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Tanzania [10]
3 years ago
11

if 1/4 of a gallon of paint is needed to paint 2/3 of a fence, how many gallons are needed to paint the entire fence? site:socra

tic.org
Mathematics
2 answers:
FinnZ [79.3K]3 years ago
8 0

Answer:3/8 gallons of paint is needed to paint the entire fence.

Step-by-step explanation:

Let x represent the entire area of the fence that is to be painted.

If 1/4 of a gallon of paint is needed to paint 2/3 of a fence, it means that 1/4 of a gallon of paint is needed to paint 2x/3

The number of gallons needed to paint the entire fence would be

(x/4)/(2x/3) = x/4 × 3/2x = 3/8 gallons

trasher [3.6K]3 years ago
7 0

\bf \begin{array}{ccll} \stackrel{paint}{gallons}&fence\\ \cline{1-2} \\\frac{1}{4}&\frac{2}{3}\\\\ x&1 \end{array}\implies \cfrac{~~\frac{1}{4}~~}{x}=\cfrac{~~\frac{2}{3}~~}{1}\implies \cfrac{~~\frac{1}{4}~~}{\frac{x}{1}}=\cfrac{2}{3}\implies \cfrac{1}{4}\cdot \cfrac{1}{x}=\cfrac{2}{3} \\\\\\ \cfrac{1}{4x}=\cfrac{2}{3}\implies 3=8x\implies \cfrac{3}{8}=x

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AlladinOne [14]

Answer:

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So on this case the 98% confidence interval would be given by (3.767;4.233)

Step-by-step explanation:

Previous concepts

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".

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Solution to the problem

The confidence interval for the mean is given by the following formula:

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

Since the Confidence is 0.98 or 98%, the value of \alpha=0.02 and \alpha/2 =0.01, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.01,0,1)".And we see that z_{\alpha/2}=2.326

Now we have everything in order to replace into formula (1):

4-2.326\frac{1}{\sqrt{100}}=3.767    

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So on this case the 98% confidence interval would be given by (3.767;4.233)

   

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