Many track runners believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on until the outermost lane, Lane 6. The data lists the number of wins for track runners in the different starting positions. Calculate the chi-square test statistic to test the claim that the number of wins is uniformly distributed (equally likely) across the different starting positions. The results are based on 240 races.

Answer:

Step-by-step explanation:

From the given information:

The domain D of integration in polar coordinates can be represented by:

D = {(r,θ)| 0 ≤ r ≤ 6, 0 ≤ θ ≤ 2π) &;

The partial derivates for z = xy can be expressed  as:

[tex]y =\dfrac{\partial z}{\partial x} , x = \dfrac{\partial z}{\partial y}[/tex]

Thus, the area of the surface is as follows:

[tex]\iint_D \sqrt{(\dfrac{\partial z}{\partial x})^2+ (\dfrac{\partial z}{\partial y})^2 +1 }\ dA = \iint_D \sqrt{(y)^2+(x)^2+1 } \ dA[/tex]

[tex]= \iint_D \sqrt{x^2 +y^2 +1 } \ dA[/tex]

[tex]= \int^{2 \pi}_{0} \int^{6}_{0} \ r \sqrt{r^2 +1 } \ dr \ d \theta[/tex]

[tex]=2 \pi \int^{6}_{0} \ r \sqrt{r^2 +1 } \ dr[/tex]

[tex]= 2 \pi \begin {bmatrix} \dfrac{1}{3}(r^2 +1) ^{^\dfrac{3}{2}} \end {bmatrix}^6_0[/tex]

[tex]= 2 \pi \times \dfrac{1}{3} \Bigg [ (37)^{3/2} - 1 \Bigg][/tex]

[tex]= \dfrac{2 \pi}{3} \Bigg [37 \sqrt{37} -1 \Bigg ][/tex]

The equation of the line is y = -1/3 x.

Answer:

A graph represents a relation that is also a function if only and if every vertical line intersects the graph at most once.

Step-by-step explanation:

The vertical line test should be used to get an idea about the nature of a graph whether it represents a function or not. A vertical line must not intersect the graph multiple times as it would violate the definition of a function.

If a vertical line intersects the graph multiple times, it means the graph is having the same repeated inputs, which is against the definition of a function. A function can not have repeated input values.

Thus, we conclude that a graph represents a relation that is also a function if only and if every vertical line intersects the graph at most once.

Answer: 500

Step-by-step explanation: use the equation y=mx+b.

B = cost of the plan per month

X = number of minutes

M = price per minute

The first plan is a flat rate of $25 a month. Whereas the second is $10 plus $0.05 a minute.

Plug in the answers until you get a price that is equal to $25.

Y = 0.05(300) + 10

Y = 25

therefore after 300 minutes the other plan is cheaper

Answer:

x= 5.25

Step-by-step explanation:

You have to get x alone, so do inverse operations.

(Basically, reverse what it is)

4(x-3)=9

divide 4 by both sides to get rid of 4 on left side

9/4 = 2.25

(x-3) = 2.25

Now add 3 to both sides, to get x alone

2.25 + 3 = 5.25

x=5.25

Check work

4(5.25-3) = 9

4(2.25) = 9

9=9

Answer:

52% play video games on their personal computer.

Step-by-step explanation:

884/1700 = 52%

Answer:

x = 8/3 and y = 32/3

Step-by-step explanation:

Add the two equations, getting -3y = -32, thus y = 32/3

Sub for y in first equation, getting 5x + 32/3 = 24

5x = 40/3

x = 8/3

9514 1404 393

Answer:

  2x +y = -4

Step-by-step explanation:

The equation of the given line can be simplified by dividing all of the numbers by 2:

  2x +y = -5

The parallel line can have the same coefficients of x and y, but will have a different constant. The constant will be appropriate to the given point, so will be ...

  2x +y = constant

  2(-3) +(2) = constant = -6 +2 = -4

The parallel line is ...

