Use the linear regression feature on a graphing calculator to find the correlation coefficient for the data. Round your answer to three decimal places.

x y
8.2 1
1.6 98
9.0 3
7.3 13
3.6 77
1.9 79
1.4 86
The correlation coefficient is about
_______


Question 2
This means that there is __________
between the variables.

need urgent help!!!

Answer:

The answer you're looking for is 8,200cm

Step-by-step explanation:

Answer:

The least amount of fencing needed for the rectangular pen is 72.19 feet.

Step-by-step explanation:

The area and perimeter equations of the pen are, respectively:

[tex]p = 2\cdot (x + y)[/tex] (1)

[tex]A = x\cdot y[/tex] (2)

Where:

[tex]p[/tex] - Perimeter, in feet.

[tex]A[/tex] - Area, in square feet.

[tex]x[/tex] - Width, in feet.

[tex]y[/tex] - Length, in feet.

Let suppose that total area is known and perimeter must be minimum, then we have a system of two equations with two variables, which is solvable:

From (2):

[tex]y = \frac{A}{x}[/tex]

(2) in (1):

[tex]p = 2\cdot \left(x + \frac{A}{x}\right)[/tex]

And the first and second derivatives of the expression are, respectively:

[tex]p' = 2\cdot \left(1 -\frac{A}{x^{2}} \right)[/tex] (3)

[tex]p'' = \frac{4\cdot A}{x^{3}}[/tex] (4)

Then, we perform the First and Second Derivative Test to the function:

First Derivative Test

[tex]2\cdot \left(x - \frac{A}{x^{2}} \right) = 0[/tex]

[tex]2\cdot \left(\frac{x^{3}-A}{x^{2}} \right) = 0[/tex]

[tex]x^{3} - A = 0[/tex]

Given that dimensions of the rectangular pen must positive nonzero variables:

[tex]x^{3} = A[/tex]

[tex]x = \sqrt[3]{A}[/tex]

Second Derivative Test

[tex]p'' = 4[/tex]

In a nutshell, the critical value for the width of the pen leads to a minimum perimeter.

If we know that [tex]A = 169\,ft^{2}[/tex], then the value of the perimeter of the rectangular pen is:

[tex]x = \sqrt[3]{169\,ft^{2}}[/tex]

[tex]x \approx 5.529\,ft[/tex]

By (2):

[tex]y = \frac{A}{x}[/tex]

[tex]y = \frac{169\,ft^{2}}{5.529\,ft}[/tex]

[tex]y = 30.566\,ft[/tex]

Lastly, by (1):

[tex]p = 2\cdot (5.529\,ft + 30.566\,ft)[/tex]

[tex]p = 72.19\,ft[/tex]

The least amount of fencing needed for the rectangular pen is 72.19 feet.

Answer:

87.9°

Step-by-step explanation:

arctan(50/40)=87.9°

Answer: About 15 feet off the ground

The more accurate value is 14.6167273222817 but even this value is not fully exact.

======================================================

Work Shown:

Refer to the diagram below.

sin(angle) = opposite/hypotenuse

sin(66) = x/16

16*sin(66) = x

x = 16*sin(66)

x = 14.6167273222817

x = 15

The ladder reaches roughly 15 feet off the ground, when rounding to the nearest whole number.

I'm rounding to the nearest whole number since the other length (16 ft) is a whole number. Round however you need to if your teacher instructs otherwise.

Answer:

since angle x and y are the same the answer will be

A: x=y

Answer:

15x^2 + 23x = 4

Step-by-step explanation:

NOT BOX METHOD :

(-5x-1)(-3x-4)

=15x^2+20x+3x+4

=15x^2+23x+4

Answer: £3.38

Step-by-step explanation:

In the first year, the pocket money goes up by:

= 1 + (1 * 50%)

= £1.50

In the second year:

= 1.50 + (1.50 * 50%)

= £2.25

In the third year:

= 2.25 * ( 2.25 * 50%)

= £3.38

Answer:

65 degree angle but when straight 180 degree angle

Step-by-step explanation:

sry if wrong :)

Answer:

We have to:

"All of the plots are the same length, x"

L = x

"and the width of each plot is 5 yards less than the length"

W = x-5

"The total number of plots Liam owns is 20 more than the length of a plot"

20 + x

"the total area of all the plots Liam owns is 2,688 square yards"

A = (20 + x) * (x) * (x-5)

A = (20x - 100 + x ^ 2 -5x) * (x)

A = (x ^ 2 + 15x - 100) * (x)

2688 = (x ^ 3 + 15x ^ 2 - 100x)

x ^ 3 + 15x ^ 2 - 100x = 2688

x ^ 3 + 15x ^ 2 - 100x - 2688 = 0

Answer:

*** The equation x3 + 15x2 - 100x - 2.688 = 0 can be used to find the length of each plot.

Answer:x^3+15x^2-100x-2,688=0

Step-by-step explanation:

Answer:

v . u = < v1 , v2 > . <u1 , u2> = v1 u1 + v2 u2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step 1: Add -4y to both sides.

2x+4y+−4y=1+−4y

2x=−4y+1

Step 2: Divide both sides by 2.

2x

2

=

−4y+1

2

x=−2y+

1

2

Step 1: Add 5y to both sides.

3x−5y+5y=7+5y

3x=5y+7

Step 2: Divide both sides by 3.

