Show that postage of 6 cents or more can be achieved by using only 2-cent and 7-cent stamps.

Find the second derivative of the given function. $f(x)=e^{2 x}+2 e^{-x}$

Water is pumped through a pipe of diameter 15.0 cm from the Colorado River up to Grand Canyon Village, on the rim of the canyon. The river is at 564 m elevation and the village is at 2 096 m. What additional pressure is necessary to deliver this flow? Note: You may assume the free-fall acceleration and the density of air are constant over the given range of elevations.

Give an argument using rules of inference to show that the conclusion follows from the hypotheses. Hypotheses: Everyone in the class has a graphing calculator. Everyone who has a graphing calculator understands the trigonometric functions. Conclusion: Ralphie, who is in the class, understands the trigonometric functions.

A round pencil lying on its side is in neutral equilibrium relative to displacements perpendicular to its length. What is its stability relative to displacements parallel to its length?

Hydrogen chloride, HCl, is a gas at room temperature. Would you expect it to be very soluble or not very soluble in water?

A drug manufactured by a pharmaceutical company is sold in bulk at a price of $150 per unit. The total production cost (in dollars) for x units in one week is$C ( x ) = 0.02 x ^ { 2 } + 100 x + 3000$ How many units of the drug must be manufactured and sold in a week to maximize the profit? What is the maximum profit?

Start by drawing a number line that shows integers from -5 to 5. Then graph each of the following integers on your number line. -4

Prove that 1/(2n) ≤ [1 · 3 · 5 · · · · · (2n − 1)]/(2 · 4 · · · · · 2n) whenever n is a positive integer.

Consider subsonic Fanno flow accelerated to sonic velocity $(M_a = 1)$ at the duct exit as a result of frictional effects. If the duct length is increased further, will the flow at the duct exit be supersonic, subsonic, or remain sonic? Will the mass flow rate of the fluid increase, decrease, or remain constant as a result of increasing the duct length?

Distinguish between a vein and a venule.

Find the sum of the finite geometric series $a+a r+a r^{2}+\cdots+a r^{n-1}$. Write the answer as a quotient of integers. $30+3+\frac{3}{10}+\frac{3}{100}+\dots+\frac{3}{1,000,000}$

A salesperson figures that the probability of her making a sale is during the first contact with a client is .4 but improves to .55 on the second contact if the client did not buy during the first contact. Suppose this salesperson makes one and only one callback to any client. If she contacts a client, calculate the probabilities for these events: a. The client will buy. b. The client will not buy.

Problem 4

a. Is the following statement a good definition? Explain.

A square is a figure with four right angles.

b. How can you rewrite the statement "Obtuse angles have greater measures than acute angles" so that is it a good definition.