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Nostrana [21]
3 years ago
8

Use geometric mean to find the 7th term in a geometric sequence if the 6th term is 12 and the 8th term is 27

Mathematics
1 answer:
Darya [45]3 years ago
3 0

Answer:

18

Step-by-step explanation:

<em>First, use the equation for geometric mean; an=a1r^n-1</em>

*where is an is the number at an n term, r is the ratio and a1 is the first number of the sequence.*

12 = a1 r^5

27 = a1r^7

From the equations above,

a1 = 128/81

r = 3/2

Therefore, the 7th term is:

an = (128/81) (3/2)^6

an = 18

hope this helps :)

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The government of Preon (a small island nation) was voted in at the last election with 58% of the votes. That was 2 years ago, a
mel-nik [20]

Answer:

a) z=\frac{0.684 -0.58}{\sqrt{\frac{0.58(1-0.58)}{114}}}=2.250  

b) p_v =2*P(z>2.250)=0.0244  

If we compare the p value and the significance level given we see that p_v we have enough evidence to reject the null hypothesis at 5% of significance.

Step-by-step explanation:

Data given and notation

n=114 represent the random sample taken

\hat p=0.684 estimated proportion of people that their approval rating might have changed

p_o=0.58 is the value that we want to test

\alpha=0.05 represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

Hypothesis

We need to conduct a hypothesis in order to test the claim that true proportion of people that their approval rating might have changed is 0.58 or no.:  

Null hypothesis:p=0.58  

Alternative hypothesis:p \neq 0.58  

Part a

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.684 -0.58}{\sqrt{\frac{0.58(1-0.58)}{114}}}=2.250  

Part b: Statistical decision  

The significance level provided \alpha=0.05. The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

p_v =2*P(z>2.250)=0.0244  

If we compare the p value and the significance level given we see that p_v we have enough evidence to reject the null hypothesis at 5% of significance.

7 0
3 years ago
Simplify (x+2)(x+6) using grouping, and write the resulting expression in standard form
Vlad1618 [11]

Answer:

(x+8)

Step-by-step explanation:

8 0
3 years ago
4x + 5y = 12 and 3x + 4y = 9.25 . Solve for systems of equations
masha68 [24]

Answer:

y=1

x=7/4

Step-by-step explanation:

4x + 5y = 12

3x + 4y = 9.25

4x + 5y = 12

12x + 16y =37

-12x -15 y =-36

12x + 16y =37

y=1

x=7/4

8 0
3 years ago
Read 2 more answers
What is the slope of this line?
Lynna [10]

\frac{ - 2}{2}
8 0
3 years ago
In a group of equal number of men and women 10% men and 45% women are suffering from Malaria.What is probability a peraon select
Kaylis [27]

Answer:

The probability a person selected random is not suffering from Malaria  is 0.725.

Step-by-step explanation:

Denote the events as follows:

X = a person is suffering from Malaria

M = a man

W = a woman

The information provided is:

P (M) = P (W) = 0.50

P (X|M) = 0.10

P (X|W) = 0.45

Compute the probability a person selected random is suffering from Malaria as follows:

P(X)=P(X|M)P(M)+P(X|W)P(W)

         =(0.10\times 0.50)+(0.45\times 0.50)\\\\=0.05+0.225\\\\=0.275

Then the probability a person selected random is not suffering from Malaria  is:

P (X') = 1 - P (X)

         = 1 - 0.275

         = 0.725

4 0
3 years ago
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