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Georgia [21]
3 years ago
8

Solve 3^n=5. How to solve n?

Mathematics
1 answer:
Ne4ueva [31]3 years ago
8 0

Answer:

\huge\boxed{n=\log_35}

Step-by-step explanation:

3^n=5\Rightarrow\log_33^n=\log_35\qquad\text{use}\ \log_ab^n=n\log_ab\\\\n\log_33=\log_35\qquad\text{use}\ \log_aa=1\\\\\boxed{n=\log_35}

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Obtain or compute the following quantities.
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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

e) F_{0.99,8,12}=4.50

f) F_{0.01,8,12}=0.18

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

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

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

(g) P(F ≤ 6.26) for v1 = 5, v2 = 4 (Round your answer to two decimal places.)

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

(h) P(0.177 ≤ F ≤ 4.74) for v1 = 10, v2 = 5 (Round your answer to two decimal places.)

For this case we want to find the probability that the F distribution with 10 degrees on the numerator and 5 on the denominator would be between 0.177 and 4.74. We can use the following excel code: "=F.DIST(4.74,10,5,TRUE)-F.DIST(0.177,10,5,TRUE)". And we got

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

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