The market research department of the Better Baby Buggy Co. predicts that the demand equation for its buggies is given by q=−0.5p+140, where q is the number of buggies it can sell in a month if the price is $p per buggy. At what price should it sell the buggies to get the largest revenue? What is the largest monthly revenue?

What type of research answers scientific questions by testing a hypothesis?

A. experimental

C. technical.

D. anahytical Viraite

If the revenue function for a particular commodity is $R(p)=-50 p^{2}+60 p$, what is the (linear) demand function? Give a reason for your answer.

You can sell 90 pet chias per week if they are marked at $1 each, but only 30 each week if they are marked at$2/chia. Your chia supplier is prepared to sell you 20 chias each week if they are marked at $1/chia, and 100 each week if they are marked at$2 per chia. a. Write down the associated linear demand and supply functions. b. At what price should the chias be marked so that there is neither a surplus nor a shortage of chias?

The following table shows projected worldwide sales of (all) cell phones and wholesale prices:

$$\begin{matrix} \text{Year} & \text{2004} & \text{2008}\\ \text{Wholesale Price (\$)} & \text{100} & \text{80}\\ \text{Sales (millions)} & \text{600} & \text{800}\\ \end{matrix}$$

a. Use the data to obtain a linear demand function for cell phones, and use your demand equation to predict sales if the price was set at $85. b. Fill in the blanks: For every ____ increase in price, sales of cell phones decrease by ___ units.

A bacteria culture starts with 1,000 bacteria and doubles in size every 3 hours. Find an exponential model for the size of the culture as a function of time t in hours and use the model to predict how many bacteria there will be after 2 days.

The joint probability mass function of the random variables X, Y, Z is

$$p ( 1,2,3 ) = p ( 2,1,1 ) = p ( 2,2,1 ) = p ( 2,3,2 ) = \frac { 1 } { 4 }$$

Find (a) E[XYZ], and (b) E[XY+XZ+YZ].

A sporting goods store finds that if it sells x exercise machines per day, its costs will be $C(x)=100 x+3200$ and its revenue will be $R(x)=-2 x^{2}+300 x$ (both in dollars). a. Find the store’s break-even points. b. Find the number of sales that will maximize profit, and the maximum profit.

Assume a curve is given by the parametric equations x=f(t) and y=g(t), where f and g are twice differentiable. Use the Chain Rule to show that $y ^ { \prime \prime } ( x ) = \frac { f ^ { \prime } ( t ) g ^ { \prime \prime } ( t ) - g ^ { \prime } ( t ) f ^ { \prime \prime } ( t ) } { \left( f ^ { \prime } ( t ) \right) ^ { 3 } }$.

Four equal charges of

$$5.0 \mu \mathrm { C }$$

are placed at the vertices of a square of side 10 cm. a. Calculate the value of the electric potential at the centre of the square. b. Determine the electric field at the centre of the square. c. How do you reconcile your answers to a and b with the fact that the electric field is the derivative of the potential?

For each demand equation, express the total revenue R as a function of the price p per item, sketch the graph of the resulting function, and determine the price p that maximizes total revenue in each case. q=−3p+300

Without looking at the electron affinity table, arrange the following elements in order of decreasing electron affinities: C, O, Li, Na, Rb, and F.

Lane 1 at your local track is 0.25 mi long. You live 0.5 mi away from the track. Which of the following results in the shortest jog? F. jogging 6 times around the track in Lane 1 G. jogging to the track and then 5 times around the tracking Lane 1 H. jogging to the track, 3 times around the track in Lane 1, and then home I. jogging 8 times around the track in Lane 1

Find each limit algebraically. $\lim _{x \rightarrow-1}\left(8 x^{5}-7 x^{3}+8 x^{2}+x-4\right)$