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Delvig [45]
3 years ago
14

Please answer this question​

Mathematics
1 answer:
Free_Kalibri [48]3 years ago
5 0

Answer:

3

Step-by-step explanation:

log(3x^{3}) - log(x^{2}) = log(\frac{3x^{3}}{x^{2}})\\log(27) - log(x) = log(\frac{27}{x} )\\

therefore,

\frac{3x^{3} }{x^{2} } = \frac{27}{x} \\3x=\frac{27}{x} \\3x^{2} =27\\x= +3\\x=-3

however, since logarithms cannot have negative arguments, x can only be +3

i.e. log(-3) is impossible, and will return MATH ERROR on a calculator.

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Answer:

We reject the Null and conclude that at α = 0.1, the is enough evidence to support th claim that miles per gallon has improved between 2017 and 2019

Step-by-step explanation:

This is a paired t test:

H0 : μx - μy = 0

H1 : μx - μy > 0

The test statistic :

dbar / (Sd/√n)

d = Xi - Yi

d = 2.4, 0.3, 1.7,3,-0.2, 1.1, -0.5, -3.2, 1.4, 2, 1.6, 2.2

dbar = Σd / n = 11.8 / 12 = 0.983

Sd = Σ(d - dbar)²/ (n - 1) = 1.685 (calculator)

Hence,

Test statistic = 0.983 / (1.685/√12)

Test statistic = 0.983 / 0.4864176

= 2.021

Using the test statistic score, we could obtain the Pvalue using the Pvalue FROM Tscore calculator :

Degree of freedom, df = n - 1 = 12 - 1 = 11

Pvalue(2.021, 11) = 0.03415

α = 0.1

Pvalue < α ; We reject the Null and conclude that at α = 0.1, the is enough evidence to support th claim that miles per gallon has improved between 2017 and 2019

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