  2x +y = -4

Answer:

y=×2-6×+7 is the answer

Answer:

The elevation of the surf shop is 12.8

Step-by-step explanation:

I hope this helps

Answer:

i think there would be 14  stations

Step-by-step explanation:

sorry f i am wrong

i did 7/8/ 1/16

7/8 * 16/1 =14

Answer:

14

Step-by-step explanation:

7/8 divided by 1/16 becomes 7/8 multiplied by 1/16, which equals 14

Answer:

Answer:

So you have a box, with weight Wb and you have a right force of 6N and a left force of Fl

With sum of forces you get that to maintain equilibrium the force Fl must be 6 therfore to maintain moving right the left force must be 5N

Rate positively and give brainlist

Answer:

The answer is 5n

Step-by-step explanation:

Since the force on the right would have to be greater, and the force on the right is 6n, the left force would have to be less. Therefore, the answer is 5n.

Answer:

i know

Step-by-step explanation:

bro

Answer:

y = 15 - 2x

Step-by-step explanation:

The starting temp is 15, and we expect it to fall 2 degrees each night. We substitute x and y, y = total temp at the end of the examined time period, x = number of hours.

Please give me thanks by clicking the heart button! :)

Answer:

15 - 2(x)

x = hours

Step-by-step explanation:

Step-by-step explanation:

I tried. if I got this wrong I might need to go back to kindergarten

Answer:

16/3

Step-by-step explanation:

Answer:

5 1/3

Step-by-step explanation:

Convert any mixed numbers to fractions.

Then your initial equation becomes:

−8/3 ÷ −1/2

Applying the fractions formula for division,

=−8×2/3×−1

=−16/−3

Simplifying -16/-3, the answer is

=5 1/3

Answer:

D. 4x + 4y

Step-by-step explanation:

2x + 2x = 4x

3y + y = 4y

So, 4x + 4y is the answer!

Answer:

That’s sad. Option c

Step-by-step explanation:

Step-by-step explanation:

The given function is :

[tex]y=\dfrac{-1}{8}(x-1)^2-4[/tex] ...(1)

It is an equation of parabola. The vertex form for equation of parabola is given by :

[tex]y=a(x-h)^2+k[/tex] ...(2)

Here,

Vertex = (h,k), axis = h and rate = a

From equation (1) and (2) :

a = -1/8, h = 1 and k = -4

The atached graph shows the graph for the given equation.

Answer:

C. 80

Step-by-step explanation:

5x10x.5=25

25x2=50

3x10=30

50+30=80

Answer:

C

Step-by-step explanation:

Split the shape into normal shapes such as a rectangle and two triangles

use there formulas for area for each shape

rectangle L x W

10 x 3 = 30

for triangles it’s side a times the base divided by 2

5 x 10 / 2 = 25

so it’s 50 because there is two triangles

add 50 and 30

so it’s 80ft so C

Answer:

4x and -2x

Step-by-step explanation:

Answer:

The like terms are 4x and 2x.

Step-by-step explanation:

4x and 2x have x as their variable.

Answer:

81

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

Answer:

[tex] (x, y) = (2, 1) [/tex]

Step-by-step explanation:

Given vertices of a triangle:

[tex] (x_1, y_1) = (-4, -2) [/tex]

[tex] (x_2, y_2) = (1, 0) [/tex]

[tex] (x_3, y_3) = (9, 5) [/tex]

Using the centroid formula:

[tex] (x, y) = (\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}) [/tex]

Plug in the values into the formula

[tex] (x, y) = (\frac{-4 + 1 + 9}{3}, \frac{-2 + 0 + 5}{3}) [/tex]

[tex] (x, y) = (\frac{6}{3}, \frac{3}{3}) [/tex]

[tex] (x, y) = (2, 1) [/tex]

Answer:

0.425

Step-by-step explanation:

40x2.5=100

17x2.5=42.5

So the fraction is 42.5/100 which is 0.425