Mathematics: A. show that the ratios 10/20 and 30/60 form a proportion by finding a common multiplier. b. show that the ratios in part (a) are equal by writing them in simplest form.

A. show that the ratios 10/20 and 30/60 form a proportion

babygail0818

06.01.2022

$\text{(A) Hence, The ratio }\frac{10}{20}\text{ form a proportion by common multiplier 3 to get }\frac{30}{60}$

$\text{(B) Hence, Both ratio are equal to }\frac{1}{2}\text{ in simplest form. }$

Step-by-step explanation:

(A) We need to show both fraction of same proportion.

Ratio 1: $\frac{10}{20}$

If we multiply by 3 at numerator and denominator

$\RIghtarrow \frac{10\times 3}{20\times 3}$

$\RIghtarrow \frac{30}{60}$

$\RIghtarrow \frac{30}{60} \text{ is equivalent ratio of second one }\frec{30}{60}$

$\text{Hence, The ratio }\frac{10}{20}\text{ form a proportion by common multiplier 3 to get }\frac{30}{60}$

(B) Now we simplify both ration into simplest form

$\Rightarrow \frac{10\div 10}{20\div 10}=\frac{1}{2}$

$\Rightarrow \frac{30\div 30}{60\div 30}=\frac{1}{2}$

$\Rightarrow \frac{1}{2}=\frac{1}{2}$

$\text{Hence, Both ratio are equal to }\frac{1}{2}\text{ in simplest form. }$

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alexandrarosete7

06.05.2023

0.5705

Step-by-step explanation:

Margin of error is expressed as M.E = $z * \sqrt{\frac{\sigma}{n} }$ where;

z is the z score at 95% confidence

$\sigma$ is the standard deviation

n is the sample size

Given n = 349, $\sigma = 42$ and z score at 95% confidence = 1.645

Substituting this values into the formula above we will have;

M.E = $1.645*\sqrt{\frac{42}{349} }$

$M.E = 1.645*\sqrt{0.1203} \\\\M.E = 1.645*0.3468\\\\M.E = 0.5705 (to\ four\ dp)$

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