table shows the widget s

elling price, x, and the total profit earned at that price, y. Write a quadratic regression equation for this set of data, rounding all coefficients to the nearest hundredth. Using this equation, find the profit, to the nearest dollar, for a selling price of 28.25 dollars

1 answer:

Neporo4naja [7]3 years ago

4 0

Answer:

y = -7.235451 x^2 + 402.5542 x - 2382.736

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Consider the following two ordered bases of R3:

grigory [225]

Answer:

Let $A = (a_1, ..., a_n)$ and $B = (b_1, ..., b_n)$ bases of V. The matrix of change from A to B is the matrix n×n whose columns are vectors columns of the coordinates of vectors $b_1, ..., b_n$ at base A.

The, we case correspond to find the coordinates of vectors of C,

$\{\left[\begin{array}{ccc}2\\-1\\-1\end{array}\right], \left[\begin{array}{ccc}2\\0\\-1\end{array}\right], \left[\begin{array}{ccc}-3\\1\\2\end{array}\right] \}$

at base B.

1. We need to find $a,b,c\in\mathbb{R}$ such that

$\left[\begin{array}{ccc}2\\-1\\-1\end{array}\right]=a\left[\begin{array}{ccc}1\\-1\\0\end{array}\right]+b\left[\begin{array}{ccc}-2\\2\\-1\end{array}\right]+c\left[\begin{array}{ccc}2\\-1\\1\end{array}\right]$

Then we find these values solving the linear system

$\left[\begin{array}{cccc}1&-2&2&2\\-1&2&-1&-1\\0&-1&1&-1\end{array}\right]$

Using rows operation we obtain the echelon form of the matrix

$\left[\begin{array}{cccc}1&-2&2&2\\0&-1&1&-1\\0&0&1&1\end{array}\right]$

now we use backward substitution

$c=1\\-b+c=-1,\; b=2\\a-2b+2c=2,\; a=4$

Then the coordinate vector of $\left[\begin{array}{ccc}2\\-1\\-1\end{array}\right]$ is $\left[\begin{array}{ccc}4\\2\\1\end{array}\right]$

2. We need to find $a,b,c\in\mathbb{R}$ such that

$\left[\begin{array}{ccc}2\\0\\-1\end{array}\right]=a\left[\begin{array}{ccc}1\\-1\\0\end{array}\right]+b\left[\begin{array}{ccc}-2\\2\\-1\end{array}\right]+c\left[\begin{array}{ccc}2\\-1\\1\end{array}\right]$

Then we find these values solving the linear system

$\left[\begin{array}{cccc}1&-2&2&2\\-1&2&-1&0\\0&-1&1&-1\end{array}\right]$

Using rows operation we obtain the echelon form of the matrix

$\left[\begin{array}{cccc}1&-2&2&2\\0&-1&1&-1\\0&0&1&2\end{array}\right]$

now we use backward substitution $c=2\\-b+c=-1,\; b=3\\a-2b+2c=2,\; a=4$

Then the coordinate vector of $\left[\begin{array}{ccc}2\\0\\-1\end{array}\right]$ is $\left[\begin{array}{ccc}4\\3\\2\end{array}\right]$

3. We need to find $a,b,c\in\mathbb{R}$ such that

$\left[\begin{array}{ccc}-3\\1\\2\end{array}\right]=a\left[\begin{array}{ccc}1\\-1\\0\end{array}\right]+b\left[\begin{array}{ccc}-2\\2\\-1\end{array}\right]+c\left[\begin{array}{ccc}2\\-1\\1\end{array}\right]$

Then we find these values solving the linear system

$\left[\begin{array}{cccc}1&-2&2&-3\\-1&2&-1&1\\0&-1&1&2\end{array}\right]$

Using rows operation we obtain the echelon form of the matrix

$\left[\begin{array}{cccc}1&-2&2&-3\\0&-1&1&2\\0&0&1&-2\end{array}\right]$

now we use backward substitution $c=-2\\-b+c=2,\; b=-4\\a-2b+2c=2,\; a=-2$

Then the coordinate vector of $\left[\begin{array}{ccc}-3\\1\\2\end{array}\right]$ is $\left[\begin{array}{ccc}-2\\-4\\-2\end{array}\right]$

Then the change of basis matrix from B to C is

$\left[\begin{array}{ccc}4&4&-2\\2&3&-4\\1&2&-2\end{array}\right]$

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4 years ago

Tresset [83]

The car part would be 120 inches long

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MissTica

Answer:

C: 28 inches

Step-by-step explanation:

Perimeter is when you add the length of each sides together.

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2 years ago

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In a poll, 22% of 714 surveyed adults said that . What is the actual number of adults who said that

Eva8 [605]

Answer:

<h2> 157 surveyed adult </h2>

Step-by-step explanation:

IF 22% of 714 surveyed adult made a statement, the actual number of those that made the statement can be gotten by simply evaluating 22% of 714 as shown below;

= 22% of 714

= 22/100 * 714

= (22*714)/100

= 15708/100

= 157.08

≈ 157 surveyed adult

<em>This means that about 157 surveyed adults made the statement. </em>

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4 years ago

Pls help with my geometry

Sati [7]

Least to greatest is mB,mD,mC

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