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RoseWind [281]
3 years ago
10

Evaluate the geometric series. Please help me!!

Mathematics
1 answer:
o-na [289]3 years ago
6 0

Answer:

- 85

Step-by-step explanation:

The n th term of a geometric series is

a_{n} = a(r)^{n-1}

where a is the first term and r the common ratio

1(-2)^{n-1} ← is the n th term of a geometric series

with a = 1 and r = - 2

The sum to n terms of a geometric series is

S_{n} = \frac{a(r^{n}-1) }{r-1}

    = \frac{1((-2)^{8}-1 }{-2-1}

    = \frac{256-1}{-3}

    = \frac{255}{-3}

    = - 85

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a) F_{0.05,4,7}=0.16

b) F_{0.05,7,4}=0.24

c) F_{0.95,4,7}=4.12

d) F_{0.95,7,4}=6.09

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Step-by-step explanation:

(a) F0.05, 4, 7 (Round your answer to two decimal places.)

For this case we need a valueof the F distribution with 4 degrees of freedom for the numerator and 7 for the denominator that accumulates 0.05 of the area on the left tail. We can use the following excel code: "=F.INV(0.05,4,7)". And we got:

F_{0.05,4,7}=0.16

(b) F0.05, 7, 4 (Round your answer to two decimal places.)

For this case we need a valueof the F distribution with 7 degrees of freedom for the numerator and 4 for the denominator that accumulates 0.05 of the area on the left tail. We can use the following excel code: "=F.INV(0.05,7,4)". And we got:

F_{0.05,7,4}=0.24

(c) F0.95, 4, 7 (Round your answer to three decimal places.)

For this case we need a valueof the F distribution with 4 degrees of freedom for the numerator and 7 for the denominator that accumulates 0.95 of the area on the left tail. We can use the following excel code: "=F.INV(0.95,4,7)". And we got:

F_{0.95,4,7}=4.12

(d) F0.95, 7, 4 (Round your answer to three decimal places.)

For this case we need a valueof the F distribution with 7 degrees of freedom for the numerator and 4 for the denominator that accumulates 0.95 of the area on the left tail. We can use the following excel code: "=F.INV(0.95,7,4)". And we got:

F_{0.95,7,4}=6.09

(e) the 99th percentile of the F distribution with v1 = 8, v2 = 12 (Round your answer to two decimal places.)

So for this case we need a value on the F distribution with 8 degrees of freedom for the numerator and 12 for the denominator that accumulates 0.99 of the area on the left tail. And we can use the following excel code: "=F.INV(0.99,8,12)". And we got:

F_{0.99,8,12}=4.50

(f) the 1st percentile of the F distribution with v1 = 8, v2 = 12 (Round your answer to three decimal places.)

So for this case we need a value on the F distribution with 8 degrees of freedom for the numerator and 12 for the denominator that accumulates 0.01 of the area on the left tail. And we can use the following excel code: "=F.INV(0.01,8,12)". And we got:

F_{0.01,8,12}=0.18

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For this case we want to find the probability that the F distribution with 5 degrees on the numerator and 4 on the denominator would be less or equal than 6.26. We can use the following excel code: "=F.DIST(6.26,5,4,TRUE)". And we got

P(F_{5,4} \leq 6.26)=0.95

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P(0.177 \leq F_{10,5} \leq 4.74)=0.94

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