Provide a CMOS logic gate circuit that realizes the function $Y=\overline{A} B C+A \overline{B} C+A B \overline{C}.$ How many transistors are required? Explore the possibility of reducing the number of the transistors required.

Draw a NAND logic diagram that implements the complement of the following function: $F(A, B, C, D)=\Sigma(0,1,2,3,6,10,11,14)$

The Bureau of the Census reports that the median family income for all families in the United States during the year 2003 was $43,318. That is, half of all American families had incomes exceeding this amount, and half had incomes equal to or below this amount. Suppose that four families are surveyed and that each one reveals whether its income exceeded$43,318 in 2003. List the points in the sample space.

Graph and label each point.

$$X(1.75,-0.75)$$

If G = (V, E) is a forest with |V| = v, |E| = e, and k components (trees), what relationship exists among v, e, and k?

Will an amide be the final product obtained from the reaction of an acyl chloride with pyridine in an aqueous solution? Explain your answer.

At a certain time

$$t_0,$$

the path of a moving particle is tangent to the y-axis in the positive direction. The particle's speed at time

$$t_0$$

is 4 m/s, and its acceleration vector is

$$\mathbf { a } = \langle 5,4,12 \rangle.$$

Determine the curvature of the path at

$$t_0.$$

Find an equation of the following hyperbolas, assuming the center is at the origin. Sketch a graph labeling the vertices, foci, and asymptotes. Use a graphing utility to check your work. A hyperbola with vertices

$$( \pm 1,0 )$$

that passes through

$$\left( \frac { 5 } { 3 } , 8 \right)$$

An experimenter measures the weights of a random sample of 20 items and uses the information to estimate the overall population mean. Is the experimenter using probability theory or statistical inference?

Determine whether the given matrix is in row echelon form. If it is, state whether it is also in reduced row echelon form.

$$\left[ \begin{array} { l l l } { 1 } & { 2 } & { 3 } \\ { 1 } & { 0 } & { 0 } \\ { 0 } & { 1 } & { 1 } \\ { 0 } & { 0 } & { 1 } \end{array} \right]$$

Give the CMOS circuit for a three-input NAND gate.

You and your uncle are fishing. You are using 22-N fishing line, which means the line can support that much tension without breaking. Your uncle challenges you to catch the biggest fish you can land in the boat with that line, with the provision that you have to hoist the fish out of the water with the line and not with a net. You finally hook a fish that looks to have the right inertia, and you start to reel it in slowly. Just as you get the fish up into the air, though, the line snaps and the fish gets away. You accuse your uncle of having behind your back switched your pole to a line weaker than the 22-N line you thought you were working with, but he denies it. He then points out that you were accelerating the fish upward at $1.0 \mathrm { m } / \mathrm { s } ^ { 2 }$.

Explain the restrictions on x for the expressions.

$$\frac { 2 x + 4 } { x ^ { 2 } - 25 } \cdot \frac { x ^ { 2 } - 5 x - 50 } { 4 x ^ { 2 } - 16 }$$

$$\frac { 6 x ^ { 2 } } { 3 x ^ { 2 } - 27 } \div \frac { 2 x + 2 } { x ^ { 2 } - 2 x - 3 }$$