the baseball team equipment manager received a shipment of new baseballs. out of 200 balls 12.5% had defects. How many baseballs were without defects?​

Answer:

76.9

Step-by-step explanation:

tan(α) = opposite leg/adjacent leg

tan(70°) = x/28

x = 28* tan(70°) = 76.9

Answer:

76.9  or 77

Step-by-step explanation:

tan(α) = opposite leg/adjacent leg

tan(70°) = x/28

x = 28* tan(70°) = 76.9

Answer:

[tex]\boxed{x = 251.4 cm}[/tex]

Step-by-step explanation:

Part 1: Sketching the triangle

We are given the angle of elevation, 70°, and the distance along the ground, 86 centimeters. Our unknown is a ladder leaning against the building. Buildings are erected vertically, so the unknown side length is the hypotenuse of the triangle.

We can then sketch this triangle out to visualize it (attachment).

Part 2: Determining what trigonometric ratio can solve the problem

Now, we need to refer to our three trigonometric ratios:

[tex]sin = \frac{opposite}{hypotenuse}[/tex]

[tex]cos = \frac{adjacent}{hypotenuse}[/tex]

[tex]tan = \frac{opposite}{adjacent}[/tex]

Visualizing the sketched triangle, we can assign the three sides their terms in correspondence to the known angle -- this angle cannot be the right angle because the hypotenuse is opposite of it.

Therefore, we know our unknown side length is the hypotenuse of the triangle and because the other side is bordering the 70° angle, it is the adjacent side.

By assigning the sides, we can see that we need to use the trigonometric function that utilizes both the hypotenuse and the adjacent side to find the angle. This is the cosine function.

Part 3: Solving for the unknown variable

Now that we have determined what side we need to solve for and what trigonometric function we are going to use to do so, we just need to plug it all into the equation.

The cosine function is provided: [tex]cos( \alpha) = \frac{adjacent}{hypotenuse}[/tex], where [tex]\alpha[/tex] is the angle. We just need to plug in our values and solve for our unknown side; the hypotenuse.

[tex]cos (70) = \frac{86 cm}{x}[/tex], where x is the unknown side/the hypotenuse.

[tex]x * cos (70) = \frac{86 cm}{x} * x[/tex] Multiply by x on both sides of the equation to eliminate the denominator and make the unknown easier to solve for.

[tex]\frac{xcos (70)}{cos(70)} = \frac{86 cm}{cos(70)}[/tex], Evaluate the second fraction because the first one cancels down to just the unknown, x.

[tex]\frac{86}{cos(70)} = 251.4[/tex], round to one decimal place.

Your final answer is [tex]\boxed{x=251.4cm}[/tex].

Step-by-step explanation:

The probability that either Jack or Jill will be selected on the first draw is 2/30.

The probability that the other person will be selected on the second draw is 1/29.

The probability of both events is (2/30) (1/29), which simplifies to 1/435.

Answer:

Step-by-step explanation:

by looking at the given image...

the shape ABCD is a parallelogram.

Required:

is to prove ∡A and ∡B are supplementary

and ∡C and ∡D are supplementary.

so, m∠A + m∠B = 180°

and m∠C + m∠D = 180°

the  Statement    

1. ABCD is a parallelogram                

the reason is..    

It is Given!

the  Statement  

2.m∠A=m∠C and m∠B=m∠D        

the reason is..

Definition of parallelogram.

the  Statement  

3.m∠A+m∠B+m∠C+m∠D=360°    

the reason is..

Definition of quadrilateral

the  Statement  

4. m∠A+m∠B+m∠A+m∠B=360°    

the reason is..

By substitution

⇒ 2( m∠A + m∠B ) = 360°

⇒ m∠A + m∠B = 180°

it is also similar  m∠C + m∠D = 180°

the  Statement  

5.∠A and ∠C are supplementary

the reason is..

by the definition of Supplementary   ∠ B and ∠D are supplementary

Hope it helps!

Answer:

see below

Step-by-step explanation:

by looking at the given image...

the shape ABCD is a parallelogram.

