Write an equation of the line in STANDARD FORM with a slope of 3 and passes through the point (6,-2) in standard form using the formula
y-y1 = m (x-x1) please!

The 90% confidence interval for the difference in population proportions of fans who actively disliked the champion in 2000 and 2010 is (-0.087, -0.013).

To compute the confidence interval, first calculate the sample proportions:

Then, calculate the standard error of the difference in sample proportions:

Using a t-distribution with degrees of freedom equal to the smaller of n1-1 and n2-1 (i.e. 1249), and a confidence level of 90%, the margin of error is:

Finally, the confidence interval for the difference in population proportions is given by:

This means we are 90% confident that the true difference in population proportions of fans who actively disliked the champion in 2000 and 2010 is between -0.087 and -0.013. Since the interval does not contain 0, we can conclude that there is strong evidence that the proportion of fans who actively disliked the champion in 2000 was higher than in 2010.

To learn more about confidence interval, here

https://brainly.com/question/24131141

#SPJ1

Answer:

after working for at least 10 1/4 years

Step-by-step explanation:

After working for at least  10 1/4 years  a project manager would be eligible for a $20,000 monthly salary.

A quadratic equation, \(ax^{2} +bx+c=0\) is solved by

\(x=\frac{-b \pm \sqrt{b^2-4ac} }{2}\)

Given function \(f(x)=x^4-10x^2+10000\)

Function that has monthly salary $20,000 will be \(x^4-10x^2+10000=20000\)

\(x^4-10x^2+10000-20000=0\)

\(x^4-10x^2-10000=0\)

Now using the formula \(x=\frac{-b \pm \sqrt{b^2-4ac} }{2}\)

\(x^2=\frac{10 \pm \sqrt{10^2+40000} }{2}\)

\(x^2=\frac{10 \pm \sqrt{40100} }{2}\)

\(x^2=\frac{10 \pm 200.2}{2}\)

\(x^2=5 \pm 100.1\)

\(x^2=105.1\)

\(x=\sqrt{105.1}\)

\(x=10.25\)

Hence, after working for at least  10 1/4 years  a project manager would be eligible for a $20,000 monthly salary.

Learn more about quadratic equation here:

https://brainly.com/question/1214333

#SPJ2

The graph of the equation is plotted and attached

The solution of the equation is at the point (-7, -8)

To find the solution of a graph, you need to identify the point or points where the graph intersects the axis or axes, depending on the number of dimensions of the graph.

The given equation is a linear equation hence the graph will be straight lines. The equations are

-2x  y = 6

x - y = 1

Examining the graph the point of the intersection of the two graphs is seen to be at the point (-7, -8)

Therefore we say that the solution of the equation plotted is (-7, -8)

Learn more about graphs at:

https://brainly.com/question/25184007

#SPJ1

Step-by-step explanation:

please mark me as the brainliest answer and please follow me

Answer:

the first one is wrong.

Step-by-step explanation:

Answer:

\( 3x + y = 2 \)

Step-by-step explanation:

\( y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1) \)

\( y - 5 = \dfrac{-7 - 5}{3 - (-1)}(x - (-1)) \)

\( y - 5 = \dfrac{-12}{4}(x + 1) \)

\( y - 5 = -3(x + 1) \)

\( y - 5 = -3x - 3 \)

\( 3x + y = 2 \)

We discovered the value, which is \(-31/6\), to solve the equation.

The process of equating or creating equality; Equalization is the idea of equating death with darkness. Equilibrium: a state of equal balance. Mathematics. an assertion that two quantities are equal by an expression or statement, frequently mathematical.

In mathematics, an equation is an expression or even a statement that consists of two algebraic expressions that have the same value and are divided from one another by the equal symbol. It is an otherwise stated proposition that has been quantitatively quantified. A chemical equation is said to be balanced if the quantity of each kind of atom in the reaction is identical on both the reactant and product sides.

To solve the given equation we get

\(3\frac{1}{3}*(-2\frac{1}{4} ) +1\frac{5}{6}\)

To convert these fraction value (mixed fraction) into simple fraction

\(\frac{10}{3} *-\frac{9}{4}+\frac{11}{6}\)

\(-\frac{15}{2}+\frac{11}{6}\)

Take LCM of 2 and 6

\(\frac{-45+11}{6}\)

\(=\frac{-34}{6}\)

To know more about equation visit:

https://brainly.com/question/10413253

#SPJ1

Answer:

  9/4

Step-by-step explanation:

You want to know the value required to complete the square in the equation 1 = x² -3x.

