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2 years ago

What is log x + log y - 2 log z written as a single logarithm?

Mathematics

1 answer:

Mademuasel [1]2 years ago

3 0

Answer:

D) log (xy/z^2)

Step-by-step explanation:

The given expression is log x + log y - 2 log z

Here we use log rules to simplify this.

Product rule: log x + log y = log (xy)

Quotient rule : log x - log y = log(x/y)

Power rule: log(x^y) = y.log(x)

Using the product rule

log x + log y - 2 log z

= log(xy) - 2 log z

Use the power rule now.

= log(xy) - log z^2

Now we have to use the Quotient rule and simplify.

= log $\frac{xy}{z^{2} }$

Answer: D) log (xy/z^2)

Thank you.

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2 years ago

Type the correct answer in each box. Use numerals instead of words.

Alex_Xolod [135]

Answer:

Step-by-step explanation:

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3 years ago

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Answer:

a. We reject the null hypothesis at the significance level of 0.05

b. The p-value is zero for practical applications

c. (-0.0225, -0.0375)

Step-by-step explanation:

Let the bottles from machine 1 be the first population and the bottles from machine 2 be the second population.

Then we have $n_{1} = 25$ , $\bar{x}_{1} = 2.04$ , $\sigma_{1} = 0.010$ and $n_{2} = 20$ , $\bar{x}_{2} = 2.07$ , $\sigma_{2} = 0.015$ . The pooled estimate is given by

$\sigma_{p}^{2} = \frac{(n_{1}-1)\sigma_{1}^{2}+(n_{2}-1)\sigma_{2}^{2}}{n_{1}+n_{2}-2} = \frac{(25-1)(0.010)^{2}+(20-1)(0.015)^{2}}{25+20-2} = 0.0001552$

a. We want to test $H_{0}: \mu_{1}-\mu_{2} = 0$ vs $H_{1}: \mu_{1}-\mu_{2} \neq 0$ (two-tailed alternative).

The test statistic is $T = \frac{\bar{x}_{1} - \bar{x}_{2}-0}{S_{p}\sqrt{1/n_{1}+1/n_{2}}}$ and the observed value is $t_{0} = \frac{2.04 - 2.07}{(0.01246)(0.3)} = -8.0257$ . T has a Student's t distribution with 20 + 25 - 2 = 43 df.

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$-0.03\pm t_{0.025}0.012459\sqrt{\frac{1}{25}+\frac{1}{20}}$

where $t_{0.025}$ is the 2.5th quantile of the t distribution with (25+20-2) = 43 degrees of freedom. So

$-0.03\pm(2.0167)(0.012459)(0.3)$ , i.e.,

(-0.0225, -0.0375)

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