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Mekhanik [1.2K]
3 years ago
8

A three-dimensional model of Arthur's apartment is

Mathematics
2 answers:
Ilya [14]3 years ago
5 0

Answer: The volume of the apartment is 2,160 ft3.

An hourly rating of 2.5 BTUs per cubic foot is required, so multiply the total volume by 2.5.

Arthur needs an air conditioner that will provide 5,400 BTUs to properly cool his apartment

Step-by-step explanation:

gayaneshka [121]3 years ago
5 0

Answer:

2,160

multiply the total volume by 2.5

5,400 BTUs

Step-by-step explanation:

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Answer:

3694.5 yd^3

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Your friend Alex is planning a fundraising game night to raise money for a local children's hospital. She invites a few of your
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Step-by-step explanation:

(a) You win $5 if you roll a six, $1 if you roll an odd number, and $0 if you roll a 2 or a 4, and you pay $1.50 for every roll.  The expected value is the sum of each outcome multiplied by its probability.

E = (5.00)(1/6) + (1.00)(3/6) + (0)(2/6) + (-1.50)(1)

E = -0.167

You are expected to lose on average about $0.17 per roll, which means Alex has the advantage.

(b) The probability of rolling a 2 or 4 on a fair die is 2/6 or 1/3.  The probability of this happening five times is:

P = (1/3)⁵

P = 1/243

P ≈ 0.41%

There is approximately a 0.4% probability that a fair die will roll a 2 or 4 five times.

(c) The confidence interval for a proportion is:

CI = p ± ME

ME = CV × SE

The margin of error is the critical value times the standard error.

The critical value for 95% confidence is z = 1.960.

The standard error for a proportion is:

SE = √(pq/n)

Given p = 1/6, q = 5/6, and n = 100:

SE = √((1/6) (5/6) / 100)

SE = 0.037

So the confidence interval is:

CI = 1/6 ± (1.960) (0.037)

CI = 0.167 ± 0.073

0.094 < p < 0.240

Since the observed proportion of 0.08 is outside of this interval, we can conclude with 95% confidence that the die is not fair.

(d) Under the current game rules and die probabilities, the expected value is:

E = (5.00)(0.08) + (1.00)(0.33) + (0)(0.59) + (-1.50)(1)

E = -0.77

To make the game fairer, but to still give Alex the advantage so she can make money for her fundraiser, we need to change the rules of the game so that the expected value is less negative.

One simple way to do this is to pay players $2.00 if they roll a 2.

Now the expected value is:

E = (5.00)(0.08) + (1.00)(0.33) + (2.00)(0.29) + (0)(0.30) + (-1.50)(1)

E = -0.19

Now instead of expecting to lose on average $0.77 per roll, players can expect to lose on average $0.19 per roll.  This means they have a better chance of winning money, but Alex still has the advantage.

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3 years ago
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Step-by-step explanation:

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3 years ago
A rectangle is twice as long as it is wide. it's width is 5 1/2 cm. find the area of the rectangle.
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  <span>A rectangle is twice as long as it is wide. it's width is 5 1/2 cm. find the area of the rectangle.</span>   
 
answer: 60 1/2 cm.
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