Your picture shows the required value: (-3/2)² = 9/4.

<95141404393>

The depth of the river is 3.612 feet.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.

Since last year the depth of the river was 4.2 feet deep and year it dropped 14%. The depth will be:

\(= 4.2 - (14\% \times 4.2)\)

\(= 4.2 - 0.588\)

\(= 3.612 \ \text{feet}\)

Learn more about percentages on:

brainly.com/question/24877689

Answer:

Step-by-step explanation:

We are given the sequence

\(15, 29, 49, 75, 107\\15->29 = 14\\29 -> 49 = 20\\49->75 = 26\\75 -> 107 = 32\\14, 20, 26, 32\\14 -> 20= 6\\20 -> 26 = 6\\26 -> 32 = 6\\\\6, 6, 6\\6->6 = 0\)

Since we had to find the differences twice, it is a second degree polynomial

\(y = an^2 + bn + c\\plugging \: in \: n = 1, 2, 3...\\the \: sequence \: is \\a+b+c, 4a + 2b + c, 9a + 3b + c...\\the \: diff \: under \: is \\3a + b, 5a + b, 7a + b...\\the \: diff \: under \: is \\2a, 2a, 2a...\\so, \\2a = 6\\a = 3\\3(3) + b = 14\\b = 5\\\\a +b + c = 15\\3 + 5 + c = 15\\c = 7\\\)

so,

\(y = 3n^2 + 5n + 7\)

The approximate value of √3 is 1.732 which is an irrational number.

Given that,

We have to find the value of root3.

√3 is an irrational number.

Real numbers that cannot be represented as a ratio are referred to as irrational numbers. Or to put it another way, irrational numbers are actual numbers that defy logic.

Irrational numbers are real numbers that cannot be represented by a straightforward fraction. These can't be stated as ratios, like p/q, where p and q are both integers, q≠0. In terms of statistics, it defies reason.

The approximate value of √3 is 1.732.

Therefore, The approximate value of √3 is 1.732 which is an irrational number.

To learn more about irrational visit: https://brainly.com/question/15837135

#SPJ9

A substitute is a good or service that buyers can quickly swap out for another. For instance, a one-dollar bill can be used in place of another dollar bill.

In business and economics, a replacement, or substitutable good, is a good or service that consumers perceive as just being substantially the same as or reasonably similar to some other good. Consumers are given options and alternatives through substitutes, which also spur competition and lower prices in the market.

Here are a few examples of replacement goods:

1. A $1 bill can be exchanged for four quarters.

2. Coke against Pepsi

3. Regular vs. premium gas

4. Butter and lard

5. Tea and coffee

6. Apples and oranges

7. Comparing driving a car to riding a bike

8. Books in general and e-books

To learn more about substitute link is here

brainly.com/question/18330729

#SPJ4

The mean weight of the Labrador Retrievers is approximately 80.4 lb, the standard deviation is approximately 4.63 lb, and the variance is approximately 21.44 lb2.

To calculate the mean, standard deviation, and variance of the weights of the Labrador  Retrievers, we can use the following formulas:

Mean (μ):

μ = (x1 + x2 + x3 + ... + xn) / n

Standard Deviation (σ):

σ = sqrt(((x1 - μ)2 + (x2 - μ)2 + (x3 - μ)2 + ... + (xn - μ)2) / n)

Variance (σ^2):

σ^2 = ((x1 - μ)2 + (x2 - μ)2 + (x3 - μ)2 + ... + (xn - μ)2) / n

where x1, x2, x3, ..., xn are the individual weights, n is the number of weights.

Given the weights of the Labrador Retrievers: 74 lb, 80 lb, 82 lb, 78 lb, and 88 lb, we can plug these values into the formulas to calculate the mean, standard deviation, and variance.

Mean (μ):

μ = (74 + 80 + 82 + 78 + 88) / 5 = 402 / 5 = 80.4 lb

Standard Deviation (σ):

σ = sqrt(((74 - 80.4)2 + (80 - 80.4)2 + (82 - 80.4)2 + (78 - 80.4)2 + (88 - 80.4)2) / 5)

= sqrt(((-6.4)2 + (-0.4)2 + (1.6)2 + (-2.4)2 + (7.6)2) / 5)

= sqrt((40.96 + 0.16 + 2.56 + 5.76 + 57.76) / 5)

= sqrt(107.2 / 5)

= sqrt(21.44)

≈ 4.63 lb

Variance (σ2):

σ^2 = ((74 - 80.4)2 + (80 - 80.4)2 + (82 - 80.4)2 + (78 - 80.4)2 + (88 - 80.4)2) / 5

= (40.96 + 0.16 + 2.56 + 5.76 + 57.76) / 5

= 107.2 / 5

≈ 21.44 lb2

Therefore, the mean weight of the Labrador Retrievers is approximately 80.4 lb, the standard deviation is approximately 4.63 lb, and the variance is approximately 21.44 lb2.

