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When n gallons of milk was added to a tank that was already 1/8 full, the tank was filled to 12/16 of its capacity. In terms of n, what is the capacity of the tank, in gallons?
Assume the capacity of the tank is: \( x \)
\[ \frac{1}{8}x+n=\frac{12}{16}x \implies n=(\frac{12}{16}\frac{2}{16})x=\frac{10}{16}x \implies x=\frac{16}{10}n \]
Assume the capacity of the tank is: \( x \)
\[ \frac{1}{8}x+n=\frac{12}{16}x \implies n=(\frac{12}{16}\frac{2}{16})x=\frac{10}{16}x \implies x=\frac{16}{10}n \]

What is the value of \( x \) for the given \( \begin{cases} \frac{3}{4}x\frac{1}{2}y=1\\ \frac{5}{6}x=\frac{3}{5}y+2 \end{cases} \)?
\[ y=\frac{1}{x^31} \implies x^31=\frac{1}{y} \implies x^3=\frac{1}{y}+1 \implies x=\sqrt[3]{\frac{1}{y}+1} \\ f^{1}(x)=\sqrt[3]{\frac{1}{x}+1} \]
\[ y=\frac{1}{x^31} \implies x^31=\frac{1}{y} \implies x^3=\frac{1}{y}+1 \implies x=\sqrt[3]{\frac{1}{y}+1} \\ f^{1}(x)=\sqrt[3]{\frac{1}{x}+1} \]

Which of the following is a solution to \( (\frac{1}{3})^{2x4}=3 \times 27^x \)?

World Wide Insurance Company found that 53% of the residents of a city had homeowner’s insurance with the company. Of these clients, 27% also had automobile insurance with the company. If a resident is selected at random, find the probability that the resident has both homeowner’s and automobile insurance with World Wide Insurance Company.

An effervescent tablet has a diameter of 1 inch and a thickness of 0.2 inches. A cylindrical container is designed for protecting 20 tablets. What is the minimum height of this container in inches?

What is the sum of \( 2.56 \times 10^{4}+(\frac{1.2 \times 10^{2}}{2}) \times 10^{3} \)?

A glass of water is filled with 25% water. The volume of this glass can contain 800 milliliters liquid. If a milliliter equals 1000 cubic millimeters, what portion of the glass is empty in a cubic meter?

A circle is defined by the equation, \( (x+3m)^2+(y+2)^2=m+4 \). Which of the following “m” makes the circle to be tangent to the horizontal axis in the standard xy coordinate, and lead the circle to the quadrant III?

Which of the following is NOT correct?

Of all the employees in a company, 1/8 are technical staff and the rest are the nontechnical staff. If 40% of the technical staff have been working in the company for less than three years and if the fraction of nontechnical staff who have been working in the company for more than three years is 2 times the fraction of technical staff who have been working in the company for more than three years, what fraction of all the employees in the company are nontechnical staff who have not been working in the company for more than three years?

A survey represented that the proportion of the number of research papers in dentistry to the number of researchers was 3.4. If the growth rate is 1.3% per year, then how much will it change after 8 years? In each year, just two decimal point is considered.

A grocer has 500 pounds of coffee in stock, 25% of which is decaffeinated. If the grocer buys another 300 pounds of coffee of which 30% is decaffeinated. What is the approximate value of decaffeinated coffee in grams?

\( 11<x<17 \) 

Quantity A  Quantity B 
\( \frac{x+17}{x} \)  \( \frac{x+11}{11} \) 
