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omeli [17]
3 years ago
15

How do I solve for x: (4/9)^(x) • (8/27)^(1-x) =2/3

Mathematics
2 answers:
asambeis [7]3 years ago
8 0

(\frac{4}{9})^x\cdot (\frac{8}{27})^{1-x} =\frac{2}{3}\\((\frac{2}{3})^2)^x\cdot ((\frac{2}{3})^3)^{1-x} =\frac{2}{3}\\(\frac{2}{3})^{2x}\cdot (\frac{2}{3})^{3-3x} =\frac{2}{3}\\(\frac{2}{3})^{2x+3-3x} =\frac{2}{3}\\(\frac{2}{3})^{-x+3} =\frac{2}{3}\\-x+3=1\\-x=1-3\\-x=-2\ /:(-1)\\x=2

exis [7]3 years ago
7 0
X=2

All this stuff is wrong I screwed up somewhere:
IGNORE EVERYTHING BELOW THIS:
take the natural log of both sides of the equation.

ln(( \frac{4}{9})^{x}  )   \times  \ ln(( \frac{8}{27})^{(1 - x)} ) =  ln( \frac{2}{3} )
Remembering your log rules:

ln( {a}^{b} )  = b  \: ln(a)
Using this rule we rewrite the first equation:
x \:  ln( \frac{4}{9} )  \times (1 - x) \:  ln( \frac{8}{27} )  =  ln( \frac{2}{3} )
Simplify:
x ln( \frac{4}{9} )  \times ( ln( \frac{8}{27}) - x \:  ln( \frac{8}{27} )  )
Solve for some of these ln's to make life easier:

- .81x \:  \times ( - 1.22 - 1.22x) =  - .41
Distribute:
(.988x + .988x^{2} ) =  - .41

Factor out .988
.988(x +  {x}^{2} ) =  - .41 \\ (x +  {x}^{2} ) =  \frac{ - .41}{.988}  \\ (x +  {x}^{2} ) = -  .415
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hram777 [196]
Given that for each <span>$2 increase in price, the demand is less and 4 fewer cars are rented.

Let x be the number of $2 increases in price, then the revenue from renting cars is given by
(48 + 2x) \times (150 - 4x)=7,200+108x-8x^2.

Also, given that f</span><span>or each car that is rented, there are routine maintenance costs of $5 per day, then the total cost of renting cars is given by
5(150-4x)=750-20x

Profit is given by revenue - cost.
Thus, the profit from renting cars is given by
</span><span>(7,200+108x-8x^2)-(750-20x)=6,450+128x-8x^2

For maximum profit, the differentiation of the profit function equals zero.
i.e.
</span><span>\frac{d}{dx} (6,450+128x-8x^2)=0 \\  \\ 128-16x=0 \\  \\ x= \frac{128}{16} =8

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3 0
3 years ago
You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable preliminary estim
pogonyaev

Answer:

n=\frac{0.5(1-0.5)}{(\frac{0.025}{1.28})^2}=655.36  

And rounded up we have that n=656

Step-by-step explanation:

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 80% of confidence, our significance level would be given by \alpha=1-0.80=0.20 and \alpha/2 =0.10. And the critical value would be given by:

z_{\alpha/2}=\pm 1.28

Solution to the problem

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)  

Since we don't have prior info for the proportion of interest we can use \hat p=0.5 as estimator. And on this case we have that ME =\pm 0.025 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)  

And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.025}{1.28})^2}=655.36  

And rounded up we have that n=656

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Hello!!

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