To know more about Labrador Retrievers refer here:

https://brainly.com/question/15735245#

#SPJ11

The amount of orange that Manny and Josh have leftover after eating lunch is 1.

A fraction is a non-integer. A fraction usually has a numerator and a denominator. The numerator is the number above. While the denominator is the number below

Oranges Manny has left = 1 - 4/9 = 5/9

Oranges Josh has left = 1 - 5/9 = 4/9

Oranges they both have left = 5/9 + 4/9 = 1

To learn more about subtraction of fractions, please check: https://brainly.com/question/915789

The line that is tangent to the circle D is: line segment AB.

The straight line that "just touches" the curve at a particular location is known as the tangent line (or simply tangent) to a plane curve in geometry. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.

At any given location, a line that is tangent to a circle contacts the curve of the circle.See image 1 below, which explains what a tangent is.

According to the second diagram's representation of circle D, line segment AB touches circle D's curve at point B.

As a result, line segment AB is the line that is perpendicular to the circle D.

Your question is incomplete but most probably your full question was

Circle D is shown. Line segment F E goes through point D. Line segment C D is shown. Line segment G H goes from one side of the circle to the other side. Line segment A B is outside of the circle and intersects the circle at point B. In circle D, which is tangent to the circle? Line G H Line segment A B CD EF

Learn more about tangent on:

brainly.com/question/16507124

#SPJ4

Answer:

B

Step-by-step explanation:

Line segment AB

9514 1404 393

Answer:

  (a)  x = (3 -ln(3))/5 ≈ 0.819722457734

  (b)  y = 10

Step-by-step explanation:

(a) Taking the natural log of both sides, we have ...

  2x +1 = ln(3) +4 -3x

  5x = ln(3) +3 . . . . . . . . add 3x-1

  x = (ln(3) +3)/5 ≈ 0.820

__

(b) Assuming "lg" means "log", the logarithm to base 10, we have ...

  log(y -6) +log(y +15) = 2

  (y -6)(y +15) = 100 . . . . . . . taking antilogs

  y^2 -9x -190 = 0 . . . . . . . . eliminate parentheses, subtract 100

  (y -19)(y +10) = 0 . . . . . . . . factor

The values of y that make these factors zero are -19 and 10. We know from the first term that (y-6) > 0, so y > 6. That means y = -19 is an extraneous solution.

The solution is ...

  y = 10

__

When solving equations using a graphing calculator, it often works well to define a function f(x) such that the solution is f(x) = 0, the x-intercept(s). That form is easily obtained by subtracting the right side of the equation from both sides of the equation. In part (a) here, that is ...

  f(x) = e^(2x+1) -3e^(4-3x)

Answer:

Step-by-step explanation:

e^(2x + 1) = 3e^(4 - 3x)

e^(2x + 1) = e^3(4-  3x)

lne^ (2x + 1) =ln e^3(4-  3x)

2x + 1 = 3*(4 - 3x)

2x + 1 = 12 - 9x

11x + 1 = 12

11x = 12 - 1

11x = 11

x = 1

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

I've never worked with binary logs but I'll give this my best shot. If someone comes along and gives you a different answer, use it.

lg(y-6) + lg(y + 15) = 2

lg (y - 6)(y + 15) = 2

inverse (y - 6)(y + 15) = 2^2

(y - 6)(y + 15) = 4

y^2 + 9y - 90 - 4 = 0

y^2 + 9y - 94 = 0

y = 6.19

y = -15,19

Answer:

(2, 3 )

Step-by-step explanation:

Given the 2 equations

x - 2y = - 4 → (1)

2x + y = 7 → (2)

Multiplying (2) by 2 and adding to (1) will eliminate the y- term

4x + 2y = 14 → (3)

Add (1) and (3) term by term to eliminate y, that is

5x = 10 ( divide both sides by 5 )

x = 2

Substitute x = 2 into either of the 2 equations and evaluate for y

Substituting into (2)

2(2) + y = 7

4 + y = 7 ( subtract 4 from both sides )

y = 3

Solution is (2, 3 )

Answer:

The value of x is 6.

