A: $521.80
B:513.60
C: 467.90
D: 435.70

Answer:

[tex]E(Y)=\frac{1}{25}[/tex]

Step-by-step explanation:

Let's start defining the random variables for this exercise :

[tex]X_{1}:[/tex] '' The proportion of the particulates that are removed by the first pass ''

[tex]X_{2}:[/tex] '' The proportion of what remains after the first pass that is removed by the second pass ''

[tex]Y:[/tex] '' The proportion of the original particulates that remain in the sample after two passes ''

We know the relation between the random variables :

[tex]Y=(1-X_{1})(1-X_{2})[/tex]

We also assume that [tex]X_{1}[/tex] and [tex]X_{2}[/tex] are independent random variables with common pdf.

The probability density function for both variables is [tex]f(x)=4x^{3}[/tex] for [tex]0<x<1[/tex] and [tex]f(x)=0[/tex] otherwise.

The first step to solve this exercise is to find the expected value for [tex]X_{1}[/tex] and [tex]X_{2}[/tex].

Because the variables have the same pdf we write :

[tex]E(X_{1})= E(X_{2})=E(X)[/tex]

Using the pdf to calculate the expected value we write :

[tex]E(X)=\int\limits^a_b {xf(x)} \, dx[/tex]

Where [tex]a=[/tex] ∞ and [tex]b=[/tex] - ∞ (because we integrate in the whole range of the random variable). In this case, we will integrate between [tex]0[/tex] and [tex]1[/tex] ⇒

Using the pdf we calculate the expected value :

[tex]E(X)=\int\limits^1_0 {x4x^{3}} \, dx=\int\limits^1_0 {4x^{4}} \, dx=\frac{4}{5}[/tex]

⇒ [tex]E(X)=E(X_{1})=E(X_{2})=\frac{4}{5}[/tex]

Now we need to use some expected value properties in the expression of [tex]Y[/tex] ⇒

[tex]Y=(1-X_{1})(1-X_{2})[/tex] ⇒

[tex]Y=1-X_{2}-X_{1}+X_{1}X_{2}[/tex]

Applying the expected value properties (linearity and expected value of a constant) ⇒

[tex]E(Y)=E(1)-E(X_{2})-E(X_{1})+E(X_{1}X_{2})[/tex]

Using that [tex]X_{1}[/tex] and [tex]X_{2}[/tex] have the same expected value [tex]E(X)[/tex] and given that [tex]X_{1}[/tex] and [tex]X_{2}[/tex] are independent random variables we can write [tex]E(X_{1}X_{2})=E(X_{1})E(X_{2})[/tex]   ⇒

[tex]E(Y)=E(1)-E(X)-E(X)+E(X_{1})E(X_{2})[/tex] ⇒

[tex]E(Y)=E(1)-2E(X)+[E(X)]^{2}[/tex]

Using the value of [tex]E(X)[/tex] calculated :

[tex]E(Y)=1-2(\frac{4}{5})+(\frac{4}{5})^{2}=\frac{1}{25}[/tex]

[tex]E(Y)=\frac{1}{25}[/tex]

We find that the expected value of the variable [tex]Y[/tex] is [tex]E(Y)=\frac{1}{25}[/tex]

Answer:

The volume for a cone and pyramid are the same, V = 1/3 Bh where B is the area of the base.

Step-by-step explanation:

So even though the base is a different shape, as long as the areas and heights are the same, they will have the same volume.

Given:

Consider the given expression is:

[tex]10n-\dfrac{1}{3}(9n-12)[/tex]

To find:

The simplified form of the given expression.

Solution:

We have,

[tex]10n-\dfrac{1}{3}(9n-12)[/tex]

Using distributive property, it can be written as:

[tex]=10n-\dfrac{1}{3}(9n)-\dfrac{1}{3}(-12)[/tex]

[tex]=10n-3n+4[/tex]

[tex]=7n+4[/tex]

Therefore, the correct option is A.

Answer:

x=76

Step-by-step explanation:

y+8=3y

-2y=-8

y=4

104*2=208

360-208=152

152/2=76

x=76

Answer:

The answers to your questions are given below.

Step-by-step explanation:

1. (3x + 8)(3x + 8) = 0

3x + 8 = 0 or 3x + 8 = 0

3x = –8 or 3x = –8

x = –8/3 or –8/3

2. (3x – 8)(3x + 8) = 0

3x – 8 = 0 or 3x + 8 = 0

3x = 8 or 3x = –8

x = 8/3 or –8/3

3. x(3x – 8) = 0

x = 0 or 3x – 8 = 0

x = 0 or 3x = 8

x = 0 or 8/3

4. (3x – 8)(3x – 8) = 0

3x – 8 = 0 or 3x – 8 = 0

3x = 8 or 3x = 8

x = 8/3 or 8/3

Answer:

Step-by-step explanation:

x^1/3( x^1/2 + 2x^2)

x^(1/2 + 1/3) + 2x^(2 + 1/3)

x^(5/6) + 2x^(7/3)

Answer:

the ans is 4 hope it may help u

Step-by-step explanation:

x =-6

x= - × -6 -2

x=+ 6 -2

x= +4

Answer:

85 i thinkkkk

Step-by-step explanation:

Answer:

This

Step-by-step explanation:

let x = rate of the slower plane (First plane!)

x+25 = rate of the faster plane (Second plane!)

