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Irina18 [472]
3 years ago
10

Insert five numbers between 1/27 and 27 to form a geometric sequence. there are 2 answers

Mathematics
1 answer:
sattari [20]3 years ago
6 0

Answer:

1/27, 1/9, 1/3, 1, 3, 9, 27

27, 9, 3, 1, 1/3, 1/9, 1/27

Step-by-step explanation:

The nth term of a geometric sequence is:

aₙ = a₁ rⁿ⁻¹

If 1/27 is the first term, and 27 is the 7th term, then:

27 = 1/27 r⁷⁻¹

27 = 1/27 r⁶

27² = r⁶

27 = r³

r = 3

This sequence is 1/27, 1/9, 1/3, 1, 3, 9, 27.

On the other hand, if 27 is the first term, and 1/27 is the 7th term, then:

1/27 = 27 r⁷⁻¹

1/27 = 27 r⁶

1/27² = r⁶

1/27 = r³

r = 1/3

This sequence is 27, 9, 3, 1, 1/3, 1/9, 1/27.

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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
3 years ago
Please help!
mariarad [96]

Answer: 1,045 passengers

Step-by-step explanation:

This question involves multiple steps. Let's first try to figure the number of children on the cruise.

The ratio of girls to the total number of children was 2:5. There are 198 boys.

This information tells me that for every 5 children, there's 2 girls and 3 boys.

Based off of this information, we can divide the total number of boys by 3 in order to find the number of children.

198÷3=66

Let's multiply 66 by 5 since that's the number of groupings based off the ratio.

66×5=330

Let's check the number of children. Since the ratio of girls to total children is 2:5 and we already confirmed there's 198 boys, there should be 132 girls. We can turn this ratio into a fraction where 2/5 of the children are girls. we can confirm this by multiply 330 by 2/5 (0.4) and getting 132.

There are 330 children on the cruise.

The ratio of the number of adults to the number of children was 13:6.

For every 6 children, there were 13 adults. Let's divide the number of children by 6 in order to find the number of groupings.

330÷6=55

Let's now multiply the groupings by 13 to find the number of adults.

55×13=715

So there should be 715 adults and 330 children on the cruise.

715+330=1,045

5 0
3 years ago
What is 4,726,000 rounded to the nearest million?
just olya [345]

Answer:

5,000,000

Step-by-step explanation:


6 0
3 years ago
Briainliest Simplify 15√90/√125<br> options<br> 9√2<br> 18√5<br> 18√2/5<br> 27√2/5
nekit [7.7K]

Answer:

9√2

Step-by-step explanation:

simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

Exact form:9√2

Decimal form: 12.72792206

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3 years ago
E = ( m V2)/2 rewrite this equation to solve for v<br><br><br><br> HELPP!!!!!
Vaselesa [24]

Answer: V 3

Step-by-step explanation:

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