Algebra Answers

8^4/3=(2^5x-4)/√2 solve for x

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At a certain fast food chain, every order of fries comes with a game piece. If every game piece has a 1/4 chance of winning a prize, and your family just ordered three orders of fries, what is the probability that someone in your family won a prize today?

When polluted water begins to flow into an unpolluted pond, the concentration of pollutant, c, in the pond at t minutes is modelled by c(t) = 27t / 10000 + 3t, where c is measured in kilograms per cubic metre. Determine the rate at which the concentration is changing after

a) 1 h b) one week

The equation f(t) = 5t / t^2 + 3t + 2 models the bacteria count, in thousands, for a sample of tap water that is left to sit over time, t, in days. The equation g(t) = 15t / t^2 + 9 models the bacteria count, in thousands, for a sample of pond water that is also left to sit over several days. In both models, t > 0. Will the bacteria count for the tap water sample ever exceed the bacteria count for the pond water? Justify your answer.

Solve l x / x - 4l ≥ 1.

An economist for a sporting goods company estimates the revenue and cost functions for the production of a new snowboard. These functions for the production of a new snowboard. These functions are R(x) = -x^2 + 10x and C(x) = 4x + 5, respectively, where x is the number of snowboards produced, in thousands. The average profit is defined by the function AP(x) = P(x)/x, where P(x) is the profit function. Determine the production levels that make AP(x) > 0.

Three employees work at a shipping warehouse. Tom can fill an order in s minutes. Paco can fill an order in s - 2 minutes. Carl can fill an order in s + 1 minutes. When Tom and Paco work together, they take about 1 minute and 20 seconds to fill an order. When Paco and Carl work together, they take about 1 minute and 30 seconds to fill an order.

a) How long does each person take to fill an order?
b) How long would all three of them, working together, take to fill an order

Tayla purchased a large box of comic books for $300. She gave 15 of the comic books to her brother and then sold the rest on an Internet website for $330, making a profit of $1.50 on each one. How many comic books were in the box? What was the original price of each comic book?

The Turtledove Chocolate factory has two chocolate machines. Machine A takes s minutes to fill a case with chocolates, and machine B takes s + 10 minutes to fill a case. Working together, the two machines take 15 minutes to fill a case. Approximately how long does each machine take to fill a case.