Algebra Answers

which of the following statements are true justify your answer

a) For any three set A,B,C in a universal set U,(A\B)×C=A×(B\C)

b) the operation of conjugation is closed on C

c) if f(x) and g(x) are polynomials for which f(0)= g(0) and f(t)= g(t) ,then f(x)=g(x)

d) the solution set of 2x= 1,y+5=x,x=y+3 is a singleton

A company has decided to produce a new cereal called ‘Nuts and Bran’ which contains only nuts (N) and bran (B). The company has RM15000 to spend on nuts and bran. The cost of nuts is RM1200 and RM800 for bran.

     a.   Draw an isocost curve showing the different combinations of nuts and bran that the company can purchase.

(10 marks)

    b.   What will hapeen to the original isocost line if:

1.     the capital reduce by 25%?
2.     the price of nuts increase by RM200?
3.     the price for both nuts and bran reduce by 15%?

To break even in a manufacturing​ business, income or revenue R must equal the cost of production C. The cost C to produce x skateboards is C=63+22x. The skateboards are sold wholesale for ​$25 ​each, so revenue R is given by R=25x. Find how many skateboards the manufacturer needs to produce and sell to break even.​ (Hint: Set the cost expression equal to the revenue expression and solve for​ x.)

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Part 1

The manufacturer needs to produce and sell

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skateboards to break even.

​(Simplify your​ answer.)

The average annual number of cigarettes smoked by an adult in some country continues to decline. For the years​ 2000-2009, the equation y=−94.2x+1555 approximates this data.​ Here, x is the number of years after 2000 and y is the average annual number of cigarettes smoked. Predict the average annual number of cigarettes smoked by an adult in this country in 2015. To do​ so, let  x=15 ​(since 2015−2000=15​) and find y.

The average annual number of cigarettes smoked by an adult in the country in 2015 is predicted to be

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. ​(Simplify your​ answer.)

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.

Question content area bottom

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.)