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3 years ago

(a+b+c)(d+e+f)(a+b+c)(d+e+f)(a+ b+ c) ( d+e+ f)

Mathematics

1 answer:

8090 [49]3 years ago

8 0

Hi the expanded form is

$d^3 a^3 + e^3 a^3 + f^3 a^3 + 3 d e^2 a^3 + 3 d f^2 a^3 + 3 e f^2 a^3 + 3 d^2 e a^3 + 3 d^2 f a^3 + 3 e^2 f a^3 + 6 d e f a^3 \\+ 3 b d^3 a^2 + 3 c d^3 a^2 \\+ 3 b e^3 a^2 + 3 c e^3 a^2 + 3 b f^3 a^2 \\+ 3 c f^3 a^2 + 9 b d e^2 a^2 + 9 c d e^2 a^2 + 9 b d f^2 a^2 + 9 c d f^2 a^2\\ + 9 b e f^2 a^2 + 9 c e f^2 a^2 + 9 b d^2 e a^2 + 9 c d^2 e a^2 + 9 b d^2 f a^2 + 9 c d^2 f a^2 \\+ 9 b e^2 f a^2 + 9 c e^2 f a^2 + 18 b d e f a^2$

$+ 18 c d e f a^2 + 3 b^2 d^3 a + 3 c^2 d^3 a \\+ 6 b c d^3 a + 3 b^2 e^3 a + 3 c^2 e^3 a + 6 b c e^3 a + 3 b^2 f^3 a \\+ 3 c^2 f^3 a + 6 b c f^3 a + 9 b^2 d e^2 a \\+ 9 c^2 d e^2 a + 18 b c d e^2 a + 9 b^2 d f^2 a\\ + 9 c^2 d f^2 a + 18 b c d f^2 a + 9 b^2 e f^2 a + 9 c^2 e f^2 a + 18 b c e f^2 a + 9 b^2 d^2 e a \\+ 9 c^2 d^2 e a + 18 b c d^2 e a + 9 b^2 d^2 f a + 9 c^2 d^2 f a + 18 b c d^2 f a \\+ 9 b^2 e^2 f a + 9 c^2 e^2 f a + 18 b c e^2 f a$

$+ 18 b^2 d e f a + 18 c^2 d e f a + 36 b c d e f a \\+ b^3 d^3 + c^3 d^3 + 3 b c^2 d^3 + 3 b^2 c d^3 + b^3 e^3 + c^3 e^3 \\+ 3 b c^2 e^3 + 3 b^2 c e^3 + b^3 f^3 + c^3 f^3 + 3 b c^2 f^3 + 3 b^2 c f^3 + 3 b^3 d e^2 \\+ 3 c^3 d e^2 + 9 b c^2 d e^2 + 9 b^2 c d e^2 + 3 b^3 d f^2 + 3 c^3 d f^2 + 9 b c^2 d f^2 \\+ 9 b^2 c d f^2 + 3 b^3 e f^2 + 3 c^3 e f^2$

$+ 9 b c^2 e f^2 + 9 b^2 c e f^2 + 3 b^3 d^2 e \\+ 3 c^3 d^2 e + 9 b c^2 d^2 e + 9 b^2 c d^2 e + 3 b^3 d^2 f + 3 c^3 d^2 f \\+ 9 b c^2 d^2 f + 9 b^2 c d^2 f + 3 b^3 e^2 f + 3 c^3 e^2 f + 9 b c^2 e^2 f \\+ 9 b^2 c e^2 f + 6 b^3 d e f + 6 c^3 d e f + 18 b c^2 d e f + 18 b^2 c d e f$

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Here the variable total is declared and initialized with a value zero

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An automobile manufacturer has given its jeep a 50.5 miles/gallon (MPG) rating. An independent testing firm has been contracted

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Answer:

$z=\frac{50.7-50.5}{\frac{1.3}{\sqrt{280}}}=2.574$

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Step-by-step explanation:

Data given and notation

$\bar X=50.7$ represent the sample mean

$\sigma=1.3$ represent the population standard deviation for the sample

$n=280$ sample size

$\mu_o =50.5$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

Sytem of hypotheses.

We need to conduct a hypothesis in order to check if the true mean is different from 50.5, the system of hypothesis would be:

Null hypothesis: $\mu = 50.5$

Alternative hypothesis: $\mu \neq 50.5$

The statistic is given by:

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Replacing we got:

$z=\frac{50.7-50.5}{\frac{1.3}{\sqrt{280}}}=2.574$

P-value

Since is a two tailed test the p value would be:

$p_v =2*P(Z>2.574)=0.010$

Conclusion

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is different from 50.5 mpg

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