Step-by-step explanation:

You have to use Pythagorean Theorem, a² + b² = c². Make (4x+1)cm as the hypotenuse because any values substitute into x will give the highest length among these 3 expressions of length :

\( {a}^{2} + {b}^{2} = {c}^{2} \)

Let a = side = (x+1)cm,

Let b = side = 4x cm,

Let c = hypotenuse = (4x+1)cm,

\( {(x + 1)}^{2} + {(4x)}^{2} = {(4x + 1)}^{2} \)

\( {x}^{2} + 2x + 1 + 16 {x}^{2} = 16 {x}^{2} + 8x + 1\)

Then you have to simplify :

\(17 {x}^{2} + 2x + 1 = 16 {x}^{2} + 8x + 1\)

\(17{x}^{2} + 2x + 1 - 16 {x}^{2} - 8x - 1 = 0\)

\( {x}^{2} - 6x = 0\)

Next you have to solve it :

\( {x}^{2} - 6x = 0\)

\(x(x - 6) = 0\)

\(x = 0 \: (rejected)\)

\(x - 6 = 0\)

\(x = 6cm\)

The value of x in the right triangle is 6 cm.

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

Right triangle:

The three sides are:

x + 1, 4x and 4x + 1

Applying the Pythagorean theorem.

(x + 1)² + (4x)² = (4x + 1)²

x² + 2x + 1 + 16x² = 16x² + 8x + 1

17x² + 2x + 1 = 16x² + 8x + 1

17x² - 16x² = 8x - 2x

x² = 6x

x gets canceled.

x = 6

Thus,

The value of x is 6.

Learn more about the Pythagorean theorem here:

https://brainly.com/question/14930619

#SPJ2

Answer:

15c+3b=66 and 25c+5b=110

Step-by-step explanation:

The approximate volume of the sphere is 6.01 ft³.

A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.

The volume of a sphere is expressed as:

Volume =  (4/3)πr³

Where r is the radius of the sphere and π is the mathematical constant pi (approximately equal to 3.14).

Given that the surface area of the sphere is 16 square feet.

First, we determine the radius r:

Surface area = 4πr²

Hence

16 = 4πr²

Dividing both sides by 4π, we get:

r² = 16/4πr

r = √( 16/4πr )

r = 1.128 ft

Plugging in the value of r that we just found, we get:

Volume =  (4/3)πr³

Volume =  (4/3) × 3.14 × (1.128 ft)³

Volume =  6.01 ft³

Therefore, teh volume is 6.01 ft³.

Learn about volume of hemisphere here: brainly.com/question/22886594

#SPJ1

Answer:h

Step-by-step explanation:

Answer:

The legnth of side AB would be 3 units

Step-by-step explanation:

First, you would determine that both point A and point B would have the same y-coordinate of 1.   Then you would determine the difference between the x values of points A and B.  Since 5 (the x-value for B) minus 2 (the x-value for A) is 3, the legnth of side AB would be 3 units.

Step-by-step explanation:

I recommend using Desmos to quickly graph things (it's much faster than doing it yourself, I use it often. You can graph points and everything).

The picture ends up looking like the attachment I have below.

This is now a simple subtraction.

A is at 2 on the x-axis and B is at 5.

5-2=3

Answer:

3 units

The total amount that would be found in the account after 4 years, would be $ 641. 69

The total amount after 4 years in Arik's account can be found by the formula :

= A = Amount invested x ( 1 + r /n )ⁿ

The variables are:

Amount invested = $ 500

r = 6.25% = 0. 0625

n = 12

t = 4 years

The total amount is then :

A = 500 x ( 1 + 0. 0625 / 12 ) ^ ⁽¹² ˣ ⁴ ⁾

A = $ 641. 69

Find out more on interest compounded at https://brainly.com/question/24274034

#SPJ1

Answer:

1) £2 = €2.32

£5 = €5.80

£50 = €58

2) The graph will be a straight line

3) (0, 0)

4) Label the independent variable, £ on the x-axis and dependent variable € on the y-axis

Step-by-step explanation:

1) The given conversion factors is £1 = €1.16

Therefore;

£2 = 2 × €1.16 = €2.32

£2 = €2.32

£5 = 5 × €1.16 = €5.80

£5 = €5.80

£50 = 50 × €1.16 = €58

£50 = €58

2) The shape of the plot of the directly proportional currencies graph will be a straight line

3) Given that the £ is directly proportional to the € and that the value of the € can be found directly by multiplying the amount in £ by 1.16, without the addition of a constant, the graph crosses the axes at the origin (0, 0)

4) The y-axes which is the dependent variable should be labelled €, while the x-axis which is the independent variable should be labelled £

Answer:

see explanation

Step-by-step explanation:

To prove the equation id true, solve both sides and if they are equal then the equation is true.

left side = 6 × 8 = 48

right side = 3 × 2 × 2 × 2 × 2

               = 6 × 2 × 2 × 2

              = 12 × 2 × 2

              = 24 × 2

=             = 48

Since both sides are equal then the equation is true

Answer:

S=32.5

W=97.5

Step-by-step explanation:

S=speed of plane in still air

W=speed of wind

-----------------------------------------

3(S+W)=130

6(S-W)=130

-----------------------------------------

S+W=43.33333...

