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An airline charges the following baggage fees: $25 for the first bag and $35 for the second. Suppose 51% of passengers have no c

Orlov [11]

Answer:

The average revenue per passenger is about $13.85

μ = $13.85

The corresponding standard deviation is $14.51

σ = $14.51

The airline should expect revenue of $1,662 with a standard deviation of $14.51 for a flight of 120 passengers.

Expected revenue = $1,662 ± 14.51

Step-by-step explanation:

An airline charges the following baggage fees:

$25 for the first bag and $35 for the second

Suppose 51% of passengers have no checked luggage,

P(0) = 0.51

33% have one piece of checked luggage and 16% have two pieces.

P(1) = 0.33

P(2) = 0.16

a. Build a probability model, compute the average revenue per passenger, and compute the corresponding standard deviation.

The average revenue per passenger is given by

μ = 0×P(0) + 25×P(1) + 35×P(2)

μ = 0×0.51 + 25×0.33 + 35×0.16

μ = 0 + 8.25 + 5.6

μ = $13.85

Therefore, the average revenue per passenger is about $13.85

The corresponding standard deviation is given by

σ = √σ²

Where σ² is the variance and is given by

σ² = (0 - 13.85)²×0.51 + (25 - 13.85)²×0.33 + (35 - 13.85)²×0.16

σ² = 97.83 + 41.03 + 71.57

σ² = 210.43

So,

σ = √210.43

σ = $14.51

Therefore, the corresponding standard deviation is $14.51

b. About how much revenue should the airline expect for a flight of 120 passengers? With what standard deviation?

For 120 passengers,

Expected revenue = 120×$13.85

Expected revenue = $1,662 ± 14.51

Therefore, the airline should expect revenue of $1,662 with a standard deviation of $14.51 for a flight of 120 passengers.

6 0

2 years ago

Find the absolute extrema of the function over the region R. (In each case, R contains the boundaries.) Use a computer algebra s

algol [13]

f(x, y) = x ² - 4xy + 5

has critical points where both partial derivatives vanish:

∂f/∂x = 2x - 4y = 0 ==> x = 2y

∂f/∂y = -4x = 0 ==> x = 0 ==> y = 0

The origin does not lie in the region R, so we can ignore this point.

Now check the boundaries:

• x = 1 ==> f (1, y) = 6 - 4y

Then

max{f (1, y) | 0 ≤ y ≤ 2} = 6 when y = 0

max{f (1, y) | 0 ≤ y ≤ 2} = -2 when y = 2

• x = 4 ==> f (4, y) = 12 - 16y

Then

max{f (4, y) | 0 ≤ y ≤ 2} = 12 when y = 0

max{f (4, y) | 0 ≤ y ≤ 2} = -4 when y = 2

• y = 0 ==> f (x, 0) = x ² + 5

Then

max{f (x, 0) | 1 ≤ x ≤ 4} = 21 when x = 4

min{f (x, 0) | 1 ≤ x ≤ 4} = 6 when x = 1

• y = 2 ==> f (x, 2) = x ² - 8x + 5 = (x - 4)² - 11

Then

max{f (x, 2) | 1 ≤ x ≤ 4} = -2 when x = 1

min{f (x, 2) | 1 ≤ x ≤ 4} = -11 when x = 4

So to summarize, we found

max{f(x, y) | 1 ≤ x ≤ 4, 0 ≤ y ≤ 2} = 21 at (x, y) = (4, 0)

min{f(x, y) | 1 ≤ x ≤ 4, 0 ≤ y ≤ 2} = -11 at (x, y) = (4, 2)

5 0

3 years ago

Help quickly please

Margarita [4]

Weathering-the process of wearing or being worn by long exposure to the atmosphere.

3 0

3 years ago

Read 2 more answers

Big Ben, the famous clock tower in London, has a minute hand that is 14 feet long. How far does the tip of the minute hand of Bi

ycow [4]

Answer:

36.65 ft (2 dp)

Step-by-step explanation:

Angles around a point sum to 360°
1 hour = 60 minutes

Therefore, the minute hand of a clock travels 360° in 60 minutes

Number of degrees the minute hand will travel in 25 minutes:

$\sf =\dfrac{360}{60} \times 25=150^{\circ}$

To find how far the tip of the minute hand travels in 25 minutes, use the Arc Length formula:

$\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right)$

$\textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in degrees)}$

Given:

r = length of minute hand = 14 ft
$\theta$ = 150°

$\begin{aligned}\implies \textsf{Arc length} &=2 \pi (14)\left(\dfrac{150^{\circ}}{360^{\circ}}\right)\\ & = 28\pi \left(\dfrac{5}{12}\right)\\ & = \dfrac{35}{3} \pi \\ & = 36.65\: \sf ft\:(2\:dp)\end{aligned}$

4 0

2 years ago

4(r+3)-3r=19 help me plz

bulgar [2K]

Since ur using r as a variable the answer is r = 7.

6 0

3 years ago

Read 2 more answers