If i have $2.69 how much more money do i need to have $7.99 show work

The Coast Starlight Amtrak train runs from Seattle to Los Angeles. The mean travel time from one stop to the next on the Coast S

Goshia [24]

Solution :

a).

Given :

R = 0.636, $S_x = 99$ , $S_y=113, M_x=108, M_y=129$

Here R = correlation between the two variables

$S_x , S_y$ = sample standard deviations of the distance and travel time between the two train stops, respectively.

$M_x, M_y$ = means of the distance and travel between two train stops respectively.

The slope of the regression line is given by :

Regression line, $b_1$ $=R \times \left(\frac{S_y}{S_x}\right)$

$=0.636 \times \left(\frac{113}{99}\right)$

= 0.726

Therefore, the slope of the regression line $b_1$ is 0.726

The equation of the regression line is given by :

$\overline {y} = b_0+b_1 \overline x$

The regression line also has to pass through the two means. That is, it has to pass through points (108, 129). Substituting these values in the equation of the regression line, we can get the value of the line y-intercept.

The y-intercept of the regression line $b_0$ is given by :

$b_0=M_y-(b_1 \times M_x)$

= 129 - (0.726 x 108)

= 50.592

Therefore, the equation of the line is :

Travel time = 20.592 + 0.726 x distance

b). $\text{ The slope of the line predicts that it will require 0.726 minutes}$ for each additional mile travelled.

The intercept of the line, $b_0$ = 0.529 can be seen as the time when the distance travelled is zero. It does not make much sense in this context because it seems we have travelled zero distance in 50.529 minutes, but we could interpret it as that the wait time after which we start travelling and calculating the distance travelled and the additional time required per mile. Or we could view the intercept value as the time it takes to walk to the train station before we board the train. So this is a fixed quantity that will be added to travel time. It all depends on the interpretation.

c). $R^2=0.404$

This means that the model accounts for around 40.4% variation in the travel time.

3 0

3 years ago

PLEASE HELP!!! Trapezoid ABCD was dilated to create trapezoid A'B'C'D'. Which statements are true about the trapezoids? Check al

hichkok12 [17]

Answer:

Option A , B and D are true.

The statement which are true:

The length of side AD is 4 units

The length of side A'D' is 8 units.

The scale factor is, $\frac{1}{2}$

Step-by-step explanation:

Given in figure trapezoid ABCD;

The coordinates of ABCD are:

A= (-4, 0)

B = (-2, 4)

C = (2,4)

D = (4, 0)

Since, trapezoid ABCD was dilated to create trapezoid A'B'C'D' as shown in figure;

The coordinates of A'B'C'D' are;

A' =(-2, 0)

B'=(-1, 2)

C' = (1, 2)

D' = (2, 0)

First calculate the length of AD

Using Distance formula for any two points i.e,

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Since, A = (-4, 0) and D = (4, 0)

then;

Length of AD = $\sqrt{(4-(-4))^2+(0-0)^2} = \sqrt{(4+4)^2} =\sqrt{64}=8$ units

Therefore, the length of side AD is, 8 units.

Similarly find the length of A'D'.

Where A' = (-2, 0) and D' =(2,0)

Using distance formula:

Length of A'D' = $\sqrt{(2-(-2))^2+(0-0)^2} =\sqrt{(2+2)^2}= \sqrt{4^2} = 4$

Therefore, the length of side A'D' is, 4 units.

Now, find the slope of CD and C'D'

where C =(2, 4) , D = (4, 0) , C' = (1, 2) and D' =(2,0)

using slope formula for any two points is given by:

$Slope = \frac{y_2-y_1}{x_2-x_1}$

$Slope of CD = \frac{0-4}{4-2} = \frac{-4}{2} = -2$

Similarly,

$Slope of C'D' = \frac{0-2}{2-1} = \frac{-4}{2} = -2$

Since, Sides CD and C'D' have same slope i.e, -2

Scale factor(k) states that every coordinate of the original figure has been multiplied by the scale factor.

If k > 1, then the image is an enlargement.

if 0<k< 1, then the image is a reduction.

If k = 1, then the figure and the image are congruent.

The rule for dilation with scale factor(k) is;

$(x, y) \rightarrow (kx , ky)$

To find the scale factor:

A = (-4, 0) and A' = (-2, 0)

$(-2, 0) \rightarrow (-4k , 0)$

On comparing we ghet;

-4k = -2

Divide -4 both sides we get;

$k = \frac{1}{2}$

∴ The Scale factor is, $k = \frac{1}{2}$

Since, k < 1 which implies the image is a reduction.

Therefore, the statements which are true regarding about trapezoids are;

The length of side AD is 4 units

The length of side A'D' is 8 units.

The scale factor is, $\frac{1}{2}$

6 0

3 years ago

The cylinder and the sphere below have the same radius and the same volume. What is the

oee [108]

The answer would be 8 or A

Step by Step Explanation:

First you have to find the volume of the Sphere.

Set the problem up like this: V = Volume
V= 4/3 • pi (3.14) • 6(3)
= 904.32

Now you have to volume and as stated the volume and radius is the same for both the cylinder and sphere. So now you plug in the answers for the letters.
Formula for (V) Volume of Cylinder is:
V= Pi (3.14) • R (radius) (2) • H (height)
So plug in for what you know
904.32 = 3.14 • 6(2) • H
904.32 = 3.14 • 36 • H
113.04/904.32 = 113.04 • H/113.04
8 = H

The answer is A

7 0

3 years ago

Can someone tell me what the blue lines mean?

Radda [10]

Answer:

It means the two lines are equal in length.

7 0

3 years ago

Read 2 more answers

How state the roots as points when I have <br> x=6 and x=-2

dem82 [27]

I don't really know what you're trying to ask because

x = -2 and x=6 are your roots.

But if you want to convert them back to their equation form,

get the other side of the equation to be 0.

x = 6

x - 6 = 0

x = -2

x + 2 = 0

so your original equation had something like (x+2)(x-6)

6 0

3 years ago