Consider the sequence below

Mathematics

1 answer:

GalinKa [24]3 years ago

5 0

Answer: option D is the correct answer

Step-by-step explanation:

In the given sequence, the consecutive terms differ by a common difference.

The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + (n - 1)d

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = - 351

d = - 343 - - 351 = - 343 + 351

d = 8

Therefore, the explicit function which defines the sequence is

f(n) = - 351 + 8(n - 1)

f(n) = 8n - 8 - 351

f(n) = 8n - 359

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Answer:

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Step-by-step explanation:

Given two random variables X and Y, it is possible to calculate the covariance as Cov(X, Y) = E(XY)-E(X)E(Y). We have E(X)=5, E(Y)=6 and E(XY)=21. Therefore Cov(X,Y)=21-(5)(6)=21-30=-9. On the other hand, we know that the correlation of X and Y is the number defined by $Cov(X,Y)/\sqrt{Var(X)}\sqrt{Var(Y)}$ and because in this particular case we have V(X)=9 and V(Y)=10, we have $-9/\sqrt{9}\sqrt{10}$ = -0.9487. Therefore, we have a strong negative relationship between the variables.