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3 years ago

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Ellis is painting wooden fenceposts before putting them in his yard. They are each 6 feet tall and have a diameter of 1 foot. Th

ere are 12 fenceposts in all. How much paint will Ellis need to paint all the surfaces of the 12 fenceposts? Use 3.14 for π, and round your answer to the nearest hundredth. Provide an explanation and proof for your answer to receive full credit.

1 answer:

katen-ka-za [31]3 years ago

4 0

Answer:

244.92 ft^2

Step-by-step explanation:

Find out the surface area of 1 fence post.

It has 2 circular parts (a bottom and a top)

r = d / 2

r = 1 / 2

r = 0.5 feet.

Area = 3.14 * 0.5^2

area = 3.14 * 0.25

Area = 0.785

Each post has 2 such shapes. 2 * 0.785 = 1.57

There are 12 posts with areas of 1.57 on the bottom and top = 18.84 ft^2

Find the area of the long part of the post

h = 6 feet

circumference = 2* pi * r

circumference = 2* 3.14 * .5

circumference = 3.14

The height is 6 feet.

The area of the body of the pole 6 *circumference = 6 * 3.14 = 18.84 ft^2

There are 12 poles.

Total area = 12 *18.84 ft^2 = 226.08

Total area = 12 bodies + 24 ends

Total area = 226.08 + 18.84

Total area = 244.92

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ololo11 [35]

Answer:

a) $p = (3/4)^5 *(1/4) =0.0593$

b) $P(X=6) = (6C6) (0.25)^6 (1-0.25)^{6-6}= 0.000244$

c) $P(X \geq 1)$

And we can use the complement rule like this:

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

$P(X=0) = (6C0) (0.25)^0 (1-0.25)^{6-0}= 0.17798$

And replacing we have:

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

Step-by-step explanation:

Previous concepts

A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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

The complement rule is a theorem that provides a connection between the probability of an event and the probability of the complement of the event. Lat A the event of interest and A' the complement. The rule is defined by: $P(A)+P(A') =1$

We can model the number of correct questions answered with a binomial distribution $X \sim Binom(n = 6, p = 1/4=0.25)$

Solution to the problem

Assuming the following questions:

a) the first question she gets right is the 6th question?

For this case we want the first 5 questions incorrect and the last one correct, assuming independence we have:

$p = (3/4)^5 *(1/4) =0.0593$

(b) she gets all of the questions right?

For this case we want all the questions right so then we want this:

$P(X=6) = (6C6) (0.25)^6 (1-0.25)^{6-6}= 0.000244$

(c) she gets at least one question right?

For this case we want this probability:

$P(X \geq 1)$

And we can use the complement rule like this:

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

$P(X=0) = (6C0) (0.25)^0 (1-0.25)^{6-0}= 0.17798$

And replacing we have:

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

7 0

3 years ago

Find the quotient of <br><br> -85^2-27n+76 / -17n-19

bagirrra123 [75]

<u><em>Answer:</em></u>
5n-4

<u><em>Explanation:</em></u>
<u>The given expression is:</u>
$\frac{-85n^2-27n+76}{-17n-19}$

<u>1- Take the negative as a common factor from both the numerator and the denominator. This will give us:</u>
$\frac{-(85n^2+27n-76)}{-(17n+19)}$

<u>2- Cancel out the negative sign (common factor) from the numerator and denominator. This will give us:</u>
$\frac{(85n^2+27n-76)}{(17n+19)}$

<u>3- Factor the numerator. This wil give:</u>
$\frac{(5n-4)(17n+19)}{(17n+19)}$

<u>4- Finally, cancel out the (17n+19) which common in both numerator and denominator. This will give us the final expression:</u>
5n-4

Hope this helps :)

6 0

3 years ago

You are asked to do a study of shelters for abused and battered women to determine the necessary capacity in your city to provid

ohaa [14]

Answer:

Using the normal probability distribution, with a capacity of 350, it is enough for all abused on 90.82% of nights.

274 shelters will be needed.

Step-by-step explanation:

Problems of normally distributed samples are 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.

In this problem, we have that:

$\mu = 250, \sigma = 75$

If the city’s shelters have a capacity of 350, will that be enough places for abused women on 95% of all nights?

What is the percentile of 350?

This is the pvalue of Z when X = 350.

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

$Z = \frac{250 - 150}{75}$

$Z = 1.33$

$Z = 1.33$ has a pvalue of 0.9082.

Using the normal probability distribution, with a capacity of 350, it is enough for all abused on 90.82% of nights.

If not, what number of shelter openings will be needed?

The 95th percentile, which is X when Z = 1.645. So

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

$1.645 = \frac{X - 150}{75}$

$X - 150 = 1.645*75$

$X = 274$

274 shelters will be needed.

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Answer:

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