A rectangular box without a top (a topless box) is to be made from 12 $\mathrm { ft } ^ { 2 }$ of cardboard. Find the maximum volume of such a box.

Which of the following statements starts a polygon named pol at the coordinates 20 and 290?

pol.moveTo(20F, 290F);
pol.lineTo(20F, 290F);
pol = new Path(20F, 290F);
pol.newPath(20F, 290F);

Look at the figure at the right. Where do planes A C E and B C D intersect?

(A) $\overleftrightarrow{A D}$

(B) $\overleftrightarrow{C B}$

(C) $\overleftrightarrow{C D}$

(D) $\overleftrightarrow{B F}$

You are asked to construct a segment congruent to $\overline{A B}$. As a first step, you draw a ray. Which of the following, if true of the ray, would be most helpful? (A) The ray is drawn on the paper shorter than $\overline{A B}$. (B) The ray is drawn on the paper longer than $\overline{A B}$. (C) The ray is drawn parallel to $\overline{A B}$. (D) The ray is drawn perpendicular to $\overline{A B}$.

Find three positive numbers whose sum is 100 and whose product is a maximum.

Find a counterexample to show that each statement is false.

The sum of any three odd numbers is even.

When an even number is added to the product of two odd numbers, the result will be even.

When an odd number is squared and divided by 2, the result will be a whole number.

Steam enters a nozzle at 400$^\circ{}$C and 800 kPa with a velocity of 10 m/s, and leaves at 375$^\circ{}$C and 400 kPa while losing heat at a rate of 25 kW. For an inlet area of 800 cm^2, determine the velocity and the volume flow rate of the steam at the nozzle exit. Answers: 260 m/s, 1.55 m^3/s

Find a counterexample for the following statements. All numbers are greater than 0 and less than or equal to 1.

Locate the turning point or vertex for each of the following quadratic functions: $y=2 x^{2}-10 x+3$

A lidless cardboard box is to be made with a volume of 4 $m^3$. Find the dimensions of the box that requires the least amount of cardboard.

In the course of a mammal's lifetime, its heart beats about 1 billion times, regardless of the mammal's size or weight. (This excludes humans.) a. An elephant's heart beats approximately 25 times a minute. How many years would you expect an elephant to live? Use scientific notation to calculate your answer. b. A pygmy shrew's heart beats approximately 1150 times a minute. How many years would you expect a pygmy shrew to live? c. If this relationship were true for humans, how many years would you expect a human being with a heart rate of 60 beats per minute to live?

Find the dimensions of the box with volume 1000 cm^3 that has minimal surface area.

Minimize the function $f(x, y, z)=x^{2}+y^{2}+z^{2}$ subject to the constraints x + 2y + 3z = 6 and x + 3y + 9z = 9.

Which of the following statements does NOT have a counterexample?