Required:

is to prove ∡A and ∡B are supplementary

and ∡C and ∡D are supplementary.

so, m∠A + m∠B = 180°

and m∠C + m∠D = 180°

the  Statement    

1. ABCD is a parallelogram                

the reason is..    

It is Given!

the  Statement  

2.m∠A=m∠C and m∠B=m∠D        

the reason is..

Definition of parallelogram.

the  Statement  

3.m∠A+m∠B+m∠C+m∠D=360°    

the reason is..

Definition of quadrilateral

the  Statement  

4. m∠A+m∠B+m∠A+m∠B=360°    

the reason is..

By substitution

⇒ 2( m∠A + m∠B ) = 360°

⇒ m∠A + m∠B = 180°

it is also similar  m∠C + m∠D = 180°

the  Statement  

5.∠A and ∠C are supplementary

the reason is..

by the definition of Supplementary   ∠ B and ∠D are supplementary

Hope it helps!

Answer:

[tex] x+2-2 <-5-2[/tex]

And after operate we got:

[tex] x <-7[/tex]

And then the solution would be [tex]x<-7[/tex]

Step-by-step explanation:

For this problem we have the following inequality:

[tex] x+2 <-5[/tex]

The first step would be subtract 2 from both sides of the equation and we got:

[tex] x+2-2 <-5-2[/tex]

And after operate we got:

[tex] x <-7[/tex]

And then the solution would be [tex]x<-7[/tex]

Answer:

Age of teacher = 32 years

Step-by-step explanation:

Average age of 15 students = 16 years

Sum of age of 15 students = 16 * 15 = 240 years

Average of age 15 students and a teacher = 17 years

Sum of age  15 students and a teacher = 17 * 16 =  272 years

Age of teacher = 272 - 240 = 32 years

Answer:

Age of teacher = 32 years

Therefore, the correct answer is (b)

Step-by-step explanation:

We know that average is given by

Average age = Sum of ages /no. of students

We are given that the average age of 15 students is 16 years.

16 = Sum of ages/15

Sum of ages = 16×15

Sum of ages = 240

We are given that If teacher’s age is included the average increases by 1.

16 + 1 = New sum of ages/15 + 1

17 = New sum of ages/16

New sum of ages = 17×16

New sum of ages = 272

So the age of the teacher is found by

Age of teacher = New sum of ages - Sum of ages

Age of teacher = 272 - 240

Age of teacher = 32 years

Therefore, the correct answer is (b)

Answer:  The level of the dose be after 3 hours=  0.03125 mg.

Step-by-step explanation:

General exponential decay equation : [tex]y=A(1-r)^x[/tex] , where A = initial value , r= rate of decay , x =Time period.

Here, drug’s effectiveness  is decreasing exponentially.

AS per given , we have

A= 250 mg

x=3

r= 95% = 0.95

Then, [tex]y=250(1-0.95)^3 = 250(0.05)^3=250*0.000125=0.03125[/tex]

Hence, the level of the dose be after 3 hours = 0.03125 mg.

Answer:

214.34 about (213.75 on calculator)

Step-by-step explanation:

95% of 250=237.5

95% of 237=225.15

95% of 225=213.75

Answer:  The value of b= 15.6

Step-by-step explanation:

The given equation:  [tex]4\dfrac{1}{3}b+b=6b-10.4[/tex]

To find : Value of b.

Since, we can write [tex]4\dfrac{1}{3}=\dfrac{13}{3}[/tex]

So, the given equation becomes [tex]\dfrac{13}{3}b+b=6b-10.4[/tex]

[tex]\Rightarrow\dfrac{13b+3b}{3}=6b-10.4\Rightarrow\dfrac{16b}{3}=6b-10.4[/tex]

Subtract 6b from both sides , we get

[tex]\Rightarrow\dfrac{16b}{3}=6b-10.4\\\\\Rightarrow\dfrac{16b-18b}{3}=-10.4\\\\\Rightarrow\dfrac{-2b}{3}=-10.4\\\\\Rightarrow b=-10.4\times\dfrac{-3}{2}\\\\\Rightarrow\ b= 15.6[/tex]

hence, the value of b= 15.6

Answer:

[tex]\boxed{\sf Option \ 4}[/tex]

Step-by-step explanation:

[tex]\sqrt{2x-3} +x=3[/tex]

Subtract x from both sides.

