In Fig. 12–29, solve for the load voltage, $V_\text{L}$, the load current, $I_\text{L}$, and the current supplied by each cell in the battery.

Two dice are rolled. John gets $\$ 5$ if they show the same number; he pays $\$ 1$ if they show different numbers. What is the expected value of this game?

What is the current LTV of a mortgage loan?

What is the source of the leakage current in a transistor?

Your boat departs from the bank of a river that has a swift current parallel to its banks. If you want to cross this river in the shortest amount of time, you should direct your boat
A. perpendicular to the current.
B. upstream.
C. downstream.
D. so that it drifts with the current.

Combine the below complex numbers.

(5 + 2i) - (3 + 6i)

Let

$$S_1\text{ and }S_2$$

be subsets of a vector space V. Prove that

$$span (S_1 \cap S_2) \subseteq span(S_1) \cap span(S_2).$$

Give an example in which

$$span(S_1 \cap S_2)\text{ and } span(S_1) \cap span(S_2)$$

are equal and one in which they are unequal.

Consider $u$ and $v$ arc vectors. Show that the span of $u, v$, and $0$ is the same as the span of $u$ and $v$.

Combine the below complex numbers.

(11 - 6i) - (2 - 4i)

Will the current in a lightbulb connected to a $220\text{-}\mathrm{V}$ source be greater or less than the current in the same bulb when it is connected to a $110\text{-}\mathrm{V}$ source?

In the following problem, graph the given complex number.

6 +7i

Chordates share all of the following body plan characteristics except for A. bilateral body symmetry at some stage of life. B. deuterostome development. C. specialized tissue. D. two germ layers.

Determine the missing amounts in each of these four separate situations a through d.

Prove that if c is a nonzero scalar, then span{u} = span{cu}.