If 3a=11b and b= 2c, find the ratio of a:b, a:b:c

Mathematics

1 answer:

pav-90 [236]2 years ago

5 0

Answer:

a:b = 11:3 and a:b:c = 11:3:2

Step-by-step explanation:

a:b is equal than write a/b. So a/b=11/3 it means a:b = 11:3

b:c is then b/c = 2

For a:b:c the ratio must be maintained. Ratio is equals reasons or divides. We already know a:b is 11:3. What about a:c?

3a=11b then a=11/3 b, b=2c then c=1/2 b hence a/c =22/3 if we pay attention this reason is 2*11/3 so a:b:c is 11:3:2

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Lady bird [3.3K]

Answer:

$10.08-1.64\frac{0.1}{\sqrt{6}}=10.013$

$10.08+1.64\frac{0.1}{\sqrt{6}}=10.147$

So on this case the 90% confidence interval would be given by (10.013;10.147)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma =0.1$ represent the population standard deviation

n represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=10.08$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=1.64$