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frosja888 [35]
3 years ago
13

Ethanol fuel mixtures have "E" numbers that indicate the percentage of ethanol in the mixture by volume. For example, E10 is a m

ixture of 10% ethanol and 90% gasoline. How much E5 should be mixed with 6000 gal of E10 to make an E9 mixture?
Mathematics
1 answer:
liberstina [14]3 years ago
8 0

According to the problem we start with 6000 gal of E10 which means there is 10% of ethanol  in this 6000, with ths information we can calculate the amount of ethanol already in the mixture:

6000gal*0.1=600gal

The relationship between ethanol and total fluid can be represented like this:

\frac{600}{6000} =0.1

Based on this relationship we can build the one that we are looking for:

E9=9Ethanol91Gasoline=\frac{Ethanol}{Total}=0.09

\frac{TotalEthanol}{TotalSolution} =0.09

the total solution will be:

TotalSolution=6000+X

where X is the E5 solution volume

and the TotalEthanol would be:

TotalEthanol=600+E5Ethanol

where E5ethanol (5% Ethanol 95% Gasoline) would be:

\frac{E5Ethanol}{X}=0.05\\E5Ethanol=0.05X

Now replacing in the relationship we found before:

\frac{600+0.05X}{6000+X}=0.09

Solving for X:

600+0.05X=0.09(6000+X)\\600+0.05X=540+0.09X\\0.09X-0.05=600-540\\0.04X=60\\X=\frac{60}{0.04} \\X=1500

We should mix 1500 gal of E5 to make an E9 mixture

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Answer:

Step-by-step explanation: X and Y represent the digits.

The tens digit is twice the units digit.

The digit in the Tens place has 10× its base value, so we can set up equations to model the information given.

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X = 2y means the Tens digits is twice the units digit.

10y + x +2 = 10x +y - 34 models the statement: The reversed number plus two is 34 less than the original number.

Substitute 2y for x to solve for y

10y +2y +2= 10(2y) + y -34

Distribute and combine like terms

12y + 2 = 20y +y - 34

34 +2 = 21y -12y

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X = 8

Original number: 84 Reversed number: 48

Substitute into equation model

48 +2= 84 -34

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True!

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Step-by-step explanation:

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Answer:

92°

Step-by-step explanation:

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The average homicide rate for the cities and towns in a state is 10 per 100,000 population with a standard deviation of 2. If th
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Answer:

P(X>8)=P(\frac{X-\mu}{\sigma}>\frac{8-\mu}{\sigma})=P(Z>\frac{8-10}{2})=P(Z>-1)  

And we can find this probability with the complement rule:  

P(Z>-1)=1-P(Z  

Step-by-step explanation:

Previous concepts  

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".  

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem  

Let X the random variable that represent the average homicide rate for the cities of a population, and for this case we know the distribution for X is given by:  

X \sim N(10,2)  

Where \mu=10 and \sigma=2  

We are interested on this probability  

P(X>8)  

And the best way to solve this problem is using the normal standard distribution and the z score given by:  

z=\frac{x-\mu}{\sigma}  

If we apply this formula to our probability we got this:  

P(X>8)=P(\frac{X-\mu}{\sigma}>\frac{8-\mu}{\sigma})=P(Z>\frac{8-10}{2})=P(Z>-1)  

And we can find this probability with the complement rule:  

P(Z>-1)=1-P(Z  

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