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podryga [215]
3 years ago
12

Given a sphere with radius r, the formula 4pi r^2 gives

Mathematics
1 answer:
Shkiper50 [21]3 years ago
8 0

Answer:

Step-by-step explanation:

That's B:  the surface area.

The volume of the sphere is V = (4/3)πr³; A = 4πr² happens to be the derivative of V with respect to r.

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We learned in that about 69.7% of 18-20 year olds consumed alcoholic beverages in 2008. We now consider a random sample of fifty
maw [93]

Answer:

(1) The expected number of people who would have consumed alcoholic beverages is 34.9.

(2) The standard deviation of people who would have consumed alcoholic beverages is 10.56.

(3) It is surprising that there were 45 or more people who have consumed alcoholic beverages.

Step-by-step explanation:

Let <em>X</em> = number of adults between 18 to 20 years consumed alcoholic beverages in 2008.

The probability of the random variable <em>X</em> is, <em>p</em> = 0.697.

A random sample of <em>n</em> = 50 adults in the age group 18 - 20 years is selected.

An adult, in the age group 18 - 20 years, consuming alcohol is independent of the others.

The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 50 and <em>p</em> = 0.697.

The probability mass function of a Binomial random variable <em>X</em> is:

P(X=x)={50\choose x}0.697^{x}(1-0.697)^{50-x};\ x=0,1,2,3...

(1)

Compute the expected value of <em>X</em> as follows:

E(X)=np\\=50\times 0.697\\=34.85\\\approx34.9

Thus, the expected number of people who would have consumed alcoholic beverages is 34.9.

(2)

Compute the standard deviation of <em>X</em> as follows:

SD(X)=\sqrt{np(1-p)}=\sqrt{50\times 0.697\times (1-0.697)}=10.55955\approx10.56

Thus, the standard deviation of people who would have consumed alcoholic beverages is 10.56.

(3)

Compute the probability of <em>X</em> ≥ 45 as follows:

P (<em>X</em> ≥ 45) = P (X = 45) + P (X = 46) + ... + P (X = 50)

                =\sum\limits^{50}_{x=45} {50\choose x}0.697^{x}(1-0.697)^{50-x}\\=0.0005+0.0001+0.00002+0.000003+0+0\\=0.000623\\\approx0.0006

The probability that 45 or more have consumed alcoholic beverages is 0.0006.

An unusual or surprising event is an event that has a very low probability of success, i.e. <em>p</em> < 0.05.

The probability of 45 or more have consumed alcoholic beverages is 0.0006. This probability value is very small.

Thus, it is surprising that there were 45 or more people who have consumed alcoholic beverages.

6 0
2 years ago
What are the solutions of the equation x² = 49
olga55 [171]
To find x you do √49=x
5 0
3 years ago
Give a counterexample for the statement: 'All square roots are irrational numbers'. Explain your reasoning.
galben [10]
A counterexample for the statement 'All square roots are irrational numbers.' is the square root of 9.  This is because when simplified, the answer is 3.  

For a number to be irrational, it can't be expressed in fractional form.  However, 3 can be expressed in fractional form as 3/1.
5 0
3 years ago
I NEED HELP ASAP PLZZZZZZZZZZZZ ON ALLLLLLLLLLLL
r-ruslan [8.4K]

Answer:

ree

Step-by-step explanation:

4 0
3 years ago
Numbers divisible by 100 are divisible by 5.
Reptile [31]

The additional true statement that would need to be given in order to state the conclusion using the law of detachment is 49,700 is divisible by 100.

<h3 /><h3>What is law of detachment?</h3>

Law of detachment states that if a facts is true and its hypothesis is true, then its conclusion is true.

For instance,

Statement A: If there's an increase in Mr Charles salary.

Statement B: Mr Charles buys bicycle for his son.

This means Mr Charles buying bicycle for his son is true because of the increase in income.

Learn more about law of detachment:

brainly.com/question/13966470

#SPJ1

8 0
2 years ago
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