[tex]\sqrt{2x-3} +x-x=-x+3[/tex]

[tex]\sqrt{2x-3}=-x+3[/tex]

Square both sides.

[tex]( \sqrt{2x-3})^2 =(-x+3)^2[/tex]

[tex]2x-3=x^2-6x+9[/tex]

Subtract x²-6x+9 from both sides.

[tex]2x-3-(x^2-6x+9 )=x^2-6x+9-(x^2-6x+9)[/tex]

[tex]-x^2 +8x-12=0[/tex]

Factor left side of the equation.

[tex](-x+2)(x-6)=0[/tex]

Set factors equal to 0.

[tex]-x+2=0\\-x=-2\\x=2[/tex]

[tex]x-6=0\\x=6[/tex]

Check if the solutions are extraneous or not.

Plug x as 2.

[tex]\sqrt{2(2)-3} +2=3\\ \sqrt{4-3} +2=3\\\sqrt{1} +2=3\\3=3[/tex]

x = 2 works in the equation.

Plug x as 6.

[tex]\sqrt{2(6)-3} +6=3\\ \sqrt{12-3} +6=3\\\sqrt{9} +6=3\\3+6=3\\9=3[/tex]

x = 6 does not work in the equation.

Answer:

option d

Step-by-step explanation:

[tex]\sqrt{2x-3}+x = 3\\\\\sqrt{2x-3} = 3 -x\\[/tex]

Square both sides

[tex](\sqrt{2x-3})^{2}=(3-x)^{2}\\\\\\2x-3=9-6x+x^{2}\\\\0=x^{2}-6x + 9 - 2x + 3\\[/tex]   {Add like terms}

[tex]x^{2} - 8x + 12 = 0[/tex]

Sum = -8

Product = 12

Factors =  -2 , - 6

x² - 2x - 6x + (-2) * (-6) = 0

x(x -2) - 6(x -2) = 0

(x -2) (x - 6) = 0

x - 2 =0   ; x - 6 = 0

x = 2      ; x = 6

roots of the equation : 2  , 6

But when we put x = 6, it doesn't satisfies the equation.

When x = 6,

[tex]\sqrt{2x-3} + x = 3\\\\\sqrt{2*6-3}+6 = 3\\\\\sqrt{12-3}+6=3\\\\\sqrt{9}+6=3\\\\[/tex]

3 + 6≠ 3

Therefore, x = 2  but x = 6 is extraneous

Answer:

Rectangle

Step-by-step explanation:

Well if point A is on (2,3) and you reflect it over the x axis point B would be located at (2,-3).

Then over the y axis point C would be located at (-2,-3), then reflecting that over the x axis point D is (-2,3)

Points

__________

A. (2,3)

B. (2,-3)

C. (-2,-3)

D. (-2,3)

__________

So graphing all these points we get a rectangle.

Because it has 4 sides that are 90 degrees and the sides opposite from each other are the same.

The most precise name of the quadrilateral will be rectangle .

Given,

Point A : (2,3) .

Here,

If point A is on (2,3) and you reflect it over the x axis point B would be located at (2,-3).

Then over the y axis point C would be located at (-2,-3), then reflecting that over the x axis point D is (-2,3)

Points

A. (2,3)

B. (2,-3)

C. (-2,-3)

D. (-2,3)

So, graphing all these points we get a rectangle.

Because it has 4 sides that are 90 degrees and the sides opposite from each other are the same.

