For a one-way within-subjects ANOVA, the mean difference attributed to the manipulation is in the ________, and the mean difference attributed to individual differences is in the ________ of the test statistic. numerator; numerator denominator; numerator numerator; denominator denominator; denominator

Answer:

[tex]\displaystyle \left(\alpha+1\right)\left(\beta + 1\right) = \frac{a+c-b}{a}\:\: \left(\text{ or } 1+\frac{c-b}{a}\right)[/tex]

Step-by-step explanation:

We are given the equation:

[tex]ax^2+bx+c=0[/tex]

Which has roots α and β.

And we want to express (α + 1)(β + 1) in terms of a, b, and c.

From the quadratic formula, we know that the two solutions to our equation are:

[tex]\displaystyle x_1 = \frac{-b+\sqrt{b^2-4ac}}{2a}\text{ and } x_2=\frac{-b-\sqrt{b^2-4ac}}{2a}[/tex]

Let x₁ = α and x₂ = β. Substitute:

[tex]\displaystyle \left(\frac{-b+\sqrt{b^2-4ac}}{2a} + 1\right) \left(\frac{-b-\sqrt{b^2-4ac}}{2a}+1\right)[/tex]

Combine fractions:

[tex]\displaystyle =\left(\frac{-b+2a+\sqrt{b^2-4ac}}{2a} \right) \left(\frac{-b+2a-\sqrt{b^2-4ac}}{2a}\right)[/tex]

Rewrite:

[tex]\displaystyle = \frac{\left(-b+2a+\sqrt{b^2-4ac}\right)\left(-b+2a-\sqrt{b^2-4ac}\right)}{(2a)(2a)}[/tex]

Multiply and group:

[tex]\displaystyle = \frac{((-b+2a)+\sqrt{b^2-4ac})((-b+2a)-\sqrt{b^2-4ac})}{4a^2}[/tex]

Difference of two squares:

[tex]\displaystyle = \frac{\overbrace{(-b+2a)^2 - (\sqrt{b^2-4ac})^2}^{(x+y)(x-y)=x^2-y^2}}{4a^2}[/tex]

Expand and simplify:

[tex]\displaystyle = \frac{(b^2-4ab+4a^2)-(b^2-4ac)}{4a^2}[/tex]

Distribute:

[tex]\displaystyle = \frac{(b^2-4ab+4a^2)+(-b^2+4ac)}{4a^2}[/tex]

Cancel like terms:

[tex]\displaystyle = \frac{4a^2+4ac-4ab}{4a^2}[/tex]

Factor:

[tex]\displaystyle =\frac{4a(a+c-b)}{4a(a)}[/tex]

Cancel. Hence:

[tex]\displaystyle = \frac{a+c-b}{a}\:\: \left(\text{ or } 1+\frac{c-b}{a}\right)[/tex]

Therefore:

[tex]\displaystyle \left(\alpha+1\right)\left(\beta + 1\right) = \frac{a+c-b}{a}[/tex]

Answer: A x> -2

Step-by-step explanation:

Answer:

1. a) x^2 + 6x + 27

b) 4x^2 - 4x + 1

c) x^2 - 4y^2

d) x^3 + 6x^2 + 12x + 8

e) x^3 - 9x^2 + 27x - 27

Answer:

Total number in favour:

Probability:

Total number in against:

Probability:

If two parallel lines are intersected by a transversal, then internal opposite angles are equal.

So, x° = 61°

=> x = 60

Because they are internal opposite angles.

Answer:

Probability of dying on the birthday is:

Probability of not dying on the birthday is:

Probability of blue-eyed boy is:

Total frequencies = 10

Frequency of 7 and greater is 4: 7, 8, 9, 10

Required probability:

Answer:

slope: -3

y-intercept: 9

Step-by-step explanation:

To find the slope and y-intercept, we can manipulate the equation to slope-intercept form. Slope-intercept form is y=mx+b where m is slope and b is y-intercept.

[tex]3x+y-9=0[/tex]        [subtract both sides by 3x]

[tex]y-9=-3x[/tex]            [add both sides by 9]

[tex]y=-3x+9[/tex]

Now, our equation is in slope-intercept form. We can see that the slope is -3 and the y-intercept is 9.

Answer:

17

Step-by-step explanation:

8+2+(3×3-2)=8+2+(9-2)=8+2+7=17

mistake in the first step

firstly we do × and ÷

then + and -

Answer:

option 3

Step-by-step explanation:

Given

3x + 5 + 7x + 2 ← collect like terms

= (3x + 7x) + (5 + 2)

= 10x + 7 → option 3

According to the question

=3x + 5+7x + 2

Combining Like terms

= (3x + 7x) +(5+2)

= 12x + 7

Therefore the correct option is third

10x + 7

Answered by Gauthmath must click thanks and mark brainliest

Answer:

I think the answer is B

The students could use what they know of triangle rectangles, in the image below you can see the diagram that the students could use to estimate the height of the tower.

