Rachel is putting 3,902 bagels into a box if she puts 8 bagels in each box how many boxes can she fill in total.

Use the given data to find the equation of the regression line. examine the scatterplot and identify a characteristic of the dat

kari74 [83]

Answer:

y = 1.5x + 3.2009

Step-by-step explanation:

I plotted your points and drew a linear regression line.

Its equation is

y = 1.5x + 3.2009

The regression line ignores the fact that the points fall along a smooth curve.

A parabolic regression line fits the data much better.

The equation for that line is

y = - 0.1647x² + 4.1357x - 5.6946

It is the equation for a vertical parabola opening downward.

7 0

3 years ago

Consider the linear transformation T from V = P2 to W = P2 given by T(a0 + a1t + a2t2) = (2a0 + 3a1 + 3a2) + (6a0 + 4a1 + 4a2)t

Svet_ta [14]

Answer:

$[T]EE=\left[\begin{array}{ccc}2&3&3\\6&4&4\\-2&3&4\end{array}\right]$

Step-by-step explanation:

First we start by finding the dimension of the matrix [T]EE

The dimension is : Dim (W) x Dim (V) = 3 x 3

Because the dimension of P2 is the number of vectors in any basis of P2 and that number is 3

Then, we are looking for a 3 x 3 matrix.

To find [T]EE we must transform the vectors of the basis E and then that result express it in terms of basis E using coordinates and putting them into columns. The order in which we transform the vectors of basis E is very important.

The first vector of basis E is e1(t) = 1

We calculate T[e1(t)] = T(1)

In the equation : 1 = a0

$T(1)=(2.1+3.0+3.0)+(6.1+4.0+4.0)t+(-2.1+3.0+4.0)t^{2}=2+6t-2t^{2}$

$[T(e1)]E=\left[\begin{array}{c}2&6&-2\\\end{array}\right]$

And that is the first column of [T]EE

The second vector of basis E is e2(t) = t

We calculate T[e2(t)] = T(t)

in the equation : 1 = a1

$T(t)=(2.0+3.1+3.0)+(6.0+4.1+4.0)t+(-2.0+3.1+4.0)t^{2}=3+4t+3t^{2}$

$[T(e2)]E=\left[\begin{array}{c}3&4&3\\\end{array}\right]$

Finally, the third vector of basis E is $e3(t)=t^{2}$

$T[e3(t)]=T(t^{2})$

in the equation : a2 = 1

$T(t^{2})=(2.0+3.0+3.1)+(6.0+4.0+4.1)t+(-2.0+3.0+4.1)t^{2}=3+4t+4t^{2}$

Then

$[T(t^{2})]E=\left[\begin{array}{c}3&4&4\\\end{array}\right]$

And that is the third column of [T]EE

Let's write our matrix

$[T]EE=\left[\begin{array}{ccc}2&3&3\\6&4&4\\-2&3&4\end{array}\right]$

T(X) = AX

Where T(X) is to apply the transformation T to a vector of P2,A is the matrix [T]EE and X is the vector of coordinates in basis E of a vector from P2

For example, if X is the vector of coordinates from e1(t) = 1

$X=\left[\begin{array}{c}1&0&0\\\end{array}\right]$

$AX=\left[\begin{array}{ccc}2&3&3\\6&4&4\\-2&3&4\end{array}\right]\left[\begin{array}{c}1&0&0\\\end{array}\right]=\left[\begin{array}{c}2&6&-2\\\end{array}\right]$

Applying the coordinates 2,6 and -2 to the basis E we obtain

$2+6t-2t^{2}$

That was the original result of T[e1(t)]

8 0

3 years ago

How would I do this problem? In trapezoid PQRS, PQ is parallel to SR. Find the area of PQRS. Leave your answer is simplest radic

Mrac [35]

Can u take its pictures and post it bcuz it might be easer to answer

7 0

3 years ago

Read 2 more answers

The temperature of a liquid in an experiment starts at 0 degrees. The temperature of the liquid changes at a rate of -0.2 per mi

Ilia_Sergeevich [38]

Initial temperature of the liquid = 0 degrees.

Rate of changes of liquid temperature = -0.2 per minute.

Rate of change also represents slope of a linear function.

We know, slope-intercept form of a linear equation

y=mx+b, where m is the slope (rate of change) and b is y-intercept(initial temprature).

With respect to given problem, y represents temperature of a liquid after x number of minutes.

According to given problem, slope(rate of change) = -0.2 per minute and y-intercept(initial temprature)=0.

Plugging values of m and b in the above slope-intercept form of a linear equation.We get,

y=-0.2x+0

or y=-0.2x.

Final temprature is given -14.6 degrees and we need to find time when temprature reach -14.6 degrees.

As y represents temperature of a liquid , we need to plug y=-14.6 in above equation.

We get,

-14.6=-0.2x.

Dividing both sides by -0.2.

-14.6/-0.2=-0.2x/-0.2

x=73.

We got 73 minutes.

73 minutes can be convert in hours.

We have 60 minutes in an hour.

Therefore, 73 = 60+13.

So, 1 hour and 13 minutes will it for the liquid to reach -14.6 degrees.

In minutes answer is 73 minutes.

3 0

2 years ago

Kevin rented a truck for one day. there was a base fee of $17.99, and there was an additional charge of 95 cents for each mile d

Darina [25.2K]

Answer:

Step-by-step explanation:

Base fee = $17.99

Additional charge = $0.95 for each mile driven

If Kevin paid $157.64 when he returned the truck and we want to find out how many miles he drove the truck, step 1 would be to subtract the base fee.

157.65 - 17.99 = 139.65

This means that the remaining $139.65 is how much he paid for the miles he drove.

Since we know each mile costs $0.95.

Simply divide $139.65 by $0.95 to work out how many miles he drove.

Miles driven = 139.65 / 0.95 = ?

4 0

3 years ago