Know more about rectangle,

https://brainly.com/question/15019502

#SPJ6

Answer:

[tex]\large \boxed{\sf \ \ \ a+b+c=3 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

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

As

[tex](x+\dfrac{1}{4})^2=x^2+\dfrac{2}{4}x+\dfrac{1^2}{4^2}=x^2+\dfrac{2}{4}x+\dfrac{1}{4^2} \ \ So \\\\x^2+\dfrac{2}{4}x=(x+\dfrac{1}{4})^2-\dfrac{1}{4^2}[/tex]

Let 's go back to the first equation

[tex]4x^2+2x-1=4[(x+\dfrac{1}{4})^2-\dfrac{1}{4^2}]-1=4(x+\dfrac{1}{4})^2-\dfrac{1}{4}-1\\\\=4(x+\dfrac{1}{4})^2-\dfrac{1+4}{4}=\boxed{4(x+\dfrac{1}{4})^2-\dfrac{5}{4}}[/tex]

a = 4

[tex]b=\dfrac{1}{4}\\\\c=-\dfrac{5}{4}[/tex]

[tex]a+b+c=4+\dfrac{1}{4}-\dfrac{5}{4}=\dfrac{4*4+1-5}{4}=\dfrac{12}{4}=3[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

No.

Step-by-Step Explanation:

When two lines are parallel, they might or might not be equal. It is not necessary that they should be equal.

See the triangle below in which two lines are parallel to each other.

Answer:

15 miles

Step-by-step explanation:

Speed is the ratio of distance traveled to the time taken to reach the distance. The formula for speed is given by:

Speed = distance / time

Distance = speed × time

Claire is cycling at a speed of 12 miles per hour. Han is cycling at a speed of 8 miles per hour. At time t = 45 minutes = 45/ 60 hour = 0.75 hour, the distance traveled by Claire and Han is given as:

For Claire:

Distance = speed × time = 12 miles / hour × 0.75 hour = 9 miles

For Han:

Distance = speed × time = 8 miles / hour × 0.75 hour = 6 miles

Since both Han and Claire are traveling in opposite directions, the distance between them after 45 minutes = 9 miles + 6 miles = 15 miles

Answer:

Step-by-step explanation:

Add the equations in order to solve for the first variable. Plug this value into the other equations in order to solve for the remaining variables.

Point Form:

(

−

1

,

10

3

)

Equation Form:

x

=

−

1

,

y

=

10

3

Tap to view steps...

image of graph

Tap to hide graph...

Answer:

A

Step-by-step explanation:

Given

f(x) = [tex]\frac{3+x}{x-3}[/tex]

To evaluate f(a + 2), substitute x = a + 2 into f(x)

f(a + 2) = [tex]\frac{3+a+2}{a+2-3}[/tex] = [tex]\frac{5+a}{a-1}[/tex] → A

Answer:

96

Step-by-step explanation:

800*0.12=96

Answer:

96

Step-by-step explanation:

12% of 800 is 96

Answer:

260

Step-by-step explanation:

By PEMDAS, we know multiplican comes first. 53*5=265. Then, subtract 5 to get 260.

If you want additional help with math or another subject for FREE, check out growthinyouth.org.

Answer:

260

Step-by-step explanation:

the rule is to start with multiplication first 53*5=265 then subtract 5

53 × 5-5= 265-5=260

Answer:

(2,1)

Step-by-step explanation:

Well first we single out y or x in one of the equations,

we’ll use 2x + y = 5 and single out y.

2x + y = 5

-2x to both sides

y = -2x + 5

So we can plug in -2x + 5 into y in 2x - 2y = 2.

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

2x + 4x - 10 = 2

combine like terms,

6x - 10 = 2

Communicarice property

+10 to both sides

6x = 12

divide 6 to both sides

x = 2

If x is 2 we can plug 2 in for x in 2x + y = 5.

2(2) + y = 5

4 + y = 5

-4 to both sides

y = 1

(2,1)

Thus,

the solution is (2,1).

