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Problem 1

Find the point of intersection of each pair of straight lines. $$ \begin{array}{l} y=3 x+4 \\ y=-2 x+14 \end{array} $$

Expert verified

The point of intersection of the given pair of straight lines is \((2, 10)\).

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Chapter 1

The quantity demanded of a certain brand of DVD player is \(3000 /\) wk when the unit price is \(\$ 485\). For each decrease in unit price of \(\$ 20\) below $\$ 485$, the quantity demanded increases by 250 units. The suppliers will not market any DVD players if the unit price is \(\$ 300\) or lower. But at a unit price of \(\$ 525\), they are willing to make available 2500 units in the market. The supply equation is also known to be linear. a. Find the demand equation. b. Find the supply equation. c. Find the equilibrium quantity and price.

Chapter 1

Sketch the straight line defined by the linear equation by finding the \(x\) - and \(y\) -intercepts. $$ 3 x-2 y+6=0 $$

Chapter 1

Use the results of Exercise 63 to find an equation of a line with the \(x\) - and \(y\) -intercepts. $$ x \text { -intercept } 3 ; y \text { -intercept } 4 $$

Chapter 1

For each pair of supply-and-demand equations, where \(x\) represents the quantity demanded in units of 1000 and \(p\) is the unit price in dollars, find the equilibrium quantity and the equilibrium price. $$ p=-0.3 x+6 \text { and } p=0.15 x+1.5 $$

Chapter 1

The amount of corn used in the United States for the production of ethanol is expected to rise steadily as the demand for plant-based fuels continue to increase. The following table gives the projected amount of corn (in billions of bushels) used for ethanol production from 2005 through \(2010(x=1\) corresponds to 2005 ): $$ \begin{array}{lcccccc} \hline \text { Year, } \boldsymbol{x} & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text { Amount, } \boldsymbol{y} & 1.4 & 1.6 & 1.8 & 2.1 & 2.3 & 2.5 \\\ \hline \end{array} $$ a. Find an equation of the least-squares line for these data. b. Use the result of part (a) to estimate the amount of corn that will be used for the production of ethanol in 2011 if the trend continues.

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