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Ber [7]
3 years ago
10

Circle O has a circumference of 36pi cm

Mathematics
1 answer:
iogann1982 [59]3 years ago
8 0

Circumference = 2 pi r , so

36 pi = 2 pi r

r = 36 pi / 2 pi

= 18 cm  answer

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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
Use the differential equation given by dy/dx=xy/3, y&gt;0<br><br> complete the table of values
melisa1 [442]
The \dfrac{\mathrm dy}{\mathrm dx} row is filled by just plugging in the corresponding values of x and y into the ODE.

For example, when x=-1 and y=1, you have

\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{xy}3\implies\dfrac{\mathrm dy}{\mathrm dx}\bigg|_{x=-1,y=1}=\dfrac{(-1)(1)}3=-\dfrac13

and so on.
6 0
3 years ago
Sandy is helping her uncle at this coffee shop. She observes that, when ordering coffee, 13 of customers select chocolate flavor
valkas [14]
The answer is 2/5 :)

Have A Good Day
 
Please stay in school

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Love you dudes <3
6 0
3 years ago
Read 2 more answers
Juan invest $3700 in a simple interest account at a rate of 4% for 15 years
OleMash [197]

<em><u>Question:</u></em>

Juan Invest $3700 In A Simple Interest Account At A Rate Of 4% For 15 Years. How Much Money Will Be In The Account After 15 Years?

<em><u>Answer:</u></em>

There will be $ 5920 in account after 15 years

<em><u>Solution:</u></em>

<em><u>The simple interest is given by formula:</u></em>

S.I = \frac{p \times n \times r }{100}

Where,

p is the principal

n is number of years

r is rate of interest

From given,

p = 3700

r = 4 %

t = 15 years

Therefore,

S.I = \frac{3700 \times 4 \times 15 }{100}\\\\S.I = 37 \times 4 \times 15\\\\S.I = 2220

<em><u>How Much Money Will Be In The Account After 15 Years?</u></em>

Total money = principal + simple interest

Total money = 3700 + 2220

Total money = 5920

Thus there will be $ 5920 in account after 15 years

8 0
3 years ago
Is 5/6 close to 1, 0, or 1/2. Explain
Brums [2.3K]
5/6 is closest to 1 because it it 1/6 away from 1 and is 5/6 away from 0 and is 2/6 away from 1/2 (referring 1/2 as 3/6) Hope this helps!
5 0
3 years ago
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