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Lady bird [3.3K]

3 years ago

8

Which value is equivalent to ...

1 answer:

Lemur [1.5K]3 years ago

8 0

The given expression is equivalent to 100/9

Step-by-step explanation:

Given expression is:

$(\frac{7.5.2}{7.3})^2 * (\frac{5^0}{2^{-3}})^3*2^{-9}$

First of all we will apply the exponents in the fraction

So the new fractions will be:

$=\frac{7^2.5^2.2^2}{7^2.3^2} * \frac{5^{(0*3)}}{2^{(-3*3)}}*2^{-9}\\=\frac{5^2.2^2}{3^2} * \frac{5^0}{2^{-9}}*2^{-9}\\=\frac{25.4}{9} * 1\\=\frac{100}{9}$

Hence,

The given expression is equivalent to 100/9

Keywords: Exponents, fractions

Learn more about exponents at:

#LearnwithBrainly

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Solution :

$n_1=178, \hat p_1 = 0.48$

$n_2=427, \hat p_2 = 0.38$

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a). Yes, the sample sizes are large enough to use the large sample confidence interval so as to estimate the difference in the population proportions.

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Where the $\text{subscript indicates}$ the age $18-29$ group and the 2 - subscript indicates the age $50-64$ group.

Since $n_1 \hat p_1 = 85.44$

$n_1(1- \hat p_1)=92.56, \ \ n_2\hat p_2 = 162.26, \ n_2(1-\hat p_2) = 264.74$

are all at least 10, the sample sizes are large enough to use the large sample confidence interval.

$P_0=\frac{x_1+x_2}{n_1+n_2}$

$=\frac{85.44+162.26}{178+427}$

= 0.409421

$P_0 = 0.4074$

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= 0.5906

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$=\left( \hat p_1- \hat p_2 \pm \frac{z \alpha}{2} \times \sqrt{P_0Q_0\left(\frac{1}{n_1}+\frac{1}{n_2}}\right) \right)$

$=\left( 0.48-0.38 \pm \frac{z \times 0.10}{2} \times \sqrt{0.4094 \times 0.5906\left(\frac{1}{178}+\frac{1}{427}}\right) \right)$

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