First, the students could use the measuring tape to find the distance between the base of the tower and them, this distance is represented with the variable S in the image below.

Now, using the clinometer, they could find the elevation angle between their viewpoint and the tip of the tower. This would be the angle θ in the image (notice that they should do this from the ground).

So at this point, we know one angle and the adjacent cathetus to that angle.

And we want to find the height of the tower, which is the opposite cathetus to the known angle.

Then we can remember the trigonometric relation:

tan(a) = (opposite cathetus)/(adjacent cathetus)

Replacing these by the things we know:

tan(θ) = H/S

tan(θ)*S = H

Then, by measuring θ and S, we can find the height.

If you want to read more about triangle rectangles, you can see:

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[tex]\displaystyle \Large \boldsymbol{} a) \ \underline{x^2-3x}+\underline{2x-6}-\underline{xy+3y}=\\\\\\x(x-3)+2(x-3)-y(x-3)=\boxed{(x-3)(x-y+2)} \\\\\\b) \ mn-mx-n+x=m(n-x)-(n-x) =\boxed{ (m-1)(n-x)}[/tex]

Answer:

45 / 27 = 30 / 18 = x / 24

x = 40

Step-by-step explanation:

Hi there!

The question here states that the two polygons are similar

Polygons that are similar have similar side length ratios.

If we want to find a side length we must create a proportional relationship

We are already given a partial proportional relationship.

Which is...

45 / __ = __ / 18 = x / __

First let's fill in the blanks

The side that is corresponding to the side with a length of 45 has a length of 27. So it would be 45/27

The side that is corresponding to the side with a length of 18 has a length of 30. So it would be 30/18

The side corresponding to side labeled "x" has a length of 24. so it would be x/24

So we would have

45 / 27 = 30 / 18 = x / 24

Now let's find x

We only need 2 ratios ( the one including x of course, and the other one can either be 30/18 or 45/27)

30 / 18 = x / 24

Now let's solve for x

Cross multiply

30*24=720

18*x=18x

We now have 18x = 720

Divide both sides by 18

18x / 18 = x

720 / 18 = 40

x = 40

To check our answers we can see if the ratios are similar

If they are then we are correct

45/27 = 1.66

30/18 =1.66

40/24 = 1.66

They are all equivalent meaning that our answers are correct

Answer:

3x+ 7 =49

Step-by-step explanation:

49-7= 42

42 divided by 3 = 14

her daughter is 14 years old

I truly hope this helped, it makes sense to me. I wasn't sure whether or not you needed a more detailed equation, but that's one.

have a great day!

Answer:

SOH-CAH-TOA

[tex]\sin \left(x\right)=\frac{6}{\sqrt{49+36}}[/tex] = 40.60°

SOH = SIN = OPP/HYP

SIN(Θ) = 6/[tex]\sqrt{49+36 }[/tex]

Step-by-step explanation:

Answer:

b=3

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

b = 3

Step-by-step explanation:

3(9+9b)=69+136

27+27b = 205

27b = 205-27

27b = 178

b = 178/27

*slaps face*

In the comments you said the "136" is "13b" so ok...

3(9+9b)=69+13b

27+27b = 69 + 13b

27+14b = 69

14b = 69-27

14b = 42

b = 3

Answer:

9

Step-by-step explanation:

We know that a^b / a^c = a^(b-c)

9^8 / 9^7

9^(8-7)

9^1

9

Answer:

[tex]y = \frac{1}{4}x -2[/tex]

Step-by-step explanation:

Step 1:  Find the standard form of the equation

The equation that was given made no sense so I will recreate the entire equation using the point slope formula.

Use the point slope formula

[tex]y - y_{1} = m(x - x_{1})[/tex]

[tex]y - (-3) = m(x - (-4))[/tex]

[tex]y +3 = m(x + 4)[/tex]

Find the slope

[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m = \frac{1-(-3)}{12-(-4)}[/tex]

[tex]m = \frac{1+3}{12+4}[/tex]

[tex]m = \frac{4}{16}[/tex]

[tex]m=\frac{1}{4}[/tex]

Combine them together

[tex]y +3 = \frac{1}{4}(x + 4)[/tex]

Convert to standard form

[tex]y +3 = \frac{1}{4}x + 1[/tex]

[tex]y +3 - 3 = \frac{1}{4}x + 1 - 3[/tex]

[tex]y = \frac{1}{4}x -2[/tex]

Answer:  [tex]y = \frac{1}{4}x -2[/tex]

Answer:

10/3

Step-by-step explanation:

rate of change = gradient

(17-7)/(6-3) = 10/3

basically difference of y values / difference of x values

Answer:

D

Step-by-step explanation:

It is because work is done when a force cause an object to move in the direction of the applied force.

so work is equal to force × distance

Answer:

4√3

Step-by-step explanation:

5√27-2√48-5√3-(√3-2√3)2

= 5√(3x9)-2√(3x16)-5√3-2√3+4√3

= 5(3)√3-2(4)√3-5√3-2√3+4√3

= 15√3-8√3-5√3-2√3+4√3

= 4√3

Answer:

134.1

Step-by-step explanation:

Area of the circle = 49π = 153.9 (rounded to the nearest tenth)

Segment area,

49/2(150π/360-sin(150))

= 19.8 (rounded to the nearest tenth)

Subtracting them,

153.9-19.8

= 134.1 cm²

Answered by GAUTHMATH

The area of the shaded region is 134.1 cm²

'A segment of a circle is the region that is bounded by an arc and a chord of the circle.'

