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Svetllana [295]
2 years ago
14

What is the next term of the geometric sequence?

Mathematics
1 answer:
Basile [38]2 years ago
8 0

Answer:

The next term of the given geometric sequence is -12.

Step-by-step explanation:

Given that,

A geometric sequence, \dfrac{4}{9},\dfrac{-4}{3},4

To find,

The next term of the geometric sequence.

Solution,

We have,

First term, a=\dfrac{4}{9}

Common ratio,

r=\dfrac{-\dfrac{4}{3}}{\dfrac{4}{9}}\\\\r=-3

The next term of the sequence is :

T_4=ar^{n-1}\\\\=\dfrac{4}{9}\times (-3)^3\\\\T_4=-12

So, the next term of the given geometric sequence is -12.

Reference,

brainly.com/question/13008517

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Answer:

Correct options is (A).

Step-by-step explanation:

A (1 - <em>α</em>)% confidence interval can be constructed to determine whether there is any difference between the average GPA of seniors and the average GPA of sophomores.

The hypothesis can be defined as:

<em>H₀</em>: There is no difference between the average GPA of seniors and the average GPA of sophomores, i.e. <em>μ</em>₁ - <em>μ</em>₂ = 0.

<em>Hₐ</em>: There is a difference between the average GPA of seniors and the average GPA of sophomores, i.e. <em>μ</em>₁ - <em>μ</em>₂ ≠ 0.

The (1 - <em>α</em>)% confidence interval for the difference between two means is:

CI=(\bar x_{1}-\bar x_{1})\pm z_{\alpha /2}\times SE

Decision rule:

If the confidence interval contains the mull value, i.e. 0, then the null hypothesis will be failed to be rejected and vice-versa.

The 95% confidence interval for the difference between the true average GPAs (seniors - sophomores) is (0.53, 1.61).

The 95% confidence interval dos not contains 0. Thus, the null hypothesis will be rejected.

Conclusion:

There is a significant difference between the average GPA of seniors and the average GPA of sophomores.

The 95% confidence interval for the difference between the true average GPAs (0.53, 1.61), implies that there is a 95% confidence that the average GPA of seniors is greater than the average GPA of sophomores.

Thus, the correct options is (A).

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