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Vinvika [58]
3 years ago
10

Which ratio is greater? 4:3 or 7:9. (Show necessary steps and calculations for your answer)

Mathematics
2 answers:
scoundrel [369]3 years ago
8 0

Answer:

4 : 3 > 7 : 9

Step-by-step explanation:

In order to compare two ratios or fractions, we make their denominators equal and then equate their numerators.

4 : 3 =  \frac{4}{3}  =  \frac{4 \times 3}{3 \times 3}  =  \frac{12}{9}  \\  \\ 7 : 9 =  \frac{7}{9} \\  \\  \because \: 12 > 7 \\  \\  \therefore \:  \frac{4}{3} > \frac{7}{9} \\  \\  \implies \: 4 : 3  > 7 : 9

stiks02 [169]3 years ago
7 0
4:3

= 4/3

= 1.333333...


7:9

= 7/9

= 0.777777...



4:3 is greater than 7:9
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A programmer plans to develop a new software system. In planning for the operating system that he will​ use, he needs to estimat
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a) n = 9604

b) n = 381

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

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The margin of error is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

90% confidence level

So \alpha = 0.1, z is the value of Z that has a pvalue of 1 - \frac{0.1}{2} = 0.95, so Z = 1.645.

a. Assume that nothing is known about the percentage of computers with new operating systems. n = ?

When we do not know the proportion, we use \pi = 0.5, which is when we are going to need the largest sample size.

The sample size is n when M = 0.01.

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.01 = 1.96\sqrt{\frac{0.5*0.5}{n}}

0.01\sqrt{n} = 1.96*0.5

\sqrt{n} = \frac{1.96*0.5}{0.01}

(\sqrt{n})^{2} = (\frac{1.96*0.5}{0.01})^{2}

n = 9604

b. Assume that a recent survey suggests that 99% of computers use a new operating system. n = ?

Now we have that \pi = 0.99. So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.01 = 1.96\sqrt{\frac{0.99*0.01}{n}}

0.01\sqrt{n} = 1.96*\sqrt{0.99*0.01}

\sqrt{n} = \frac{1.96*\sqrt{0.99*0.01}}{0.01}

(\sqrt{n})^{2} = (\frac{1.96*\sqrt{0.99*0.01}}{0.01})^{2}

n = 380.3

Rouding up

n = 381

7 0
3 years ago
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