The Patterson family has 3 kids, 1 boy and 2 girls. Suppose that for each birth, the probability of a boy birth is 1/2, and the probability of a girl birth is also 1/2. What is the fractional probability of having 1 boy and 2 girls, in any order, in a family's first 3 births?

Answer:

3

Step-by-step explanation:

Answer:

The SQ Root of 493

Step-by-step explanation:

Becaues this triangle is a right triangle, we can find the missing side usiing the pythagorean theorum.

The pythagorean theorun states A^2 + B^2 = C^2, so 18^2 + 13^2= 439

Then all you have to do is find the sq root of 439, but this question askes you not to.

Hope this helps :)

Answer

See below :)

Step-by-step explanation:

Experimental Verification

Step 1 : Three triangles with different shapes and sizes are drawn. Suppose the name of each triangle is ABC.

( Draw the triangles in such a way that you can each angle by using a protractor )

( See attached picture )

Step 2 : Measure each angle of these three triangles with the help of protractor and fill up the following table.

_________________________________

Figure < A < B < C < A + <B + <C Result

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( i ) 180°

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( ii ) 180°

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(iii) 180°

________________________________

Conclusion : The sum of the angles of any triangle is equal to 180°

Theoretical proof

( See attached picture )

Given : <ABC , <BCA and <BAC are the angles of ∆ABC.

To prove : <ABC + <BCA + <BAC = 180°

Construction : Through the vertex A , a straight line XY parallel to BC is drawn.

Proof :

_________________________________

Statements Reasons

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

1. < XAB = <ABC 1. XY // BC and alternate

angles

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2. <YAC = <BCA 2. XY//BC and alternate

angles

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

3. <XAB + <BAC + 3. whole part axiom

<YAC = <XAY

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

4. <XAB + <BAC + 4. < XAY is a straight angle.

<YAC = 180°

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

5. <ABC + <BAC + 5. from statements ( 1 ),

<BCA = 180° ( 2 ) and (4)

_______________________________

Proved

Hope I helped!

Best regards!!

Answer:

x = 6, PLEASE MARK AS BRAINLIEST

Step-by-step explanation:

Let this number be x:

1) Increase x by 30 = x + 30

2) Divide the result by 2 = [tex]\frac{x+30}{2}[/tex]

3) The number obtained is 3 times the original number =

[tex]\frac{x + 30}{2} = 3x[/tex]

[tex]{x + 30} = 6x[/tex]

[tex]30 = 5x[/tex]

[tex]x = \frac{30}{5}[/tex]

[tex]x = 6[/tex]

Answer:

[tex]r=8[/tex]

Step-by-step explanation:

[tex]r-7=1[/tex] add seven to both sides

[tex]r=1+7\\r=8[/tex]

Hope this helps

Answer:

The correct answer to this problem is r = 8.

Step-by-step explanation:

To solve this problem, we have to remember that our goal is to get the variable (in this case, r) by itself on one side of the equation.  To do this, we have to get rid of the -7 on the left side of the equation.  Therefore, our first step is to add 7 to both sides of the equation.  This gives us:

r - 7 = 1

r - 7 + 7 = 1 + 7

r = 8

Thus, your answer is r = 8.

Hope this helps!

Answer:

no because it has 2 of the same x-intercepts.

Step-by-step explanation:

Answer:

Below.

Step-by-step explanation:

Left side = 2 cos^2 ( π/4 - A/2) - 1

= 2 ( cos π/4  cos A/2 + sin π/4  sin A/2)^2 - 1

Now sin π/4 and cos π/4 = 1 /√2 so:

= 2 ( 1/√2 cos A/2 + 1/√2 sin A/2)^2 - 1

= 2  * 1/2( cos^2 A/2 + sin^2 A/2 + 2 sin A/2 cos A/2) - 1

But cos^2 a/2 + sin^2 A/2 = 1 so we have:

2 * 1/2( 1 +  2sin A/2 cos A/2) - 1

= 1  + 2 sin A/2 cos A/2 - 1

=  2 sin A/2 cos A/2

Using the identity 2 sin A cos A = sin 2A

2 sin A/2 cos A/2 = sin A  = right side.

So left side = right side and the identity is proved.

