What are all the values for $x$ such that $x^2<3 x+18 ?$ (A) $x<-3$ (B) $-3<x<6$ (C) $x>-3$ (D) $x<6$

Let $g(t, u, v)=\ln (t+u+v)-\tan (t u v)$ and find the indicated quantities. $g_t(0,0,1)$

Determine whether $p_1$ or $P_2$ is the better approximation.

$$f(x)=\cos x,\ a=\frac{\pi}{3}$$

Which is the better value? Circle it.

Dollar 5.00 for 4 mangoes dollar 6.00 for 5 mangoes.

Find each of the following quantities.

$$a) log_2 1024 b) log_2 1/4 c) log_4 8$$

Predict the major products of the following reactions, including stereochemistry where appropriate. (a) 2.2.-dimethyloxirane $+\mathrm{H}^{+} / \mathrm{H}_{2}^{18} \mathrm{O}$ (oxygen-labeled water). (b) 2.2-dimethyloxirane+$\mathrm{H}^{18} \mathrm{O}^{-} / \mathrm{H}_{2}^{18} \mathrm{O}$. (c) (2S,3R)-2-ethyl-2,3-dimethyloxirane$+\mathrm{CH}_{3} \mathrm{O}^{-} / \mathrm{CH}_{3} \mathrm{OH}$. (e) (2S,3R)-2-ethyl-2,3-dimethyloxirane$+\mathrm{H}^{+} / \mathrm{CH}_{3} \mathrm{OH}$

Five hundred smartphone owners were asked if they use their phones to download sports scores. The responses are summarized in the following table:

a. What is the probability that a randomly sampled respondent from this group has used his or her smartphone to download sports scores?

b. What is the probability that a randomly sampled respondent from this group is female?

c. Given that a randomly sampled respondent has not used the smartphone to download sports scores, what is the probability that he or she is male?

d. Are the responses Yes and No independent of the respondent's gender?

According to Freud, dream symbols are typically erotic in nature.

A. True
B. False

Each of the following expressions defines a function D on the set of $3 \times 3$ matrices over the field of real numbers. In which of these cases is D a a-linear function? (a) $D(A)=A_{11}+A_{22}+A_{33}$; (b) $D(A)=\left(A_{11}\right)^{2}+3 A_{11} A_{22}$; (c) $D(A)=A_{11} A_{12} A_{33}$; (d) $D(A)=A_{13} A_{22} A_{32}+5 A_{12} A_{22} A_{32}$; (e) $D(A)=0$; (f) $D(A)=1$.

Find the given integral.

The indefinite integral of (x^3 + 3x + 4)/(square root of x) dx

What did you think would happen next?

What stereochemistry would you expect for the product of the Diels–Alder reaction between (2E,4E)-2,4-hexadiene and ethylene? What stereochemistry would you expect if (2E,4Z)-2,4-hexadiene were used instead?

In the following sentences, eliminate any double negatives by crossing out incorrect words and writing the correct forms above them if necessary.

Example 1. I couldn’t see $\overset{\textit{\color{#c34632}{anyone}}}{\sout{\text{no one}}}$ around to help me.

She looked for graph paper everywhere in the house, but she didn’t find none.

Suppose that $\int_{0}^{4} f(x) d x=5 \text { and } \int_{0}^{2} f(x) d x=-3$ and $\int_{0}^{4} g(x) d x=-1$ and $\int_{0}^{2} g(x) d x=2.$ in the following exercise, compute the integrals. $\int_{0}^{2}(3 f(x)-4 g(x)) d x$