S-W=21.66666...

2S=64.999...

S=32.5(simplified)

-----------------------------------------

32.5+W=130

W=97.5

-----------------------------------------

Answer:

\(a) x=15\\b) AD\ is\ not\ parallel\ tp BC\)

Step-by-step explanation:

\(As\ we\ know\ that,\\Angle\ D=3x\\Angle\ A=2x\\Angle\ B=90\\Angle\ C=x\\The\ Angle\ Sum\ Property\ Of\ A\ Quadrilateral\ states\ that\ the\ sum\ of\ all\\ the\ interior\ angles\ of\ a\ quadrilateral\ is\ 180.\\Hence,\\ \angle D+ \angle A + \angle B + \angle C=360\\3x+2x+90+x=180\\3x+2x+x=180-90\\6x=90\\x=15\\Hence, x=15\)

\(Hence,\\As\ Angle\ A\ and\ Angle\ B\ are\ co-interior\ angles, if\ they\ are\\ supplementary\ then\ AD \parallel BC.\ Lets\ check\ that\ out.\\Hence,\\Angle\ A=2x=2*15=30\\Angle\ B=90\ [Given]\\Hence,\\As\ 90+30\neq 180,\\Angle\ A +Angle\ B\neq 180\\Hence,\\As\ Angle\ A and\ Angle\ B\ are\ not\ supplementary, AD\ will\ not\ be\ parallel\ to\ CB.\)

In linear regression, one variable, called a dependent variable, is related to one or more independent variables by a linear equation.

A function has the following format: y = f(x).

In which each value of y is a function of one value of x, and thus, x is the independent variable and y is the dependent variable.

That is, the input of the function is the independent variable and the output is the dependent variable.

In the case of multiple inputs, all the inputs are independent variables.

More can be learned about functions at https://brainly.com/question/24808124

#SPJ1

Answer:

The graphs and the table is missing in the question.

Step-by-step explanation:

The guidelines for interpreting correlation  co-efficient r are :

1. Strong correlation    0.7<|r|≤1

2. Moderate correlation   0.4<|r|<0.7

3. Weak correlation   0.2<|r|<0.4

4. No correlation  0≤|r|<0.2

Logarithmic regression

(i). Mean : \($ {\overset{-}{ln}x} = \frac{\sum ln x_i}{n}, \ \ \ {\overset{-}y} = \frac{\sum y_i}{n} $\)

(ii) Trend line : \($ y = A +B \ln x, \ \ B = \frac{S_{xy}}{S_{xx}}, \ \ A={\overset{-}y-B{\overset{-}{\ln x}}}$\)

(iii). Correlation coefficient : \($ r = \frac {S_{xy}}{\sqrt{S_{xx}} \sqrt{S_{yy}}} $\)

\($ S_{xx} = \sum (\ln x_i - {\overset{-}{\ln x}})^2 = \sum (\ln x_i)^2-n. ({\overset{-}{\ln x}})^2$\)

\($ S_{yy} = \sum(y_i - {\overset{-}y})^2 = \sumy_i^2 - n. {\overset{-}y^2}$\)

\($ S_{xy} = \sum(\ln x_i - {\overset{-}{\ln x}})(y_i-{\overset{-}y}) = \sum \ln x_i y_i - n. {\overset{-}{\ln x}}{\overset{-}y} $\)

Now using the technology we can calculate

The equation of the regression curve is y = A + B(lnx)

we get A = 30.72 , B = 17.19

The equation of regression curve is \($ \hat y$\) = 30.72 + 17.19(lnx)

Answer:

2.1use bodmas

32/32=1

-25*25=-625

96+-96==0

ans=1-625

=-624

Answer:

- 624

Step-by-step explanation:

96+(-96)+32/32 - 25*25

-> 0+32/32-(25)(25)

-> 32/32 - (25)(25)

-> 1-(25)(25)

-> 1- 625

-> -624