Hope this helps :)

Answer:

A = 55

B = 60

Step-by-step explanation:

We know that 55+ b+ other angle = 180 since they make a straight line

The other angle = 65 since they are alternate interior angles

55+ B+ 65 = 180

Combine like terms

120 + B = 180

B = 60

A + B + 65 = 180 interior angles of a triangle must equal 180 degrees

A +60+ 65 =180  

Combine like terms

A +125 = 180

A = 55

Answer:

[tex]\boxed{A = 55\°}[/tex]

[tex]\boxed{B = 60\°}[/tex]

Step-by-step explanation:

Exterior Angle with A = 180 - 55 = 125 degrees  (Angles on a straight line)

The measure of exterior angle is equal to the sum of non-adjacent interior angles.

So,

125° = B + 65°

B = 125 - 65

B = 60°

Now,

A = 180 - 60 - 65     (Interior angles of a triangle add up to 180 degrees)

A = 55°

Answer:

La Tasha has 27 rabbit stickers. She splits the stickers

evenly among 3 pieces of paper. How many stickers

did La Tasha put on each piece of paper?​

Step-by-step explanation:

Answer:

$2,500 was invested in the first account while $7,500 was invested in the second account

Step-by-step explanation:

Here in this question, we want to find the amount which was invested in each of the accounts, given their individual interest rates and the total amount that was accorded as interest from the two investments

Now, since we do not know the amount invested , we shall be representing them with variables.

Let the amount invested in the first account be $x and the amount invested in the second account be $y

Since the total amount invested is $10,000, this means that the summation of both gives $10,000

Mathematically;

x + y = 10,000 ••••••(i)

now for the $x, we have an interest rate of 5%

This mathematically translates to an interest value of 5/100 * x = 5x/100

For the $y, we have an interest rate of 6% and this mathematically translates to a value of 6/100 * y= 6y/100

The addition of both interests, gives 575

Thus mathematically;

5x/100 + 6y/100 = 575

Multiplying through by 100, we have

5x + 6y = 57500 •••••••••(ii)

From 1, we can have x = 10,000-y

let’s substitute this into equation ii

5(10,000-y) + 6y = 57500

50,000-5y + 6y = 57500

50,000 + y = 57500

y = 57500-50,000

y = 7,500

Recall;

x = 10,000-y

so we have;

x = 10,000-7500 = 2,500

Answer:

y = 3/4( x+5)( x+4) ( x-1)

Step-by-step explanation:

The formula for the polynomial is

y = c( x- a1)( x- a2) ( x-a3)  where c is a constant and a1,a2,a3 are the zeros

We have zeros -5,-4 and 1

y = c( x- -5)( x- -4) ( x-1)

y = c( x+5)( x+4) ( x-1)

We have a y intercept of -15

That means x=0 and y = -15

-15 = c ( 0+5)( 0+4) ( 0-1)

-15 = c( 5) ( 4) (-1)

-15 = c( -20)

Divide each side by -20

-15/-20 = c

3/4 =c

The equation is

y = 3/4( x+5)( x+4) ( x-1)

Step-by-step explanation:

If the line is parallel to y=2/3x+4 then,

m=m

slope of eqn y=2/3x+4

m=2/3(On comparing with y= mx + c)

the passing point is (3,7) then,

y-y1 = m(x-x1)

y-7=2/3(x-3)

y-7=2/3x -2

y-7= -4x/3

3y-7= -4x

4x + 3y - 7=0

So, The reqd eqn is 4x + 3y - 7 = 0

Answer:

Step-by-step explanation:

We have f(x) and g(x). We are to evaluate each of these functions at the domain values given (1, 2, 3, 4, 5, and 6) and see where the output is the same.

