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If the probability of rain on any given day in city x is 50 percent, what is the probability it will rain on exactly 3 days in a five day period?

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If $$\\\\frac{5}{4x+6} = \\\\frac{3}{5}$$, what is the value of $$x$$?

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Evaluate the expression:
$${1\\\\frac{2}{3} - \\\\frac{1}{2}} \\\\over {\\\\frac{1}{2} - \\\\frac{2}{3}}$$

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A rectangular box is $$6\\\\sqrt{2}$$ inches high, $$6\\\\sqrt{2}$$ inches wide, and 5 inches deep. What is the greatest possible straight-line distance, in inches, between any two points on the box?

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If a potato peeler peels 4 potatoes in $$\\\\frac{3}{4}$$ of a second, how many potatoes does it peel in 5 minutes?

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What is the value of $$2a^2+4a$$ if $$(x-a)(x-7)=x^2-4x-21$$ for all $$x$$ and $$a$$ is a constant?

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What is the largest possible value of $$z$$ if $$4x+(z-27)^2=36$$ and $$-7\\\\le x\\\\le 8$$?

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Three vertices of a rectangle are given in the standard $$x,y$$ coordinate plane: $$(0,3), (6,-1), (8,2)$$. What are the coordinates of the fourth vertex?

$\"\"$

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In the diagram below, triangle ABC is equilateral and triangle BCD is isosceles. What is the measure of angle BDC?

$\"\"$

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Given that $$\\\\cos\\\\angle E = \\\\frac{1}{3}$$ for right triangle DEF, what is the value of $$\\\\sin\\\\angle E$$?

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