The planes fly for 2 hours, where Distance = R*T

Distance between the planes = SUM of the distances.

R*T + R*T= 470 miles

2*x + 2*(x+25)=470

2x+2x + 50 = 470

4x+50=470

4x=420

x=105 mph First plane

x+25= 105+25=130 mph Second plane.

Answer:

4x+50=470

4x=420

x=105 mph First plane

x+25= 105+25=130 mph Second plane.

R^2

Step-by-step explanation:

Answer:

Yessir

Step-by-step explanation:

Answer:

0.3425 = 34.25% probability it will be off probation in February 2020

Step-by-step explanation:

We have these desired outcomes:

Off probation in July 2019, with 0.25 probability, then continuing off in January, with 1 - 0.08 = 0.92 probability.

Still in probation in July 2019, with 1 - 0.25 = 0.75 probability, then coming off in January, with 0.15 probability.

What is the probability it will be off probation in February 2020?

[tex]p = 0.25*0.92 + 0.75*0.15 = 0.3425[/tex]

0.3425 = 34.25% probability it will be off probation in February 2020

Answer:

the ans is 21 hope it may help u

Step-by-step explanation:

g = 6

x=6

x= 3x + 3

x = 3 × 6 +3

x = 18 + 3

x= 21

Answer:

Step-by-step explanation:

answer= 1

5 x 2 - 3^2

1. First simplify exponents

= that is nine

2. Then Do 5 x 2- 9

5 x 2=10

10-9

= 1

Answer:

Can you add a picture if there are any?

Step-by-step explanation:

Answer:

Step-by-step explanation:

Do you have any measurements?

1) 180-Angle 2 = Angle 1

3) Same as Angle 2

6) Same as Angle 2

Answer: 720 ways

Step-by-step explanation:

Given

Leroy wants to teach his puppy 6 new tricks

Considering each trick is different from other

The first trick can be taught in 6 different ways

After learning the first trick, there are 5 tricks remaining which can be taught in 5 different ways

Similarly, for the remaining tricks, it is 4, 3, 2, and 1 way

So, the total number of ways is [tex]6\times 5\times 4\times 3\times 2\times 1=720\ \text{Ways}[/tex]

Answer:

12 inches

Step-by-step explanation:

All you have to do is divide 72 by 6.

72 divided by 6 equals 12.

So your answer would be D.12 inches

Answer:

B. 14 ft

Step-by-step explanation:

I calculated it logically

Answer:

the last one- 4/24

Step-by-step explanation:

ive answered this question before and got it correct

Answer:

62739.3 cm3

Step-by-step explanation:

Volume of a Sphere:

V=43πr3V=\frac{4}{3}\pi r^3V=34​πr3

radius=diameter2=49.32=24.65\text{radius} = \frac{\text{diameter}}{2} = \frac{49.3}{2}=24.65radius=2diameter​=249.3​=24.65

centimeters

Plug in:\text{Plug in:}Plug in:

43π(24.65)3\frac{4}{3}\pi (24.65)^334​π(24.65)3

62739.258293562739.258293562739.2582935

Use calculator

≈62739.3 cm3\approx 62739.3\text{ cm}^3≈62739.3 cm3

Round to the nearest tenth

Answer:

why does no one ever answer these questionsss?? it's always math to, like I'm just trying to pass my quick check, let alone the class. you know how much easier my life would be it's people just answered the questions. I'm gonna run away, to some Scottish Isle and live a quiet life, in a cozy home with the wind outside ruffling through the grass, and the tired tired sea crashing onto the shoreline. I'll only visit my family and friends once a year, but the rest of the time, I'll be there, in the quiet. eventually a young visitor will stumble through my b & b and he'll end up staying there for weeks, for reasons unknown to me. Then, we'll fall in love, to the quiet sound of the ocean outside. And it'll be just us, it'll be our place, our secret. we won't have to deal with the loud, crazy, hectic world. and it will be perfect. but for now I'm stuck trying to pass this math class.

Answer:

The volume of one dime is 340.11 mm3. The volume of 50 dimes is 17.005.32 mm3.

Step-by-step explanation:

Answer:

20x^2 +19xy+3y^2

Step-by-step explanation:

See Image below :)

9514 1404 393

Answer:

  20x² +19xy +3y²

Step-by-step explanation:

Use the distributive property.

  (4x +3y)(5x +y)

  = 4x(5x +y) +3y(5x +y)

  = 20x² +4xy +15xy +3y²

Collect terms.

  = 20x² +19xy +3y²

Answer:

Step-by-step explanation:

Answer: 55

Step-by-step explanation:

180 = 125 + x

x = 55

Answer:

113 meters long

Step-by-step explanation:

If each part is all equal in length, then each part is 1/4 the total length of the obstacle course. Therefore, each part of the course was 1/4(452)=113 meters long

Answer:

48 years

Step-by-step explanation:

Let the ratio of their ages be

4:2:1

Sum up the numbers

4+2+1

= 7

Their total ages is 84

7/84

= 1/12

Therefore Jim age can be calculated as follows

= 12×4

= 48

Hence Jim is 48 years