[tex]f(1)=-(1)^2+4(1)+12[/tex] and f(1) = 15

[tex]f(2)=-(2)^2+4(2)+12[/tex] and f(2) = 16

[tex]f(3)=-(3)^2+4(3)+12[/tex] and f(3) = 15

[tex]f(4)=-(4)^2+4(4)+12[/tex] and f(4) = 12

[tex]f(5)=-(5)^2+4(5)+12[/tex] and f(5) = 7

[tex]f(6)=-(6)^2+4(6)+12[/tex] and f(6) = 0

Now for g(x) at each of these domain values:

g(1) = 1 + 2 and g(1) = 3

g(2) = 2 + 2 and g(2) = 4

g(3) = 3 + 2 and g(3) = 5

g(4) = 4 = 2 and g(4) = 6

g(5) = 5 + 2 and g(5) = 7

g(6) = 6 + 2 and g(6) = 8

It looks like the outputs are the same at f(5) and g(5). Actually, the domains are the same as well! f(5) = g(5)

Answer:

-28.

Step-by-step explanation:

(x^2 + 3) / (x + 6)

x = -9

[(-9)^2 + 3] / (-9 + 6)

= (81 + 3) / (-3)

= 84 / (-3)

= -28

Hope this helps!

Answer:  the value of the expression is 80

Step-by-step explanation:

[tex]x^2 +3/ x+6[/tex]

(-9)² + 3 / (-9 + 6) .  PEMDAS: figure  parentheses and exponents  first

81 + 3/-3    division   3/-3  = –1

81 + (–1) .adding a negative is the same as subtracting

81 –1

80

Answer:

78.5 yds

Step-by-step explanation:

The circumference is given by

C = pi *d

C = 3.14 * 25

C =78.5

Answer:

[tex]\huge\boxed{C=25\pi\ yd\approx78.5\ yd}[/tex]

Step-by-step explanation:

The formula of a circumference of a circle:

[tex]C=d\pi[/tex]

d - diameter

We have d = 25yd.

Substitute:

[tex]C=25\pi\ yd[/tex]

Use [tex]\pi\approx3.14[/tex]:

[tex]C\approx(25)(3.14)=78.5\ yd[/tex]

Answer: A y = -(2x+8)

Step-by-step explanation:

The first line is y=-2x-8

Thus, the answer that simplifies to y = -2x-8 is the answer.  

a) y=-(2x+8)

Distribute

y=-2x-8

Because it works, no need to try the others.

Hope it helps <3

Answer:

[tex]\boxed{y = -(2x + 8)}[/tex]

Step-by-step explanation:

For the two lines to have infinite [tex]\infty[/tex] solutions, the two equations must be the same.

First equation : y = -2x - 8

A. y = -(2x + 8)

   y = -2x - 8 correct

B. y = -2(x - 8)

   y = -2x + 16 incorrect

C. y = -2(x - 4)

   y = -2x + 8 incorrect

D. y = -(-2x+8)

    y = 2x - 8 incorrect

y = -2x - 8 and y = -(2x + 8) when graphed are the same, they intersect at infinite points and there are infinite solutions.

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

Explanation:

Jane does the job alone and she can finish it in 5 hours. Her rate is 1/5 of a job per hour. By "job", I mean painting the entire fence. Notice that multiplying 1/5 by the number of hours she works will yield the value 1 to indicate one full job is done.

Through similar reasoning, Paul's rate is 1/6 of a job per hour.

Let x be the time, in hours, it takes Peter to get the job done if he worked alone. His rate is 1/x of a job per hour.

Combining the three individual rates gives

1/5 + 1/6 + 1/x = (6x)/(30x) + (5x)/(30x) + (30)/(30x)

1/5 + 1/6 + 1/x = (6x+5x+30)/(30x)

1/5 + 1/6 + 1/x = (11x+30)/(30x)

The expression (11x+30)/(30x) is the total rate if the three people worked together. This is assuming neither worker slows another person down.

Set this equal to 1/2 as this is the combined rate (based on the fact everyone teaming up gets the job done in 2 hours). Then solve for x

(11x+30)/(30x) = 1/2

2(11x+30) = 30x*1 .... cross multiply

22x+60 = 30x

60 = 30x-22x

60 = 8x

8x = 60

x = 60/8

x = 7.5

It takes Peter 7.5 hours, or 7 hours 30 minutes, to get the job done if he worked alone.

