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3 years ago

Find E[x] when x is sum of two fair dice?

Engineering

1 answer:

Ksenya-84 [330]3 years ago

4 0

Answer:

When two fair dice are rolled, 6×6=36 observations are obtained.

P(X=2)=P(1,1)=

P(X=3)=P(1,2)+P(2,1)=

P(X=4)=P(1,3)+P(2,2)+P(3,1)=

P(X=5)=P(1,4)+P(2,3)+P(3,2)+P(4,1)=

P(X=6)=P(1,5)+P(2,4)+P(3,3)+P(4,2)+P(5,1)=

P(X=7)=P(1,6)+P(2,5)+P(3,4)+P(4,3)+P(5,2)+P(6,1)=

P(X=8)=P(2,6)+P(3,5)+P(4,4)+P(5,3)+P(6,2)=

P(X=9)=P(3,6)+P(4,5)+P(5,4)+P(6,3)=

P(X=10)=P(4,6)+P(5,5)+P(6,4)=

P(X=11)=P(5,6)+P(6,5)=

P(X=12)=P(6,6)=

Therefore, the required probability distribution is as follows.

Then, E(X)=∑X

⋅P(X

)

=2×

+3×

+4×

+5×

+6×

+7×

+8×

+9×

+10×

+11×

+12×

+1+

E(X

)=∑X

⋅P(X

)

=4×

+9×

+16×

+25×

+36×

+49×

+64×

+81×

+100×

+121×

+144×

+5+

+9+

121

987

329

=54.833

Then, Var(X)=E(X

)−[E(X)]

=54.833−(7)

=54.833−49

=5.833

∴ Standard deviation =

Var(X)

5.833

=2.415

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A car is moving at 68 miles per hour. The kinetic energy of that car is 5 × 10 5 J.How much energy does the same car have when i

Blababa [14]

Answer:

The car has an energy of 1.017 × 10⁵ J when it moves at 97 miles per hour

Explanation:

Given the data in the question;

Initial velocity v₁ = 68 miles per hour = 30.398 meter per seconds

let mass of the car be m

kinetic energy of that car is 5 × 10⁵ J

E₁ = $\frac{1}{2}$ mv²

we substitute

5 × 10⁵ = $\frac{1}{2}$ × m × ( 30.398 )²

5 × 10⁵ = m × 462.019

m = 5 × 10⁵ / 462.019

m = 1082.2065 kg

Now, Also given that; v₂ = 97 miles per hour = 43.362 meter per seconds

E₂ = $\frac{1}{2}$ mv₂²

we substitute

E₂ = $\frac{1}{2}$ × 1082.2065 × ( 43.362 )²

E₂ = $\frac{1}{2}$ × 1082.2065 × 1880.263

E₂ = 1.017 × 10⁵ J

Therefore, The car has an energy of 1.017 × 10⁵ J when it moves at 97 miles per hour

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3 years ago

The vertical force P acts on the bottom of the plate having a negligible weight. Determine the shortest distance d to the edge o

Greeley [361]

Answer:

The shortest distance d to the edge of the plate is 66.67 mm

Concepts and reason

Moment of a force:

Moment of a force refers to the propensity of the force to cause rotation on the body it acts upon. The magnitude of the moment can be determined from the product of force’s magnitude and the perpendicular distance to the force.

Moment(M) = Force(F)×distance(d)

Moment of inertia ( I )

It is the product of area and the square of the moment arm for a section about a reference. It is also called as second moment of inertia.

First prepare the free body diagram of sectioned plate and apply moment equilibrium condition and also obtain area and moment of inertia of rectangular cross section. Finally, calculate the shortest distance using the formula of compressive stress (σ) in combination of axial and bending stress

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4 years ago

A three-point bending test is performed on a glass specimen having a rectangular cross section of height d = 5.4 mm (0.21 in.) a

Fudgin [204]

Answer:

5.21e-2mm

Explanation:

Please see attachment

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4 years ago

Whats 47,000 resistance converted to kilo or mega ohms.

Julli [10]

The conversion of 47,000 Ohms to kilo-ohms is equal to 47 kilo-ohms.
The conversion of 47,000 Ohms to mega-ohms is equal to 0.047 kilo-ohms.

<h3>What is resistance?</h3>

Resistance can be defined as an opposition to the flow of current in an electric circuit. Also, the standard unit of measurement of the resistance of an electric component is Ohms, which can be converted to kilo-ohms or mega-ohms.

For Ohms to kilo-ohms, we have:

1 Ohms = 0.001 kilo-ohms

47,000 Ohms = X kilo-ohms

Cross-multiplying, we have:

X = 0.001 × 47000

X = 47 kilo-ohms.

For Ohms to mega-ohms, we have:

1,000,000 ohms = 1 mega-ohms

47,000 Ohms = X mega-ohms

Cross-multiplying, we have:

X1,000,000 = 47,000

X = 47,000/1,000,000

X = 0.047 kilo-ohms.

Read more resistance here: brainly.com/question/19582164

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2 years ago

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2 years ago