Explain why there is 1/3 cup of fruit i. Half a smoothie

The time between arrivals of small aircraft at a county airport is exponentially distributed with a mean of one hour. Round the

navik [9.2K]

Answer:

a) 0.019

b) 0.563

c) x = 1.966 hours

Step-by-step explanation:

E(X) = 1

Exponential random variable's probability function is given as

P(X=x) = λ e^(-λ.x)

The cumulative distribution function is given as

P(X ≤ x) = 1 - e^(-λ.x)

a) The time between the arrivals of small aircraft at a county airport that is exponentially distributed.

But the number of planes that land every hour will be obtained using the Poisson distribution formula.

It is the best for discrete systems.

Poisson distribution formula is given as

P(X = x) = (e^-λ)(λˣ)/x!

λ = 1 aircraft per hour.

The probability that more than three aircraft arrive within an hour = P(X > 3)

P(X > 3) = 1 - P(X ≤ 3) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]

P(X > 3) = 1 - 0.98101 = 0.01899 = 0.019 to 3 d.p

b) If 30 separate one-hour intervals are chosen, what Is the probability that no interval contains more than three arrivals

Probability of one 1-hour interval not containing more than 3 arrivals = 1 - P(X > 3)

= 1 - 0.01899 = 0.98101

Probability that thirty 1-hour intervals will not contain more than 3 arrivals = (0.98101)³⁰ = 0.5626 = 0.563 to 3 d.p

c) Determine the length of an interval of time (In hours) such that the probability that no arrivals occur during the interval is 0.14

We can now use the cumulative distribution function for exponential random variable for this

P(X ≤ x) = 1 - e^(-λ.x)

P(X > x) = 1 - P(X ≤ x)

P(X > x) = e^(-λ.x)

λ = 1, x = ?,

0.14 = e⁻ˣ

e⁻ˣ = 0.14

In e⁻ˣ = In 0.14 = -1.966

-x = -1.966

x = 1.966 hours

Hope this Helps!!!

4 0

2 years ago

Given: ΔABC, AC = BC, AB = 3 CD ⊥ AB, CD = √3 Find: AC

valina [46]

Answer:

$\boxed{AC = 2.3}$

Step-by-step explanation:

AD = BD (CD bisects AB means that it divides the line into two equal parts)

So,

AD = BD = AB/2

So,

AD = 3/2

AD = 1.5

<u><em>Now, Finding AC using Pythagorean Theorem:</em></u>

$c^2 = a^2+b^2$

Where c is hypotenuse (AC), a is base (AD) and b is perpendicular (CD)

$AC^2= (1.5)^2+(\sqrt{3} )^2$

$AC^2 = 2.25 + 3$

$AC^2 = 5.25$

Taking sqrt on both sides

$AC = 2.3$

3 0

2 years ago

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Leona purchased a $1,000 bond having a quoted price of 99.875. She had to pay a 5.5% brokerage fee (of the selling price). What

Zina [86]

Answer:

The total cost of the bond is none of the given choices.

Step-by-step explanation:

The selling price of a $1000 bond = $99.875

The brokerage fee = 5.5 %

Now, 5.5% of $99.875 = $\frac{5.5}{100} \times 99.875 = 5.493$

So, the brokerage fee = $5.493

Now, to find out the total cost of the bond:

Total Cost = The selling Price + Brokerage Price

= $99.875 + $5.493

= $105.368

or, the total price of the $1000 bond is $ 105.368.

Hence, the total cost of the bond is none of the given choices.

7 0

2 years ago

A rectangular floor tile is shown it dimensions are given to the nearest 0.1 metres the tile is only able to sustain maximum pre

egoroff_w [7]

Answer:

736 N

Step-by-step explanation:

The dimensions of the rectangular tile are:

Length = 2.3m

Width = 1.6m

The pressure exerted on a surface is given by the formula

$p=\frac{F}{A}$

where

p is the pressure

F is the force exerted

A is the area on which the force is exerted

In this problem, we have:

$p=200 N/m^2$ is the maximum pressure that the tile is able to sustain

A is the area of the tile, which can be calculated as the product between length and width, so:

$A=L\cdot w =(2.3)(1.6)=3.68 m^2$

Re-arranging the formula for F, we can find the maximum force that can be safely applied to the tile:

$F=pA=(200)(3.68)=736 N$

4 0

2 years ago

A rare first-edition book is currently priced at $200. After one year, the price of the book is anticipated to be 1.15 times the

Ber [7]

Answer is Graph Y, NOT Graph W

4 0

2 years ago

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