Answer:  see proof below

Step-by-step explanation:

Use the Double Angle Identity:  cos 2A = 2cos²A - 1

Use the Difference Identity:  cos (A - B) = cosA · cosB + sinA · sinB

Use the Unit Circle to evaluate:  cos (π/2) = 0   &     sin (π/2) = 1

Proof  LHS → RHS

[tex]\text{Given:}\qquad \qquad \qquad \qquad 2\cos^2\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)-1\\\\\\\text{Double Angle Identity:}\quad \cos2\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)\\\\\\\text{Simplify:}\qquad \qquad \qquad \quad \cos\bigg(\dfrac{\pi}{2}-A\bigg)\\\\\\\text{Difference Identity:}\qquad \cos\dfrac{\pi}{2}\cdot \cos A+\sin \dfrac{\pi}{2}\cdot \sin A\\\\\\\text{Unit Circle:}\qquad \qquad \qquad 0\cdot \cos A+1\cdot \sin A\\\\\\\text{Simplify:}\qquad \qquad \qquad \qquad \sin A[/tex]

LHS = RHS:   sin A = sin A   [tex]\checkmark[/tex]

Step-by-step explanation:

g(x) = y = 8 - 2x

(A) First transform the function in terms of x :

x = y - 8 / 2

(B) Replace x with y :

[tex] {g}^{ - 1} (x) = y = \frac{x}{2} - 4[/tex]

Answer:

Yes

Step-by-step explanation:

Answer:

Second choice

Step-by-step explanation:

f(x) = (1/4)(x + 4)^2 - 9

f(x) = (1/4)(x^2 + 8x + 16) - 9

f(x) = (1/4)x^2 + 2x + 4 - 9

f(x) = (1/4)x^2 + 2x - 5

(1/4)x^2 + 2x - 5 =

= (1/2 x + 5)(1/2 x - 1)

Answer: Second choice

no❤️   ,,,,,,,,,,,,,,,,,,,      

8 dimes 4 nickels

ur crazy bb why’d you even ask this question

Answer:15

Step-by-step explanation: We know L+B+E=53 books

Loryn=L

Enda=2L

Brian=L-7

L+2L+L-7=53

Then solve for L

Leaving you with L=15

Check

15+2(15)+(15-7)

15+30+8=53

Answer:

0.34 ends in the hundredths place. so the fraction will be over one hundred

34/100 -- simplify this by dividing each side by 2: 17/50

0.252525... is a repeating decimal

set up an equation so the numbers to the right of the decimal place are the same

100x = 25.2525...

x = 0.2525...

subtract

99x = 25

divide

x = 25/99

5.7777... is also a repeating decimal

set up an equation so the numbers to the right of the decimal place are the same

10x = 57.777...

x = 5.777...

subtract

9x = 52

x = 52/9

Answer:

1X+2Y

Step-by-step explanation:

3x - 2x = 1x

3y - 1y = 2Y

Answer:

3x+2y

Step-by-step explanation:

Let's simplify step-by-step.

3x+3y−y

=3x+3y+(−y)

Combine Like Terms:

=3x+3y+(−y)

=(3x)+(3y+(−y))

=3x+2y

Answer:

=3x+2y

HOPE THIS HELPS!!!!!! :)

<333333

Answer:

7 hours

Step-by-step explanation:

810 - 180 = 630

630/ 90 = 7

Answer:

x = 7 h

Explanation:

First, we write the data of the problem.

Alex travels 810 miles away

Train - 90 miles / h

Alex covers 180 miles.

How many hours does Alex walk in the distance?

1. Calculate the distance Alex still has to travel.

 810 miles - 180 miles = 630 miles

2. We take into account the speed of the train to calculate how many hours Alex will cover the remaining distance.

90 miles .... 1 h

630 miles .... x h

x = 630 milesx1h / 90 miles

x = 7 h

Answer: (1,-1/2)

Step-by-step explanation:

Point C on the coordinate plane has the coordinates (4,-2) after a dilation with a scale factor of 1/4 we will have to multiply the coordinates each by 1/4 to find the new coordinates.

So x =  4 * 1/4 = 1   Now the new x coordinate is 1  

-2 * 1/4 =  -2/4 = -1/2      Now the new coordinate for y is also -1/2

So we will now have the coordinates (1,-1/2)

Answer:

1/26 ; 1/26 ; 1/52

Step-by-step explanation:

Given the following :

A deck of 52 cards contains :

Red hearts, Red stars, black triangles, black circles

Each type of card is numbered from 1 - 13

Therefore,

Number of each type of card = 13, all numbered distinctly with digits between 1 - 13

Probability = (number of required outcomes / total number of possible outcomes)

If one card is drawn from the deck:

Probability of picking a red one :

This is either a red heart numbered 1 or a red red star numbered 1,

Therefore, Required outcomes = 2

Total possible outcomes = 52

P(a red one) = 2 / 52 = 1/26

B) A black three

This is either a black triangle numbered 1 or a black heart numbered 1,

Therefore, Required outcome = 2

Total possible outcomes = 52

P(a black three) = 2 / 52 = 1/26

C.) A six of hearts :

A hearts numbered six = 1

Therefore, Required outcome = 1

Total possible outcomes = 52

P(a black three) = 1 / 52 = 1/52

Answer:

b + 18 = 7

77 = 7b

9 = b - 2

Answer:

No a greater slope is not always steeper

Step-by-step explanation:

If line A has a slope of 10 and line B has a slope of 6. The slope of line A will definetely be steeper than line B. In a negative slope, if line A's slope is -20 and line b's slope is 5 the line A will be steeper even though it is actually less than 5.

