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4 years ago

I need help finding the answer. Please tell me what it is and how you got it

Mathematics

1 answer:

guapka [62]4 years ago

3 0

rather simple, simply count how many zeros are there in each and that'll be the exponent of the base 10.

$\bf 1\stackrel{\leftarrow \qquad \textit{23 zeros}\qquad \to }{00,000,000,000,000,000,000,000}\implies \stackrel{Mars}{10^{23}~Kgs} \\\\\\ 1\stackrel{\leftarrow \qquad \textit{26 zeros}\qquad \to }{00,000,000,000,000,000,000,000,000}\implies \stackrel{Neptune}{10^{26}~Kgs}$

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4 years ago

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Which of these can't be formed and if they can....what type of triangle are they?!!!

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4 years ago

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Marizza181 [45]

Answer:

$n=\frac{0.5(1-0.5)}{(\frac{0.04}{1.64})^2}=420.25$

And rounded up we have that n=421

Step-by-step explanation:

We know that the sample proportion have the following distribution:

$\hat p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.1$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.04$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We assume that a prior estimation for p would be $\hat p =0.5$ since we don't have any other info provided. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.04}{1.64})^2}=420.25$

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4 years ago

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3 years ago

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A store sold a case of candles for $17.85 that had been marked up 10%. what was the original price?

Aleonysh [2.5K]

Step-by-step explanation:

The original price was $16.23

Explanation:

We can rewrite this problem as:

110% of what is $17.85.

"Percent" or "%" means "out of 100" or "per 100", Therefore 110% can be written as

110 x/100

When dealing with percents the word "of" means "times" or "to multiply".

Finally, lets call the number we are looking for "n".

Putting this altogether we can write this equation and solve for

while keeping the equation balanced:

110/100 × n = $17.85

110/100 × n = $17.85

110/100 × n = $17.85 100/110 × 110/100 × n = 100/110 × $17.85

110/100 × n = $17.85 100/110 × 110/100 × n = 100/110 × $17.85

100/110 <¬ cross out × 110/100 <¬ cross out × n = $ 1785/110

× n = $ 1785/110

n = $16.23n rounded to the nearest penny.

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3 years ago