3x

3

=

5y+7

3

x=

5

3

y+

7

3

Answer:

y = 4x+ 5 is the equation that describes the data...

that is a linear equation ... the slope is 4 thus "the y value increases 4 for every 1 unit increase in x"

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

(whole secant) x (external part) = (tangent)^2

(x+5) *x = 6^2

x^2 +5x = 36

Subtract 36 from each side

x^2 +5x - 36 = 0

Factor

( x-4) (x+9) = 0

Using the zero product property

x-4 = 0  x+9 =0

x = 4  x=-9

Cannot be negative since that is negative length

x=4

9514 1404 393

Answer:

  27

Step-by-step explanation:

For point (x, y) and slope m, the y-intercept can be found from the equation ...

  b = y -mx

  b = 0 -(-3)(9) = 27

The y-intercept is +27. The corresponding ordered pair is (0, 27).

Answer:

120 different ways

Step-by-step explanation:

The first person can be 5 different ways

Now there are 4 people left

The second person can be 4 different ways

And so on

5*4*3*2*1

120 different ways

Answer: proportionate

Step-by-step explanation:

Proportional quota sampling is when the total number of people that are to be surveyed are decided in advance. This form of sampling is usually used in opinion polls and surveys.

Since due to the fact that there are many more women in teaching jobs than men, the researcher selected more women than men for her study to ensure that it represented the actual distribution of men and women teachers in the job, then this was decided in advance and indicates the proportionate quota sampling.

Answer:

e and f

Step-by-step explanation:

there is a great app to use called algebrator it helps me everyday for things like this <3

Answer:

2x-3

Step-by-step explanation:

f (x) = 3x - 1

g(x) = x + 2

(f - g)(x) = 3x-1 - ( x+2)

Distribute the minus sign

       = 3x-1 -x-2

Combine like terms

       = 3x-x-1-2

       = 2x-3

(f - g )( x ) = 2 x - 3

f ( x ) = 3x - 1

g ( x ) = x + 2

remove unnecessary parantheses

collect like terms

Answer:

x-intercept (2, 0)

Step-by-step explanation:

y = 2x² - 6x + 4

Factor

(2x - 2)(x - 2) = 0

2x - 2 = 0

2x = 2

x = 1

x-intercept (1, 0)

x - 2 = 0

x = 2

x-intercept (2, 0)

By using the factor method,

the other x-intercept of the parabola is (2, 0).

A parabola is a curve drawn in a plane. Where any point is at an equal distance from a fixed point (the focus) and a fixed straight line (the Directrix ).

Given:

One x-intercept for a parabola is at the point (1,0).

In factor form : (x - 1)

And the quadratic function,

y = 2x² - 6x + 4.

To find the factor of the equation:

2x² - 6x + 4 ÷ (x - 1)

We get,

(2x - 4) = 0

x = 4/2

x = 2

The other intercept of the parabola is (2, 0).

Therefore, the other x-intercept of the parabola is (2, 0).

To learn more about parabola;

https://brainly.com/question/21685473

#SPJ2

Answer:

5%

Step-by-step explanation:

Given that:

Theoretical probability = 50%

The experimental probability = number of desired outcome / number of trials

Hence, experimental probability = 45 / 100 = 0.45

0.45 = 0.45 * 100% = 45%

Percentage difference in theoretical and experimental probability :

Theoretical - experimental

50% - 45% = 5%

Answer:A

Step-by-step explanation:

m=(14-11)/(8-2)

m=3/6

m=1/2

y = 1/2x+b substitute one of the points

11=1/2(2)+b

11=1 + b

b=10

y = 1/2x+10

Answer:

8,24 metros cuadrados de vidrio

Step-by-step explanation:

Área de un rectángulo = Largo × Ancho

De la pregunta anterior

Longitud = 3,23 m

Ancho = 2,55 m

Área del rectángulo = 3,23 m × 2,55 m

= 8.2365 m²

Aproximadamente = 8,24 m²

Por tanto, Ramiro tiene que comprar 8,24 metros cuadrados de vidrio

Answer:

10 years

Step-by-step explanation:

Given :

Population of Canyon falls = 22500

Rate of decrease = 740 per year

Population after x years :

f(x) = 22500 - 740x ; x = number of years

Population of Swift Creek = 15200

Rate of Increase = 1500 per year

Population after x years :

f(x) = 15200 + 1500x ; x = number of years

Number of years when, population of swift creek will be twice that of Canyon falls

15200 + 1500x = 2(22500 - 740x)

15200 + 1500x = 45000 - 1480x

15200 - 45000 = - 1480x - 1500x

-29800 = - 2980x

x = 29800 / 2980

x = 10

After 10 years

Answer:

6

Step-by-step explanation:

(whole secant) * (external part) = (tangent)^2

(KL) * (KM) = KJ^2

(KM+ ML) * KM = KJ^2

(2+ ML) * 2 = 4^2

(2+ ML) * 2 =16

Divide each side by 2

(2+ ML)  = 8

Subtract 2 from each side

ML = 6

Answer:

2

Step-by-step explanation:

Divide by 4 on each side.

4x/4 and 8/4

Now we have just x on one side and 2 on the other.

So, x = 2.

Answer:

65 + 30x.

Step-by-step explanation:

The $65 is a one-time fee for when you first purchase the instrument. The $30 is every month you rent it, and x = the months you rent it.

Therefore, to find the whole cost over time, you would do

65 (first month) + 30x (how much you'll spend over the time you rent the instrument).

Answer: $ 91.50.

Step-by-step explanation:

Let x be the original price.

Since discount is applied before tax.

New price = (Original price - Discount)-Tax rate (Original price - Discount)

, where Discount = Discount rate x Original price.

Substituting values, we get

[tex]62.28=(x-0.25x)-0.0925(x-0.25x)[/tex]

[tex]62.28=(0.75x)-0.0925(0.75x)[/tex]

[tex]62.28=0.75x-0.069375x[/tex]

[tex]62.28=0.680625x[/tex]

[tex]x=\frac{62.28}{0.680625}[/tex]

[tex]x=91.50[/tex]

Hence, the original price was  $ 91.50.