According to the given problem,

Area of the circle = πr²

                              = π × 7 × 7 cm²

                              = 153.9 (rounded to the nearest tenth)

Area of the Shaded region,

= [tex]\frac{r^{2} }{2}( \frac{angle in degrees * \pi }{360 - sin(angle in degrees)} )[/tex]

=[tex]\frac{49}{2}(\frac{150\pi }{360 - sin(150)})[/tex]

= 19.8 (rounded to the nearest tenth)

Subtracting them,

= 153.9 - 19.8

= 134.1 cm²

Hence, we can conclude that the area of the shaded region is 134.1cm²

Learn more about segment of a circle here: https://brainly.com/question/4910703

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Answer:

My fellow Americans

I'm from India and I'm hre to take q look at America's Brainly :)

Answer:

I could only solve up to this this topic we will read tomorrow .I might send you tomorrow. I don't know that if the solved parts rule is right or not .If it is wrong forgive me.

Step-by-step explanation: Notice that we have a 30° angle and we're given that the side opposite the 30° angle has a length of h and the side adjacent to the 30° angle has a length of 18.

Remember than [tex]tan =[/tex] [tex]\frac{opp}{adj}[/tex] so we can setup the equation tan 30° = h/18.

Solving for h, we multiply both sides of the

equation by 18 and we have (18)(tan 30°) = h.

From here, we enter this into our calculator to get 10.3923 or 10.4.

Instead of using trigonometry here, we could have also noticed that this is a special right triangle, a 30° - 60° - 90° triangle, which means that the long leg is √3 times the length of the short leg, so we could have setup an equation to find the value of h. Either way should be acceptable.

Step-by-step explanation:

9 a = soln

3:9 = 6:n

or, 3/9 = 6/n

or, 3n = 54

or, n = 54/3

so, n = 18

b = soln

n/10 = 6/15

or, 15n = 60

or, n = 60/15

so, n= 4

10) a = 15% of 450

= 15/100 * 450

= 15/10 * 45

or, 15/2 * 9

or,  135/2

= 67.5 g

b= 125% of 60

= 125/100 * 60

= 5/4 * 60

= 5*15

= $75

Answer:

x^2 +2x+xy +2y

Step-by-step explanation:

(x + y) (x + 2)

FOIL

first x*x = x^2

outer  x*2 =2x

inner y*x= xy

last = y*2 =2y

Add together

x^2 +2x+xy +2y

Answer:

Step-by-step explanation:

F - First ; O - Outside ;  I - inside  ; L -last

(x + y)(x + 2) = x*x + x*2 +y*x +y*2

                    = x² + 2x + xy +2y

Answer:

P.=2(2x+5)+2(x-10)=80cm

6x-10=80

x=90/6=15cm

Area= L*W= 35*5=175 squared cm= 0.0175 squared m

Cost= 0.24 * 0.0175 = GHc 0.0042

A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle.  The cost of weeding the rectangular plot is 0.0042 GHc.

That parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.

A.) The perimeter of a rectangular plot of land whose length is (2x+5) and width is (x-10) is 80cm. Therefore, we can write,

Perimeter of the rectangel = 2(L+W)

80 = 2[(2x+5)+(x-10)]

80/2 = 2x+5+x-10

40 = 3x -5

40+5 = 3x

x = 15

Hence, the value of x is 15.

B.) The length of the rectangle = (2x+5) = 2(15)+5 = 35 cm = 0.35 m

The width of the rectangle = (x-10) = 15-10 = 5 cm = 0.05 m

Now, the area of the rectangle = L×B = 0.35m × 0.05m  = 0.0175m²

C.) Given the cost of weeding 1m² is 0.24, therefore, the cost of weeding the rectangular plot is

Cost = 0.0175 × 0.24 = 0.0042 GHc

Hence, the cost of weeding the rectangular plot is 0.0042 GHc.

Learn more about Rectangle:

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Answer:

either 5 or 6

Step-by-step explanation:

I can't have a direct answer because you didn't get all of the histogram in there, but from what I can conclude from just this there's definitely either 5 or 6.

Answer:

1/3

Step-by-step explanation:

Slope is rise over run

your rise is 1 (because you only go up one block each time)

your run is 3 ( because you go right three times)

so 1/3

Answer:

C

Step-by-step explanation:

f is neither even nor odd