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2 years ago

4 7/9 divided by 1 7/12

Mathematics

1 answer:

sesenic [268]2 years ago

6 0

Answer:

2 19/5

Step-by-step explanation:

4 7/9 ÷ 1 7/12

start by turning them into improper fraction by multiplying the denominator to the whole number and adding the product to the numerator , you will get :

42/9 ÷ 17/12

42/9 * 12/17 ( reciprocal )

42/3 * 4/17 (9 and 12 can be cut smaller because both are in 3's table)

= 172/51

turn this into mixed fraction by -

Divide the numerator by the denominator.

Write down the whole number answer

Then write down any remainder above the denominator

you will get = 2 19/5

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The 90% confidence interval would be given by (57.006;62.994)

Step-by-step explanation:

Previous concepts

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".

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".

$\bar X=60$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=10$ represent the population standard deviation

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Assuming the X follows a normal distribution

$X \sim N(\mu, \sigma=10)$

The sample mean $\bar X$ is distributed on this way:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

The confidence interval on this case is given by:

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

The next step would be find the value of $\z_{\alpha/2}$ , $\alpha=1-0.90=0.1$ , $\alpha/2 =0.05$ and $z_\alpha/2=1.64$

Using the normal standard table, excel or a calculator we see that:

$z_{\alpha/2}=1.64$

Since we have all the values we can replace:

$60 - 1.64\frac{10}{\sqrt{30}}=57.006$

$60 + 1.64\frac{10}{\sqrt{30}}=62.994$

So on this case the 90% confidence interval would be given by (57.006;62.994)

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2 years ago

What is the zero in the quadratic function f(x)= 9x^2-54x-19?

Alex17521 [72]

Answer:

6.33... and 0.333...

Step-by-step explanation:

The quadratic formula is

$x=\frac{-b+\sqrt{b^2-4ac} }{2a}$ .

It is important because while some quadratics are factorable and can be solved not all are. The formula will solve all quadratic equations and can also give both real and imaginary solutions. Using the formula will require less work than finding the factors if factorable. We will substitute a=9, b=-54 and c=-19.

$x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}\\x=\frac{-(-54)+/-\sqrt{(-54)^2-4(9)(-19)} }{2(9)}\\x=\frac{54+/-\sqrt{2916+684} }{18}$

We will now solve for the plus and the minus.

The plus,,,

$x=\frac{54+\sqrt{3600}}{18}\\x=\frac{54+60}{18}\\x=\frac{114}{18}\\x=6.3$

and the minus...

$x=\frac{54-\sqrt{3600}}{18}\\x=\frac{54-60}{18}\\x=\frac{-6}{18}\\x=-0.333...$

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