Answer:

Rational numbers: fractions with an integer numerator and a nonzero integer denominator.

Irrational numbers: numbers that are not rational such as π, root 3, and any non repeating, non ending decimal.

Answer:

-216

Step-by-step explanation:

-6 x -6 =36

36 x -6 = -216

Answer:

-216

Step-by-step explanation:

Answer:

A: =105

Step-by-step explanation:

Answer:

[tex]K(6,8)[/tex]

Step-by-step explanation:

Given

Midpoint, M = (8,9)

J = (10,10)

Required

Find K

The midpoint of segments is calculated using;

[tex]M(x,y) = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})[/tex]

Where [tex]x = 8[/tex] and  [tex]y = 9[/tex]

Take J as J(x1,y1);

So:

[tex]x_1 = 10[/tex]     [tex]y_1 = 10[/tex]

Substitute values for x and y in the given formula

[tex](8,9) = (\frac{10 + x_2}{2}, \frac{10 + y_2}{2})[/tex]

Solving for x2, we have

[tex]8 = \frac{10 + x_2}{2}[/tex]

Multiply both sides by 2

[tex]2 * 8 = \frac{10 + x_2}{2} * 2[/tex]

[tex]2 * 8 = 10 + x_2[/tex]

[tex]16 = 10 + x_2[/tex]

Make x2 the subject of formula

[tex]x_2 = 16 - 10[/tex]

[tex]x_2 = 6[/tex]

Solving for y2

[tex]9 = \frac{10 + y_2}{2}[/tex]

Multiply both sides by 2

[tex]2 * 9 = \frac{10 + y_2}{2} * 2[/tex]

[tex]2 * 9 = 10 + y_2[/tex]

[tex]18 = 10 + y_2[/tex]

Make y2 the subject of formula

[tex]y_2 = 18 - 10[/tex]

[tex]y_2 = 8[/tex]

So,

[tex](x_2,y_2) = (6,8)[/tex]

So, the coordinates of K is

[tex]K(6,8)[/tex]

Answer:

La altura del globo con respecto al suelo es 449,6 metros.

Step-by-step explanation:

La afirmación está incompleta. El enunciado completo es: "Un globo vuela entre dos ciudades A y B, que distan entre sí 1.500 m. Los tripulantes del globo ven la ciudad A con un ángulo de depresión de 27°, mientras que para ver la ciudad B es de 36°. ¿Cuál es la altura aproximada del globo con respecto al suelo?

El diagrama geométrico de la situación se encuentra descrita en el archivo adjunto. La altura aproximada del globo puede obtenerse con ayuda de las funciones trigonométricas, en este caso, se recomienda utilizar la función tangente de los ángulos de depresión:

Ciudad A

[tex]\tan 27^{\circ} = \frac{h}{1500\,m-x}[/tex]

[tex]0,510 = \frac{h}{1500\,m-x}[/tex]

Ciudad B

[tex]\tan 36^{\circ} = \frac{h}{x}[/tex]

[tex]0,727 = \frac{h}{x}[/tex]

Donde [tex]h[/tex] y [tex]x[/tex] son la altura con respecto al suelo y la distancia horizontal con respecto a la ciudad A.

A continuación, se elimina la altura de ambas ecuaciones por igualación y se determina la distancia horizontal del globo con respecto a la ciudad A:

[tex]0,727\cdot x = 0,510\cdot (1500\,m-x)[/tex]

[tex]1,237\cdot x = 765\,m[/tex]

[tex]x = 618,432\,m[/tex]

Finalmente, la altura del globo con respecto al suelo es:

[tex]h = 0,727\cdot x[/tex]

[tex]h = 0,727\cdot (618,432\,m)[/tex]

[tex]h = 449,600\,m[/tex]

La altura del globo con respecto al suelo es 449,6 metros.

Answer:

  5 years

Step-by-step explanation:

Simple interest on a loan of P for t years at rate r per year is ...

  I = Prt

  4800 = 12,000(0.08)(t)

  4800/960 = t = 5

It will take Joel 5 years to pay off the loan.

Answer:

6

Step-by-step explanation:

log ₐ (aˣ) = x

3 log ₂ (4)

3 log ₂ (2²)

3 * 2

6

Answer:

Step-by-step explanation:

Rationalization.  

                                                                              2 + i

For example:  " rationalize the denominator of ---------  "

                                                                               -3 + i