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3 years ago

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Which one of the following best defines hardness: (a) energy absorbed by a material when an object strikes its surface, (b) resi

stance to bending, (c) resistance to permanent indentation, or (d) resistance to scratching

1 answer:

MrRa [10]3 years ago

5 0

Resistance to permanent indentation

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A continuous random variable, X, whose probability density function is given by f(x) = ( λe−λx , if x ≥ 0 0, otherwise is said t

Ganezh [65]

Answer:

a) $F(x) = \lambda \int_0^{\infty} e^{-\lambda x} dx= -e^{-\lambda x} \Big|_0^{\infty} = 1- e^{-\lambda x} \$

b) $P(10 < X$

Explanation:

Previous concepts

The cumulative distribution function (CDF) F(x),"describes the probability that a random variableX with a given probability distribution will be found at a value less than or equal to x".

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution".

Part a

Let X the random variable of interest. We know on this case that $X\sim Exp(\lambda)$

And we know the probability denisty function for x given by:

$f(x) = \lambda e^{-\lambda x} , x\geq 0$

In order to find the cdf we need to do the following integral:

$F(x) = \lambda \int_0^{\infty} e^{-\lambda x} dx= -e^{-\lambda x} \Big|_0^{\infty} = 1- e^{-\lambda x} \$

Part b

Assuming that $X \sim Exp(\lambda =0.1)$ , then the density function is given by:

$f(x) = 0.1 e^{-0.1 x} dx , x\geq 0$

And for this case we want this probability:

$P(10 < X$

And evaluating the integral we got:

$P(10 < X$

4 0

4 years ago

A cone penetration test was carried out in normally consolidated sand, for which the results are summarized below: Depth (m) Con

Cerrena [4.2K]

Answer:

hello your question is incomplete attached below is the missing equation related to the question

answer : 40.389° , 38.987° , 38° , 39.869° , 40.265°

Explanation:

<u>Determine the friction angle at each depth</u>

attached below is the detailed solution

To calculate the vertical stress = depth * unit weight of sand

also inverse of Tan = Tan^-1

also qc is in Mpa while σ0 is in kPa

Friction angle at each depth

2 meters = 40.389°

3.5 meters = 38.987°

5 meters = 38.022°

6.5 meters = 39.869°

8 meters = 40.265°

6 0

3 years ago

What’s Statistics<br> What are the 2 Source of error in data collection

FromTheMoon [43]

Answer:

<em>The main sources of error in the collection of data are as follows : Due to direct personal interview. Due to indirect oral interviews. Information from correspondents may be misleading.</em>

4 0

3 years ago

Read 2 more answers

A city engineer knows that she will need $25 million in 3 years to replace toll booths on a toll road in the city. Traffic on th

Andreas93 [3]

Answer:

$1.38

Explanation:

She will spend $25 million in 3 years at 10% interest is a case of Future Value of Annuity.

Therefore,

FV = A*((1+r)^n-1)/r

Where A = 25,000,000

r=10%=0.1

n=3

FV= 25000000*((1+0.1)^3-1)/0.1

FV=25000000*(1.331-1)/0.1

FV=25000000*(0.331/0.1)

FV=25000000*3.31

FV=$82,750,000

So it is estimated that 20million cars passes through the toll per year

Therefore,

Toll per vehicle per year = 82750000/2000000

=$4.14

Toll for the duration of the project

=4.14/3 =$1.38

4 0

3 years ago

2. What of the following demonstrates a

Dmitry_Shevchenko [17]

B. Always cut away from the body

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3 years ago