For the following loans, make a table showing the amounts of each monthly payment that go toward principal and interest for the first 3 months of the loan. A student loan of $\$ 24,000$ at a fixed APR of $8 \%$ for $15$ years

When the thermal conductivity of a medium varies linearly with temperature, is the average thermal conductivity always equivalent to the conductivity value at the average temperature?

In the sentence below, identify the principal part of the underlined verb by writing above it $BF$ for base form, $Pres P$ for present participle, $P$ for past, or $Past P$ for past participle.

The staff has compiled a diverse group of photographs.

The particles of which gas have the highest average speed? The lowest average speed? nitrogen trifluoride at $30^{\circ} \mathrm{C}$

Jain Enterprises honors a short-term note payable. Principal on the note is $425,000, with an annual interest rate of 3.5%, due in 6 months. What journal entry is created when Jain honors the note?

Use the rule of 70 to estimate the time required for the given principal P to double at the annual percent interest rate R. Check your answer by using the continuously compounded interest formula.

$$P=\$1200, R=14\%$$

Suppose that two variables, X and Y, are negatively associated. Does this mean that above-average values of X will always be associated with below-average values of Y? Explain.

Compare the average speed and average translational kinetic energy of $\mathrm{O}_2$ with that of $\mathrm{CCl}_4$ at $298 \mathrm{~K}$.

Use the rule of 70 to estimate the time required for the given principal P to double at the annual percent interest rate R. Check your answer by using the continuously compounded interest formula.

$$P=\$2000, R=7\%$$

If the average cost to manufacture one grand piano increases as the production level increases, which is greater, the marginal cost or the average cost?

Recognizing Participial Phrases. Each of the following sentences contains a participial phrase. Underline each participial phrase and draw an arrow pointing from it to the word it modifies. Chosen by the principal. Marie represented our school.

Show analytically that if marginal cost is greater than average cost, then the derivative of average cost with respect to quantity satisfies $a^{\prime}(q)>0$.

Use the Fundamental Theorem of Calculus to find the average value of $f(x)=e^{0.5 x}$ between x=0 and x=3. Show the average value on a graph of f(x).

For each deposit, find the future value (that is, the final amount on deposit) when compounding occurs $\textbf{(a)}$ annually, $\textbf{(b)}$ semiannually, and $\textbf{(c)}$ quarterly.