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3 years ago

Which graph represents y=⌈x⌉ over the domain 3≤x≤6 ?

Mathematics

2 answers:

Yakvenalex [24]3 years ago

5 0

Answer:The third graph (left of the bottom) represents $y=\left \lceil x \right \rceil$ over the domain 3≤x≤6.

Step-by-step explanation:

The Least Interger Function is represented by $y=\left \lceil x \right \rceil$ .

The least integer function is a discontinuous function whose value at any number x is the smallest integer greater than of equal to x .It is denoted by $\left \lceil x \right \rceil$ .and It is also known as ceiling of x. For example

$\left \lceil3.4\right \rceil=4,\left \lceil5.6\right \rceil=6. \left \lceil4.4\right \rceil=5$

So the third graph (left of the bottom) represents $y=\left \lceil x \right \rceil$ over the domain 3≤x≤6.

[we can see all the value of x starting from 3 pointed at y=3 and for x≤ 4 are converging to y=4 which is represented by solid dot and so on ... ]

Nataly_w [17]3 years ago

4 0

Im pretty sure the answer would be the fourth one. because a greater than or equal to. is a solid dot and just greater than is just a circle. and it get higher. so That is what im thinking the answer would be.
Hope this helps.

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Step-by-step explanation:

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3 years ago

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Suppose small aircraft arrive at a certain airport according to a Poisson process with rate a 5 8 per hour, so that the number o

timurjin [86]

Answer:

(a) P (X = 6) = 0.12214, P (X ≥ 6) = 0.8088, P (X ≥ 10) = 0.2834.

(b) The expected value of the number of small aircraft that arrive during a 90-min period is 12 and standard deviation is 3.464.

Step-by-step explanation:

Let the random variable X = number of aircraft arrive at a certain airport during 1-hour period.

The arrival rate is, λt = 8 per hour.

(a)

For t = 1 the average number of aircraft arrival is:

$\lambda t=8\times 1=8$

The probability distribution of a Poisson distribution is:

$P(X=x)=\frac{e^{-8}(8)^{x}}{x!}$

Compute the value of P (X = 6) as follows:

$P(X=6)=\frac{e^{-8}(8)^{6}}{6!}\\=\frac{0.00034\times262144}{720}\\ =0.12214$

Thus, the probability that exactly 6 small aircraft arrive during a 1-hour period is 0.12214.

Compute the value of P (X ≥ 6) as follows:

$P(X\geq 6)=1-P(X$

Thus, the probability that at least 6 small aircraft arrive during a 1-hour period is 0.8088.

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

$P(X\geq 10)=1-P(X$

Thus, the probability that at least 10 small aircraft arrive during a 1-hour period is 0.2834.

(b)

For t = 90 minutes = 1.5 hour, the value of λ, the average number of aircraft arrival is:

$\lambda t=8\times 1.5=12$

The expected value of the number of small aircraft that arrive during a 90-min period is 12.

The standard deviation is:

$SD=\sqrt{\lambda t}=\sqrt{12}=3.464$

The standard deviation of the number of small aircraft that arrive during a 90-min period is 3.464.

(c)

For t = 2.5 the value of λ, the average number of aircraft arrival is:

$\lambda t=8\times 2.5=20$

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

$P(X\geq 20)=1-P(X$

Thus, the probability that at least 20 small aircraft arrive during a 2.5-hour period is 0.5298.

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

$P(X\leq 10)=\sum\limits^{10}_{x=0}(\frac{e^{-20}(20)^{x}}{x!})\\=0.01081\\\approx0.0108$

Thus, the probability that at most 10 small aircraft arrive during a 2.5-hour period is 0.0108.

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3 years ago

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never [62]

Answer:

5x = 100°

4x = 80°

Step-by-step explanation:

We are given a diagram with a straight line AC being intersected by another line BD and we are to find the two mentioned angles.

We know that the two angles (5x° and 4x°) are supplementary so their sum would be equal to 180°.

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$5x+4x=180$

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$x=\frac{180}{90}$

$x=20$

Finding the measure of both the angles:

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