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3 years ago

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A rectangular one-story house covers an area of 3,700 square feet. The ceilings are 8 feet high. The owners add a second floor t

o the house. The second floor is 50 feet long and 30 feet wide with ceilings that are 9 feet high. What is the total volume of the interior of the house?

2 answers:

JulsSmile [24]3 years ago

7 0

I’m sorry i don’t know the answer i need to ask more questions though

o-na [289]3 years ago

6 0

This is a thought question

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Leakage from underground gasoline tanks at service stations can damage the environment. It is estimated that 25% of these tanks

Gnesinka [82]

Answer:

a) 3.75

b) 23.61% probability that fewer than 3 tanks will be found to be leaking

c) 0% the probability that at least 600 of these tanks are leaking

Step-by-step explanation:

For each tank there are only two possible outcomes. EIther they leak, or they do not. The probability of a tank leaking is independent of other tanks. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

To solve question c), i am going to approximate the binomial distribution to the normal.

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

It is estimated that 25% of these tanks leak.

This means that $p = 0.25$

15 tanks chosen at random

This means that $n = 15$

a.What is the expected number of leaking tanks in such samples of 15?

$E(X) = np = 15*0.25 = 3.75$

b.What is the probability that fewer than 3 tanks will be found to be leaking?

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{15,0}.(0.25)^{0}.(0.75)^{15} = 0.0134$

$P(X = 1) = C_{15,1}.(0.25)^{1}.(0.75)^{14} = 0.0668$

$P(X = 2) = C_{15,2}.(0.25)^{2}.(0.75)^{13} = 0.1559$

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0134 + 0.0668 + 0.1559 = 0.2361$

23.61% probability that fewer than 3 tanks will be found to be leaking

c.Now you do a larger study, examining a random sample of 2000 tanks nationally. What is the probability that at least 600 of these tanks are leaking?

Now we have n = 2000. So

$\mu = E(X) = np = 2000*0.25 = 500$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{2000*0.25*0.75} = 19.36$

This probability is 1 subtracted by the pvalue of Z when X = 600. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{600 - 500}{19.36}$

$Z = 5.16$

$Z = 5.16$ has a pvalue of 0.

0% the probability that at least 600 of these tanks are leaking

4 0

3 years ago

Cara is building a new dog house the roof is 10 4/5 feet long express this length as a decimal show work

scZoUnD [109]

Answer:

10.8 feet

Step-by-step explanation:

Multiply 4/5 by 2 on the top and bottom. Then you'll get 8/10 which is 0.8 as a decimal

7 0

2 years ago

Read 2 more answers

Is y=12(17/10)^x exponential growth or exponential decay

Keith_Richards [23]

Its an exponential growth

7 0

3 years ago

Find the value of the expression<br><br> 9.18 · z<br><br> for z = 2.

loris [4]

Answer: 18.36

Step-by-step explanation:

Replace "z" with "2":

$9.18 \cdot 2 = \boxed{18.36}$ .

8 0

2 years ago

Use a Venn diagram to answer the question. A survey of 180 families showed that 67 had a dog; 52 had a cat; 22 had a dog and a

Mice21 [21]

Answer:

There are 13 families had a parakeet only

Step-by-step explanation:

* Lets explain the problem

- There are 180 families

- 67 families had a dog

- 52 families had a cat

- 22 families had a dog and a cat

- 70 had neither a cat nor a dog, and in addition did not have a

parakeet

- 4 had a cat, a dog, and a parakeet (4 is a part of 22 and 22 is a part

of 67 and 520

* We will explain the Venn-diagram

- A rectangle represent the total of the families

- Three intersected circles:

C represented the cat

D represented the dog

P represented the parakeet

- The common part of the three circle had 4 families

- The common part between the circle of the cat and the circle of the

dog only had 22 - 4 = 18 families

- The common part between the circle of the dog and the circle of the

parakeet only had a families

- The common part between the circle of the cat and the circle of the

parakeet only had b families

- The non-intersected part of the circle of the dog had 67 - 22 - a =

45 - a families

had dogs only

- The non-intersected part of the circle of the cat had 52 - 22 - b =

30 - b families

had cats only

- The non-intersected part of the circle of the parakeet had c families

had parakeets only

- The part out side the circles and inside the triangle has 70 families

- Look to the attached graph for more under stand

∵ The total of the families is 180

∴ The sum of all steps above is 180

∴ 45 - a + 18 + 4 + 30 - b + b + c + a + 70 = 180 ⇒ simplify

- (-a) will cancel (a) and (-b) will cancel (b)

∴ (45 + 18 + 4 + 30 + 70) + (-a + a) + (-b + b) + c = 180

∴ 167 + c = 180 ⇒ subtract 167 from both sides

∴ c = 180 - 167 = 13 families

* There are 13 families had a parakeet only

5 0

3 years ago