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3 years ago

5.12 = 5w, what is W

Mathematics

2 answers:

MA_775_DIABLO [31]3 years ago

5 0

W=1.024
I hope this helps :)

boyakko [2]3 years ago

4 0

Answer:

The answer is 1.024

Step-by-step explanation:

5.12 divided by 5 = 1.024

Hope this helps.

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What are the steps to solve the quadratic equation x^2+4x-6=0

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$METHOD\ 1:\\\\Use:\\\\(*)\qquad(a+b)^2=a^2+2ab+b^2\\---------------------\\\\x^2+4x-6=0\qquad\text{add 6 to both sides}\\\\x^2+4x=6\\\\x^2+2(x)(2)=6\qquad\text{add}\ 2^2\ \text{to both sides}\\\\\underbrace{x^2+2(x)(2)+2^2}_{(*)}=6+2^2\\\\(x+2)^2=6+4\\\\(x+2)^2=10\Rightarrow x+2=\pm\sqrt{10}\qquad\text{subtract 2 from both sides}\\\\\boxed{x=-2-\sqrt{10}\ \vee\ x=-2+\sqrt{10}}$

$METHOD\ 2:\\\\\text{use the quadratic formula:}\\\\ax^2+bx+c=0\\\\\Delta=b^2-4ac\\\\if\ \Delta>0,\ \text{the equation has two solutions}\ x=\dfrac{-b\pm\sqrt\Delta}{2a}\\\\if\ \Delta=0,\ \text{then the equation has one solution:}\ x=\dfrac{-b}{2a}\\\\if\ \Delta$

$x^2+4x-6=0\\\\a=1,\ b=4,\ c=-6\\\\\Delta=4^2-4(1)(-6)=16+24=40>0\\\\\sqrt\Delta=\sqrt{40}=\sqrt{4\cdot10}=\sqrt4\cdot\sqrt{10}=2\sqrt{10}\\\\x_1=\dfrac{-4-2\sqrt{10}}{2(1)}=\dfrac{-4}{2}-\dfrac{2\sqrt{10}}{2}=-2-\sqrt{10}\\\\x_2=\dfrac{-4+2\sqrt{10}}{2(1)}=\dfrac{-4}{2}+\dfrac{2\sqrt{10}}{2}=-2+\sqrt{10}$

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3 years ago

An IQ test is designed so that the mean is 100 and the standard deviation is 18 for the population of normal adults. Find the sa

melisa1 [442]

Answer:

At least 98 people need to be sampled. It is not a huge number, that is, it is not difficult to sample 98 people, so it is a reasonable sample size for a real world calculation.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.9}{2} = 0.05$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.05 = 0.95$ , so $z = 1.645$

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

In this question:

We need a sample size of at least n.

n is found when M = 3. We have that $\sigma = 18$ .

$M = z*\frac{\sigma}{\sqrt{n}}$

$3 = 1.645*\frac{18}{\sqrt{n}}$

$3\sqrt{n} = 1.645*18$

Simplifying by 3

$\sqrt{n} = 1.645*6$

$(\sqrt{n})^{2} = (1.645*6)^{2}$

$n = 97.41$

Rounding up,

At least 98 people need to be sampled. It is not a huge number, that is, it is not difficult to sample 98 people, so it is a reasonable sample size for a real world calculation.

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3 years ago