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

Here's another equation to solve though its fairly the same idea as above

1/5 + 1/6 + 1/x = 1/2

30x*(1/5 + 1/6 + 1/x) = 30x*(1/2) ... multiply both sides by LCD

30x(1/5) + 30x(1/6) + 30x(1/x) = 30x(1/2)

6x + 5x + 30 = 15x

11x + 30 = 15x

30 = 15x-11x

30 = 4x

4x = 30

x = 30/4

x = 7.5

We get the same answer

Answer:  7 . 5 hrs

Step-by-step explanation:

It takes Jane 5 hours to finish the fence so she can get  [tex]\dfrac{1}{5}[/tex] of the job done in 1 hour.

It takes Paul 6 hours to finish the fence so he can get  [tex]\dfrac{1}{6}[/tex] of the job done in 1 hour.

It takes Peter x hours to finish the fence so he can get  [tex]\dfrac{1}{x}[/tex] of the job done in 1 hour.

Together, it takes them 2 hours to finish the fence so they can get  [tex]\dfrac{1}{2}[/tex] of the job done in 1 hour.

Jane + Paul + Peter = Together

[tex]\dfrac{1}{5}\quad +\quad \dfrac{1}{6}\quad +\quad \dfrac{1}{x}\quad =\quad \dfrac{1}{2}[/tex]

Multiply everything by 30x to eliminate the denominator:

[tex]\dfrac{1}{5}(30x) + \dfrac{1}{6}(30x) +\dfrac{1}{x}(30x) =\dfrac{1}{2}(30x)[/tex]

Simplify and solve for x:

6x + 5x + 30 = 15x

      11x + 30 = 15x

              30 = 4x

              [tex]\dfrac{30}{4}=x[/tex]

              7.5 = x

Answer:

The answer is below

Step-by-step explanation:

Since they are two green balls, x cannot assume value of 0 and 1. The minimum number of red balls must be two since there are only two green balls and we need to select 4 balls

For x = 2 (select two red balls from 4 red balls and 2 green balls from 2 green balls):

P(x = 2) = [tex]\frac{C(4,2)*C(2,2)}{C(6,2)} =\frac{6}{15}[/tex]

For x = 3 (select 3 red balls from 4 red balls and 1 green balls from 2 green balls):

P(x = 3) = [tex]\frac{C(4,3)*C(2,1)}{C(6,2)} =\frac{8}{15}[/tex]

For x = 4 (select 4 red balls from 4 red balls and 0 green balls from 2 green balls):

P(x = 4) = [tex]\frac{C(4,4)*C(2,0)}{C(6,2)} =\frac{1}{15}[/tex]

Expected value = E(x) = ΣxP(x) = (2×6/15) + (3×8/15) + (4×1/15) = 40/15 = 2.67

Variance =  Σx²P(x) - [E(x)]² = (2²×6/15) + (3²×8/15) + (4²×1/15) - (40/15)² = 80/225 = 0.36

Standard deviation = √variance = √0.36 =  0.6

Using the hypergeometric distribution, it is found that:

The marbles are chosen without replacement, hence, the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

In this problem:

The expected value is:

[tex]E(X) = \frac{nk}{N}[/tex]

Hence:

[tex]E(X) = \frac{4(4)}{6} = 2.67[/tex]

The expected value is of 2.67.

The variance is:

[tex]V(X) = \frac{nk(N-k)(N-n)}{N^2(N-1)}[/tex]

Hence:

[tex]V(X) = \frac{4(4)(2)(2)}{6^2(6-1)} = 0.356[/tex]

The standard deviation is the square root of the variance, hence:

[tex]\sqrt{V(X)} = \sqrt{0.356} = 0.596[/tex]

A similar problem is given at https://brainly.com/question/19426305

Answer:

A

Step-by-step explanation:

[tex] \frac{ {6}^{3}. {2}^{6} }{ {2}^{3 } } = \frac{ {2}^{3}. {3}^{3}. {2}^{6} } { {2}^{3} } = {2}^{6} . {3}^{3} [/tex]