Place a check next to each sentence in which the subject and verb agree. _____ One new product are beefalo.

On the basis of your calculations, explain why the shoe-shop owner might find it difficult to choose between the two locations.

$$\begin{array}{|c|c|c|} \hline \textbf { Year } & \textbf { Location A } & \textbf { Location B } \\ \hline 0 & (\$ 12000) & (\$ 12000) \\ \hline 1 & \$ 3000 & \$ 6000 \\ \hline 2 & \$ 4000 & \$ 5000 \\ \hline 3 & \$ 5000 & \$ 3000 \\ \hline 4 & \$ 6000 & \$ 2000 \\ \hline 5 & \$ 5000 & \$ 5000 \\ \hline \end{array}$$

$$\begin{array}{|l|c|c|c|c|} \hline \textbf { Year } & 1 & 2 & 3 & 4 \\ \hline \textbf { Discount factors @ 10\% } & 0.91 & 0.83 & 0.75 & 0.68 \\ \hline \end{array}$$

Sketch a graph of u, v, and u+v. Then demonstrate the triangle inequality using the vectors u and v. u = ⟨-3, 2⟩, v = ⟨1, -2⟩

Complete and balance these equations :

(a) $\mathrm{CO}_2+\mathrm{H}_2 \mathrm{O} \longrightarrow$
(b) $\mathrm{MgSO}_4 \cdot 7 \mathrm{~H}_2 \mathrm{O} \stackrel{\Delta}{\longrightarrow}$
(c) $\mathrm{C}_3 \mathrm{H}_7 \mathrm{OH}+\mathrm{O}_2 \stackrel{\Delta}{\longrightarrow}$
propyl alcohol (d) $\mathrm{HNO}_3+\mathrm{Ba}(\mathrm{OH})_2 \longrightarrow$
(e) $\mathrm{BaO}+\mathrm{H}_2\mathrm{O} \longrightarrow$
(f) $\mathrm{Ca}(\mathrm{OH})_2 \stackrel{\Delta}{\longrightarrow}$

Identify the part of speech (POS) and the use in the sentence (USE) of the italicized word or words. Be very specific. Lisa eagerly dived into the frigid water and immediately climbed $\mathit{back}$ into the boat. POS: _______ USE: _______

Which method would you choose if you wanted to prepare cyclohexyl benzoate—Fischer esterification or reaction of an acid chloride with an alcohol? Explain.

Describe as many sequences as you can whose first three terms are 4, 6, and 8.

A fair coin is tossed seven times. Find the probability of obtaining at most five heads

The function f is a continuous function on the closed interval [-1, 4]. and f(-1) = 3 and f(4) = 6. In addition, $f, f^{\prime},$ and $f^{\prime \prime}$ have the properties indicated in the table below. Sketch the graph of f, and find the locations on this interval where f attains its maximum and minimum values.

$$\begin{matrix} \text{x} & \text{-1 < x < 2} & \text{x = 2} & \text{2 < x < 4}\\ \ {f^{\prime}(x)} & \text{negative} & \text{undefined} & \text{positive}\\ \ {f^{\prime \prime}(x)} & \text{negative} & \text{undefined} & \text{negative}\\ & \text{ } & \text{ }\\ \end{matrix}$$

A diagonal aluminum alloy tension rod of diameter d and initial length l is used in a rectangular frame to prevent collapse. The rod can safely support a tensile stress of $\sigma_{\text {allow }}$. If $d=\frac{5}{8} \text { in, } l=10 \mathrm{ft}, \text { and } \sigma_{\text {allow }}=15 \mathrm{kpsi}$, determine how much the rod must be stretched to develop this allowable stress.

Using l'Hopital's rule if necessary, evaluate the limits of the sequences.

$$\lim _{n \rightarrow \infty} \sqrt[2 n]{3 n}$$

For each set of terms below, choose the one term that does not belong and explain why it does not belong. actin, melanin, myosin.

Solve the compound inequality. Graph your solutions. 3 < 2p - 3 ≤ 12

Hypotheses are best described as:

A. assumptions.

B. replications.

C. explanations.

D. predictions.