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The average annual number of cigarettes smoked by an adult in some country continues to decline. For the years 2000−​2012, the equation y=−77.8x+2051 approximates this data.​ Here, x is the number of years after​ 2000, and y is the average annual number of cigarettes smoked. If this trend​ continues, find the year in which the average annual number of cigarettes smoked reaches zero. To do​ this, substitute 0 for y in the equation and solve for x.


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Part 1


In

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​, the average annual number of cigarettes smoked will be zero.

​(Round down to the nearest​ year.)


Find the value of the following expression for the given values.

n2−m2​; n=−3​, and m=-7


A university​ president's salary for the​ 2012-2013 academic year was ​$470,000. Calculate his​ 2013-2014 salary if he received a 2.7​% raise.


The sum of three consecutive integers is 72. Find the integers.



In the last​ year, a total of 15,456 earthquakes occurred in a country. Of​ these, 88.7% were minor tremors with magnitudes of 4.9 or less on the Richter scale. How many minor earthquakes occurred in the country in the last​ year?

(Round to the nearest whole​ number.)


Use the diagram to find the angle measures of the triangle. Recall that the sum of the angle measures of a triangle is 180°

x=

(x+4)=

9x=



An element with mass 780 grams decays by 16.3% per minute. How much of the element is remaining after 16 minutes, to the nearest 10th of a gram?


A greenhouse employee has 35 ounces of a potting soil and must place equal amounts of the soil into each of 8 small clay pots. What is the weight of the potting soil that should be placed in each clay pot?


Test the series: infinity sigma n=1 (-1)^ n-1 sin nx n sqrt n for absolute and conditional convergence

Give an example of a series sigmaan such that Sigma an is not cnvergent but the sequence (an) converges to 0,

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