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3 years ago

What is the value of [-4.6]

Mathematics

2 answers:

solniwko [45]3 years ago

7 0

<h2>Answer:</h2>

The value is:

-4

<h2>Step-by-step explanation:</h2>

We are asked to find the value of the ceiling function: $\left \lceil -4.6 \right \rceil$

As we know that the ceiling function always occupy the higher value in integers.

i.e. the ceiling function act as follows:

it takes value 0 when -1< x≤0

1 when 0 < x ≤ 1

2 when 1 < x ≤2

and so on.

As we know that:

-4.6 lie between -5 and -4.

Hence, we have:

$\left \lceil -4.6 \right \rceil=-4$

NeTakaya3 years ago

5 0

Answer: -4

Step-by-step explanation:

The ceiling function (also known as the least integer function) is written as

$f(x) = [x]$

It gives the smallest integer greater than or equal to x .

For example : [5.6]=6

or [-1.9]= -1 [∵- 1 > -1.9 ]

To find : The value of [-4.6]

Clearly , [-4.6] is written in ceiling function notation.

Then, [-4.6] = smallest integer greater than or equal to -4.6

= -4 [∵ -4>-4.6]

Hence, the value of [-4.6] = -4

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3 years ago

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3 years ago

Suppose that X has an exponential distribution with mean equal to 10. Determine the following: a. P(X > 10) b. P(X > 20) c

GrogVix [38]

Answer:

(a) The value of P (X > 10) is 0.3679.

(b) The value of P (X > 20) is 0.1353.

(d) The value of x is 30.

Step-by-step explanation:

The probability density function of an exponential distribution is:

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

The value of E (X) is 10.

The parameter λ is:

$\lambda=\frac{1}{E(X)}=\frac{1}{10}=0.10$

(a)

Compute the value of P (X > 10) as follows:

$P(X>10)=\int\limits^{\infty}_{10} {0.10 e^{-0.10 x}} \, dx \\=0.10\int\limits^{\infty}_{10} { e^{-0.10 x}} \, dx\\=0.10|\frac{e^{-0.10 x}}{-0.10} |^{\infty}_{10}\\=|e^{-0.10 x} |^{\infty}_{10}\\=e^{-0.10\times10}\\=0.3679$

Thus, the value of P (X > 10) is 0.3679.

(b)

Compute the value of P (X > 20) as follows:

$P(X>20)=\int\limits^{\infty}_{20} {0.10 e^{-0.10 x}} \, dx \\=0.10\int\limits^{\infty}_{20} { e^{-0.10 x}} \, dx\\=0.10|\frac{e^{-0.10 x}}{-0.10} |^{\infty}_{20}\\=|e^{-0.10 x} |^{\infty}_{20}\\=e^{-0.10\times20}\\=0.1353$